AN OPTICAL RO C SāOR r0r 7EJPi"2 iC I, IML013PY

by

Peter Robert Harnett BSc., ARCS, MSc., DIC.

MARCH 1980

A Thesis submitted for the degree of

Doctor of Philosophy of the University of London

Physics Department

Imperial College

London SW7 2BZ

AN OPTICAL PROCESSOR FOR GEOPHYSICAL. IMAGERY

A review of the development of coherent optical

processing, with particular reference to applications in the

earth sciences, is provided. This forms a basis for defining

the extent and direction of the subsequent investigations.

The results of experimentation on a pilot optical

system are described, and utilised in choosing features to be

incorporated in the design of the main system. The construction

of the latter is explained in detail.

Several studies involving the application of the

processor to real problems are presented, These concern images

from satellite_, aerial and surface sensors. The techniques used'.

include band-pass filtering, directional filtering and the?

extraction of directional statistics.

ACIMOWLEDGEMENTS:

Many thanks to all who have helped me, but especially

- to Professor W.T. Welford, Dr. M.E.. Barnett, Dr. T.H.. Williams,

Mr. G. Talbett and many other colleagues of the

Optics Section, Imperial College;

- to Dr. J.W.. Norman and the students of the Photogeology Section,

Imperial College;_

to Dr. J. Townsend and Dr. C. Justice of the Geography

Department, Reading University;

- to suppliers of imagery acknowledged individually in

the body of this thesis:;;

to the Science Research Council and the Department of

Industry for financial support;

- and to my wife for moral support in the face of the most

ill aspects of Saturn.

CONTENTS:

VOLUME I - TEXT VOLUME II - FIGURES

CONTENTS OF VOLUME I

CONVENTION: PART 2'

CHAPTER P. Q

SECTION P.Q.R

1 INTRODUCTIONS

1.1 THEORY AND PRACTICE

1.1.1 Fourier Transform Theory

1.1.2 Some Physical Analogues

1.2 DEVELOPMENT AND APPLICATIONS

1.2.1 Development of Processors

1.2.Z.Apglications to Geophysics

1.3 THE CURRENT PROJECT

1.3.1 Main Objectives

1.3.2 Preliminary Objectives

Page

12

15

21

23

25

33,

40

49

52

56

62

64

66

2 THE PILOT BENCH Page

2.1 PRINCIPLES.

2.1.1 Mathematical Concepts

2.1.2 Physical Concepts

2.1.3 Optical Practicalities

2.2 DISPLAY

2.2.1 Experimentation

2.2.2. Recommendation

2.2.3 Implementation

2.3 VIDEO-PROCESSING

2.3.1 Problems

2.3.2 Techniques

2.'3,-..3 Roles:.

2.4 DIRECTIONAL SAMPLING

2.4.1 Design and Construction 68

2.4.2 Uniformity and Simulated Object Tests 77

2.4.3 Automation and Real Object Tests: 84

2.5 DIRECTIONAL FILTERING

2.4.1 'Inclusion' and 'Exclusion' Filtering 93

2.5.2 Tramples (Zero order passed:); 96

2.5.3 Examples: (Zero order blocked) 98

5

3 THE MAIN BENCH page

3.1 LAYOUT 100

3.2 COMPONENTS:

3.2.1 Illumination System 103

3.2.2 Transform. Lens System 109

3.3.3 Object/Filter/Image Stages 114

3.3.4 Display and Sampling System 118

3.3 SUPPLIERS 124

4 APPLICATIONS

4.1 BACKGROUND;

4.1.1 Fracture Trace Analysia 126

4.1.2 Terrain. Classification 134

4.2 DIRECTIONAL. STATISTICS.

4.2.1 Queensland Aerial Image 137

4.2.2 'FAMOUS:' Sonar Image 143

4.3 FEATURE. ENHANCEMENT

4.3.1 Botswana 'LANDSAT' Image- 145

4.3.2 Dartmoor 'LANDSAT' Image 147

4.4 CONCLUSIONS:

APPENDIX: Convolution

150

154

REFERENCES_ 157

1.1 THEORY AND PRACTICE=.

The roots of Coherent Optical Processing lie in the

mathematical concept of Fourier transform theory and in the

physical phenomenon of diffraction. This chapter serves to

introduce these themes and to demonstrate the connection

between them..

1.1.1 Fourier Transform Theory

Fourier transformation is an operation that links--

distributions in two domains, where the dimensions of one

domain are inversely proportional to the dimensions of the

other. This is shown, by the mathematical statement of the

one-dimensional Fourier transform from the distribution f(x)

in the xi-domain to the distribution F(u)) in the u-domain z

+00

La

-2niux c.x. () e Relation(1.1)1

since the exponent, involving the product ux, must be dimension-

less. The: inverse transform relation, which must be satisfied

simultaneously with Relation(1.1).1 in order for F(u). and f(x)

to constitute a Fourier pair is:.

{co fx = 150'f'2iCtU.K ~~ e CL.

Relation ( 1 .1 ) 2_ _co

A. significant aspect of these relations is that the

value of the dista bution- at any one point in one of the domains

depends on the values:of the distribution at all points in

the other domain, i.e.

-2Tri.ux r — 1 fc.x)e.

at) uvu,

Relation(1.1)3

+00 +2fl LU.x f(xt J Ftt-t)e reu.

x_x2 Relation (1.1)4

Thus: the 'information' represented by the value of F(u)

at a. single point u=u1 results from contributions of information

represented by the continuum of values3of f(x), (and vice-

versa for x=x2). Loosely speaking the information associated

with the value F(u1) can be considered to be in some sense a

'synopsis;' or 'general view' of a particular aspect, (the

"u1 aspect"), of the information associated with the whole=

distribution f(x). Similarly, the information associated with

the value ffx2) can be considered to be a particular 'synthesis',

(the "x2 synthesis")) of the information associated with the whole

distribution F(u):.

More specifically, the sinusoidal nature of the functions

e +Zttcux

and e-2Triax means that the 'synopses;' or 'syntheses*

take the form of spectral distributions; i.e.. for any parameter

x, there exists: another parameter u which is proportional to

and therefore related to the 'frequency' of x;, hence any

'reasonably well-behaved' functiont f(x) can be represented. by

a group of sine waves having a frequency distribution (spectrum)

F(u);, where the functions:f(x) and F(u) are linked by

Relations(i.1)1 and (1.1)2..

This is the essential 'philosophy'" of Fourier theory;: at

more detailed exposition of the concept, which also introduce

the major mathematical. properties of Fourier transform pairs,

is given in Section 2.1.1.

1.1.2 Some Physical Analogues.

The mathematical properties of Fourier transforms have

several important consequences, one of these being that the

transforms of periodic., functions consist of distributions of

discrete frequencies:, (rather than continuous ranges of

frequencies), i.e. periodic functions can be represented by a:

superposition of a series of harmonics of a simple sinusoid.

Fourier transforms have thus found useful application in areas

of science which involve waveforms or repetitive structures.

The one-dimensional theory has usually been applied to

situations where the dimension concerned is time, (the inverse

dimension being temporal frequency)., the most familiar examples

being the analysis of electrical waveforms: and mechanical

vibrations.

o 'reasonably well-behaved' implies that the function must bey certain common mathematical constraints on continuity, etc., •

the precise details of which can be found in the references; quoted.

The multi-dimensional theory, using spatial dimensions

(or spatial frequencies in the inverse domain) has become

prominent in materials science, where it is embodied in the

phenomena of electron and X-ray scattering or diffraction..

In this context, the regular structures are typically crystal

lattices, and 'Fourier space' is related-<to the 'reciprocal

space' of the crystallographer.

Optical diffraction resembles a 'scaled-up version' of

X-ray or electron diffraction since the wavelengths involve&

(and the diffracting structures normally under study): are=

several orders of magnitude larger. The scattering mechanisms

are not identical, but are sufficiently similar to have

prompted the construction of optical diffractometers (using

scaled-up crystal models) for use as diagnostic instruments.

The model could be adjusted to provide an optical diffraction

pattern comparable with the electron or X-ray diffraction pattern

produced:by a real crystalline substance of the (unknown)

structure to be determined, (LIPSON 1972.);

Fourier transforms have been implicitly usedi in optics:,

for a considerable time; following Abbe's explanation of

microscope resolution in terms of the filtering of optical

diffraction orders (from a periodic object), by the l:elms-aperture,

an extensive body of work known as the 'diffraction theory of

image formation' was developed (see BORN and WOLF 1970)'. Thus,

mathematically, the propagation of light through image-forming

systems came to involve Fourier transform relationships of

various degrees of complexity (depending on the degree- of

coherence of the light), being particularly simple for 'fully

coherent' light..

- 10 -

Contemporaneously with this, Fourier transforms were being

increasingly usad.in the field of electrical engineering to

describe the transmission of signals through circuits or networks:.

it was found that one of the most important ways of characterising

a network or network component was by its frequency response,

(which indicates the way in which it 'modifies' or 'filterW

sinusoidal signaissas a function of their frequency); hence

it became convenient to perform Fourier analyses on communications

signals (i.e. to break them down into sinusoidāl components.>

for treatment.-

Communications signals may be non-periodic and of arbitrary

shape (including pulses-and arbitrary modulations of

sinusoidal carrier waves)-, as opposed to pure sinusoidal waves.

Hence electrical engineers gained much experience in handling

continuous (as well. as discrete) frequency spectra.. Moveover,

since the signals; concerned could. represent 'information' of

some sort (e.g. spoken works, television pictures, instrument

readings), the concept of 'frequency filtering' of information

became familiar.

The growing realisation that optical imaging using coherent

light corresponded in form to the transmission of signals

through electrical systems}, led_to an 'en masse' transfer of

More precisely, the correspondence is between linear, isoplanatic optical systems and linear, time-invariant electrical systems.

terminology and technique from the field of electrical

engineering to that of optics. Just as electrical signals

could be conceived of as 'one-dimensional, temporal distributions.:

of information' so optical images could be represented as

'two-dimensional, spatial distributione5 of information . Hence=

spatial frequency spectra and spatial frequency filtering became

recognised as important entities in 'image processing systems)

(the optical counterpart of electrical. signal transmission

networks).

A detailed presentationof the physical process of

coherent optical imaging in terms of the mathematical concept

of Fourier transforms is given in Section 2.1.2:.

-- 12 -

1.2 DEVELOPMENT AND. APPLICATIONS;

1.2.1.Development of Processors

The concept of holography, originated by Gabor in 1948,

concerns the storage and retrieval. of (usually) optical

information via the spatial modulation of a spatial "carrier

wave" (i.e. an optical interference pattern):.. Besides serving

to attract increase&interest in the field of 'optical

information processing', it was later to be used for the construct-

ion of complicated spatial filters, in particular those known

as 'matched filters' (see below).

By .1950h,, the configuration of optical hardware

consitituting a classical coherent optical processor, as

shown in Fig..(2.117, was well established 'on paper*, but its.

appearance 'in the laboratory/ did not become common until the

invention of a reasonably powerful coherent light source

(i.e. the laser). Early papers thus tended to be theoretical,

dealing with such topics. as. deriving the general conditions_

on power spectra necessary for spatial filtering to enhancer

the signal-to-noise ratio of the optical information channel

(O'NEILL.1956) - (the coherent optical version of a.perennial

problem in electrical engineering)-. The major practical use

of optical processors at this time was as analogues: for X•-ray

diffraction or electron diffraction from (e.g..) crystals,

polymers and fibres (TAYLOR and LIPSON 1960,:

- 13 -

With the arrival of the laser, (arounth1964): coherent

optical processors began to operate at levels of intensity

appropriate to normal 'visual' images, (e.g. continuous tone

photographic transparencies):.- Their application to transparencies

of geophysical phenomena soon began to be investigated,

particularly by Pincus and Dobrin, Fontanel and Bauer, (see

Section 1.2.2)..

(VAN DER LUGT 1964) gave a theoretical_ exposition and

reported:practical demonstrations of 'matched optical

spatial filtering'. This is usually acheived by interfero-

metrically (holographiaally) recording the diffraction pattern

from an object transparency, to act as a spatial filter for a,

different object transparency;; the filtered image that results

consists of the convolution and cross-correlation between the

objects and is a measure of their similarity or 'matching'

(see. GOODMAN 1968-b/. Such operations. were seen to be of

potential value to problems in the field of character andIpattern .

recognition, (e.g. fingerprint matching/ or change detection,

(e.g. plotting cloud movement in meteorological satellite

photographs).

In addition to matched. filtering, a considerable amount

of coherent optical processing work at this time was concerned

with 'image restoration', i.e. using spatial filters to correct

images which had been degraded in some way at the time of

recording, (e.g.. by motion-blurring or misfocussing). The

progress made in this field, (particularly by contributors

such as Marechal, Preston, Cutrona, Leith and Upatnieks:), is

summarised in (TIPPETT et. al. 1960., (DE: VELIS and REYNOLDS: 1967);,

(GRASSELLI 19691 and (SHULMAN 1970):..

-14-

Another important application was found to be in the

generation of images from 'synthetic aperture radar' recordings,

(=RONA et.al. 1966).. This resulted from the similarity

between the mathematical descriptions of the propagation and

interference of the radar signals (which, in this type of radar,

form an essentially coherent recording system), and of the

light waves in a coherent optical processor employing lenses

of a special shape, (usually cylindrical and conical),,

(see GOODMAN 1968). S=ynthetic radar images have themselves

become very relevant to geophysical studies; (see? Chaper 4.1).

By 1970, coherent optical processing had become sufficiently

well-established.<to stimulate attention to technical details

and the formulation of specific designs;; e.g.. for lenses,

(BLANDFORD.1970), (VON BIEREN 1971), and liquid. gates, (to

suppressspurioussphase variations of the object transparency)`,

(HARBURN and RANNIKO. 1971);.. Large, 'purpose-built' processors

were developed: for use with geophysical image transparencies

(LENDARIS; and STANLEY 1970) , (PRESTON and DAVIS 1972):; the.

former being intended: specifically for satellite photographs (see: Section 1.2.2)..

The early 70's saw comprehensive reviews; of spatial

filtering techniques; (BIRCH 1972));; of the 'hardware' of coherent

optical processors (PRESTON JR.. 1972-a, etc.); and the emergence

of a debate on the relative merits of optical processors versus✓

digital computers with regard to the handling of textural

information, (DAVIS: and PRESTON 1972)x, (PRESTON JR. 1972)'.

It was recognised that although optical 'computers' excelled

in the ability to carry out certain parallel (associative)

operations on images at relatively high speed and low cost,

- 15 -

many pattern recognition and classification tasks also required

the adaptive programming qualities inherent in digital computing..

The conclusion was that coherent optical processors, would

prove to be of most value in such tasks if combined or 'hybridised:'

with digital systems, either as routine 'pre-processors' of

optical images (e.g. by providing diffraction-plane data as input

information to a digital programme), or as 'learning devices3'

to facilitate the selection of an optimal filtering operation

(for a specific task); which would subsequently be translated into

a digital form. Further work has tended to confirm this conclusion..

(Practical aspects of coherent optical processing equipment

are discussed in Section 2.1..5).

1.2.2_Applications to Geophysics

The main feature of coherent optical processing that ham

been found to be of importance to geophysical images is its

ability to quantify and classify texture.. A.detailed exposition

of this is given in Chapter (2.1), from which the following

synopsis is drawn.

Consider a two-dimensional image, together with its Fourier

transform (diffraction pattern) as shown in Fig«(1.2):1, where

x;y are the co-ordinates of space in the image and u,v are- the

corresponding co-ordinates of spatial frequency in the transform,

The points P in the transform plane, distant r from the origin

in direction 0/ 8+180° correspond to a sinusoidal 'grating'

pattern in the image plane, having a period*, and aligned along

e t qo° f Al-2:7e ; the amplitude of the grating being

proportional to the amplitude or 'strength of signal' at the

points P. This 'grating' can be considered to be a fundamental

16 -

component of texture, since diffraction theory showsethat

shape, texture, pattern or distribution of light in the

image can be built up by superposition of ;a: 041.1e ta'on 6f.

'gratings' such as these, with the appropriate periods, directions

and amplitudes. Thus, just as the diffraction pattern consists

of the superposition of allī.the points P, P', P" etc, so the

image consists:of the superposition of their corresponding

'gratings'.

If the image texture has strong directionality, this

will`be readily apparent in the angular distribution of the

transform, as shown by Fig.(1.2):2. Similarly, if the image

texture has a predominant granularity or scale, then this will,.

be manifested.in the radial distribution of the transform, Fig..(1.2).3.

Thus the relative directional strength of structures.: in the image

can be numerically assessed by measuring the light energy in

corresponding (90°-shifted) sectors of the diffraction pattern;

whilst the 'coarseness,' or 'fineness,' of the structures can be

similarly estimated_from measuring light energy in annular bands

of.spatial frequencies.

Methods such as these can form the basis. of a texture

classification technique: the measurements of light energy in

particular sectors, annuli or any other defined region of the

diffraction pattern (or possibly ratios and higher-order functions

of the measurements): can represent the values of a matrix or

multi-dimensional vector (i.e. a single entity, but made uip of

several components)•, that characterises the texture of the image.

Texture cLasses:can then be defined in terms of the properties;

of this matrix or vector (i.e., of the interrelationships between

its components). An example of this technique (GRAEMENOPOULOa

1975). is discussed later in this section.

-17—

Using the above terminology, spatial frequency filtering

of the Fourier plane can be consideredito be an operation that

separates or enhances textures or particular components of

textures,. For instance, Fig..(.1.2)-4 shows that directional

blocking of the diffraction pattern can be used to separate. out

features characterised. by a particular direction. (Similarly,

annular filters can be usedito enhance discrimination of image

regions having different degree•, of 'granularity' or 'scale'

of texture)).

Apt ācat .Qix „ of coherent optical processing to transparencies

of geophysical imagery was first demonstrated in the paper of

(BARBER:1949), in which the periodicities of sea-surface waves

were inferred from the diffraction patterns of verticalaEerial

photography.. The light source used was a. mercury lamp, so

photographic recording of the diffraction patterns took many

minutes; however, the advantages of this method over direct

visual. inspection of the photograph were made evident, particularly

for scenes-displaying a spread or range of periodicities.

Interest in these techniques was,revived by the advent of

the laser, with a particular emphasim on their application to

essentially 'binary' images, (e.g.. transparenciea; of maps-,

charts, etc..):, as exemplified: by (DOBBIN et.al. 1965) and

(P.INCUS.and DOBBIN 1966). The former paper demonstrated the

ability of directional spatial filtering to select particular

features or anomalies in seismographic: data traces (cf. Eig.(1.2):4).

The latter showedithat directional filtering could be used to

enhance the orientation of grain boundaries in photomicrographs

of rock samples and to isolate particular (directional) sets of

lineaments in fracture trace overlays, the value of inspecting

-18-

the diffraction patterns, of contour maps (etig. magnetic contours):,

in order to give a numerical assessment of the strength of

directional trends_:, was noted, and later work on the spatial

filtering of such maps has produce& significant results

(ARSENA.ULT et . al . 1974).

The techniques, were also applied to the analysis3of

lamination in rocks (PINCUS and ALI 1968);; and the use of

high-pass filtering on continuous tone images to enhance boundaries

or fine detail was shown in (DOBBIN 1968). (.PINCUZ 1969) described:

the plotting of contours of the diffraction pattern intensity

(;or of the density of a photographic recording of the pattern).,

as a -means=of measuring the distribution of grain sizes in rocks.

This application has been the subject of extensive study using

the fairly sophisticate&. optical bench of the Kansas. Geological

Survey, as reported in (PRESTON and DAVIS 1972).

In addition to these studiesainvolving 'micro' geophysical

features, coherent optical processing was re-applied to the

'macro' features displayed in aerial photographs. ('ONTANEL.et.al.

1967) used directional filtering to exclude dominant lineament

directions and therefore reveal sub-dominant trends, as a

pre-processing operation for photo-interpretation « CBAUER et.al..

1967) used the same operation to reveal a system of glacial

crevasses which (in the unprocessed photograph) had been obscurest

by surface relief caused by differential melting.

Analysis of sea-surface images was continued, (sTILWELL.1969Y,

being particularly stimulated by the growing availability of

satellite imagery (NOBLE,1970),.. The wide synoptic coverage

provided by these images has become of value in understanding

large-scale phenomena such as the behaviour of long-wavelength

swells; the interpretation of the diffraction pattern data haw

been treated in considerable detail by (YAS:XJRIRO SUGIMORL 1975).

f

- 19 -

The advent of the ERTS: (now LANDSAT).satellite programme

encouraged the building of processors with larger input formats

(i.e. greater than 35mm width), e.g.. the bench developed for the

General Motors Company, described by (LENDARIS:and STANLEY 1970). ;

this employed a scanning slit and photomultiplier arrangement to

measure the light energy in portions of the Fourier plane, and:

a similar system was used.by (NYBERG et.al. 1971). The latter

showed examples of its application in providing a numerical

description of the directionality in aevera iphotographs of

geological structures, including moraines, block-fields, fractures

and glacial striations.

An alternative method of measuring the light energy in

the diffraction pattern was provide&by photodetector arrays:.

(JENSEN 1973) mentioned a detector using wedge and ring shaped

array elements (now marketed: commercially),, in which the signals .

from the elements were read-in to a digital. computer in rapid

sequence. This method has been favoured for terrain-type.

(land-use): classification tasks, in which the computer uses..

diffraction-plane measurements to form a vector, whose values can make up 'spatial frequency signatures~' associated: with

particular types of terrain.. Classification can proceed via

the mathematical techniques:familiar to 'multi-spectral analysis',

simply substituting the spatial frequencies of the terrain

structure in place of the temporal frequencies of its reflected

radiation spectrum.

It has proved possible to develop promising terrain

classification algorithms-for tANDSAT imagery based on a mixture

of spectral (tonal) and spatial (textural) parameters; see.

(CORBETT 1973, GRAEMEN0P0ULO& 1975).

- 20 -

The above provides only a brief summary of the applications

of coherent optical processing to geophysics;; more comprehensive

and illustrative surveys are included in (McCŪLLAGH 1971) and

(McSEITH 1974).

- 21 -

1.3 THE CURRENT PROJECT

1.3.1 Main Objectives

The project on which this thesis is based was commenced in

1972 and its aim was the development of a coherent optical

system intended primarily for application to ERTS (LANDSAT)

imagery.. This requirement set the specifications for the

dimensions of the system, whilst great attention was paid to

the quality of the optics involved, in order to maintain the

high resolution and accurate density characteristic of the images..

Under finance from the Department of Industry, the Coherent

Optics Group at the Blackett Laboratory of Imperial College:

were able to make use of the talents and experience of

Professors W.T. Welford. and C.G.. Wynne as lens and system

designers, the manufacturing skills of Imperial Cbilege Optical

Systems for glassware and the high-precision engineering

abilities of the Applied Optics lens-mounting group for lens.

barrel design, assembly and testing. Project co-ordination was

in the charge of Dr. M.E.. Barnett.

At an early stage in the project, contact was made with

potential users of the images and information that the bench

was intended to supply.. Thus, guidance could be obtained in

developing the equipment and processing operations to produce

results in a form that would be of most practical use, (i.e.

there was a strong user-orientated factor in the development

and operation of the bench).

- 22:-

In particular, liaison was maintained with the photo-

geologists at Imperial College, under Dr. J.;./.. Norman, from

which it became clear that an azimuthal diffraction pattern

scanner of the type described by Nyberg'° should be considered

an essential part of the system.. This would provide a tool. for

the compilation of directional fracture-trace statistics in the

form of 'rose diagrams' which have been recognised as important

indicators of geological structure, e.g.. with regard to the

prediction of areas of mineralisation, (HUNTINGDON 1969),

(NORMAN and HUNTINGDON 1974)

,It was recognised that in addition to ERTS.transparencies,

the bench should be able to handle images at a variety of scales,

so that the results of carrying out diffraction pattern analysis

or filtering on a particular area of terrain, as recorded: by

different types of sensor (e.g. satellite versus aerial photography),

could be easily compared.. This requirement demanded a certain

amount of flexibility in the display system, particularly for

the Fourier plane, where it was seen to be important that the

apparatus should be capable of displaying the diffraction

pattern at a variety of scales, so that different ranges of

spatial frequency could be examined in detail. (It transpired:

that a closed circuit television system with video-processing

options played;. the major part in meeting these objectives..).

It was also decided that a holographic cross-correlation

matched filtering arrangement should be incorporated in the

bench so that change-detection studies. on time sequence images

could be pursued. It has been suggested that the distribution

-23—

of wind vectors --manifested by the change of cloud positions

in sequential scenes of meteorological satellite imagery, can

be rapidly determined by such a method..

Another objective that was envisaged in the long-term plan

was that the bench should be capable of adaptation to some

degree of automation.. This would be desirable for applications

requiring a routine operation to be repeated on a large number

of scenes (e.g. successive frames on a roll. film), or on a large

number of sub-scenes within a single frame. Thus, the design

of the equipment should make some provision for conversion to

automatic or semi-automatic operation, as options.. (The latter

was successfully demonstrated, at a fairly early stage, for the

generation of rose diagrams from azimuthal scanning of the

diffraction pattern, see Section 2.4.3).

1.3.2 Preliminary Objectives

Whilst the design of the transform lenses. was well established.

at the start of the project, (see: Section 3.2.2)., it was seen

that a considerable amount of experimentation was necessary in

order to specify details of the other components of the processing

bench.- Moreover, it was known that the high-precision manufacture

of the glassware and supporting barrels for the lenses would;

be a rather lengthy process..

Therefore it was decided to construct a temporary 'pilot'

bench, using standard laboratory components and optics of

moderate quality, for the purpose of developing and testing

components and techniques proposed for the 'main' bench. In this

context, particular priorities were the object plane/Fourier plane/

- 24 -

image plane display system and the Fourier plane (diffraction

pattern); scanner.

The pilot bench operated on a much smaller object format

than the main bench (a 35mm. diameter object plane, to accomodate

standard 35mm. x.24mm. film frames instead of the 70mm. x:70mm.

ERTS transparencies), but had a comparable Fourier plane size

and fairly good aberration correction.. The range of work

performed. on this bench is described in Part 2 of this thesis.

Construction of components for the main bench proceeded

in parallel with the pilot bench work, thus allowing a fairly

swift transition from pilot bench to main bench to be made on

completion of the main transform lenses:, (Part 3 of this thesis).

-- 25 —

2.1 PRINCIPLES.

The intention of this chapter is to demonstrate the principles

that are embodied: in the operation of an orthodox.coherent optical

processing bench. This is a subject that has been covered in great

detail by several publications (notably BRACEWELL (1965) and

GOODMAN (1968)). However it is felt necessary to include at this:

point a summary of those concepts and practical details that are

essential to the understanding of later chapters of this thesis...

The provision of a self-contained account of this nature is thus

principally intended to familiarise the subject of coherent optical

processing to its potential users from other'disciplines.

Section 2.1.1 introduces 'spatial frequency spacer and

'frequency filtering' as purely theoretical concepts, and deals

with the fundamental Fourier theorems in their one-dimensional

form, later extending the ideas into two dimensions,.. Section 2.1.2

explains how optical images and operations can be expressed in

two-dimensional 'oūrier-transform terms. Section 2..1.3 shows some

optical analogues of the theorems, and derives; practical results

for use in subsequent chapters..

Where statements are made or results presented without proof,

it is to be understood that an adequate treatment exists::either

in one of the above references, or in one of the other general

references.

2.1.1 Mathematical Concepts:

A_one-dimensional function f(x) and its Fourier transform

F(u) are related by the expressions: tco •

23-rcux FCu) = f 5<x) e. ~x

foo =+ao

IL) e 276-cix _oo

Fourier transformation

P.elation(2..1)1

Inverse Fourier transformation

Relation(2.,1)2

-26-

The symbolic shorthand for this relationship is:.f(x)ribF(u).

Alternatively, we can use the symbols T, Ti to represent

Fourier transform and inverse Fourier transform operators,

respectively, whence:.:

E(u):. = T { f (41

f(x) = T tF(.n).}

from which it is obvious that

T ACT f(41 = f(x).

also, it can be easily shown that:_

T ET f f(x)}J f(-x).

Relation(2.1)3

Relation(2.1)4

In rigorous Fourier transform theory, the functions.f(x), F(u);

must satisfy certain mathematical conditions, but these are

automatically fulfilled if the functions are physically

realisable.

Let us now suppose that the variable x:has the dimension of

length, i.e. that it represents the co-ordinate of one-dimensional

space.. Since the exponent 217C iux: used in Relations(2.1)1 and

(2.1)2 must be dimensionless, it follows that the variable u

must have the dimension of length' i.e.. that it must represent

the co-ordinate axis of one dimensional reciprocal space. It im

here worthwhile to consider the corresponding relationship that

applies to time-varying (rather than space-varying) phenomena.

-27-

For the temporal case, we can simply replace x.by t (time) and

u by f (frequency) . This allows us to analyses temporal signals

in terms of their frequency spectrum, a technique that playe&a

fundamental part in communications theory. By analogy with this,

the Fourier transform of a spatially-varying signal is known as

the spatial frequency spectrum which extends over spatial frequency

space+ or "Fourier space". Examples of some Fourier transform

pairs are shown in Fig.(2.1):1; note that the pure cosinusoidal

waveform, being composed:of only a single frequency, is represented

at only a single value of the abscissa=in spatial frequency space.

Fourier transforms exhibit a number of useful properties_•

which can be presented mathematically as follows, given that

f(x) &-u)

g(X) G(u)

Addition fl(x) g(x 7 (n) +- G(ug Relation(2.1)5

Similarity f aF(au) Relation(2.1)6

i.e. 'spreading out' a function in x (or multiplying its period)

by a factor a, 'closes up' its transform in u (or divides its

frequency). by a factor a.

-28-

Shift f(x-a)raF(u) • e -27ti u a Relation(2.1)7

i.e. shifting a function along the x axis by an amount a

multiplies its transform by a phase factor proportional to a,

but does not change the amplitude of the transform.

Qonvolutiont 4:Rx) 411 g(xx# (u) . G(ug Relation(2.1)8

i.e. the transform of a convolution of two functions is the

product of their individual transforms. (Convolution is a _

difficult operation to grasp, but it plays an important part in

Fourier theory; for those unfamiliar with the concept, I have

provided_ an explanation in the Appendix:to this thesis, thus.

avoiding a break in the natural sequence of this section). Note

that these theorems are all reversible.

A_particularly interesting result occurs when a function

f(x) is convolved with a 47—function g(x-a). The examples of

Fig.(2.1)1 show that::

O(x)~

applying the shift theorem, we sew that s

S (x-a) T e-27tiva

• The symbol @ indicates the convolution operation.

- 29 -

hence, by the convolution theorem:

i(x). @ S(m-a) F(u). e -27tiva

but the shift theorem states that t

f(x-a) P(u) e 2 g iva

hence:: f(x) @ g(x-a) - f(x..a). Relation(2.1)9

A-consequence of this is that a. string of delta functions, when

convolved with a function f(x) yields a string of 'replicas _'

of that function; i.e.

- 30 -

This 'replication' property has important consequences in the

analysis of repetitive structures of patterns. Fig.(2.1)2

demonstrates the derivation of the spatial frequency spectrum

of a square wave by representing the wave as a convolution of

a rect function with a 'Dirac comb' function. This type of

analysis can be applied to both ordered and disordered distributions;

in either case, the shape of the individual element in real space:

(i.e. the function that is replicated to form the distribution):

controls the shape of the overall envelope in spatial frequency

space; (or vice versa).

It is possible to apply Fourier transform theory to

functions in any number of dimensions;; however, for optical

diffraction theory, two-dimensional transforms are the

appropriate theoretical concept. The two-dimensional forms of

relations (2.1)1 and (2.1)2, are

—2T(i (ux + vy): f(x,y) e dx dy Relation(2.1)10

f (x,y) *27r'i (ux: * vy)

F(u,v) e du dv Relation(2.:1)11

31 -

All_the properties demonstrated for the one-dimensional theory

are valid, correspondingly, for the two-dimensional forms. Some

examples of two-dimensional Fourier transform pairs are shown in

Figs.(2.1)3,k.

The technique known as 'spatial frequency filtering' is a

method of changing a function f(x:,y), into a different function

g(x,y), by performing some operation S upon the Fourier transform

F(u,v)_ (where f(x,y) Jr& F(u,v) )

i.e.. if T=_ 2-dimensional Fourier transform: operator

I T= 2-dimensional inverse Fourier transform operator

S:ei2-dimensional frequency filtering operator

let F(u,v) = T f f(x,y)} , G(u,v). T f g(x,y)}

. also G(u,v)- = S>{ F(u,v)}

then G(u,v). =. ST f f(x,y)}

T(g(x,y)) = ST{ f(x,y)}

••• TI T{

g(x,y)} = Ti ST [f(x,y)}

-32—

But T T tg(x,y) = g(x,y);`gwo-dimensional version of

Relation(2.1)427

g(x,y) = TST ff(x,y)} Relation(2..1)-12

The mathematical formulation of 'spatial frequency filtering'

thus consists of three operations:-

a).' Fourier transformation of the function f(x,yl.

b) Operating upon the spatial frequency spectrum F(u,v) to

convert this to a modified spectrum G(u,v).

c) Inverse Fourier transformation of G(u,v) to form the new

function g(x,y).

The operator S- is commonly known as the spatial frequency filter..

The mathematical significance of spatial filtering can

by appreciated by examination of the structure of Relations..(2..1)10

and (2.1)11. The integral definitions imply that the value

of F(u,v) at any single point (ui, vi) of 'Fourier space'. depends

upon the values of f(x,y) over the whole continuous set of points

(x,y) of 'real space'. Hence a 'Fourier space' operation performed

ata single point (u1, vi)- of F(u,v) corresponds to a continuous:

set of 'real space' operations on all. points (x,y) of f(x,yY..

i.e.• Serial or 'point-sequential' operations in Fourier space

correspond to parallel or 'point-associative' operations, in

reāl space.

i oi°āeiit beami, a°-'the omTēx z~ir"+eiitz~~ on'.;o

x~c-iciēnt;oH,;d1l ~i`ats _.iaf:tYrē:' sctcēW :ēfl t3ē•ivēYi

- 33$ -

2.1.2 Physical Concepts

. The relationship between the mathematical entity of Fourier

transformation and the physical phenomenon of optical diffraction

is demonstrated in the following conceptual experiment, which

utilises a 'one-dimensional' optical model.

Consider a 'one-dimensional screen' of infinite extent

lying along the x axis, Fig..(2.1)5, (in this treatment it can be

visualised as a thin section of a two-dimensional screen lying

in the x-y plane). The screen has a complex amplitude transmittance

q(x) for light of wavelength X and is illuminated by a

collimated coherent beam of light of this wavelength, travelling

in the z direction. There is no spatial variation across the

A = Āe> IAA) t where W

c = velocity of light,

t = time

The light is diffracted by the screen, which can be considered

to give rise to a continuum of infinitesimal 'secondary sources

of 'light (as in Huyggnst rriric•i ~ e)~. Defin .ntr %the, complex-14

transmit;tpd .?4?htr~sk.gi al~ Z °a .d•irect4.o~~; ;n-Q] ~n,'P 3 a,t` i•.%•:

angle + to the z axis as A:D (4))', Fig. (2.1)5 shows that the

contribution dA D (40. from an infinitesimal element dx_

- q(1147 t) by definition

I cidet Arnr).itude

-34-

at distance =from the origin is given by:.

1,(x) e = sin

Relation(2.1)13

Integrating over the whole screen,

41)

♦0 lab

( e 2rri. )x

= A. e: dxti . —co q

where c,(x and Q(.51 ) constitute a Fourier pair.

Thus if we consider only the spatial:_ variations of the complex:

amplitude, and normalise the incident strength to unity, we find.

- Qt A' G 4) maps the Fourier transform of $(x);. i.e.. that the

diffracted complex amplitude as a function of angle, maoa the

Fourier transform of the complex amplitude transmission of the

screen. If the diffracted light is collected by a lens of focal

-35-

length f, as shown in Fig..(2.1)•6, then we can consider a parallel

beam of light, travel Ting at an angle 4 to the z axis, to be

focussed down to a single point in the back aocal.. plane of the

lens, distant x' from the z axis, where x( = f tan(+). is If +.~l:small, .then_.siin+ tan + , so that q(s

h~ ), becomee q(7 u-) f ) hence :.

q(x) # Q(- f )

Relation (2..1)14

The variable P defines a spatial frequency;: Relation(2.1)14 implies (in one-dimensional terms) that the complex_ amplitude

distribution A(x')` in the back focal plane of the lens maps_ the

Fourier transform or spatial frequency spectrum of the complex

amplitude distribution 'q(x). generated by the screen, (with a

scaling factor Xf).

The method demonstrated in deriving this result is the

basis- for a more realistic treatment using a two-dimensional

object plane and back focal plane, such as is provided by

(SHULMAN 1970-a): which parallels the diffraction theory of light

propagation as expounded in (BORN and WOLF 1970). The more

rigorous mathematics employed shows that for an aberration-free

lens of infinite aperture, there is a two-dimensional Fourier

transform relationship between the complex amplitude distributions

in its front and back focal planes, i.e.. that:

-36--

F

Q (• ' hf)~

+00

J q(x,y) e-z ic i -3►'f a e2-271i Y dx dy _ao

Relation(2.1)15

where q(x,y) represents the complex amplitude in the front focal

(x-y) plane,

ft . n: If IV n' back focal!.

(x/-51.1 ) plane,

with scaling factor Xf, as before.

Note that for an exact Fourier transform of a diffracting. object

transparency to be obtained in the back focal plane of the lens,

the position of the transparency must be restricted: to the front

focal plane; this condition dictates the 'classical' arrangement

of a Fourier analysis bench, shown in Fig..(2.117.• The first

lens forms a map of the Fourier transform of the object

(in complex amplitude) in its back focal plane, which is loosely

termed-the 'diffraction plane', 'the transform plane', 'spatial

frequency plane' or 'Fourier plane', (the latter being the most

commonly used description) of the complete system. A similar

-37-

transformation occurs through the second half of the system,

so that the complex-:amplitude distribution in the back focal

plane of the second lens consists of the transform of the transform

of the object distribution; the two-dimensional version of

Relatiōn(2.1)4, viz:-

T T { f (g'y): f(-x; -y)

shows that thissdistribution is simply the original object

distribution inverted along both axes, i.e. an inverted image

of the object.. By using a second lens of the same focal length

as the first, the scale of the image plane is the same as that

of the object plane;: (if lenses of different focal lengths are

used, there is magnification or demagnification of the image

relative to the object)'.. To conform with the mathematical

notation of Section 2.1.1, it is common practice to denote the

spatial frequency co-ordinates as (u,v), where these are related

to the actual spatial, co-ordinates(x', y), in the Fourier plane-

b7 k'' ==-Aft'

— 38 —

thus,

too

Q(u,v) = SS q(z,y) e -27r i(ux +- vy -voJ

dx dy Relation(2.1)16

X f v :.

The physical significance of 'spatial frequencies' as

descriptors of an object or image structure can be comprehended.

by reference to Figs.(2.1)8,9.. Fig.(2.1)8 demonstrates

visually how the square wave that was synthesised by a convolution

in. Fig..(2.1)2 can be analysed as a sum of a series of cosine

waves:.. Each pair of S -functions in its frequency spectrum

transform to a cosine harmonic, the amplitude of which is

governed by the sine function envelope;; the t1 (fundamental)

harmonic has the same periodicity as the square wave, whilst

the addition of the higher harmonics to it contributes to the

'squaring-up' of the edges. In this case, the function is

composed of discrete harmonics, but in general, an arbitrary

function would be composed of a continuous spectrum of these

simple cosine waves; the Fourier transform thus indicates. the

'strength' or amplitude of each of the cosinusoide.l frequency

components present in the analysis.

The nature of optical propagation makes it desirable to

represent any two=d :merisioh l." im ē ās' IDeiri ''compōsc z spectrum

of . cosinusoidal -complex amplitude 'grātin s' . From

-39--

i' 7 tu1.t :rn:; . each one of these 'gratings' produces a pair of

complex amplitude 6-functions in the Fourier plane (see

Fig.(2.1)9). The S -functions-lie along a direction in space

perpendicular to the 'grating-line' direction; their distance

of separation along this direction is proportional to the

spatial frequency of the 'grating', and their complex amplitude

strength (i.e. 'height') is proportional to the depth of modulation

or amplitude of the 'grating'. By applying the addition

theorem (Relation(2.1)5), we see that just as the image consists

of a continuous spectrum (in spatial frequency and direction)

of 'grating', so the Fourier transform of the image consiata

of a continuous distribution of the corresponding 1-function

pairs. (Note that this pairing implies 180°-rotational symmetry

in the Fourier - plane), ! This das:rr~:;but'~Gn ;z .~.thu rF .a:t,Od to:: the ''

statistical distribution Of orientations spatial frequencies

present in the image. For instance, if the Fourier plane exhibits

strong complex amplitude along a particular radial direction,

then this is an indication of a prevalence (in contrast, length

or numerousness) of features running in the perpendicular

direction in the image. Conversely, a strong annular zone of

complex:amplitude in the Fourier plane corresponds to a predominance

of a particular 'coarseness' or 'fineness'' of structure in the.

image. Hence, by making suitable measurements on the light

distribution in the Fourier plane of the system, we can gain in-

formation about the directional and textural properties of the

object/image.

40

By physically masking the Fourier plane in some way

(e.g. by opaque or partially-transmitting screens, phase-

changing plates, etc.) the techniques of optical spatial frequency

filtering can be realised.. As an example of this, if the object

transparency contains structures having a particular orientation,

then these can be eliminated from the 1:1 image by placing opaque

wedges aligned radially along the perpendicular direction in

the Fourier plane. Similarly, the textural content of an image

can be modified by placing discs, holes or annuli in the Fourier

plane, (concentric to the optical axis of the system).

A•significant fact, shown in Fig.(2.•1)7 is that diffracted:

light arising from structures of a given orientation and spatial_

frequency is collected from all. points of the object and focussuedi

to .h 14..anle irr t . FbVvi-or

Cola-Una t on of the. tyro ;factors :

a) The nature of coherent optical diffraction;

b) The focussing property of lenses;.

which makes it possible to apply controlled parallel-processing

operations to optical images.

2.1.3 Optical Practicalities.

The previous section demonstrates that image formation in

a coherent optical diffraction bench is a physical analogue of

Fourier-transform processes; the most significant asaumptionss

made are that:

-41 -

i) The object/image are of infinite extent;

ii) The lenses are of infinite extent (aperture).

and are aberration-free-.

This section will-outline the effects and limitations introducedi

by the use of a practically realisable system.

As a useful_ starting point, it must be appreciated that

the optical Fourier transform relationships of 2.1.2 apply to

distributions of complex amplitude and not intensity. Although

it is possible to 'record complex amplitude' by the use of

holographic techniques, one is most frequently concerned with

observing, recording or measuring the intensity distributions in

the various planes of the system.. Using the notation of

Fig..(2.1)7 we find. that :-

intensity distribution in object plane = i(x,y) = q(x,y), q*(x,y)

" Fourier . '!; = I(u,v) = Q(u,v) 41* (11,v)

" image nY Ei(-x,-y). = q(-x,-y). q*(-w,+y)

where * indicates complex conjugation.

The inversion relationship between object and image still holds,

but since q(x,y):* Q(u,v), it is apparent that there is no simple

direct relationship between i(x,y), and I(u,v). However, since

the overall 'shape' or 'form' of i(x,y) and I(u,v) corresponds

with that of the real parts of q(x,y) andQ(u,v) respectively

(i.e.. i(x,y) =- 1q(x,y), 2 , I(u,v) = 1 Q(u,v) 2 f ), then one finds .

-42-

that for many Fourier-analysis-based tasks, the confinement of

measurements to intensities: is not a serious- restriction; indeed,

the phase information lost is often irrelevant, making it positively

advantageous to obtain intensity measurements directly.

The distribution I(u,v) =:IQ(u,v)1 2 is often termedithe

power spectrum or Wiener spectrum.. It is also the far-field:

(Fraunhofer) diffraction pattern of the object, (although this

latter term is sometimes used ambiguously with respect to complex:

amplitude or intensity)..

We now consider the effects of substituting real conditions^

in place of the ideal ones assumed in (i) and (ii). above..

Fig.(2.1)10 shows✓ a situation in which the object is now of

finite size, although the lenses remain infinite and unaberrated

as before. A-single parallel diffracted beam of light from

the object (corresponding to a single spatial frequency in its

structure).: is focussed to a 'single point' in the Fourier plane,

and then reconverted to a parallel beam which forms a component

of the image.. Since the lenses: are: of infinite aperture, they

willi accept diffracted beams even when the angle of diffraction

approaches 90° (if we neglect such phenomena as reflection of

light from the lens surfaces, and the breakdown of the simple

'wall angle' diffraction formula); hence the diffraction pattern

is of infinite extent although the object is finite.

The Fourier transform relationship expressed in Relation(2.1)16

requires that the integration (of diffracted light contributions)

be taken over infinite limits in object space. In order to do

this, we can consider the object plane distribution to be

- 43 -

truncated by multiplication with a rect function (in one

dimension) or a pill. function (in two dimensions), having a

width or diameter equivalent to the actual width or diameter a

of the object. By reference to the convolution theorem

(Relation(2.1)8): and to Fig.(2.1)3, it is seen that the Fourier

transform of the object plane distribution is convolved with 4

sine function (in one dimension) or Airy function (in two dimen-

sions). Thus the replacement of an infinite object by a finite

object of diameter a (i.e.. limited by the 'truncation' function,

pill- (ā , ā)) I, results in the replacement of infinitesimal

points in the Fourier plane by finite:spots of light (i.e4 definedi

by the 'point-spread function', Airy (au,av))..

To obtain the image plane distribution by transformation

from the Fourier plane, it is demanded mathematically that wee

should integrate over infinite limits in the latter;,. since we have

shown that the diffraction pattern is of infinite extent (i.e.

not truncated) then the image must be a 'perfect' (i.e..

infinitely weil]_-resolved) replica of the object.. Thus 'infinite-

simal' points in the object would be rendered as 'infinitesimal'

points in the image if the lens apertures (and hence the

Fourier plane) were: infinite.

Now consider the situation of Figs.(2.1)11,12,13, where

both the object and the lenses are of finite size (but the

latter are still. required to be aberration frees)`. For angles

of diffraction up to 44 , (i.e.. spatial frequencies up to s1),

the situation in the Fourier plane is identical to the previous

'infinite lens' case, i.e. the Fourier transform relationship

is valid.. However, for angles such as c2 (where 4).0).(41* i3 ) 9

-44-

partial vignetting effects can occur, whereby contributions from

certain regions of the object may be lost from the system, leading

to a breakdown in the transform relations between object and

'Fourier' plane (and hence between 'Fourier' and image plane).

For angles of diffraction greater than + , total vignetting

takes place.

In order to obviate these vignetting effects, it is

necessary to provide a stop in the Fourier plane, as shown in

Fig..(2.1)14, which gives a sharp upper limit snot (angle of

diffraction 4 maxl to spatial frequencies passed-by the lenses

from/to all.parts of the object/image.. Thus there is effectively

a truncation function in the Fourier plane which validates the

transform relationships between object/Fourier/image planes:: in

a 'finite lens' system.. There is now finite resolution in the

image plane, since the truncation function pill.(2su ) 2sv )

max: max transforms to a point-spread function Airy (2s

max. x-, 2s mmay):..

Alternatively, (and more appropriately), we can express. the image

resolution limit by stating that Et defines the highest spatial MOt

frequency consinusoidāl complex amplitude 'grating' that can be

passed by the system (i.e. treating the image as an additive

assembly of gratings:rather than as a convolutive assembly of

point-spread functions). If::

a = Physical diameter of the object field..

b= ft I t " Fourier t r

= - Maximum spatial frequency passed by the system max

4 mare = Maximum angle of diffraction

max = Maximum semi-angle of ray cones forming points in the

Fourier plane

these parameters by:.

b 2Xfs max

a *-b

b 2f

e max 74 2f

Relation(2.1)17

Relation(2..1)18

Relation (2..1).19

Relation(2.1)20

--45 -

p = Aperture of the transform lens;

f = Focal length of the transform lens

A = Wavelength of the light usedi

Then in the situation exemplified by Fig.(2.1)14, we can relate

Relations (2.1)17-20 and Fig..(2.1)14 effectively define

the fields, ray angles and conjugates over which the lenses

must be 'aberration corrected' in order that the Fourier

transform relations be valid.. The fact that the two sets of

conjugates are symmetrical flee- Fig..(2.1)157 encourages a

symmetrical design for each transform lens, particularly in

the special case of equal diameter object and Fourier fieldst

(i.e. when a=b, D=2a =2b). This point is covered more fully in

discussion of the main bench design:, Section 3.2.2

Two other factors (also covered in greater detail later)

which are relevant to the transition from 'theoretical' to

'practical.' systems are:-

This case has been used in Figs.' 2.1)14,15

-46-

(fir_); reflection properties of the lens:surfaces

(iv) scattering tt it tt tt tt

Real glass lenses reflect some proportion of an incident

beam of light, which may thus be lost from the system; additionally,

there may be multiple reflections (particularly in multi-element

lens designs) which, given the coherent nature of the light,

can lead to optical interference effects in the system.. In

order to prevent this, it is desirable to put an anti-reflection

coating on the lens surfaces (i.e. to 'bloom' the lenses).. The

fact that Fourier transform lenses are normally designed for

use at only one wavelength makes it possible, to attain very good

reflection suppression from only moderately sophisticated

coatings.

The use of coherent light also leads to problems if there

is scattering from the lens surfaces or from bubbles, etc..

in the glass itself Ideally one should check the glass blanks

for bubbles before generating the lens surfaces, and careful

inspection of the polished surfaces should be made before

anti-reflection coatings are applied.. Features such as striae

or scratches can cause spurious linear features in the diffraction

pattern of an object, whilst 'pitting' may lead: to a more

random scattering ('speckle'), adding to the background noise

level in both the diffraction and image planes of the system.

Once coated, it is very important to protect the lenses from

dust, etc. (as far as possible) in order to keep the noise level

low.-

-47-

The beam that is used to illuminate the object should also

be reasonably 'clean'. The illumination system commonly usedi

gee Fig..(2.1)1g acheives this by focussing the 'raw' laser

beam onto a small pinhole; this acts as a 'low-pass' spatial

filter, removing high spatial frequency noise from the beam.

It is evident that the collimator should have a standard of

aberration correction (for the single conjugate set: front

focal plane-.Ó), surface finish, etc., similar to that of the

transform lenses.

Fig..(2.i)17 shows the arrangement of the principal elements

in a 'classical' coherent spatial filtering bench, having an

overall"_ magnification (image-object) of -1, The lenses are

shown as simple singlets;, but in reality would be multi-element

units (in order to attain the necessary degree of aberration

correction). Many variations on this basic layout are possible,

using different magnifications, or enabling particular types of

observation, measurement and recording of the Fourier and image

plane light distributions to be made.

To conclude this section, some practical results from

a transform bench are presentedI in Fig.(2.1).18, for comparison.

with the theoretical examples of Figs(2.1)3,4.. Note that the

'theoretical'kunctions are represented by the 'practical' point-

spread.functione3 of a finite-aperture system.

Figa.(2.1)19,20 show examples of directional and annular

filtering respectively.. In Fig..(2.1)19t, the vertical grating

t In this case convolution between the individual grating spectra has made it necessary to block all_ parts of the Fourier plane except that corresponding to the inclined grating alone..

-48..

has been eliminated by blocking the horizontal direction in the

Fourier plane (along which its spatial frequency spectrum

extends). In Fig..(2.1)•20, a low-pass-filter has been applied:

to block out all_spatial frequencies equal to or greater than

the 'fundamental' (.1st. harmonic) of the fine grating, which

is thus eliminated completely. The lower harmonics of the

coarse grating are passed by the filter, so its basic

structure is retained; however, there is obvious degradation

of the grating since the higher harmonics have been blocked

out..

-49-

2.2 DISPLAY

2.2.1 Experimentation

a), The requirement of a manageably large Fourier plane

with reasonable aberration correction but only 35mm input

format led to a choice (for the pilot bench) of a long focal:

length doublet telescope objective as the first Fourier

transform lens.. If used in the conventional arrangement, (object

in front focal plane), this would have led to a very long

overall:. system;. hence, the object was placed well_ inside: the

focal length of the transform lens. This change of conjugate

has two additional effects:-

i) There: is a departure from the strict obedience to the

exact Fourier transform of Relation(2.1)16; it can be shown

(SHULMAN 1970-a) that a quadratically varying phase error

is introduced, in the expression for the Fourier plane complex:

amplitude distribution, but does_not affect the intensity

distribution (power spectrum); since the pilot bench was not

intended for use in a holographic filtering mode (unlike the

main bench)., this factor was of no practical concern here..

ii.) One must expect some change in the image aberration

correction of the lens (this is not invariant of conjugate).;;

however since the light distribution in the major plane of

interest .(the Fourier plane) can be considered to result from

-50-

the focussing of parallel. diffracted beams from the object,

one should expect good correction in this plane from a lens

of this (telescopic) type.

The actual specification was:- focal length f = 850mm.

bens aperture D:= 55mm.., object distance u - 100mm. By

calculation using a modification of the results of Section

2.1.3 one finds that this gives a Fourier plane diameter of 42mm.

at a spatial frequency of 50c/mm. over an object plane diameter

of 50mm.. The object illumination optics consisted of a

standard microscope objective beam exp4.uder (focal length 8mm.)

and pinhole filter, with a doublet collimating lens (focal

length 250mm.)• giving a beam diameter of 35mm..

b),, In addition to the above conditions, it was decidedlto

plan for an overall: system magnification (final image planer

object plane) of about *2_, in order to obtain a final image

of a size permitting rapid visual inspection. Bearing in mind

the long focal length of the first transform lens, this require-

ment produced a very long overall system, and it was found

necessary to fold the optical path at some point; this fact

was turned to advantage as explained in paragraph (c). The

magnified final image was obtained in two stages>: a large

aperture triplet lens (focal length 200mm.) was used as the

second transform lens, the real image produced by this being

enlarged and re-imaged by a doublet relay lens (focal length

100mm.).

- 51

c): Preliminary experimentation ha& suggested the desirability

of providing some form of simultaneous display for at least

one Fourier-pair of planes in the system; it was hence decided

to make a double fold in the system, allowing simultaneous

side-by-side viewing of the Fourier plane (obtained via a

beam-splitter) and the final image plane, on a ground-glass_

observation screen, (an arrangement which also helped to

compact the system). A. scale diagram of this configuration

is shown in Fig(2.2)1. As shown in the figure, the addition

of a second beam splitter and a microscope objective allowed

projection of a magnified image. of the central region of the

Fourier plane onto the same viewing screen.. The three display

functions of the overall_system are illustrated in Figs(.2.2). 2-4.

d). As several of the lens surfaces in this system were of

only moderate quality, and possessed no antireflection

coatings, the resultant images suffered significant degradation

by speckle and double-reflection interference rings; however,

some simple filtering experiments were performed, such as:-

low-pass filtering (using an iris diaphragm),

high-pass. filtering (using a circular spot of opaque

silver paint on a glass slide),

directional filtering (using a narrow slit).

- 52 -

The test objects includeditransparencies.of simple

binary geometrical figures (regular and random arrays of

circles, lines etc. of various sizes and spacings), and

copies of actual ERTS scenes, reduced to a 25mm x 25mm format.

2.2.2 Recommendation

The quality of the filtered images obtained was considered

too: poor for serious investigation at this stage, but these

experimemis did. confirm that simultaneous display of the

Fourier transform and final image planes, at fixed magnification

should be regarded: as an essential requirement of the final

system, It was further reckoned that this should constitute

a minimal display facility, it being deemed-highly desirable

to include, in addition, some provision for viewing the

original object plane simultaneously with the Fourier and final

image planes, and also some means of displaying subsections of

all these planes at a variable magnification, the magnification

control for the Fourier plane to be independent of that for the

object/image planes. Justification for this development

rests on the following considerations:

a) Discussions with geologists had already stressedithe

importance of the ability to examine subsections of a

geophysical scene, in order to compare and relate. - analyses

of these' subsections to an analysis of the whole scene.- This

is particularly important for ERTS. pictures, where a singles

frame covers an area of a size likely to encompass several

- 53 -

major variations in terrain type and structure. Magnification

of such a subsection in real time allows easier recognition

of the features under investigation, and hence permits a

more rapid matching of a particular geological feature to

its corresponding power spectrum, as viewed in the Fourier-.

transform plane.. This facility is central to the use of the

optical bench in a 'training' mode for a terrain classification

scheme based (at least partly) on Fourier plane information,

(envisaged as a possible task for the,main bench)..

b) Tba pilot bench studies showed that the 35mm format

copies.. of 70mm original ERTS:transparencies contained very little

information 'strength' (interpreted as relative intensity

in the power spectrum) at spatial frequencies higher than about

20c/mm, and appeared., to display significant azimuthal

variations in the power spectrum only at spatial frequencies

of 5c/mm or less; similar figures were found to be typical of

other sorts of remote sensing imagery at this format;

(seeūFig.(2.3)6).. At this range of spatial frequencies, it

is reasonable to expect only a minor reduction in depth of

modulation during a 70mm to 35mm format photographic reduction,

thus suggesting (for ERTS: imagery, at least) that for a 70mm

format input, one should not expect to find major contributions

in intensity to the diffraction pattern at spatial frequencies

in excess'of 10c/mm, and that significant directional

information might be confined to spatial frequencies of

2.5c/mm or less. In studies using 70mm format ERTS imagery

- 54—

therefore, one should find it necessary to investigate in

detail this central region of the diffraction pattern,

(corresponding to a patch of approximately 6mm diameter in

the physical Fourier plane of the main bench);; hence the

need: for a magnification system for the Fourier plane display..

The emphasis on this region of the power spectrum for

70mm ERTS.imagery was however complemented by the need to

ensure an adequate Fourier plane display for non-ERTS1 object

inputs, possibly outside the field of remote sensing, (e.g..thin

rock section microstructures), in which the information

content was liable to extend to higher spatial frequencies_.

Thus it was found that in order to retain resolution of

detail in the Fourier plane, while coping with power spectra

from a variety of inputs, it would be highly desirable to

build-in a variable Fourier plane magnification system, in

addition to the object/image plane magnification system

mentioned previously.

c) The crude filtering exercises perfomed on the pilot system,

Some examples of which appear in Figs.(2.5)2,3,4,7, were

sufficient to give a suggestion of the types of operation

that might be applied to geophysical images on the main bench.

It became apparent from these exercises that the usefulness of

filtered imagery in enhancing or suppressing pictorial features

should be ascertained by comparison with the unfiltered scene.

Simultaneous display of the unfiltered and filtered: images allows

one to make a swifter general assessment of the degree of success:

-55-

of a filtering operation in extracting a given category of

feature information.. This holds good whether the filtering

operation is such as to cause only subtle modifications to the

image (in which case one can estimate its effects by reference

to the appearance of selected 'test' features belonging to the

category under investigation), or whether more drastic changes

are; implemented; compare the sets of Fig..(.2.5)2 and Fig..(2.5)4.

(1)' If simultaneous display of the Fourier plane in addition

to the unfiltered'. and filtered images is realised, then one can

monitor the changes imposed on the image by the filter, with

'real-time' reference to the size, shape, location and orientation

of the filter itself. Hence one has the basis of a rapid feed-

back system for control and optimisation of Fourier plane:

operations, with a human operator acting as an evaluative link

between the filtering operation and its result.. Lee block

diagram representation Fig.(2.47.

The significance of such a system as shown in Fig.(2.2)5

is its emphasis on the importance of the processor as an

interactive learning tool4 however it should be noted that

this does not reduce its capabilities as an automatic batch-

processing facility. In Fig.(2.2)5, the substitution of

an electronic control unit (incorporating a pre-programmed,

sequence of instructions for control over optical processing

operations and input/output data), for the human 'evaluation

unit', would allow conversion from one aspect to the other..

- 56 -

Indeed it was envisaged at this stage in the project, that many

image processing problems might best be tackled by initally

using the optical bench in its interactive learning capacity,

in order to determine a suitable sequence or group of operations

which would then be utilised in an automatic batch-processing

routine.

2.2..3 Implementation

Experience with the pilot bench had shown that although

the aforementioned displays might be obtained by the use of lenses,

beamsglitters, etc. alone, this was a somewhat clumsy and

inflexible procedure. It was decided. to carry out some trials

using a closed.circuit television system as a~ display channel,

with a view to building this into the main bench design, if

found suitable for the task. For these display tests, copies

of 70mm x:70mm ERTS. imagery was used (i.e. 55mm x 55mm picture

size), and the folded, pilot bench system was modified to give

1:1 magnification between object and final image planes.

The CCTV system chosen comprised a high resolution

separate-mesh vidicon fitted to a solid-state monochrome

television camera, and 17" (43cm) monitor of industrial quality.

The vidicon spectrall.response characteristic:under tungsten

illumination was designed to match the human visual response

curve, peaking at about 550nm; as a result its true characteristic

(independent of source), peaked at 4?5nm, conveniently close

to the 488nm wavelength of the laser.- Resolution of the complete

system was quoted at about 300 x 300 picture points over the

- 57 -

displayed field.. By racking the vidicon tube, (a control

provided on this type of camera)., a very wide range of

magnifications and field sizes could be catered:for. The

camera was used without the ground-glass:observation screen,

when displaying the Fourier plane, and protection against

damage to the vidicon tube by the intense 'zero-order' light

was afforded by either:

i) Blocking half the Fourier plane with a knife edge.

iii). Using a thin wire to block the zero-order «

iii) Projecting the Fourier plane onto a thin glass slide

bearing a small drop of silver paint to act as the 'zero-

order stop'.

It was usually found necessary to place a field lens in the

plane under observation, in order to direct all ray bundles into

the physically small aperture of the camera lens.. For

examination of very low spatial frequencies in•the-Eburier

plane, 'primary' magnification was provided by a 100mm f/4

enlarger lens and 'secondary' magnification by the:CC:TV system..

The spatial. performance of the system is summarised. in

Fig.(2.2)6,7 with particular reference to use with 55mm x.55mm

ERT. images.

Although the linear dynamic range of the system was

quoted at about 60-100 intensity units, it was realised that

use of the laser output power control would allow placement of

this anywhere within a total range of 104 intensity units,

a figure commonly reckoned to include all useful information

- 58 -

in the power spectra_ of geophysical images. In fact

(PRESTON JR. 1972-a) suggests that one can estimate the

maximum „possible signal to noise ratio in the optical Fourier

transform plane by taking as 'signal' the intensity of the

central. Airy disc lobe, for a 'uniform-field' object input;.

the same reference quotes a value for this quantity of 40dB

(104:•1) as being typical of a diffraction-limited lens system

possessing high quality surface finish and antireflection

coatings. This optical noise. is of course stationary in time;. when using the CCTV system, one has to contend also with

temporal fluctuations (as a result of the vidicon dark current

and video-signal-associated noise), which can lead to 'final'

signal-to-noise ratios of between 10041 and 1 :1 (20dB - l:dB);,

as measured: by displaying the video-signal on an oscilloscope.

Despite this, the television proved to be a very convenient display

device for both the Fourier transform plane and object/image

planes. Moreover, later studies_ on the pilot bench and main

bench, (e.g. Section 4.2.1) have suggested that in many

instances, the image information expressive of a particular

geological process (e.g. foliation, fracture-zoning etc.) can

be characterised: by a spatial frequency band of sufficient

'narrowness' that the corresponding intensity variations in the

transform plane are contained within the effective dynamic range

of the television channel, i.e. that the spatial-frequency-bandwidth

limits of the CCTV system measurements are broad enough to allow

extraction of useful_ geological information without shifting

the mean position of the band, in the Fourier domain.

-59-

A further factor that favoured the adoption of CCTV

display was its provision of contrast control, which made

possible simple intensity enhancement operations, a

particularly useful feature when examining the inherently

diffuse-Fourier transforms of quasi-random objects, as demonstrated

by the following example.

Fig..(2.2)8 is an image formed by sonar scanning of an

area of the seabed off Hartland Point, S.W. England.. The

area. shown is about 3km x 2km in size, at a depth of about

1003n and includes an exposure of faulted Palaeozoic rock

beds.

For the 35mm;format image used:in the bench, the scan-line

frequency was about 30c/mm.. Figs.(2.2)%9,10 are records of the

diffraction pattern taken directly on 35mm.'Pan F' film in

the Fourier plane at two different exposure levels=. These

are to be compared with Figs.(2.2)11,12 which show the CCTV

picture of the diffraction pattern at two.diffrent monitor

contrast settings. It can be seen that the contrast control

allows one to readily distinguish the envelope of the low-

spatial-frequency 'core' of the pattern from that of the higher

spatial frequencies; to perform the equivalent operation by

direct photographic recording generally requires-a change of

exposure and development times.

An assessment of the contrast range on the television

monitor was made by photographing the television image of a

standard neutral density step-wedge, and comparing this with

a direct photograph of the step-wedge, made using the same

illuminating source, recording emulsion, and film processing

-60-

conditions.. Defining:a s, ADĒ, A Dp , as the photographic

step-sizes of respectively: the standard step-wedge, its

direct photographic recording, and the photographic recording .

of its television image;. also, defining P as the photographic contrast co-efficient and YT as the 'effective monitor contrast',

one can putt

A D p

A D: = p

p (-ŌT Aps) D p vt~ s..

So that Zri. = A P

providing that the photographic exposure is such as to place:

the density steps on the linear part of the (H-D) characteristic

in both cases.. (This simple analysis ignores non-linearities

in the equivalent CCTV characteristic). ADI D _ (for thre

AD different monitor contrast settings) and A P

were measured by

taking densitometer traces across the photographic negatives,

and yielded the following results:

WT (typical minimum) - 1.4 (absolute minimum) = 0 (of course)

IT- (typical maximum) 2.0 (absolute maximum). = 2.7

61 —

These results were taken from the traces shdtm in Figs.(2.2):

13-16, and represent the television channel Ō value.. at the

mid;.point of the input intensity range;; comparison of the-

curved envelope of Figs.(2.2)14-16 with the linear envelope of

Fig. (2.2)13. illustrates the non-linear nature of fhe input/output

intensity characteristic of the television (i.e.. the dependence+

of f on input intensityk. It should be noted that the

departures from 'level' (uniform density)_ of the 'treads'

in the density staircase result from the systematically

non-uniform intensity distribution of the illnminaeting source

(an enlarger light-box). A consequence of this is that

measurements of åD (density range between steps) were made

at the step-edges or 'risers' in order to avoid: error due to

this effect.

In all, the CCTV system was considered to be a sufficiently

important asset to warrant its inclusion in the main bench.

In order to meet the display requirements mentioned in Section

2.2.2., it was decided to 'use two complete CCTV channels:. one

to handle the object and image plane information, the other

to deal exclusively with the Fourier plane. Details of the

main-bench display are given in Section

- 62

Z. 3 VIDEO-PROCESSING

2.3.1 Problems.

It should be mentioned at this stage that the transforms✓

shown in Figs.(2.2.)9-12 were obtained from an object

transparency that had been mounted in refractive-index-matching liquid., in order to reduce photographic grain noise

(PRESTON JR.. 1972-b)t. This noise arises from the random

variations of optical path-length through the emulsion and

film base, caused mainly by the granularity of the emulsion..

By enclosing the transparency in a 'gatis4 of transparent

fluid,of a similar refractive index, between optical flat.,

one can . compensate for thickness. (although not refractive index)`

variations. In the case of Fig.(2.2)8, aacrude gate was formed

by placing the transparency in microscope immersion oil],between

cover glass slides. Some idea of the improvement gained by using

even this simple construction can be gleaned from Figs..(2.3)1,2,

which are identically exposed. and proceesed_recordings of the

diffraction patterns from 'gated' and 'ungatedt' identical copies

of the sonar image mentioned previously. A-significant feature

of the 'ungated.image' transform is the increasedazimuthal

spread of light about the major direction of diffraction,

when compared to the 'gated image' transform.

-63-

This mounting technique was used extensively during

the pilot bench experiments, but was superseded. by an

improved liquid gate in the main bench design, details of

which are to be found in Section ;*•3.:

In addition to grain noise in the diffraction pattern,

one also expects a certain amount of scattering from the

optical elements of the transform lens, due to multiple

reflections and imperfections in the surface finish

(PRESTON JR. 1972-a).. It was recognised that this could not

be avoided on the pilot bench (which employed: 'stock' lenses)

and was considered:to be a major factor governing any difference

in quality between pilot bench and main bench results.

Underlying these factors, both of which have a bearing.

upon the task of providing a meaningful quantification of

diffraction-plane information, one must consider also the

statistical nature of the Fourier-transform itself. Since-

the individual features that comprise: any one feature-classy

or category present in remotely-sensed geophysical imagery

can be described-as 'quasi-random' in nature (i.e. possessing

w certain amount of variation in size, shape and photographic

density), it follows that the development of feature

categories based on Fourier-plane information depends not

so much on accurate 'point-by-point' intensity measurementa--

of the diffuse diffraction pattern, but rather on the

identification of intensity 'structures' or 'regions' in

the plane, which can be associated with specific feature

classes, (see GRAEMENOPOULOS; 1975),. (In this work the term

camera and monitor,- (BARIvETT AND :TILLTA!I3 1979).

- 64 -

'spatial signature' is used to describe Fourier plane

structure in a broad land-use classification context).

As mentioned before, the CCTV channel is a valuable asset

in this task; it was discovered, however, that its powers

could be greatly extended by the inclusion of an electronic

video-signal processor (developed by a colleague, Dr. T.H.. W'i.11:iams

at the Applied Optics section, Imperial College), between the

2.3.2 TechniQuew

The basic action of the video-processing unit, is

illustrated in Fig.(2.3).3; the continuous variations in

intensity of the incoming video-signal are converted to

'step-functions' by slicing the signal as shown « The mean

value about which slicing is performed is set by the

'level' control of the processor, which then assigns a

single intensity to all. points on the input signal lying

within each 'slice:' or range of intensity.. In this example,

there are four equal ranges spaced symmetrically about

'level', the size of the combined range (termed the 'window')

also being controllable. Points on the input video-signal

which lie above or below the limits set by the 'level' and.

'window' controls are assigned to the further slices:--

'peak white' and 'base black' respectively.

The data reduction operation implicit in this technique

appears to be of considerable value when applied to diffraction

-65-

plane information, as shown by the following example.

A.35mm format black and white transparency, copied from

a colour composite LANDSAT-A. frame, was used as input to

the optical bench. The area analysed, shown in Figs..(2.3)4,5,

includes the western section of the Grand Canyon, leading

into Lake Mead, Arizona. Fig.(2.3)6 shows the diffraction

pattern as displayed on the TV monitor, without the video).-

processor. As described in section 2.2.3, the intense

central portion of the plane has been stopped out to protect

the TV vidicon. The numbers on the photographically superimposed'

scale indicate spatial frequency in cycles-/mm of the transparency

(of approximate.scale 1.10 million); the region of the

Fourier plane shown thus covers spatial frequencies of about

0.1 - 1.2 cycles/km on the ground', corresponding to

spatial periods of 10 - 0.8 kms. This display suggests that

topographic structures characterised by this range of widths

are relatively strongly represented along alignments 0000 --090°

(bearing in mind the discussion of Section 2.1.21, and

weakly represented along alignments 090° - 180°.. However,

the diffuse nature of the diffraction pattern makes it

difficult to discern finer details of its structure. Fig..(2.3)7

shows a video-processed. version of the pattern, in which

the controls have been adjusted to position all four of the

'equal intensity range' slices over most of the displayed'

section of the Fourier plane. In this mode, it becomes possible

to pick out individual lobes of the diffraction pattern

(e.g. at 010°, 090°x, 130°, corresponding respectively to 100°,

180°, 040°, in object space), which may specify directions of

-66-

particular significance. An alternative form of display is

shown in Fig.(2.3)8, where the application of a further

controllable electronic operation, aptly termed. 'relief',

allows enhancement of the boundaries between the slices,

and gives a graphic representation of the 'hill of intensity'..

Figs.(2.3)7,8, show the display at one particular setting

of the 'level' and 'window' controls; manipulation of these

gives scope for the examination of more specific-regions

or parameters of the diffraction pattern.. For instance, by

making the 'window' very narrow, (effectively merging the

four equal-range slices into one), and redisplaying the

'peak-white' area as 'base-black', one can acheive the

'contouring' effect shown by Fig..(2.319, where the only part

of the pattern displayed.. is that of intensity equal to the value

of 'level'.

2.3.3 Roles

The above example demonstrates the capacity of the

video-processor to produce a very rapid, moderately accurate,

quantitative representation of Fourier plane data. Intensity

accuracy, in terms of linearity and noise, and spatial

accuracy in terms of geometrical distortion and resolution,

depend.essentially on the quality of vidiaon tube and monitor;.

signal degradation in the processor itself can be made negligible

by refinement of the electronics beyond those of the prototype

version employed in these studies. Whilst the performance

of the system, as defined by these parametersi is somewhat

- 6? -

inferior to that of the scanning sector described in the

following Chapter 2.4, it should be remembered that the latter

device was developed for the fairly specific (though important)

task of quantifying directional information from the Fourier-

plane in a routine, usually non-interactive, way. The television

display and video-processing equipment was intended to be

used ēither in a complementary role, (as a fast interactive

device to select data for more detailed measurement by the

scanner), or in its own right, to aid more diverse studies of

Fourier-plane and image plane information, (see:e.g. Section

4.3.2)..

-68-

2.4 DIRECTIONAL SAMPLING

2.4.1 Design and Construction

In pursuing the basic idea described in Sections 1.2.2

and 1.3.1, an azimuthal scanning and measurement system for

the diffraction plane was devised as follower.. (See Figs.(2.4)1,2,3.)

Discussions with photogeologists had suggested. that the

sampling sector angle should be variable within limits of

about 1° and 15° of arc, allowing the angular resolution

to be set with regard to the particular material under

investigation.. 'Eyeballed' rose diagrams are frequently

compiled in 5o or 10° steps, the choice of step-size

depending mainly on the geologist's estimate of:-

.(a) The limits of statistical variation of direction

appropriate to a given geological structure.

(b)i The amount of labour and time involved relative

to the value of the information extracted.

Regarding (a);; in many instances, a geologist's

background knowledge and experience may define the point

at which no increase of physically significant information

can be obtained by an increase in angular resolution. The

-69-

relevance of this to machine-derived roses is that 'over-

sampling' can occur, possibly necessitating subsequent

averaging of the output data, unless: the geologist's

recommended angular resolution can be implemented at the

scanning stage; (when 'eyeballing', sheer effort is an

efficient deterrent to oversampling).

In contrast there are also circumstances under which

a geologist might desire to construct rose diagrams- with

an angular resolution somewhat higher than usual, (e.g. in

order to distinguish between 'linear' and 'shallow arcuate'

macroscopic trends in a fracture trace group, by plotting

roses for a series of subsamples within the group). In

such cases., consideration (b): becomes prominent for eyeballed

material, but may be greatly relaxed by the use of machine

derived measurements of sufficient angular resolution.

In addition to the sector angle specifications, ,

one must consider also the radial limits (high and low

spatial-frequency cut-offs), of the sector aperture.. At this

stage in the project, there was little experience in relating

the spatial frequency spectrum of an image to its inherent

geophysical information content;; however, the pilot studies

discussed in Section 2.2.2, suggested coverage from the

projected design maximum of the main bench lenses

(N 80-90 c/mm) down to about 2.5 c/mm. The lower limit is

subject to both theoretical and practical constraints-as

f ollows

-

-70-

(a). In general theoretical terms, we can relate a spatial

frequency of (for example) 2.5 c/mm to structures in the

object plane transparency having a characteristic 'size'

or periodicity of 15 c/mm =0.4 c/mm. On 55mm xti55mm

ERTSima imagery, (where Imm represents about 3«36km or 2 miles):

this represents structures on the ground of characteristic

'size' 1.3 km. From the standpoint of lineament analysis

a low frequency limit of this order of magnitude would:

generally allow the sampling sector to include all features

for which statistical compilation is an appropriate technique;;

within a single ERTS.frame, linear features of this width

or wider are morem rite 1.e to analysis as specifics

individual elements—of-the terrain, since they are not

likely to forma. sample large enough for statistical parameter&

to have much meaning (we are here treading the boundary between

serial. 'Object plane' and parallel 'Fourier plane' techniques✓

of classification)). Experience has shown however (see:e.g.,

Section 4.2.1), that for lower-level imagery (e.g., aerial photos),

it may be valid to include 'on bench' spatial frequencies lower

than 2.5 c/mm in rose diagram generation.

(WI The exclusion of very low frequencies is necessary in

order to prevent their contribution to the integrated light

energy 'swamping' that of higher frequencies within the sector

of integration: it must be remembered that the power spectrum

of geological images- typically peaks sharply towards zero

spatial frequency, i.e. the energy per unit spatial

frequency range rises very rapidly at 'very low' spatial

frequencies where 'very low' is here taken to imply 'comparable

to that of the image aperture itself'; as a quantitive example,

- 71 -

one might reasonably choose to exclude all. spatial frequencies

corresponding to periods greater :hah 10 of the aperture

diameter; for a diameter of 55=1 - this would mean a low-frequency

cut-off of .v 0.2 c/mm - well within the limit suggested in

(a).; even with a 10mm diameter 'subsample' aperture, (for which

the corresponding cut-off would be A+ 1 c/mm), the geological/

statistical considerations of the previous3 paragraph still.

predominate.. Nevertheless, the radial variation of the power

spectrum must obviously be borne in mind when dealing with

measurements derived from integrations over a finite radial range,

(a point which will. be resumed later).

CO, Additionally, one is faced-with the practical difficulties

of manufacturing a scanning aperture to fit a spatial frequency

plane whose scale is pre-determined by the focal length of

the transform lens. Adapting Relation(2.1)17 we find that for

the main bench design ( A 0

r = 0.341 s

where r(mm). is the radial distance in the Fourier plane

associated with a spatial frequency s(c/mm)'. A=low-frequency

cut-off of 2.5c/mm is equivalent to an inner radius of

0.85mm for the sampling sector. This is; sufficiently small

to suggest that the sector disc-should be rotated via. a

circumferential rather than axial drive. However, if

we set a tolerance of 1%- on radial deviation, then the

inner and outer radii of the sector must be concentric to

.488 zu.103mm. f 7 x:102mm) .s-

-72--

8.5/4"; it was decided to relax this tolerance to 3%

(i.e. centring to 25pm or 0.001"), pending actual trials

of the device..

A summary of the sector specifications is given in

Fig..(2.4)a,.

Some thought was given to the possibility of.

synthesising the sector by photographic means using 'Kodak

Photoplast' material, which consists; of a very high contrast

emulsion ('Kodalith'). on a rigid, transparent plastic

substrate. This idea was rejected since it might lead to

undesirable light scatter in the transparent sector aperture:,.

and would involve a series of fixed.-sector angles rather

than a single adjustable unit..

The eventual design, Fig..(2.4)3, utilised two overlapping

thin steel discaB, which were clamped:at their circumference

into a. recess in the body of the device (for detail see

Fig.(2.4),6);; the sector angle was governed by the angular

overlap of the discs, which could be manually adjusted on

releasing the clamping ring. A. small' diameter central hole in

the discs supported. the shaft of a watchmakers' screw;, the

head of this screw, suitably smoothed and blackened, acted

as a block to the lowest frequencies in the Fourier plane «

The disc surfaces were also coated with a strongly absorbing

matt black paint.. The cylindrical body was mounted in the

inner race of a large diameter needle-race-bearing, the

latter being chosen to comply with , the narrow tolerance on

'radial wobble'.. The housing of the outer race was mounted _

- 73 -

on x..y-z translation stages (to allow precise postioning

of the sector centre), and also supported the rotational_

gear drive. Fig(2.4)4 is a schematic illustration of the

drive mechanism; use of a worm gear and circumferential gear—

ring gave a system with small angular backlash, whilst

leaving the region behind the sector disc clear for the

passage of light to the photomultiplier. The meshing waa

set to allow -0.2° angular freeplay in the sector (a wider

tolerance, since it was envisaged that the sector would,

normally be driven in only one direction).. However, the

ball-races supporting the worm shaft were seated on spacers,

adjustment of which could reduce the freeplay, (at the expense

of increased gear wear). For the initial trials of the sector,

the worm shaft was driven manually via a contrate wheel; a

stepping motor was introduc.ed_later, when the scanning system

was automated, as described-in section 2.4.3.

The transfer of light from the sector disc plane to

the photomultiplier can be accomplished in several. ways..

An obvious arrangement is to use a lens to re-image the

Fourier plane, with change of magnification if desired.,

onto the photomultiplier face; however, this sets undesirably

high tolerance limits on the photocathode uniformity, since

different sector positions image onto correspondingly different

portions of the photomultiplier face. Instead of this, one

can place the leas immediately behind the sector disc, with

the photomultiplier face in its back focal plane; it then

acts as a 'field lens' to the Fourier plane (as shown in Fig.(2.4)5),.

light from each point in the sector aperture being spread.

- 74 -

over the same region of the photomultiplier facet. The lens

aperture:A is determined by the Fourier plane diameter b

whilst its focal length F relative to a given photomultiplier

face?is set by the maximum semi-angle 6 of the ray-cones max.

forming points in the Fourier plane. An input object of radius

40mm (diagonal of ERTS transparencies) and spatial frequency

90c/mm, used with a transform lens of 700mm focal length

leads to:- (see? Relations (2.1117 and (2.1)20):

= 2 xt 0.341 x 90mm 60mm

maw _ ,an 70 radians. q0 0.06 radians

and thus

A. = 70mm minimum (allowing space for mounting)

F = 0112 mm 04175mm maximum (for 10mm photomultiplier

face radius);

in practice a stock lens of L = 75mm, F = 150mm was used,

only moderate aberration correction and surface finish

being required for this task.

t It is important to bear in mind however that the distribution of light over this region is spatially non-uniform and will. vary in a non-uniform way as the sector rotates;.see-Section 2.4.2.

-75-

In choosing a photomultiplier it was borne in mind

that the apparatus required only moderate performance in

terms of dynamic range, sensitivity, response time and

cathode area.. Preliminary measurements on the power spectra..

of ERTSsimages (F.F. GRAY - private communication) suggested

that the light level at a spatial frequency of 2.5 cycles/mm

might typically be about 103 times its value at 90 cycles/mm..

(The latter being essentially the noise level due to scattering

this can be considered a convenient maximum figure for the

required dynamic.. range, the actual angular variation in the

power spectra being, in general, considerably less« Calculations

on the absolute light levels in the main bench, (later confirmeds

experimentally), estimated a power in the collimated-object

beam of about 25mW, yielding about .25mW.in the Fourier plane

if all frequencies.below 2.5c/mm are excluded, thus giving

about 1.5e, or 1500nWin a 2° sector. For a standard 11-stager

photomultiplier, rated sensitivity is about 200 Amps/lumen or

1.6 x 105 /444#J, with a maximum allowable anode current of

102/AR , and hence a maximum allowable light level. of 0.6nW.

The 'excess gain ' would: thus be Ō 6 = 2500. if the whole

sector down to the 2.5c/mm low frequency limit were used, but

might only be about 2.5 for measurements taken in a high-frequency

annulus;, compensation could be easily effected by control of

the photomultiplier power supply, adjustment of the laser source

power, or the use of filters.

-76-

The photomultiplier tube chosen was a 30mm diameter general

purpose type with a low dark current 'S' cathode. This was

coupled to a digital panel meter which displayed the reading

in four digits and produced an output suitable for connection

to a tape punch.. Subject to the availability of extensive s

digital computing services,-this choice of output was

preferred to the alternative of an analogue voltmeter with

polar chart recorder, since it offered:

a), more flexibility in display, since the punch

tape information could be transferred_to a wide,

range of output peripherals, providing e.g.. continuous

or histogrammed polar plots on paper or microfilm;

or line-printed linear histograms and reading listings.

b); the possibility of manipulating the information

e.g., by averaging, normalising etc., and of

incorporating additional information from the tape

e.g. correction factors from monitored fluctuations

of the laser output power.

c)- easier incorporation into an automatic or

semi-automatic system.

Although this technique would not provide the 'instantaneous'

hard-copy of a chart-recorder, some form of display could

be obtained from a computer terminal within a few minutes

of tape generation, so this was not considered to be a

serious shortcoming.

-77-

Direct photomultiplier-meter coupling via a load resistor

was found= to be unsatisfactory, since the requisite resistor

value was non-negligible compared to the input impedance of

the panel meter, leading to static (D.C.). inaccuracies in the

reading; moreover, the finite capacitance of the measurement

circuits gave rise to an unduly long RG; time, (many seconds).

causing dynamic inaccuracies, i.e. inability of the meter

to follow photomultiplier signal changes at a reasonable rate..

These problems were overcome by replacing the load. resistor by

an PET 'current to voltage converter', presenting a large

input impedance to the photomultiplier and a small. output

impedance to the meter. With this modification, the

restabilisation time of the meter, following x:103 to 1 change

in photomultiplier signal level, was typically only • - 1

second, thus allowing dynamic testing of the full. sector

disc/photomultiplier/panel meter combination..

2.4.2 Uniformity and Simulated. Object Tests..

The purpose of this stage in development was to

ascertain whether the scanning unit was functioning correctly

with respect to simple object inputs, before proceeding

to more complicated. 'real.' objects; in particular, to check

that the system was free from angular bias.. The first test

transparency consisted: of a slit (clear on opaque background).

of width 0.1mm=and length 15mm, mounted in immersion oil..

Readings were taken at 5° intervals, using a sector of 5°

width, over the full spatial frequency range allowed by the

-78 -

pilot system (2.5 - 50 cycles/mm); the general form of the

photomultiplier output readings was such as displayed. in the

graphs of Fig.(2.4)7. After several scans, the following

general observationssemerged:-

1). For a fixed object location, the peak output signal

(i.e. at the two diffraction lobes of the slit), showedi

significant variations with respect to object ori:e:ntat:i.on

2)- For a fixed slit orientation, the peak output signal

showed&significant variations with respect to object

location within the object, , 1nne

31 For fixed.. slit location and orientation, the peak output signal showed significant variation between the two

opposite diffraction lobes (of theoretically equal

intensity)..

Result (3), was attributed to mechanical eccentricity of

rotation of the central stop of the sector discs, a problem

which is considered in Section 2.4.3y(until the modifications.

described therein were made, the effect was eliminated by

iteratively lining-up the centre of the Fourier plane with

the centre of eccentricity)..

- 79 -

Results 1) and 2) were thought to be due to a non-uniform

distribution of sensitivity over the photomultiplier cathode

face. Discussion of this is based on the example of Fig..(2.4)7,

which also demonstrates the order of magnitude of the variations

involved. In this figure, the four plots correspond.

to the respective radial slit positions A,B,C,D as indicated,

and the 90° shift in plots B & 11 relative to plots A-& C

has been compensated for, so that the peaks line up to

facilitate comparison. Referring now to Fig..(2.4)8, it will

be realised that the light distribution impinging on the.

diffuser in front of the photomultiplier, when used in the mode

suggested in Section 2.4.1, is effectively a demagnified image

of the object, spatially filtered by the. sector aperture in .

the Fourier plane. Although the diffuser spreads this light

out over a large region of the photomultiplier face, it is

evident that different object positions will tend to be

associated with correspondingly different regions of the

photomultiplier face; hence spatial non-uniformities of

sensitivity in the latter will_ lead to the undesirable variations.

mentioned above.

In order to put the problem on a more quantitive basis,

it was decided to construct a_map of the photocathode

sensitivity. This was done by removing the photomultiplier

from the sector disc assembly and projecting the collimated

beam (normally used for object illumination) directly onto the

diffuser;. the beam was stopped down to 2mm diameter by an iris

diaphragm, and the photomultiplier, with its diffuser, was

- 8o

traversed-on an x-y grid across the stationary light spot,

readings being taken at 2mm intervals. (This method ensured

that the intensity of the light spot remained constant over -

the scan, and was thus chosen in preference to the alternative

of scanning the light spot across the stationary photomultiplier,

which would have demanded a much higher spatial uniformity of

intensity in the initial collimated beam>. The resultant

matrix- of readings was converted to a contour plot of

sensitivity (in arbitrary units) over the photomultiplier face,

which constitutes Fig.(2.4)9..

The steep falx-off at about 25mm.diameter indicates the

approximate limit of the photocathode sensitive area.. However,.

the most interesting feature is the distinct asymmetry about

an axis trending approximately 100/190°, causing 'above

average' readings around_the 90° radius and 'below average'

around_ 270°; remembering that the filtered image isinvertedi

with respect to the original object, we can see-that this

plot tends to confirm the results of Fig.(.2.4)7.. Further

to this, by calculating the integral of the sensitivity

function along radii 0°, 90°, 180°, 270°, out to a distance

of about 3mm (corresponding to the size of the demagnified

slit image), a crude estimate of the angular bias for the

test object was obtained, and was found to agree.in order

of magnitude with the observed variations of Fig..(2.4)7.

These findings cast serious doubt on the suitability

of the photomultiplier as the detector in this application:.

in the above example, deviations of up to 10% from the mean

- 81

were observed; these were far i elow_:the •projected -:

levels of precision in other components of the main bench

optical system, and are perhaps unacceptably :low even to geologists_..

Moreover, there was no chance of applying systematic

correction factors, since the errors involved were strongly

object-dependent.

L possible escape from this quandary was provided by

noticing that if the matrix:of readings forming the basis:

of Fig,(2.4)9 was 180°-averaged about the centre.(i.e the

average of each diametrically-opposite pair of readings was

substituted in place of both members of the pair), then the

resultant contour plot, shown in Fig.(2.4)'10, became highly

symmetrical (i.e. with a much-reduced angular bias) and fairly

flat out to a diameter of 15mm. By calculating integrals of

this averaged function along several radii, out to a distance:

of 7.5mm, the maximum angular bias inherent in this plot was

estimated to be about - ; %, a quite tolerable figure.

The implication of this: is that if a light distribution

possessing 180° rotational symmetry impinges concentrically

on the photomultiplier diffuser, (within the 15mm diameter

circle), the resultant photomultiplier output will be effectively

free:from angular bias effects.. The two-dimensional power

spectrum of an object, as generated on the bench, is just such

a distribution. Moreover, use of this distribution would also

overcome the 'positional bias effects' mentioned earlier,

although in their place would be some 'spatial frequency bias'

due to the rise in averagA sensitivity towards the centre of

the photocathode. A•true demagnified re-imaging of the

diffraction pattern onto the photomultiplier diffuser would

-82-

require the addition of an extra lens in the light path through

the scanning assembly; however, it was noted that the short

depth of focus of the collecting lens allowed a good approx-

imation to the desired symmetry to be obtained, simply by strong

defocussing of the photomultiplier and diffuser relative to the

collecting lens. Subsequent test measurements were made using

this new arrangement.

In the next test, the object transparency used. was a

negative of the previous one (i.e. an opaque bar on a clear

background); this was done in order to gain some measure of

the difference in 'scattered, light level:.' between 'positive'

and. 'negative'" versions3 of the same object, 'scattered light'

here being taken to be principally light entering the Fourier

plane as a result of scattering from dust or defects on the

transform lens surfaces, (oil. immersion being used to minimise

emulsion-grain scattering at the object). The results are

shown in Fig.(2.4),11, where plots (a) and (b)• correspond to

the appropriate indicated bar positions; note the large

discrepancy in signal level between the two lobes of plot (`a):,

(approximately perpendicular to the axis of antisymmetry in

the photocathode)•. Plots (c)- and (d), are 180°-averaged versions_

prepared. from (a) and (b) respectively, and demonstrate the

effectiveness of this procedure;. their peak heights differ by

only ' 1 % from the mean, a figure almost as good as that

theoretically predicted above from Fig.(2.4)10.. The peak signal

level compared to the scattered light level for this plot is

about 3, which compares with a value of about 15 for the

-83-

'positive' object (taken as a mean from the plots of

Fig..(2.4)7).. These figures are rather low, indicating the

considerable amount of spurious scattering that was present

in the pilot system, and emphasising the desirability of a_

very high standard of surface finish and cleanliness in the

main bench.. Also, there is a marked increase in scattering

in changing from a 'positive' to a 'negative' object, which

has especial importance with regard to the prospect of applying

diffraction pattern analysis to fracture trace overlays; it

confirms that there is a significant advantage to be gainedl

in using clear 'targets' against an opaque 'background'

rather than vice-versa..

The final test in this series used: the opaque bar object

but omitted the oil immersion procedure. The result appears,

(180°--averaged), in plot (e) of Fig.(2.4).11, and shows not

only ax further large increase. in the scattered. light 'level:',

but also much broadening of the diffraction lobe due to

emulsion-grain scattering, thus confirming the necessity of

index-matching of the object transparency for making diffraction

pattern measurements. For comparison, the other results

mentioned in this section are also summarised on this graph,

normalised_ to the same peak value.

It should be emhasised that the success of the 180°-averaging

technique employed in these tests depended: on the essentially

fortuitousrantisymmetry in the spatial distribution of sensitivity

over the photomultiplier face, (although this might be a syste-

matic result of the method of manufacture of the photomultiplier).

- 84 -

A more irregular distribution would have caused a gravely

problematical situation, against which the advantages of

alternative diffraction pattern,me-asuremen.t ~•de.vic:ess_wēip;h v4*y l eavily,

(e: . the 'ROA' array - a commercially available solid-state.';' 'detector comprising arrays of wedge-snared and ,annular..elements:)'

2.4.3 Automation and Real Object Tests

The extension of diffraction pattern measurements to

the analysis of 'real' (remote sensing) imagery took place

chronologically in parallel with the conversion of the

directional sampling system to semi-automatic operation;

it is deemed convenient to deal fully with the latter subject

before proceeding to the former.

The automation of diffraction-plane scanning and

measurement was accomplished by the addition of three.

instruments to the basic system of Fig..(2.4)1, viz; a

stepping motor to provide the mechanical drive to the sector

disc;: a tape punch to transfer the output information of

the digital panel meter onto paper tape; and a control unit

to co-ordinate activities within the complete system, which

thus appears systematically as in Fig.(2.4)'12. The detailed

design and construction of the control box, together with

the integration of these instruments into the system was

undertaken by a colleague, Mr. G. Talbett, of the Appliedi

Optics Section, Imperial College; the following account is

therefore intended to briefly summarise their operation «

-85-

The stepping motor was of a stock design, requiring

200 steps per revolution of the drive spindle;; with the gear

reduction used, this entailed 35,000 steps per revolution

of the sector disc, implying a possible angular resolution

(i.e. of 1 step) of about 0.01° of arc or 0.2 milliradians.

In fact this was much less than the frenplay in the gear

train, which thus set the limit to angular accuracy; the

starting position of the sector could be set by eye to an

accuracy of about 0.1° of arc (2 milhiradians)-. The tape

punch, also a stock item, was used to generate 8-hole paper

tape in a code suitable for acceptance by a remote terminal of

the college computer, the coding operations being performedh

by the control box as explained below. The basic functioning

of the control box itself is shown schematically in Fig.(2.4),13

and proceeds as follows:

Once the starting button is pressed, the stepping motor

drive board commences sending pulses to the motor, which steps

accordingly;; the pulses are-counted by the control electronics

and terminated when they reach a number (preset by the operator).

equivalent to the required angular sampling interval. Although

the photomultiplier output follows the light level during the

sector movement, the panel meter is kept locked at the previous

reading until the stepping terminates; it is then unlocked,

allowed to reach and display the photomultiplier signal

level, and after a time interval (preset by the operator) is

relocked at this new reading. The time interval required for

settling of the meter is usually less than one second, but can

be increased_if there are extremes of variation in signal level

between successive readings. After relocking, the signal from

-86-

the panel meter is coded_by the control;_ electronics and fed into

the tape punch; when punching of the reading ceases_, the

control box checks to see if the number of readings taken has

reached the value (preset by the operator) equivalent to the

required total angular range (usually 360°). If it has

not, the cycle is repeated by reactivating the stepper,

which moves on to the next reading; if it has, the control

box resets itself, ready for restarting by the operator.

Typically, the entire. sequence of operations of sampling

a 360° range at 2° intervals takes about 5 minutes and generates 3 metres of paper tape. This speed is comparable to .

that at which the tape can be read in to the local terminal of

the college computer. 180°-averaging is then applied, and

hard-copy (generally in the form of linear or polar plots) iia-

producediin a few minutes (limited by the output speed of the

terminal). Typically, the minimum time interval between.

the start of sampling and the completion of hard-copy is about

15 mins. The complete directional sampling system thus

embodies, a'slow, interactive/non-interactive, technique,

(interaction with the data being via instructions typed on

the terminal), which complements the 'fast interactive' video—

processing option of Chapter 2.3, its advantages over the

latter being better sensitivity, linearity and geometric fidelity..

(NOTE: The computing . respō biliti46 ,iēre` h sb. ūiide'rtaltēn

-87-

The aim of the following series of angular scans of the

diffraction patterns of 'real' objects (remote sensing

imagery of some form) was to attain some initial feeling for

the relationship between the subjective assessment of the

directionality in a scene, and the corresponding 'objective'

measurements provided by the sector disc._ The principal

scene used for these scans was_- the seabed sonargraph shown in

Fig.(2.218 and here repeated as Fig..(2.4114. This was chosen

partly because it displayed an obvious directional trend;

partly because the diffraction pattern had already been

photographed and was thus conveniently available for comparison;

and partly because, (being an image composed of regular scan-lines).,

it was desired to obtain some quantitative idea of the effect

of the scan-lines on the shape of the directional plot.

The first scan shown used a sector of 10° angular width

with 10° sampling intervals, utilising the full spatial.

frequency range of the system. 2.5-50c/mm; Fig.(2.4)'15 is a

linear plot of the results and Fig.(2.4)16 is the somewhat more

informative polar plot (rose diagram). The large lobe extending

between roughly 010° and 045° of this plot clearly associates.

with the predominant rock bedding in the object scene.

Information on directional strengths is represented by the whole

of the 180° envelope, but for a 'unilobal' shape such as this,

we can take the ratio of the major to minor ordinate radii as

a crude empirical measure of the 'directionality " of the scene

(in this plot the value is about 4:11; the significance of

doing this will be appreciated from later results in this section.

Fig..(2.4)17 and Fig.(2.4)-18 are further scans of the same

-88-

pattern, taken using 5° and 2_° sector angles/sampling

intervals, respectively. The intensity of the object

illn in ating:beam was multiplied by factors of 2 and 5

respectively relative to its value for the 10° sector scan,

in order to compensate for the smaller sector angles, thereby

'normalising' the scale of the plots. As one would expect,

these scans show the effect of increased angular resolution

in defining subsidiary lobes within the main envelope;

the 'horizontal' lobe (at 273° since the original transparency

was slightly askew: in its mounting) corresponds to the

'vertical.' scan-lines of the sonar picture. The overall

directionality of the plot is of course unchanged by the

increase of angular resolution.

The next two figures are included to demonstrate the

severity of emulsion-grain scattering effects in 'real'

imagery.• Fig.(2.4)19 shows 2° sampled scans over the range

2.5-50c/mm of the diffraction patterns from oil-immersed and

non-immersed., copies of the seabed: sonar

transparency (cf. Figs.(2.3):1&2),. The same intensity of

illuminating beam was used for both scans, so if one neglects

the small difference in transmission losses between the two

objects, one can regard the plots as comparable in absolute terms.

The figure shows that within the spatial frequency range 2.5-50c/mm,

taken as a whole, there is a higher level of diffracted light

from the non-immersed object; this is presumably balanced by

a corresponding loss of light energy from the frequencies below.

2.5c/mm, relative to the oil-immersed object. The more

significant difference however lies in the 'smoothing out' of

-89-

the finer lobes for the non-immersed; object as opposed to the

oil-immersed one. This can be shown more clearly by artificially

adjusting the 'oil-immersed' plot in the following manner.

By making the assumption that the diffraction effects due to the

emulsion grains in the transparency are to a first approximation

isotropic in the Fourier plane, one can compensate for the major

size difference in the plots by adding a 'D.C. level' (i.e.

isotropic increment) to the values of the 'oil immersed.' plot.

(c=omparison between the 'modified oil-immersed:' and .!non-immersed' in

plots is madekFig.(2.4)20, which thus highlights the loss; in

angular detail which results from omitting to immerse the

transparency (and confirms that the assumption of isotropy

mentioned above is only approximate). It should be mentioned

that the photographic emulsion, used in these tests was

'Ilford pan F', which although not as fine-grained as the recording

emulsion of ERTStransparencies, was taken as representative

of the wide range of input materials that might conceivably be,

used on the bench.

The next series of scans made explored the variation in

directionality with respect to spatial frequency, in the

transform of the sonar scene. Consecutive 20 sampling scans

were taken over three bands of spatial frequency (i.e. annuli

in the Fourier plane), defined by stops over the sector, at

2.5-5c/, 5-10c/mm and 10-50c/mm. The total light energy in

each of the bands was measured using a photocell, and the

intensity of the illuminating beam correspondingly adjusted:

in order to normalise the scans relative to each other

with respect to total_ intensity in each band). By dividing

- 90

through with the normalising factor, the readings could also

be expressed in absolute form (i.e. including the effects of

the differing total energies from the different bands)-. The

absolute. plots are shown in Fig.(2.4)21 and the normalised ones.

in Fig.(2.4)22.

The ratio of total intensities between the 'high' 'medium'

and 'low' frequency bands was 1 t 3.3 5 10, the dominant

concentration of light in the low frequencies causing that

scan to be similar in shape to the previous 2.5 - 50 c/mm

measurements. The medium and high frequency bands, however,

show significant departures in the lobe distribution; as

expected, the scan-line lobe becomes- relatively very prominent

at high spatial frequencies.. The overall envelope shape also

varies somewhat with spatial frequency, the basic 'direction-

ality' (as defined previously), ranging from 6 at 2.5-5c/mm,

through 4 at 5-10c/mm to 2 at 10-50c/mm, indicating a

plausible (indeed rather expected) increase in randomness.:

of feature direction between the coarser and finer details of

the scene. The relevance of the high frequency scan is a little

suspect e b croix?ē 'the . fundamental scan-line frequency of

30c/mm is included-in-its range (although there are also many sub-harmonics), so there must be some, contribution from the

side-orders; however, since these are much dimmer than the

zero-order, the 'overlap contribution' is probably small.

For comparison with Fig..(2.4)14, the spatial frequency bands_

should be expressed in, 'real-space' as opposed to 'bench-spacer

terms; thus 1 cycle/mm is equivalent to 10 cycles/km, and the

- 91

scan-line frequency;} corne 300 cycles=/km, corresponding

to a scan spatial period of about 3.3 metres 'on the ground'.

A_significant problem that arose during these tests was

the possibility of distortion of the readings caused by mis-

centring of the sector disc relative to the Fourier plane.

Initially, lining-up was done by traversing bodily the whole

sector scanning device, using dial guages for control

measurement, until the zero-order diffraction spot was concentric

with the central stop in the sector discs. However, it was

found that scans taken following this procedure showed:

irregularities (before 180°-averaging) that were too severe to

be attributable to the cathode non-uniformities mentioned

previously. Investigation showed that the 'central' hole

by which the stop was mounted in the sectors (see: Section 2.4..1)

had not been positioned to the specified tolerance of 25turn

(the miscentring error was in fact 120/0m)!; moreover the college

workshops subsequently claimed. that they did not possess the

facilities for maintaining the tolerance in this operation..

The short-term solution was to line up the centre of the

Fourier plane with the true centre of rotation of the discs,

so that the diffraction patterns were at least scanned

symmetrically, although the eccentricity of rotation of the

stop meant that there was necessarily a residual absolute

inaccuracy in the readings.

This problem was overcome in the permanent solution,

which entailed the construction of a centring unit to fit

between the discs and the main body of the rotating assembly.

— 92

(See!Fig.(2.4)23). This allowed the discs to be adjusted:

so that the stop coincided with the centre: of rotation

(an operation performed iteratively, observing the stop

during rotation via a travelling microscope), at which point

they were clamped permanently.. The central stop was then

lined up with the centre of the Fourier plane using

translation stages as before.

The following is an example showing the effect of

miscentring on rose diagram shape. Fig..(2.4).24 is a vertical

aerial photograph of a 2km x 2km area of the Yorkshire

Pennines, showing part of a limestone plateau. Weathering

and vegetation have helped to outline several fissuresin

the surface, including the prominent sets developed along the

rectangular jointa:that are characteristic of this type of

rock.. Fig..(2.4)25 is the un-averagedx 3600 rose diagram

for the circled. area. produced~ by sampling in the range

2.5-25e/mm (25-250 c/km 'on the ground') at 2°"resolution.

The diagram has been rotated through 900" relative to the Fourier

plane so that Lobes in the diagram should be parallel to

prominent directionality in the object. The effect of

miscentring is particularly evident in the angular discrepancy

between the lobes corresponding to approximately north/south..

In. the 1800-averaged version, this gives rise to misleading

information by suggesting the prescence of two separate sets:

of roughly NA lineations. The correctly-scanned version is

shown in Fig.(2.4)27. In contrast to the single N/S. direction,

this shows several lobes in the 0700-0850 directions, corresponding

well. with observed structure in the picture..

An example of rose diagram generation from an ERTS

transparency is provided in (BARNETT AND HARNETT 1975).

-93-

2.5.- DIRECTIONAL .FILTERING

As mentioned in section 2.1.1,-the quality of the filtered:.

imagery obtained on the pilot bench was somewhat low, (though

not unaccountably so, given the nature and quality of the

components used). However, the results obtained did provide

useful guidelines to experimentation on the main bench, and.

their presentation in this chapter allows visual comparison

with those ..achj:fiv.ld on the latter (see Section 4.3.1).

2.5.1 'Inclusion' and 'Exclusion' filtering

The principal aim of these studies was to produce images

in which directions were selectively enhanced or suppressed

as an aid to the visual. detection of linear features. The

filters used wereall. of the passive, binary, amplitude-only

type (i.e. their complext. amplitude transmissivity at any given

point was real and of nominal value 1 (clear) or 0 (opaque))..

AlL filters of this type block out some proportion of the

optical information inherent in the input scene; thus the

filtering process amounts to a selective degradation of the

image in both spatial and tonal resolution.

Hence, if it is wished to enhance linear features running

in a particular direction, the modus operandi is to degrade

resolution of features running in all other directions (or

at least in directions closely adjacent to the 'desired' one),

-94-

whilst maintaining good resolution of features running in the

'desired:' direction.. The archetypal filter for this operation,

hereafter termed a 'directional inclusion filter', is shown

in Fig.(2.5).1, together with its practical derivatives;: the

latter either include or excludb the zero-order and very low

frequencies isotropically, since practical experience has

confirmed that directional filtering of 'near-zero' frequencies

causes(,usually undesirable). severe changes in the appearance of

major structures.in the picture, rather than the (desired.),

adjustment of local. detail..

The complementary 'directional exclusion' filters, also.

shown in Fig..(2.5)1, degrade resolution of structures aligned'

within a limited range of directions, whilst maintaining

resolution in other directions;; the purpose of such filters

is to block dominant directional trends in a scene to allow

easier visual inspection of weaker directions. Note that there

is no distinction between 'inclusion' and 'exclusion' for angular

band-width (Y):=900

The fact that use of. these filters produces an image built

up from 'degraded.' point-spread functions, is of significance

when the nature of the input imagery (in particular its contrast),

is considered, since the degradation may cause a loss of local_

contrast in the scene. Thus, although impressive results can

be obtained from 'binary' images (clear features on an opaque.

background or vice versa), or high-contrast continuous-tone images,

those derived from lower contrast continuous-tone images- are

somewhat less striking. In the published literature, there are

several examples of directional filtering applied to true binary

— 95 —

images such as magnetic contour maps (ARSENAULT et.al. 1974),

and lineament overlay traces (PINCUS AND DOBRIN 1966)., or to

high-contrast continuous,tone images such as seismograph records

(DOBRIN et.al. 1965),, (DOBRIN 1968), rock-section photomicrographs

(PINCUS. 1969), and aerial photographs of glaciers (BAUER et.al. 1967)..

(CHEVALLIER et.al.. 1970) provides an example of exclusion...

filtering on an aerial photograph of moderate contrast, but

in this case the structures involved are particularly well-

defined ones (later urban development on Roman field systems)..

Moreover, in the example of inclusion filtering which appears.

in the same reference, zero_-order blocking has been applied

(almost certainly of necessity)- to boost the contrast; thin

is an entirely legitimate exercise for the subject under study

(an archaeological one), but the loss of initial grey-tone

information involved might prove undesirable in a geological

context... Almost the only example of geologically relevant direct-

ional filtering on an aerial photograph of moderate contrast

is provided.-by (FONTANEL et.al. 1966). In view of this deficiency,

it has been decide&to devote the illustrations in this chapter

to examples of filtering involving continuous-tone images of

geological interest.

Initial experiments utilised a narrow slit as a directional

(inclusion) filter, but this was soon replaced by a small

/library' of carefully-cut card wedges, embodying several

different values of (inclusion and exclusion). The zero-order

was either passed through a pinhole in the card or blocked by

a spot of pa;inue deposited on a glass slide (placed adjacent to

- 96 -

the wedges along the optical axis).. The filters were

mounted in a rotational stage. After checking that the

filters operated satisfactorily upon simple test objects:

(such as.: the gratings of Fig..(2.1)19)., they were applied:

to a variety of geological image transparencies.

2.5.2 Examples (zero order passed:).

Fig..(2.5)-2b shows a portion of an unfiltered negative of

the Hartland Point' sonar scene, (which was chosen as a

representative high-contrast object);, as viewed through the

system, (i.e. including double-reflection and coherent scattering

effects). The degree of deterioration due to the latter is

apparent from comparison with the input .positive,

Figs..(2.5)2ct-h are filtered versions of the image_, using a

zero-pass inclusion filter of angular bandwidth Y =20°.

The centre direction of the included range (indicated by arrows)'

is as follows (taking the vertical direction as 000°)s—

c :000° d:030 a x060° f :090x° g 120° h :•150°. It can be seen that

in this scene, the filtering operations have emphasised the

various systems of linears quite effectively, particularly the

long faults in c and lineaments at 080° and 100° in f. Note

also the preponderance of lineation around 120° in g, compared

with the scarcity aroundz030°-060° in d. and e; this is in

agreement with the rose diagram for the region (see Figs.(2.4)16-2z).

- 97 -

An example employing an image of moderate contrast is.

provided-by Figs.(2.5)3a,b.. Fig..(2.5).3a is a negative copy

of the unfiltered: aerial photograph shown in Fig..(2.4)24;:

Fig.(2.5)3b is a directionally filtered version of the image,

using a q1=20°, zero-pass, inclusion filter, aligned;. for

0300. This has enhanced the two long linears:(arrowed);

however, one can see that the general deterioration of the

scene, brought about by filtering, is fairly severe, and may

touch on the limits of acceptability to a photo-interpreter:-

i.e. the gain in direct, 'locational' information due to

optical enhancement of the linears, may well be balanced.by

the loss of indirect,.'contextual' information pertaining to

them, (relative to the unfiltered image). ERTS images are

particularly vulnerable in this respect, owing tō their

excellent spatial and tonal resolution; under these circumstances,

directional exclusion filtering becomes preferable to inclusion.

Fig.(2.5)4a is an unfiltered ERTS image showing aportion

of S.W.: Angola gatalogue no. E1007 0036 (this is a negative

copy derived from a colour composite original). The rose✓

diagram obtained-by scanning at 1.5 - 40c/mm, (0.16 - 4.40 cycles/km

'on the ground'), is shown as Fig.(2.5)5, and Figs.,.(2.5)4b-d.

were produced by using a y =20°, zero-pass, exclusion filter. In Fig.(2.5)4b, the sector blocks directions 070° - 090°

(eliminating the major lobe of the rose diagram at 0800);

directions showing particular enhancement are around 0550 and 100°.

For Fig.(2.5)4c, the blocked range of directions is 1450 - 1650

and there is enhancement of linears in directions 125° and 180°

Finally, for Fig.(2.5)4d, blocking is at 040° - 060°,

enhancement at 0200 and 0750.

-98-

It is evident from this example that enhancement occurs

chiefly in those directions that lie adjacent to the 'blocked:'

directions in the scene. This observation was confirmed]on

other scenes, (and is in agreement with the appearance of the

filtered image that may be expected from a consideration of

the filter point-spread function, see Section 4.3.1). In

this situation, the rose diagram is a very useful guide in

choosing the alignment(s) of the filter (Sea BARNETT AND HARNETT 1975).

2.5.3, Examples (zero-order blocked)

Inclusion or exclusion filtering with a blocked

zero-order, is not commonly reported in the literature,

although it does occur in (CHE3TALLIER et.al. 1970);. The

'edge-sharpening' effect of zero-order blocking (due to the fact

that the high-frequency components forming edges are no longer

'masked' by the lower frequency components) is well-known, and

proves advantageous in the 'archaeological' imagery of the

above reference. However, when applying this technique to

geological images on the pilot bench, the result was generally

of dubious utility. A typical example is provided in

Figs.(2.5)6a,b, showing respectively, unfiltered and filtered'

versions of the sonar image used previously. The operation used:

te —10°, zero-block, inclusion filter, aligned:to pass features

running in directions 130° - 140°.

- 99 -

In common with many filtering operations, this form of

image presents a somewhat unfamiliar object'of speculation.:for

photogeologists. It is thus highly desirable to view such

images in parallel with their unfiltered versions, a

recommendation for the main bench design stressed in Section 2.2.2.

(Although this chapter is restrictedito discussion of

directional filtering, it should be mentioned that some work

on non-directional filtering (e.g. plain zero-blocking, without

wedges) was also carried out. The main bench studies that arose

from this are reported. in Section 4.3.2).

- 100 -

3.1 LAYOUT

As with the pilot bench, the design of the main bench

was based on the 'classical' system illustrated in Fig.(2.1)17,

but with certain modifications to the geometry and components_

used in order to meet the conditions imposed. at the start of

the project or developed during the pilot bench studies.

The major factors affecting the eventual choice of layout

can be summarised as follows:•

1): Minimisation of overall system length

The original specifications for the object and Fourier planes_

ledi to a telephoto lens design (see: Section 3.2.2), which gavee

an object plane to image plane distance of about 1..7 metres-

for a focal length of 0.7 metres. The possibility of further

economies in the overall-system length were therefore confined

to the illumination and collimation part of the bench..

2); Provision for holographic matched filtering:-

It had been decided at an early stage in the project to

include facilities for holographic matched filtering on the

bench (see:Section 1.3.1).

In this technique a collimated coherent reference beam

is arranged to interfere with the diffraction pattern of an

object scene o1(x,y)., (see Fig. (3..1)1) . . A-recording of the=

interference pattern on either a photographic or some other

medium constitutes a hologram of the diffraction pattern.

If the hologram is itself illuminated by the diffraction pattern

- 101 -

of either the same object scene=o1(x,y), or some other scene.

o2(x,y), (see. Fig.(3.112)., then the optical output of the

hologram in the direction of the original reference beam,

when Fourier-transformed, becomes the autocorrelation

o1(x,y1! @ o1(x,y), or the cross-correlation oa(x,y) o*(x,y)

of the input object scenes. This function has a sharply-peaked:

maximum if o1(x,y)i and o2(x,y) are very similar, ('well-matched');

in general, the height and width of the peak are measures of

the degree3 of correlation or 'matching' between o1 (x,y) and

o2.(x,y); hence the hologram is said to act as a 'matched

filter'.

In ordier to accomodāte this technique on the bench, it

was necessary to provide a reference beam, offset at an.

angle to the main axis of the bench, and a means of swinging

the second transform lens off the main axis, (using a vertical

line through the centre of the Fourier plane as the axis-

of rotation).

3) Stability of components:-

In view of the exceptional size and weight of the transform

lenses, the resultant supporting components were of massive

construction, to ensure rigidity and stability of the bench..

In addition, the matched filtering facility imposed the require-

ment of vibration stability to holographic standards.

It was decided. to mount as much of the optical equipment

as possible on a cast-iron surface table, the legs of which

rested on air•-cushions (inflated inner tubes)—a proven method:

- 102 -

of providing satisfactory vibration damping, used frequently

in Imperial College Optics section and elsewhere..

For the illumination system eventually chosen (see°Section

3.2.1) it was found desirable to provide an extension in the

form of a II-section girder which was bolted to the underside

of the table-top. The disposition of the various components

of the system on the table and extension is shown in Figs.(3.1)3

and 4. The arrangement of Fig.(3.1)3 is suitable for CCTV

examination of the diffraction pattern, filtered and unfiltered

images, and for producing rose diagrams from the azimuthal

diffraction pattern scanner. Fig.(3.1)4 shows the arrangement

used in holographic matched filtering, with the CCTV systems

used to display a test image and its cross-correlation with

a 'target' image.

For clarity, Figs.(3.1)3 and 4 omit to show the

supporting benches for the lenses, mirrors, beamsplitters, etc;

these are however covered in the appropriate sections of

Chapter 3.2 together with detailed descriptions of the other

components in the figures.

-103-

3.2 COMPONENTS

3.2.1 Illumination System

The light source chosen was an argon gas laser having

& continuous output of about 200 mW in its most powerful

lasing line (488nm.), the transform lenses therefore being

optimised to work at this wavelength. A laser of this power

was chosen to allow rapid measurement with good Fourier

space resolution using the photomultiplier/sector sampling

equipment developed on the pilot bench. The power requirement

had to take into account losses in the illuminating optics:

(see below), the likely variation of intensity with spatial

frequency (Section 2.4.1), and the sensitivity of the

photomultiplier (Section 2.4.1).

The coherence length of the laser beam was determined

by measuring the visibility of the interference fringes

formed in a: Michelson interferometer, as a function of the

optical path difference between the interferometer arms..

The visibility remained good for a path difference of up

to ±25mm (the first zeros of visibility were at +?5mm), so

it was decided to adopt the former figure as a tolerance for

the reference beam-object beam path difference in the design

of the holographic matched filtering aspect of the main bench.

- 104—

The laser was not fixed to the surface table but its position

and orientation were maintained by abutting the laser housing

feet against metal strips bolted to the table top. In the

event of it being necessary to move the laser for maintenance,

or for installation of further bench components, this arrangement

allowed the laser to be instantly re-aligned with the rest of

the illpm;nation optics.

The size of the transform lenses and their associate&

supporting unite;required the optical axis of the bench

to be in a plane some considerable height (30Smm was chosen),

above the table top. The beam from the laser was brought up to

this level via two guidance mirrors as shown in Fig.(3.211

and Fig . (.3.2) 3.. Studies on thermoplastic holograms (P.. GRAY - private

communication) indicated that reference beam angles of about

30° should be designed for in the main bench, and that, therefore,

a 'beside-the-lens' reference beam system was necessary, as

shown in Fig.(3.2)6, in contrast to the 'through-the-lens'

system of Fig.(3.2)5. The options that presented themselves

were

(a) splitting the unexpanded laser beam, expanding

and collimating object and reference beams

seperately.

(b). expanding and collimating the beam, using a small.

aperture collimating lens, and splitting off the

reference beam from the expanded object beam..

- 105 -

(c) expanding and collimating the beam, using a large

aperture collimating mirror, taking seperate

expanded-outputs from the mirror face for object

and reference beams.

(a) was clearly eliminated as requiring far more equipment

and space than the other options. (b) would have entailed

obtaining two high quality optical components (lens and

beamsplitter) versus the one (mirror) of (c).; moreover,

(b) would have placed several optical surfaces in the path of

the expanded beam in contrast to the single one of (c),

(i.e. (c) was a better choice on grounds of low coherent noise

from dust scatter); another advantage of the mirror system'

was that its inherent 180° fold could be used to make a much

more compact illumination system than (b);: in addition, large

aperture, high quality paraboloid:: (collimating)' mirrors were

available as stock items (and therefore relatively inexpensive.).

from astronomical telescope manufacturers. Option (c)- was

therefore adopted, the mirror being mounted in a support unit

bolted to the girder extension, and masked off to expose only

those parts of the surface required for the object and reference

beams, (Fig.(3.211).

For aligning the system, the mounting allowed fine tilt

adjustment of the mirror via three screws (Fig.(3.2)9);;

focussing was accomplished by mounting the self-contained beam

expander unit on a traverse table (Fig.(3.2)8), which allowed . it

to be racked along the mirror axis. A conventional beam expander

unit, consisting of a microscope objective and pinhole filter

(for beam 'cleaning') was used, (Fig.(3.2)2)..

-106-

For constructing holographic filters, (when both object

and reference beams were required>, a x40 objective was used

to spread the beam over both apertures in the mask, as in

Fig.(3.2)4. In other modes of use, (when only object illumin-

ation was required)-, a x10 objective was substituted and the

beam guidance mirrors were-adjusted: to confine the beam spread

to the 'object aperture' of the mask, i.e. off the mirror

axis, permitting a higher intensity object beam to be obtained,

as in Fig..(3.2)1.

In either arrangement, there was a variation of intensity

across the collimated beam(s), from the mirror, and the choice

of objective powers mentioned above was based on a compromise:

between the size of this variation and the amount of light

wasted at the mask. It was realised that in many applications-,

a significant intensity variation across the object plane

(e.g. ±50% ".of the central intensity) could be tolerated; this

is because:

(a) When recording images in the image plane of the

bench, the logarithmic response of photographic

emulsionspreducesthe intensity variations to

relatively small density variations..

(b) For Fourier-transformation, the object plane can be

considered to contain a product of the object amplitude

distribution with a slowly-varying illumination

amplitude distribution.. The Fourier plane thus:

consists of the transform of the object distribution

convolved with a modified point spread function

- 107 -

that corresponds to the transform of the

illumination distribution.. Since the latter is_

slowly-varying, most of the energy in the point

spread function remains confined to low spatial

frequencies;. hence there is no significant alteration

in the 'scale' of the point spread function. Thus

for most objects of interest, the 'envelope' of

the convolution is virtually identical to that which

would be obtained if using illumination of uniform

amplitude across the object.

It was, however, possible to provide more uniform object

illumination by using a higher power objective (e.g. x40)

off-axis, for applications where object/image photometric

accuracy was important.

The single angled reference? beam mirror shown in Fig.(3.2)6

suffers from several disadvantages which made it unsuitable for

incorporation into the main bench, namely:-

(a) There is no provision for equalising the reference

and object optical path lengths for holographic

recording.

(b) The shallow reference beam angle, (i.e. large angle

of incidence) requires the optical flatness of the

mirror to be maintained over an unusually large

length, compared to the other mirrors and beamsplitters

used in the display system (Section 3.2.4), which were

of a much more manageable size. Optical flatness

- 108 -

is needed.to maintain a sharp point-spread-function

in the auto/cross-correlation plane..

(c) The large area of mirror exposed to possible dust

accumulation, combined with the large angle of

incidence/reflection encourages beam noise from

dust scattering. This can adversely affect the:

signal-to-noise ratio in the auto/cross correlation..

In order to overcome these problems, the system shown

in Fig.(3.2)7 was used in practice. The individual mirror

lengths and angles of incidence were much smaller than that

of the single mirror of Fig.(3.2)6. In addition, the reference

beam path length could be adjusted by tilting and translating

the second mirror (on a sliding mount)) relative to the first,

as indicated. The mirror support unit could be bolted to the

table at several positions along the beam from the collimator

to supply a. wide range of reference beam angles= (approximately

300-60°)i, and is shown in Fig.(3.2)3 and Fig.(3.2)4. The

mirror mounts were of the designs described_ in the display

system (Section 3.2.4),.

It will be noticed that the geometrical path length of

the reference beam was considerably larger than that of the

object beam. This was necessary in order to equalise the

optical paths, since the object beam passed through a

considerable thickness of glass (transform lens and liquid: gate

windows) and index-matching liquid (in the gate).

- 109 -

3.2.2. Transform lens System

The collimated coherent object beam from the paraboloid

mirror passed-to the object plane along the principal axis of

the bench, defined by the transform lens system. The latter

is taken to consist of the lenses themselves together with

their associated_ mechanical support assemblies; discussion of

the object plane, Fourier plane and image plane stages is

deferred to Section 3.2.3.

The: original specification for the transform lenses is

given in Fig.(3.2)10. The design adopted as an initial model

was the six-element symmetrical system proposed: by (BLANDFORD 1970).,

but significant modifications (in the choice of glass types

and in the replacement of.cemented_by air-spaced doublets)- were

necessary in order to meet the specification. The design

chosen is shown in Fig.(3.2)11a.

An initial computer optimisation was made using catalogue'

glasses and this was followed by further optimisations as work

on the glassware proceeded, to take account of the real melt

refractive indices, test plate radii of curvature and element

thicknesses. Stringent inspection of the glass for bubbles and

of the worked elements for striae. was carried out in order

to minimise sources of coherent noise in the lenses, and a high-

quality stock antireflection coating, optimised to the design

wavelength of 488nm., was applied.

Fig.(3.2)11b shows a longitudinal section of a complete

mounted transform lens. It can be seen that the glass:

elements were precision mounted in a series of cells making

- 110 -

up an inner barrel, fitting into a thick-walled three-piece

outer barrel to give strength and rigidity to the assembly..

Naval brass was chosen as the barrel material in view of its

good stress resistance, thermal expansion and machining

properties.

Twyman-Green interferogram tests were carried out on

the completed lenses, .verifying them to be within specification

and therefore diffraction-limited over the desired object/image°

and transform fields.

Design of the lenses was supervised by Prof.. C..G.. Wynne

of the Optics Section at. Imperial College, and their mounting

and testing also took place in the Optics Section, primarily

under the guidance of Mr. F.D..Reavell.

It was realised that the relatively massive construction

of the transform lenses required that translation and tilt

adjustments be accomplished via a system of support units and

benches of a size and stability beyond that provided by

laboratory equipment manufacturers 1 standard items. The

solution arrived at utilised a combination of stock engineering

components and units designed and built in the Physics

department at Imperial College.

Each lens was supported by a matched pair of stock

V-blocks, the lens + V-block combination being treated as a

single unit to which the three orthogonal translations and three

orthogonal tilts were applied. The intention was to provide

a means of adjustment for intermittent rather than regular

use to allow initial precision alignment of the optical

system which would then be locked in position unless/until

realignment became necessary through possible future modifications

or additions to the system.

An identical lens support unit, shown in Fig.(3.2)12,

was used_for each transform lens. The V-blocks rested on a

flat steel plate and were kept in alignment by straightedges

(and the lens);. The horizontal adjustment screws, mounted in

one of the edging strips, provided transverse translation and

tilt in the horizontal plane.. Locking was performed by screwing

up against the opposite edging strip, using spacer blocks and

shim to give the correct alignment Of the lens to the axis,

defined by the illumination system. Vertical translation and

tilts in two orthogonal vertical planes was providediby the

three vertical adjustment screws, relying on the weight of

the lens to self-lock these adjustments. The ball,-ends of

these screws bore into slots in base plates attached to either

the fixed or the rotating optical benches respectively.

A: stock milling-machine table, bearing several precision--

parallel T-slots and V-slots, (which proved to be very useful

for mounting components)., was used as the fixed optical bench,

and was chosen to be of sufficient length to accomodate the

object and filter stages in addition to the first transform

lens assembly. Longitudinal horizontal translation of the

latter was attained by allowing its base plate to slide along

the milling-machine table, located by guides running in one of

- 112 -

the T-slots; the base plate could be clamped by a nut and bolt

also engaging in the T-slot, see Figs.(3.2),13,14. The milling

machine table stood on rubber pads on the cast-iron surface-

table; the large frictional force due to the supported load was

sufficient to make it unneccesary to bolt it to the surface.

Longitudinal translation of the second transform lens

assembly was accomplished by attaching its base plate to a stock

lathe top-slide, Fig.(3.2)15. The latter was mounted on a rotating

platform assembly, the function of which was to swing the second

transform lens horizontally off the main optical axis of the

system, when required: for holographic matched filtering. For

this operation, the axis of rotation would be defined: by a vertical

line through the centre-of the Fourier plane, and thus passing

through the fixed bench. It was therefore: decided to undercut

part of the milling-machine table to make room for a bearing

pivot beneath it. The removal of the bottom of the suds well

in the milling machine table left a hole by which the bearing

pin could be inserted.

A-full description of the rotating platform assembly is

given in Figs.(3.2)16-21. Additional points to note are

(1). The assembly, with top slide, less support unit and lens

attached, was designed to approximately balance on the line of

contact between the wheels and the surface of the cast-iron

surface table, thus avoiding excessive vertical thrust on the

bearing.

- 113 -

(ii). A detachable sighting pin could be fittest into a

vertical socket machined concentrically in the bearing pin..

During alignment of the system, the adjustment screws-in the

bearing base were used to translate the bearing pin until the

tip- of the sighting pin coincided with a focussed point of

light at the centre of the Fourier plane.

(iii) At the on-axis 'normal' and off-axis 'matched filtering'

positions, the rotating bench was locked to the surface table

by means of stock magnetic bases-:.

-

3.2.3 Object/Filter/Image stages.

Experimentation on the pilot bench (Section 2.4.2) had.

confirmed the desirability of enclosing object transparencies

in a refractive index matching liquid in order to reduce the

effect of random light scattering by the grains of the photo-

graphic emulsion. Measurements of the intensity distribution

of a slit image, made in the Optics Section; (F.G.. LEAVER:-

private communication) showed a reduction in scattered light

intensity of an order of magnitude in the case of a medium-grain

emulsion (Ilford N5.31) and by a factor of 2 or 3 for a holographic

emulsion (Agfa 10E75);. The benefits of index matching were

also reported in more detail by (WOJTOWIGZ 1971) who used an

inert silicone oil as the matching liquid; silicone oils were

also used in the liquid gate for a diffractometer described by

(HARBURN AND .RANNIK0:1971)), and it was decided to use one of

these oils for the liquid gate in this project.

The gate design chosen consisted of a tank supporting two

optical flats (windows), enclosing a slide mechanism to accept

single 70mm x 70mm mounted transparencies. The slides were

inserted andextracted: via a slot in the roof of the gate which

could be covered to minimise contamination of the liquid by

airborne dust, (Figs.(3.2)22,23):. One of the windows was.

mounted between rubber 0-rings and clamped to the gate body

by three adjustable screws:s this arrangement permittech the

window to be aligned parallel to the opposite window, of the gate,

since the elasticity of the 0-rings allowed an adequate: range

of movement, whilst maintaining _ 'ail- oil-tight seal, (Fig.(3.2)24),.

-115 -

The windows were aligned parallel to each other by

fluffing out wedge fringes in the reflections from their

inner faces of the collimated beam, before filling with oil..

The defluffed field was monitored as the gate was filled:to

check that no significant displacement of the windows took

place due to the variation in pressure of the oil at differing

depths in the gate. Only very weak reflections occurred in

the filled gate, due to the index match between oil and glass.

The outer faces of the windows were given an antireflection

coating similar to that used for the transform lenses.

it was envisaged that, should the bench be required for

batch-processing of images, an object stage that could

accomodate roll film spools, (cf. the gate manufactured by

Space. Optics Research Laboratories of Chelmsford, Massachusetts),

would be necessary: hence the tank was made thick enough to

hold spools in place of the slide mechanism.. The large

- thickness of oil and glass caused; a considerable shift between

the real and apparent object planes (as seen by the transform

lens) and also some aberration due to the variation in length

of the optical path through the gate experienced by rays within

the 'diffraction cone' from each point on the object.

Calculation showed however that the small_ angle of the diffraction

cone allowed: this to be compensated by defocussing, so that

diffraction - limite& performance could be maintained with

the gate. The large optical path increase introduced by the

gate between collimator and Fourier plane also had to be taken

into account when designing the off-axis reference beam for

holographic matched filtering (Section 3.2.1).

- 116-

The liquid gate was mounted on the fixed optical bench

via a support unit and sliding base plate designed along the

same lines as those used for the first transform lens, and

incorporating alL translation and tilt adjustments.

On extraction from the gate, a mounted object transparency

would be drained of most of its oil film in a dustproof box-.,

and then transferred to a further dustproof box for storage;

no attempt was made to remove all the oi1_from the transparency.

It was found in use that transparencies re-inserted in the gate

introduced only very slight amounts of dust, and it was thus=

possible to use the gate with a single charge of liquid for

many months. The gate was provided:: with a bottom drain hole to

allow easy replacement of the liquid when this eventually

became necessary..

It is not proposed to record here the many types and

modes of construction of spatial frequency filters, a subject

that has been well covered in the works of (BIRCH 1972);

(GOODMAN 1968), and (PRESTON 1972)..

The main intention in this project was to use passive

binary amplitude filters of directional (wedge-shaped) and

textural (annular) form, in response to their apparent utility

in geophysical image processing tasks, as mentioned in Section 1.2.2.t

t It should be mentioned, however, that the bench was also used extensively for holographic matched filtering; and that further developments, particularly in the installation of a Mach-Zender interferometer between the transform lenses, have also allowed. phase filtering operations to be implemented..

Experimentation on the pilot bench had shown that

low-pass: filters, (Fig.(3.2)25)., made by piercing sheets of

foil or thin plate were quite satisfactory.. Drops of paint

on microscope slides were testecb as_ high pass:filters, but

these were soon replaced by filters on photographic film

using 'Kodalithe high contrast emulsion. These were made

by drawing out and photographing large versions of the

desired filters. The disadvantage of these filters was that

fixed, emulsion remaining in the clear areas (after photographic

processing) caused considerable scattering of the light in

the Fourier plane, i.e.. introduced much noise into the system.

This was overcome by using a reversal bleaching process in place

of the conventional photographic processing; in addition to

producing positives rather than negatives from an original

drawing, the bleaching process.strippech the emulsion from the

clear areas, so filters made in this way contributed only an

acceptably small increment to the optical noise-,level. Using

this procedure, suites of filters based on the forms. shown in

Fig.(3.2)25 and Fig.(2.5)1 were produced.

The filters were mounted in slides which were supported.

by a translation stage made up from stock optical bench

fittings, to allow precision positioning in the Fourier plane,

Fig.(3.2)-26. The unit gave horizontal and vertical translation

within the plane and also rotation about the optical axis

(for directional filters). It was mounted on a sliding base,.

engaging with a T-slot of the fixed.. optical bench, to permit

focussing of the diffraction pattern onto the filter; se& Fig.(3.2)20.

•

...

- 118 -

Much of the observation in the image plane was performem

via one_ of the CCTV systems; but it was also found convenient

to view the plane directly on the ground glass screen of a

4" x 5" sheet film camera back, Fig.(3.2)27. This providedi a

convenient means of generating hard copy output, using a

shutter at the laser to control exposure.. The camera back formed

a free-standing unit on the table top, but could be connectem

to the rotating optical bench to prevent any relative movement

between the second transform lens and the film plane.

3.2.4-Display and Sampling System

Following the pi10t bench research of Chaper 2.2, the

display system utiliaed two closed-circuit televis_ion . systemS',

each consisting of a camera, video-processing unit and monitor •.

The use of these CCTV channels fulfilled all of the recommendations

put forwar~ in that chapter, including independent ranges of

magnification of the Fourier and object/image planes, and

simultaneous side-by-side viewing of the object and filtered

image_., As described; bel-owj, the main bench facility also

allowe'd superposit~on of a 'test' object onto its cross-­

correlation with a 'referenc~' object, when the bench was used

for matched- holographic-filtering •

The monitors, (which were interchangeable between the

cameras) comprised one monochrome and one colour set.. In the

latter, the v~deo-processed signals were used to display the

density slices in a range of distinct colours. Thus it was

- 119 -

possible to generate 'false-colour' images, or more specifically-,

to display colour-contoured maps of intensity of the image

viewed-by the camera. This had been found to provide a

valuable extension to the monochrome video-processed images

when dealing with complicated. or 'highly textured:' images

(i.e. those including relatively large amounts of high spatial

frequency information).

In order to retain photometric accuracy, both cameras

required field lenses to collect light from the physically

large aperture images in the optical bench and transfer it

through the small_ apertures of the stock T.V.. camera lenses..

The performance of the CCTV systems (particularly as

regards resolution) as summarised in Section 2.2.5, acted as a

base for specifying the mirrors and beamsplitters needed for

the various display paths, but consideration was also given to

the recording of hard copy, and direct visual observation of

the images in the display 'paths, which in general led. to a preference for spatial resolution in excesssof that which could.

be passed by the CCTV systems. The upper limit of spatial

resolution was set by the size of mirrors and beamsplitters

that it would be practical to use; for a given object size,

projection of the 'cones' of diffracted light with a semi-angle

corresponding to a particular spatial frequency, defines the

effective aperture occupied by the diffracted light at any plane

along the display paths, and hence the requiredzbeamsglitter

or mirror aperture= required to pass- that spatial frequency

over the whole of the given object format. Thus, for instance,

referring to Fig.(3.1)3, for a spatial frequency of 40c/mm

(i.e. diffraction cone semi-angle = 0.488 x 10-3 x:40 rads..

= 0.02 rads.). and object field of 60mm x 60mm, the required.

- 120 -

aperture for mirror Ml, distant 750mm from the gated object

plane, would be: (60+ 2 k.750 x` 0.02).mm =- 90mm, in the

vertical direction, and approximately 90 ;sin 45° = 130mm,

in the horizontal direction; the same aperture would also

transmit a 30mm x:30mm object field at 80c/mm;:(these figures

were the ones actually adopted in practice for this path)•.

Similar calculations were.used.to specify the apertures

of all the mirrors, beamsplitters and lenses used in the display

and sampling paths; those. applied to the diffraction pattern

covered the full. spatial frequency range passed by the transform

lenses.

Consideration was given to the possibility of employing

pellicle (membrane) mirrors and beamsplitters, but these were

rejected on the grounds of: (a) insufficient thickness:

uniformity of the beamsplitters (tolerances quoted amounted to

several fringes over the required apertures); (b) possible

susceptibility to vibration (from sound waves)• - undesirable-_:

in holographic matched filtering.. Therefore, optical flats

of good quality were used for the mirrors and beamsplitters,

to keep aberrations to a minimum; it was decided however,

(referring to Figs.(3.1)3,4) to mount at least the elements

B1,B2 and M4, (which interpose in the main axis of the transform

lens system)•, on sliding mounts, so that they could be retracted

when not in use to give the true diffraction-limited path

through the transform lenses.

In practice, all of the elements were mounted on specially-

designed sliding saddles of a uniform pattern, which fitted onto

- 121 -

a system of lightweight optical benches, bolted to the surface

table top, and running perpendicular to the transform lens

axis. The saddles could be locked in position, but allowed some

translation and rotation adjustment to aid alignment of the

system;: many of the mounts were of a simple type in which the

mirror or beamsplitter was lightly clamped in position by nylon

screws. against: rubber cushions, (Fig..(3.2) 28, 29) ; however, some

of the mirrors were supported in kinematic mounts to allow

fine adjustment of horizontal and. vertical tilt, (Fig.(3.2)301.

The mounts were distributed such as to ensure that sufficient

degrees of freedom were provided in each of the display/sampling

paths, to allow accurate alignment.

The beamsplitters were antireflection coated on their rear

surfaces and the front surface treatment was as described below,

(the following descriptions all_ refer to Figs.(3.2)3,4);-

(a) Fourier Plane Display - via beamsplitter B2: this had

an uncoated front surface so that only a small_

fraction of the light from the (bright). diffraction

pattern would be diverted into the T.V.. camera. This

helped to protect the camera and also caused only a

small lose of light from the filtered image viewed,

by the other camera. When viewing very low spatial

frequencies, an additional beamsplitter could be

used, as shown in Fig.(3.2)-31, for .a further reduction

in intensity at the first camera, whilst simultaneously

providing an extra image of the diffraction pattern

for e.g.. hard-copy recording.

- 122 - .

(b). Fourier Plane Sampling - via mirrors M4, M5 and

transfer lens L4, (see Fig.(3.2).32). By changing

the power and position of L4 (normally, telescope

doublets were used)., a range of magnifications of

the Fourier plane could be obtained at the sector

disc, to facilitate sampling at differing spatial

frequency ranges, particularly low spatial frequencies..

(gee.also Figs.(3.2)33,34)..- (c)" Object/Image plane Display - via beamsplitter BI,

mirrors M1,M2,M3 and re-imaging lens L3, (see?

Figs.(3.2)35,36,37,38). Beamsplitter BI was coated.

for 55% transmittance, 4% reflectance, at its working

angle of. 45°;,the departure: from 50%/50% was intendedi

to compensate for losses in the transmitted beam at

B2. and at the large number of (albeit coated). surfaces

of the transform lenses and liquid gate, so that in

the absence of filters, images of approximately equal

intensity could be viewed-side by-side at the image

stage I. The effect of filtering operations could

thus be monitored: in direct comparison with the

adjacent unfiltered image of the object provided:

by this display path..

Initial experiments used a single doublet lens

for L3, but it was decided-to replace this by two

separate matched-doublet lenses'`, arranged to place

the object in the front focal plane of the first

lens and the image in the back focal plane of the

fi The double lens system for L3 was tried experimentally but permanent mountings for the lenses had not been constructed at the time of the authorts"departure from the project.

- 123 -

second. The advantage of this system was that axial

movement of the second lens relative to the first

allowed the re-imaging path length to be altered

for (d) below..

(d) Object/Cross-correlation Plane Display - via

beamsplitters B1, B3, mirrors -M1 1 M2 and re-

imaging lens L3. (See Figs.(3.2)39,). By

shortening the separation of the two lenses

comprising L3, an unfiltered image of an object

could be focussed in the auto or cross-correlation

plane J. The beamsplitter B3 had an uncoated

front surface so that a 'reduced-intensity' image

could be superimposed on a 'full-intensity' auto/

cross-correlation pattern, the intention being to

allow the object to be simultaneously visible with

its auto/cross-correlation, in registered superposition.

In practice, it was usually found necessary to use

neutral density filters to balance the beam intensities

in order to acheive this.

A general view of the main bench is given in Figs.(3.2)41,42«

- 124 - 3.3 SUPPLIERS

Many of the components described in Chapter 3.2 were

manufactured in the Optics section and PhysicsDepartment workshops.

A list of the outside suppliers of items mentioned is included

at this stage.

'Crown' 8' x 4' Cast Iron Surface Table..

'Bridgeport' 42!' x. 9" Milling Machine Table

'Mascot' 12" x.5" Lathe Top Slide

Roller Bearings for, Rotating Optical Bench and. Sampling Unit .

Model 54 Argon Ion Laser

Beam Expander and Pinhole Filter Unit

10" aperture, 40" focus Paraboloid Mirror

Windley Bros. Ltd. Crown Works; Beach's Drive= Chelmsford Essex:

- Adcock-Shipley P.O. Box: 22_ Forest Road Leicester _LE5 OFJ

Colchester Lathe Co.. Hythe Colchester Essex_

I.N.A.. Bearing Co. Ltd. Maybrook Road,. Castle Vale Industrial Estate, Minworth Sutton Coldfield " Warks

- Windley Bros. Ltd. (as above)

Delta (Manganese Bronze) Ltd. Handford: Worker Hadleigh Road Ipswich

- Suffolk

- Coherent (UK) Ltd. 13 The Mall Bar Hill. Cambridge CB3 8DZ:

Scie-Mechs 8a Wheatash Road Addlestone' Surrey

- Astronomical Eauipment Ltd. 26 Guildford Street Luton Beds.

Vee Blocks 4" Height, 4" Gap 2 Matched Pairs

Rolled Naval Brass for Transform Lens Barrels

- 125-

Liquid Gate Windows:, Transform Lens Elements, Mirrors, Beamsplitters

Coatings for windows, lenses and beamsplitters

Liquid Gate medium:. Dow Corning 710 silicone oil

Stepping Motor for Sampling Unit

Photomultiplier

Power Supply

Digital Panel Meter

Tape Punch

Link Electronics CCTV Cameras

- I.C.- Optical Systems Ltd. Franklin Road., London SE20 8HW

- Balzers High Vacuum Ltd:. Northbridge Road Berkhamste& Herts.

- Hopkin and Williams Freshwater Road:. Chadwell.Heath Romford Essex

- Unimatic Engineers Ltd. 122 Granville Roadh London NW2

- E.M.I.. Ltd. Electron Tutee Division Bury Street Ruislip Middlesex:

V.G. Electronics Ltd. Menzies Road. Hastings Sussex.

Advanced Electronics Ltd.. Raynham Road. Bishops Stortford Herts.

- Data Dynamics Ltd. Springfield Road Hayes Middx.

Studio 99 Video Ltd. 73 Fairfax; Road London NW6

Shibaden 15" monochrome= CCTV Monitor

- Studio 99 Video (as above)

Ltd.

Sony 'Trinitron' colour Television Receiver

- Modified, by Dr. T.H.- Williams Optics Section, Blackett Laboratory

- 126 -

4.1 BACKGROUND

The following chapters describe a number of 'case studies'

demonstrating the performance of the completed main bench in

operating on imagery of practical significance, using the

techniques of diffraction pattern sampling and filtering.

The purpose of this chapter is to provide a few accompanying

notes on the geophysical background to these studies, in order

to indicate the relevance of the techniques to the particular

practical situations.

4.1.1 Fracture Trace Analysis

SEE::. (HUNTINGDON 1969). ,

(NORMAN AND HUNTINGDON 1974).,

(NORMAN 1976).

In the geological sciences, the investigation of linear

features in the earth's szrfāce-- as indicators of its structure

and history is now a familiar and well;-established technique..

It is a particularly important theme in the branch of photogeology,

since in many cases, linears that may be difficult to establish

by field survey techniques can be detected relatively easily

from aerial or satellite photography..

The use of such remotely-sensed imagery in lineament

analysis makes possible the simultaneous evaluation of large

tracts of territory, including areas where prospective ground_

surveys are relatively difficult to mount, (e.g. jungle, desert,

mountain), and therefore difficult to justify unless preceded.

by indications of the importance of the area from other sources:

of data; in fact, remote sensing images are usually the major

-127-

'other source', which reinforces the importance of a thorough

analysis of the images. Another important feature of such

analyses is that they may reveal traces of fracture patterns

in formations that are buried beneath a (sometimes substantial)

covering of surface rocks. The latter frequently have their own,

unrelated, stress patterns, which may drastically obscure the

buried fractures in a ground survey.

By making composites of high-altitude aerial photographs,

or more recently, satellite imagery, extensive major lineaments

often running to several tens of kilometres. in length have been

discovered.. In contrast, lower altitude photographs can be used

for revealing the pattern of smaller scale lineaments in local

areas; these may resolve finer details of the regional stress

patterns indicated by the major lineaments and may therefore

allow detection of anomalous areas. in the pattern, which can

represent features of structural of mineralogical interest.

Of course, not all linear features appearing in remotely -

sensed imagery may be directly associated with fractures, faults

or joints, (which are the 'target' features). One of the major

tasks in traditional 'eyeballed' fracture trace analysis is to

separate fracture traces from unrelated and/or irrelevant

lineaments, such as exposed bedding planes, glacial striae',

buried drainage channels, gullying and other erosional or

depositional forms, and:. artifacts such as field boundaries..

In certain types of imagery, e.g. side-looking radar, or sonar

images, it may also be necessary to compensate for lineation

due to instrumental effects (e.g. scanning, or,movement of the

detector,1 involved in generating the image; (See section 4.2.21.

-128-

Conversely, fracture traces may appear in a variety of

forms, (in addition to obvious cracks), such as tonal (rock

or soil). and vegetal lineations;. or textural boundaries; or

may be manifested. in the shape of landforms and drainage

(e.g. the classic example of unusually straight sections in

a meandering stream)..

Consequently, the traditional 'eyeballing' procedure,

normally entails the compilation of a map of all_ 'genuine'

lineaments:, constructed by plotting the lineaments on a

transparent overlay attached to the image under interpretation.

The lineament map is a very useful representation of structural

information; it may:. allow areas having similar stress patterns

to be interrelated; aid verification of the existence of single

long lineaments from a series of separate (discontinuous) traces;

define the boundaries,of anomalous regions in the stress pattern;

or _enhance groupings of lineaments characteristic of specific

geological entities, (e.g. shatter zones over intrusion boundaries).

In addition to the. above, in areas of dense lineament data

it has been found advantageous to adopt a statistical approach

to the analysis, and parameters such as lineament density (e.g..

number or cumulative length of lineaments per unit area), or

histograms of lineament length, have proved to be useful

indicators of the geophysical situation.

Lineament overlays frequently display several superimposed.

fracture systems, each with possibly independent directional

characteristics;: directional statistics have therefore been

found to be of considerable value in separating the various

- 129-

geophysical events involved, and in assessing the relative strength

of the stress patterns, or their relative significance in

locating possible zones of mineralisation. These statistics.

are frequently expressed as rose diagrams or directional

histograms, plotting (e.g.) the total number or total length

of linears within successive compasa sectors.

It should be emphasised_ that fracture-trace analysis;

generally constitutes only one facet of a geologist's investigations

of a study area;; in developing conclusions, its results would

be combined with those from any other available data such as

geochemical samples: or aeromagnetic measurements, plus the

background knowledge of the interpreter in relating the observed'

or inferred structures to those of previous experience.

It can be deduced from previous chapters of this thesis

that coherent optical diffraction techniques offer broadly two

important prospects to fracture trace analysis:

11: Rose diagram generation, (i.e. compiling directional lineament

statistics), via azimuthal sampling in the Fourier plane.

2) Feature enhancement, (of particular directions or particular

concentrations of lineaments)• via directional or textural frequency

filtering in the Fourier plane..

Considering rose diagram generation, comparisons between

eyeballing and coherent optical methods can be made as follows:-

— 130—

a) Objectivity. A very significant weakness of eyeballedi

fracture-trace data is the inevitable subjectivity of the

interpreter. This can take the form not only of perceptual

inconsistencies, e.g. resulting in an overlay where particular

directions are over-or under-represented due to differences in

appearance (e.g. contrast, whether vegetated, whether coinciding

with tonal boundaries, etc.) of the lineaments on the remotely

sensed images; but also of spurious bias effects due to the

background knowledge of the interpreter (e.g. a tendency to

preferentially select lineaments which support hypotheses drawn

from other data in the image, or from other sources).

However, background knowledge also confers significant

value to eyeballing methods of interpretation, since it enable

the-mass,of indisputably irrelevant data (e.g. bedding planes,

field boundaries) to be rejected and can allow valid weighting

corrections to be applied to particular directions as a result .

of data from other sources. (It is well known that the prominence

of a fracture trace in an image may be only loosely related to -

its geological relevance).

B6 blc these aspects must be contrasted against the results

of the coherent optical techniques which assesses the directional

characteristics of the totality of features in an image, and

which therefore avoids interpreter bias at the expense of losing

interpreter discrimination. It should be noted that any differences

between the results obtained by coherent optical versus,

eyeballed methods will_be to some extent scene-dependent - i.e.

they will_be affected by the nature of the features making up

the particular scene or image under analysis, e.g. the proportion

-131-

of 'irrelevant' data, or the proportion of valid features liable

to be mis-interpreted. In scenes where such factors: are at

least not obviously prominent, one might anticipate some degree

of correlation between results derived: from the two methods.

Section 4.2.1 reports a pilot experiment to investigate whether

a useful degree:of correlation can be obtained in practice

under these circumstances.

b). Speed Assuming'that the coherent optical method can.be

demonstrated as capable of producing useful statistical results,

speed becomes its most obvious other advantage over eyeballing.

The superiority of coherent optical processing for the particular

task of rose diagram generation is not only due to the fact that

the data is compiled by the parallel nature of the diffraction

process: and because of the relatively rapid response of the

photodetection and measurement system, but also because of the

possibility of deriving the information directly from the remote

sensing image, bypassing the lengthy stage of fracture trace

overlay production.

The sampling system designed for the bench in this project

was capable of generating a rose diagram in a few minutes, and

it would be quite possible to modify the system to reduce-this

time to a few seconds if required. By traditional eyeballing,

the derivation of a rose diagram from an overlay might take many

hours although this could obviously be significantly shortened

by (e.g.) the use of semi-automatic plotting tables or, if

video input/output to a conventional computer is available, by

a simple line identification and measurement programme.

- 132 -

However one might notionally ad&.to this the considerable

time required to construct the overlay itself from the remote-

sensing image, although in many instances this task would be

considered an essential part of the full interpretation of the

area, irrespective of its use in generating further groupings

of information, (such as rose diagrams). Thus the speed

advantages of the coherent optical method are likely -to find

their greatest use in generating statistics for areas in advance

of full: interpretation, and therefore to provide some

guidance in selecting those areas.

Allied to this is the ease with which certain compilation

parameters, such as sector angular size and diameter of sample

area,: can be adjusted, e.g. to take account of variations in the

numerical density of lineaments or to subsample areas in order

to track gradual variations in directional trends and isolatee.

directionally anomalous regions - (see Section 4.2.2).

It should be noted that the time required for any serial

form of analysis, such as eyeballing, increases linearly with

the number of lineaments involved, but remains constant for thea

parallel form embodied by coherent optical processing. Hence

the speed advantages of the latter method increase with the

density of lineaments and the size of the area under. study, and

may make it possible to apply rose diagram compilations to a

greater extent than would otherwise be practicable «

Turning to the aspect of feature enhancement by spatial

frequency filtering, it is apparent that for linear features,

133 -

directional filtering is of obvious importance. Applications,

to fracture trace: analysis can occur both in the remote sensing

image prior to interpretation and in the fracture trace overlay.

When dealing with the 'raw' image, spatial filtering can

provide an aid to the conventional 'eyeballed' overlay

construction procedure by producing modified images in which:

(i) the application of a narrow angular pass-band filter

allows only lineaments running within a specified narrow range

of directions to be resolved, hence enhancing such lineaments

relative to the rest of the detail in the scene.

This operation is particularly useful for identifying

connections or continuations between apparently discontinuous,

sections of a lineament, or for clarifying the appearance of

'en echelon' fractures,..

OR

(ii) angular blocking filters act to eliminate irrelevant or

spurious linear features which may obscure or be confused:

with true fracture traces in the original (unfiltered) image;:

or to suppress. the stronger fracture trace directions thus

allowing easier perception of the weaker trends in the scene..

Similar operations can also be applied to fracture trace

overlays, in order to define or mag zones of similar directionality

within a scene, or to remove dominant trands if these obscure

other traces under study (as above)-.

0. An example of directional filtering, applied togremote sensing

image, using the main bench optics, is described in Section 4.3.1..

-134-

4.1.2 Terrain Classification

See: (CORBETT 1973).

(GRAEMENOPOIILOS, 1975)

(McKEITH 1974)

One of the major fields of application of remote sensing

data, particularly the LANDSAT series satellite imagery, is in

terrain or land-use classification, for such purposes as:•

crop forecasting, water resource and drainage planning, and

monitoring forest inventories, urban development and desertification..

These studies are extensively based on the techniques of

multi-spectral analysis, in which measurements of spectral

reflectance: in various wavebands are used to categorise target

areas into terrain or land-use classes, (e.g. healthy/diseased

wheat, shallow/deep water, coniferous/deciduous woodland,

bare earth/scrub etc. etc..).'

A. multitude of computer-based methods of analysing the input

data to optimise the accuracy and consistency of such classifications

has been developed, and have been described in a vast range of

literature. The success of these methods using satellite imagery

has also stimulated research using lower level (e.g. aircraft)`

imagery.

It has long been recognised that classification procedures

would be improved if textural information were utilised as well_

as tonal, i.e. that, in addition to the reflectancesat each

point la the scene, the nature of the relationship between

the reflectance at a point and that at neighbouring points,

is a valuable descriptor of terrain/land use. Indeed,defining

-135-

textural boundaries is a frequent task 'In eyeballedlphoto-'

interpretation for geological and geographical studies..

Using digital techniques, the;:general.approach is to

compare or associate point values with 'nearest neighbour'

point values, then 'second nearest neighbour' point values, and

so on, with the computing effort rising steeply as a function

of the number of points included in the association, i.e. as

the operation becomes increasingly 'parallel' in nature. The

limit of this trend is given by whole-scene operations or

transformations, where all pointsof the image are considered

in association, of which Fourier techniques are an important

example.

Since coherent optics provides the possibility of rapid

parallel whole-scene operations, there have been several invest-

igations involving its application to the field of terrain

classification. Measurements at various points in the diffraction

pattern representing the spatial frequency spectrum of an

input image can be used as the basis_.for textural signatures,

in the same manner that 'spectral' or tonal signatures are

derived from a multispectral set of imput images; i.e. spatial

frequency spectrum measurements can be manipulated using similar

mathematical tools as those regularly applied to measurements

of the electromagnetic spectrum (i.e. 'tonal' or reflectance

values of the input scene)•.

In addition, optical spatial filtering allows rapid

separation of textural classes, definition of textural boundaries,

etc, and may thus yield images suitable for mapping directly;

-136-

or as 'preprocessed-images', for further eyeballed or

computer-aided interpretation. This aspect highlights;a

notable advantage of coherent optics over digital techniques:

i.e. that of providing an optical image output directly from

an optical image input, obviating the need for optical-digital

input/output conversion stages.

Both annular and directional spatial filters, or a

combination, may be of interest in the field of terrain

texture analysis;- a report of an experiment using annular

filtering is given in Section 4.3.2.

- 137 -

4.2 DIRECTIONAL STATISTICS

4.2.1 Queensland Aerial Image

The input material used in this study (an aerial photograph,

eyeballed fracture trace overlay and manually summed rose

diagrams) was supplied by Dr. E.J.. Heidecker and Mr. T. Supazjanya

of the Department of Geology and Mineralogy at the University of

Queensland, who had previously reported promising correlations

between the cumulative length rose diagrams and the optical

diffraction patterns of corresponding areas of the fracture

trace overlay (HEIDECKER and SUPAJANYA 1975). In this paper,

they compared the general shape of the diffraction pattern

(i.e. presence and position of lobes) with that of the-corresponding

eyeballed rose, but had not measured the azimuthal energy

distribution in the diffraction pattern, and were not therefore

able to give a numerical: comparison. The first part of the

present experiment therefore used the azimuthal sampling unit

in order to provide numerical values to build up an optical

rose diagram from the overlay.

The fracture trace overlay Fig.(4.2)1 was received in thee

form of a Xerox copy from the hand-plotted original, and was

subsequently reduced onto a 70mm x 70mm format lith-film

transparency for use in the object stage of the bench. The

width of the traces on the transparency was measured at typically

- 138 -

0.05mm suggesting that its diffraction pattern should extend:

out to about 20 cycles per mm at least. The diffraction

pattern of 'Area A!' of the overlay is shown in Fig. (4.2) 2

from which it can be seen that there was considerable energy

at spatial frequencies up to and beyond 10 cycles per mm..

The diffraction pattern was sampled using a 2° sector in

the spatial frequency band 7.5-20 cycles per mm, chosen•.

by reference to video-processed images of the diffraction

pattern, which had suggested that this range would give better

discrimination between the Lobes- than if the pattern were

sampled down to lower spatial frequencies;; (this was confirmed;,

experimentally by a.. trial run including low frequencies, on

the sampling unit). The resultant optical rose diagram for

Area A is shown superimposed on the manually-summed rose in

Fig.(4.2)3.

The plots agreed well in picking out the major directional

lobe 060°-09et, but showed- significant disagreement in the

region 110°=150°,- where the optical rose gave much lower readings,

than the manual one. The explanation offered for this

discrepancy was the existence of reprographic errors in the

input, as follows:

It was noticed that the contrast and continuity of the=

fracture traces on the photocopy were somewhat dependent on

their direction, and in general, that lines running in the

range of directions 0900-180° were poorly reproduced compared

to those in the range 0000-0900.. Microscopic examination

confirmed that this condition had been transferred (and

t All direction measurements refer to True North in the object plane (i.e.-Diffraction pattern measurements have been 90°-shifted).

- 139 -

possibly exaggerated by the nature of the lith exposure

characteristic) to the transparency, which might therefore

be expected to give rise to a rose diagram with systematically

weakened readings in the range 0900-1800, (i.e. including the

observed. 1100-1500, 'weak' region).

Circumstantial evidence for attributing the discrepancy

to this cause rather than to any other factor was given by

the relatively good 'Area:. A' optical - manual correlation

obtained when using the aerial photograph (see below): as

input; (since the latter would otherwise:be expected to give

less good correlation than the fracture trace overlay)..

The more important part of this experiment concerned the

optical derivation of rose diagrams direct from the uninterpretedi

aerial photograph.

The terrain covered by the photo was a part of the Owenee

granite batholith in north-eastern Queensland, and is shown in

Fig.(4.2).4. A. reduced negative transparency (on 70mm format

continuousatone fine grain film) was made from the photographic

print and used.in the object stage of the bench.. The diffraction

pattern of 'Area A' is shown in Fig. (4.2)•5, from which it is

obvious that much of the energy is contained in lower spatial

frequencies (under 3 cycles per mm) compared to 'Area. A'' of

the overlay. This is to be expected, since the appearance~ of

the lineaments on the airphoto is in general not as fine (narrow),

nor of such high contrast, as on the overlay. Much of the

high spatial` frequency information in this pattern is due to

the fine details of the picture such as boulders and scrub..

-14o-

Both these factors suggested that successful measurement

of the directionality due to lineations in the airphoto was more

likely to be achieved by scanning the diffraction pattern at

considerably lower spatial frequencies than those employed for

the overlay, and this was confirmed in practice, as shown by

the following plots..

Fig.(4.2)6 shows the optical rose diagram derived from

'Area A' of the airphoto, prepared by scanning in the spatial.

frequency. range 3-5 cycles per mm.(corresponding to about

13.5 - 22 cycles per km 'on the ground'%, superimposed on the

manual rose from 'Area A' of the overlay. This figure-

suggested that these frequencies, although not as high as those

used in the scanning of the overlay diffraction pattern, were

still too high for a satisfactory representation to be obtainedz'

from the airphoto diffraction pattern; (there is little

correspondence in shape apart from the general elongation along

the E-Wt axis compared to the N-S axis).

Fig.(4.2)7'shows:. the 'Area A-' optical rose derived from

scanning at 0.5 --1.0 cycles per mm (about 2.2-4.4 cycles per

km 'on the ground') with the comparison manual rose.. At these

frequencies there was quite close agreement, even some of the

smaller peaks being picked out by the optical method.

To provide a rough estimate of consistency, the same

spatial frequency range was used in generating an optical rose

for 'Area B' of the airphoto, and this is shown superimposed

on the corresponding manual rose in Fig.(4.2)8. General

agreement was again fairly good, but in this case there were

also substantial differences in certain directions..

It was deduced from the above results that the spatial

frequency spectrum characteristic of 'lineament information'

in this case was such as to allow some degree of separability

of that information from the other details of the scene over

a certain frequency range, i.e. that 'lineament information'

was dominant over certain spatial frequencies, presumably

related to the typical spacing and apparent width of the

lineaments. However the degree of separability might be

somewhat dependent on the particular nature of the scene, or

portion of a scenes under analysis.. To take a hypothetical.

extreme example, in a scene consisting of fairly broad fracture

features on a background composed mainly of fine rock detritus

or scrub, it might be possible to choose a spatial frequency

band that includes almost all. f the lineament information and

almost none of the background; whereas-in a scene where the

background contains a large number of bedding-plane traces

having a similar apparent width to the fractures, separation

of the 'wanted' and 'unwanted' information in the diffraction

plane might be impossible.

Other points to be noted in connection with this experiment

were that:.

(i) The 'truth' against which the optical method was

checked was a photogeologist's subjective interpretation, and

was therefore itself subject to sources of error, which must

affect the validity of the comparison to some extent..

(ii) The choice of the spatial frequency band scanned

was essentially an empirical one, based on a 'reasonable guess'

as to the nature of the image information in diffraction plane.

- 142 —

terms, i.e. the likely scale or texture of the lineament

information relative to other detail in the scene.. This

process was aided by studying the diffraction pattern (and video-

processed versions of it) via the CCTV channel, and it was thought

that this was a factor in which the knowledge and experience

of a photogeologist should play a vital part in continuing

future studies-.

(iii) Only a particular rock type/geological structure

was considered; it was anticipated that further trials of the

technique should be applied to a wide variety of geological_

situations (e.g.. with varying degrees of superficial cover);

and other forms of imagery.

In conclusion, the experiment demonstrated that in comparing

the optical rose from an uninterpreted image and an 'eyeballs-d'

interpreted rose, it was possible to obtain a degree of

correlation of practical importance to geologists. However,

the criteria for selecting the spatial frequency range to be

scanned, and the consistency of the results as a function of

the particular geological situation under analysis, are subjects

on which considerable further work wilL be required if optical

rose diagram generation is to become a routinely accepted tool

for the photogeologist..

This work was communicated to the geological disciplines

in (HARNETT AND BARNETT 1977),..

- 143 -

4.2.2 'FAMOUS' Sonar Image

This section reports work involving a sonar image supplied

by Dr. R.B..Whitmarsh of the Institute of Oceanographic

Sciences. The image of the 'FAMOUS' area (French-American

Mid Ocean Undersea:Study) was produced as part of an extensive-

project for the study of the Mid-Atlantic Ridge in the region

of the Azores, (Fig.(4.2).9), and was generated by a long-range,

side-scan sonar system, known as

Many of the features in this image are-:thought to be fault

scarps, and their distribution and directional statistics are

of significance in contributing to theories concerning the

geological evolution of the area (WHITMARSH AND LAUGHTON 1975).

It was therefore proposed to produce rose diagrams by

azimuthal diffraction pattern sampling for several test area

in the scene, (three of which are indicatediin Fig.(4.2)9)..

A problem known to be inherent in this image was that the

features shown were distorted by yaw of the sonar source/receiver..

The effect of this was to cause a biasuin the image towards

the vessel's tracking direction (055?/235o) i.e. isolated point.

features became drawn out into short lines parallel to the

track in the image, and straight scarp lines appeared to be

modulated by fine 'wiggles' or zig-zags'. Initially, sampling

was done in the spatial frequency range 0.5.-7.5 cycles per mm (0.22-3.3 cycles per km 'on the ground')., and the yaw effect was

manifested by showing the track as the strongest direction in

the rose, (see Fig.(4.2).10a).

It was reasoned that since the distortion was a high

spatial frequency effect, a better result might be obtained by

'GLORIA', (LAUGHTON AND RUSHY 1975)..

-144 -

confining the azimuthal scan to low spatial frequencies. The

band chosen was:0.5-1.5 cycles per mm, (0.22-0.66 cycles per

km 'on the ground:')., corresponding to detail of characteristic

size/stiacing of 1.5-4.5 kms, and therefore including most of

the features of interest to the geologists in this context.

The resultant rose diagram, (Fig.(4.2)10b), showed a significant

reduction in the 'track' direction and was much more in accord

with the anticipated geological. result; the remaining test area&

were therefore scanned using the low,:pass spatial frequency

band.

Another factor affecting the results obtained from scanning

was that the various test areas specified were of differing

sizes=; thus, for a constant illumination intensity, average lineament

density, and spatial frequency spectral distribution, the rose:

diagrams. would be scaled to the size of the test area.. Therefore,

in order to normalise the individual test area roses, the

illumination intensity was adjusted in inverse-ratio to the mag-

nitude of the test area. The roses, from test area?s:2 and 3, •

for instance, (Fig.(4.2)10c,d1 could then be compared in

absolute magnitude with that from test area. l(Fig.(4.2).10b).

The resultant rose diagrams have been incorporated into

a comprehensive report on the 'FAMOUS' area in (WHITMARSH and

LAUGHTON 1976), in which the geological implications are

discussed in detail.

- 145 -

4..3 FEATURE_ ENHANCEMENT

4.3.1 Botswana 'LANDSAT' Image

The input material used in this section was a portion of

a3LANDSAT satellite image supplied by Dr. Mallick of they

Institute of Geological Sciences..

The scene consisted of a region of BotswanaĀapproximate-ly

90 x_60 miles in extent (Fig.(4.3)1). The problem here was an example of a situation that often troubles photogeologists,

i.e. that features of interest, particularly possible linears „

and tonal boundaries=, may be partially obscured by overlying

material such as glacial drift, desert sand, etc. In this case:

the superficial cover consisted of vegetated_ sand-dunes, which

interfered with interpretation over a sizeable area of the image..

Prevailing winds had caused the dunesito assume a.unidirectionaS..

form, so a directional exclusion (blocking). filter (40° of arc

with zero order pass) was used in the Fourier plane to eliminate:

the dune-crest direction, resulting in the image shown in

Fig.(4.3)2. The effect of the filtering operation can be seen

at higher magnification by comparing the unfiltered and

filtered images of Figs.(4.3)3 and 4. In addition to eliminating

the dunes, the filter has imparted a 'grain' on the scene, one

of the effects of which has been to enhance the LANDSAT scan

lines, aligned at about 20° to the (missing). dune crest direction.

This can be explained by considering the nature of the point

spread function produced by the filter, from which the filtered_.

image was built up, as follows.

- 146 -

Figs.(4.3)5 and 6 show, respectively, 10° inclusion and

exclusion filters (zero order pass) with their corresponding

diffraction patterns i.e. intensity point spread functions,

(produced by photographing the Fourier plane with the filters

placed in the object plane of the bench):. As expected the

diameter of the point spread function is 'small' or 'large='

respectively in directions at 90° to the resolved or blockech

range of directions. However, a notable feature of both point.

spread functions is the pair of sharp lobes caused by diffraction

from the 'discontinuity' corresponding to the wedge edges..

When the wedges are used as filters, the filtered image

consists of a convolution of the unfiltered image with the

modified'(filtered> point spread function.. Hence there is a,

tendency for enhancement of linears running in or near to the

direction of the long lobes in the filtered point spread:

function. This effect operates independently of any lineament

enhancement that occurs due to the preferential exclusion or

inclusion of directions over the whole angular range covered:

by the filter. The effect does not seem to have been previously

recorded: in the literature, evem though it has been observed

to be fairly pronounced in certain types of image (particularly

high contrast or 'binary' images such as fracture trace overlays);;

it appears to be= the cause of the 'directional grain' in the

filtered: images of Figs. (4.3 ).2 and 4. A significant consequence of this effect is that, whilst

it can enhance 'genuine' linear features, it can also introduce

spurious directionality, of no geological importance, by its

tendency to 'join up' features lying chance along lines in or

near the lobe directions. Whether such spurious directionality

-147-

is sufficiently innocuous as to be outweighed by the benefits

of the filtering operation (or can be easily discounted from

geological background: information), or whether it is sufficiently

serious as to degrade the value of the filtering operation to

an unacceptable extent, may depend partly upon the nature of the

image involved (contrast, etc.)- and partly upon the skill and

geological background knowledge of the interpreter.

4:3.2 Dartmoor 'LANDSAT' Image

This section reports an experiment to test the ability

of coherent optical filtering to provide textural separations,

which are meaningful. in the context of terrain classification..

A common requirement in this type of analysis is the demarcation

of boundaries:between zones of differing field size, which may

indicate differing schemes of agricultural land use. This is

particularly important in regions of the world where agricultural_

development is proceeding relatively rapidly and which are

otherwise not well_-mapped. However, for this example, a fairly

well-mapped area that of Dartmoor and its environs, has been

employed..

Fig.(4.3)7a shows a simplified map of the area)on which

the boundary between open moorland (including the 'bracken, heath

and rough grassland' category of the Ordnance Survey)., and enclosed

fields, has been taken from Ordnance.Survey 1:.50,000 scale

maps, (revised_ 1970). Figs.(4.3)7b,c show the corresponding

portion of a LANDSAT image, in MSS. wavelength Bands5 and 7

- 148 -

respectively. It can be seen that for the season of the year

at which this image was received, the moorland/enclosure

boundary was somewhat more distinct in Band .5 than.Band..7.

Normal multispectral classification techniques would

probably use data from all bands to define the boundary. For

this example the degree:of correlation between 'map truth'

(as represented by the boundary shown in Fig.(4.3)7a) an&

the Band 5 image, was taken as a standard against which to

compare the results obtained by textural separation. The latter

were generated as follows....

It was reasonedthat the moorland. area should be characterised

by relatively low spatial frequencies, (i.e. slowly-varying

tones)_ representing broad expanses of a few types of vegetation

(e.g.-bracken, heather, grass, forestry).; whereas the enclosed:

field areas wouldicontain a greater proportion of relatively

high spatiali. frequencies (i.e. rapidly-varying tones) due to

the spatially rapi&changes in vegetation type (e.g. crop/pasture/

woodland)-. This was confirmed by the appearance of the diffraction

patterns of the areas-, and is also apparent in a simple visual

inspection of Figs.(4.3)-7b,c;. it was noticed that the 'textural

contrast' appeared to be greater in Band 7 than Band 5;. hence:

the Band 7 image was used for the spatial filtering operation..

Fig.(4.3)8a, shows the Band 7 image subjected to spatial

filtering using an annular filter of pass band1.5-7.5 cycles

per mm. (1.5-7;5 cycles per km 'on the ground' since 1:• 1 million

scale imagery was used), as seen via the CCTV system.. This,

spatial frequency range corresponds to features of characteristic

size in the range 130-650 metres on the ground; therefore the

filter passes much of the 'enclosed field' detail but blocks

the low frequency 'moorland' area, resulting in an image in

0.1

z

- 149 -

which moorland appears tonally dark compared to the enclose&.

field region.

It should be noted that this filter was chosen from a

''standard! library and that the accuracy of moorland/field

separation might be improved by using a filter specifically

tailored to exploit the differences between the moorland/field,

spatial frequency spectra. Nevertheless, the moorland/field

boundary derived from Fig.(4.3).8k7_correlates quite well with

the 'map truth' of Fig..(4.3)7a.

Further enhancement of the boundary was obtained by

'intensity slicing' the image using the video-processor, with

either a.monochrome or 'false-colour' output, as shown in

Figs..(4.3)8b,c, respectively.. It should be emphasised that

the tonal slices here represent regions of differing textural

character in the original image (Fig.(4.3)7c)', and therefore

do not necessarily bear any relationship to its (low-frequency)

tonal composition.

Thus, it has been demonstrated that annular spatial

filtering combined with video-processing can generate

'textural.. slices' which can therefore be used to aid separation

of terrain classes that are distinguishable on textural criteria.

The technique has also been applied to side-looking-radar imagery,

as reported in (HARNETT, MOUNTAIN and BARNETT, 1978);.

- 150_ -

4.4 CONCLUSIONS

Following the successful completion of the main bench, the

latter chapters of this thesis have demonstrated its operation

on remote sensing imagery in the manner originally planned..

These concluding remarks are therefore devoted to a brief

assessment of the extent to which the proposed advantages of

coherent optical techniques have been (or may be) displayed:

in the-real optical processor..

Spemd: The processor has so far been developed to the status-

of a 'research tool.', providing filtered images in seconds

and rose diagrams in tens of seconds, but with manual

setting-up of the input, output and filter stages adding somewhat

to these times. However, should it be required to use the

system for batch processing (e.g. to generate an array of

'subsample' rose diagrams from a single. input image, or to

apply a fixed spatial filtering operation to a series of input

images),, then the conversion of these stages to semi-automatic

operation should be a:fairly straightforward task. A point

to be noted in this connection-is that recent work

(G.D. MOUNTAIN - private communication) has suggested that for

input records on ultra-fineegrain photographic emulsion, the

emulsion grain noise level over the spatial frequency range

of interest may be low enough for the use of a liquid gate to

be unnecessary.

- 151

It should be remembered that the speed of coherent optical

processing compared to serial processing methods should be judged:

in relation to the density of image information in the scene

under investigation. For scenes such as LANDSAT and much other

remote sensing imagery, the amount of data to be handled in

parallel is sufficiently high for the present processor to

maintain an advantage over digital processors in this respect,..

for the immediate future..

Objectivity:. With regard to the compilation of directional

statistics, studies using the main bench have shown promising

agreement between results derived optically and those from

eyeballedd interpretation However, there is: a need for

considerable further testing, using input imagery that includes:.

aAvaried,selection of geological situations,, if the validity

and degree of accuracy of the coherent optical technique is to

be established with sufficient confidence to become a, routinely

accepted tool.

Should this prove to be the case, then it can be envisaged,:

that the coherent optical processor could perform a task that

by present eyeballed methods is arduous, time-consuming and

open to subjective influence; thus allowing a greater proportion

of the photo-interpreter's effort to be concentrated on those

aspects of the work which are less amenable to machine analysis

i.e. association of ideas, and judgement on the basis of

geological knowledge and experience.

- 152 -

Similar remarks can be attached to the results of spatial

filtering operations on geophysical imagery.. It should also be.

borne in mind that spatiaL filtering is equivalent to modifying

the point spread function of an image and may therefore introduce

undesirable optical artifacts into a scene.. A comprehensive

photo-interpretive assessment of the benefits and hazards of

spatial filtering is now desirable=..

Relevance:. It is felt that the most important factors govern-

ing the degree to which the coherent optical processor described

in this thesis: may provide meaningful contributions to image

analysis, both in the geophysical sciences and elsewhere, are:

). C:ontinued testing of the techniquesdescribed:in

the foregoing chapters, their assessment by experienced_.

photo-interpreters and other specialists in the

disciplines•,for which the results are intended, and

possible modifications of the techniques in response

to such assessment.

b) Continued improvements to the input, filter and

output stages, in order to increase the speed and

convenience of use of the apparatus..

c) Increased emphasis on the interaction between

'users' from other disciplines and 'operators' familiar

with the optical technology involved. It is important

that 'operators' understand clearly the nature of the

information that 'users' try to obtain from the imagery,

in order tc develop appropriate techniques for those tasks..

- 153 -

Conversely, 'users' may be able to benefit by the incorporation

of optical concepts such as 'spatial frequency spectra' into

their specialist notions of image descriptors (such as

'granularity', 'directionality', etc.), since they provide a

precise quantitative definition of image properties.

- 154 -

APPENDIX - Convolution The convolution of the two functions f(x). and g(x) is

another function h(x) defined by the relation: +40

h(x). _ S f(x!).g(x-x!)dx'

for which the symbolic shorthand is h(x) =f(x) © g(x).

The convolution operation can be comprehended in terms of the

following pictorial representation;

Suppose that we start with the functions:-

Using the above definition, we see that we first need, to plot

the function 800) .g(x-x/17.

Now g(x'1 looks like this: 9 Cxi)

But g(-x') is simply this function reversed, hence g(-30) looks,

like this:

- 155 -

But g(x-x'): is simply this function displaced by an amount

+-x along the x!' axis, hence g(x-x') looks like this:

9(x-x')

Also f(x') looks like this:.

Thus f (x')jg(x-x' ); looks like this:.

Note that this product function is finite only over the regions:

where f(x') and g(xi-x!) are both finite;, the value of h(x) is:

the integral of the product function with respect to x' between

the limits ± i.e. simply the area:. under the product function:

50x9.'Cx x.')

h(x)

N!

Referring to the above diagram, we can see that as .x changes, so

the function g(x-x.'): 'slides across' the function f(x'), resulting

in a continuous change in the shape of the product function f(x').g(x-x')

and hence of the area-under it.. Note that in general, the

convolution function h(x), is large for values: of m that provide a

high degree of overlap between the functions f(x') and g(xrx'),

I- x

function curves corresponding to

the above-mentioned values of xl.

3(x )e)

Cx') D

• •

•• •• 4.r••

es. xFY tt

-156-

and falls to zero at values of x_that provide no overlap between

these functions. For example;-

A, B, C, D, label positions of

the function g(x-x')

corresponding to the values

x =.0e, 0, , ō , respectively: A

x=-d X=o

A, B, C, D,. label the product

A, B, C, D, label the values of the

convolution function h(x). at the hGH)'

above-mentioned values of xw B

—ōc 6

If f(x) and g(x) both have finite widths Wf and Wg respectively,

we can see that the width of h(x) is given by Wh == Wf + Wg.

From the above, one can consider the convolution operation

to be a form of 'blurring' in which each discrete'point along

the curve of the function f(x) is replaced.. by a 'blur' whose

shape is the reversed curve of the function g(x); h(x) is the

function resulting from the superposition of all_ these 'blurred'

points.

- 157 -

REFERENCES

ARSENAULT, U.H., SEGUIN, M.K. and BROUSSEAU, N

Optical Filtering of Aeromagnetic Maps.

Applied Optics, 13, pp. 1013-1017

. (1974)

BARBER, N.F. (1949) Diffraction Analysis-of a Photograph of the Sea..

Nature, 164, p. 485

BARNETT, M.E. and HARNETT, P.R. (1975 ). Diffraction Pattern Sampling and-. its Application to

Directional Enhancement -4 Geological Image Transparencies.

Trans. I.M..M.;, 84z pp. B53-B55

BARNETT:_, M.E., HARNETT, P.R.., WELFORD, W.T. and WYNNE, C.G. (1976)

An. Interactive Hybrid Processing Facility for Geological

and Geographical Applications.

Proc. S .P.S.E..., 74, (Image. Processing)•, pp. 130-136

BARNETT, M.E. and HARNETT', P.R. (1977).

Optical Processing as an, aid to Photo-Interpretation

in 'Environmental Remote Sensing 2: practices and problems'

(eds. Eric C. Barrett and Leonard F. Curtis); 2nd Bristol Symposium on Remote Sensing, Dept. of Geography, University

of Bristol; Edward Arnold.

BAUER, A.., FONTANEL, A.. and GRAU, G. (1967)

The Application of Filtering in Coherent Light to the

Study of Aerial Photographs of Greenland Glaciers.

Journal of Glaciology, 6, pp. 781-793

BIRCH, K.G.. (1972)

Spatial Filtering in Optical Data Processing.

Rep. Prog.. Phys:, 35, pg. 1265 - 1314

'BARN TT-, N.E. and-WILLIAMS,. T.H.(19797 Video Rate' Image Processing, in •'Rank Prize: Fund 'Symposium on 'E]:ec ron-ia ieds. Schagen apd`ticLean), Press,

- 158

BLANDFORD ,. B- (1970 ) A New Lens System for use in Optical Data Processing, in 'Optical Instruments and Techniques', (ed. J. Home Dickson),

Oriel Press, pp. 435 - 443

BORN, M. and WOLF, E. (1970).

Principles of Optics, (4th Edition) Pergamon,

BRACEWELL., R.. (1965)

The Fourier Transform and its Applications. McGraw-Hill_.

CHEVALLIER, R., I+'ONTATIE L., A., GRAU, G.. and GUY, M.. (1970). Application of Optical'_ Filtering to the Study of Aerial; Photographs..

Photogramme_tria, 26, pp. 17 - 35

COLLIER, R.J., BURCKHART, C.B. and LIN, L.H. (1971) Optical Holography. Academic Press. a ch.7, pp. 164 - 166

CORBETT, F.. (1973): Terrain. Recognition in ERTS-T Imagery by Diffraction Pattern Analysis.. American Society of Photogrammetry, Fall Convention and. Symposium

on Remote Sensing in Oceanography, pp, 431 - 436

CUTRONA:, L.J. et.a1N.. (1966) On the Application of Coherent Optical Processing Techniques to Synthetic Aperture Radar. Proc. I.E.E..E-, 54, pp. 1026 - 1032

DAVIS, J.... and PRESTON, F.W.. (1972)

Optical Processing: An Alternative to Digital Computing.

Geological Society of America, Special Paper 146, pp. 49-68

DE VELIS , J . B .. and REYNOLDS, G.0- (1967 ) Theory and Applications. of Holography. Addison Wesley.

- 159

DOBRIN, M..B.., INGALLS, A.L . and LONG, J.A. (1965)

Velocity and Frequency Filtering o.f Seismic Data using Laser light.

Geophysics, 22, pp. 1144 - 1178

DOBRIN, M.B. (1968)

Optical Data Processing in the Earth Sciences.

I .E.E..E Spectrum, 5, (9) , pp.. 59 - 66

FONTANEL A., GRAU, G.., LAURENT, J. and MONTADERT, L.. (1967)

Etude et Depouillement des Photographies Aeriennes par

Diffraction de la Lumiere Coherente-issue d'un Laser.

(Actes du II e Symposium International de Photo-Interpretation,

Sept. 1966)1..

Archives Internationales de Photogrammetrie, 16, (III), pp. 13 - 22

GOODMAN, , J .W. (1968)? Introduction to Fourier Optics.. McGraw-Hill.

-. ch.7, pp. 154 - 155 b ck74 pp, 171 184

GRAEMENOPODIiO.S , . N._ (1975)

Automated.Thematic Mapping and Change Detection of ERTS.A.Imagess..

Final Report, Itek Corp., N?5-20797

GRASSELLT2, A.., ed. (1969)

Automatic Interpretation and Classification of Images..

Academic Press..

HARBURN, G. and RANNIKO,. J.K. (1971)

Details for an Optical Gate..

Journal of Physics E: Scientific Instruments, 4, pp 394 - 395

HARNETT, P.R. and BARNETT, M.E - (1977)

Optical Rose Diagrams for Lineament Analysis.

Trans. I.M.M., 86, pp. B102 - B106

HARNETT, P.R, MOUNTAIN, G.D. and BARNETT, N.E.. (1978)

Spatial Filtering Applied to Remote Sensing Imagery.

Optica Acta, 25, (8), pp. 801 - 809

-16o -

HEIDECKER, E.J. and SUPAJANYA, T. (1975) A Simple Optical Method for Routine Analyses of Fracture Traces-.

Trans. I.M.M.., 84, pp. B56 - B58

HUNTINGDON, J.F.. (1969) Methods and Applications of Fracture-Trace Analysis. in

the quantification of Structural Geology..

Geological Magazine, 106, pp. 430 - 451

JENSEN, N. (1973) High Speed Image Analysis Techniques.

Photogrammetric Engineering, 22, pp. 1321 - 1328

LAUGHTON, A.S. and RUSBY, J.S.M. (1975). Long-Range Sonar and Photographic Studies3of the Median Valley

in the FAMOUS Area of the Mid-Atlantic Ridge near 37°N. Deep Sea Research, 22, pp,.. 279 - 298

LENDARIS:, G.G ► and; STANLEY, G.L... (1970) Diffraction Pattern Sampling for Automatic Pattern Recognition. Proc. I.E.E,, 58, pp. 198 --;216

LIPSON, H., ed. (1972): Optical Transforms. Academic.. Press..

McCULLAGH,. M..J . (.1971): Optical Data Processing: A-New Geographical Tool.

Unpublished report for Kansas Geological Survey/Department

of Geography, University of Kansas_

McKEITH, P.L.C. (197 .)• Texture and Pattern in Earth Imagery.. MSc. Thesis, University of London..

- 161 -

NOBLE, V.E. (1970)-

Ocean Swell Measurements from Satellite Photographs.

Remote Sensing of Environment, 1, pp.. 151 - 154

NORMAN, J.W. ands HUNTINGDON, J.F. (1974): Possible Applications of Photogeology to the Study of Rock Mechanics..

Quarterly Journal of Engineering Geology, 7, pp. 107 - 119

NORMAN, J.W.. (1976)_ Fracture Trace_Analysis as a Subsurface Exploration Technique..

Trans. I.M.M.., 85, pp. B52 - B6a

NYBERG , S:.`, ORHAUG , T and S VENSSON , H.. (1971)

Optical Processing for Pattern Properties..

Photogrammetric Engineering, 7, pp.. 547 - 554

O'NEILL:, E.Iw.. (1956)'

Spatial Filtering in Optics..

I..E.E..E.. Trans. Inf.. Theory, (2), pp. 55 - 56

PINCUS, and DOBRIN, M.B. (1966);

Geological Applications of Optica]. Data Processing.

Journal of Geophysical Research, 71, pp. 4861 - 4869

PINCUS, H..J .. and ALI, S.A.. (1968) Optical Data,Processing of Multi-Spectral Photographs•.

of Sedimentary Structures...

Journal of Sedimentary Petrology, 38, pp. 457 - 461

PINCUS, H.J. (1969)

Sensitivity of Optical Data.Processing to Changes in Rock Fabric.

International Journal of Rock Mechanics and Minine Science,

6, pp. 259 - 276

PRESTON, F.W.. and DAVIS, J..0 . (1972)

Application of Optical Processors to Geological Images, in

'Machine Perception of Patterns and Pictures', (ed. P.A. Walker) ,

Institute of Physics, pp. 223 - 232

- 162 —'

PRESTON Jr., K. (1972).

A Comparison of Analog and Digital Techniques for Pattern Recognition..

Proc. I,E.F.Ef, 60, pp. 1216 - 1231

PRESTON Jr., K. (1972).

Coherent Optical Computers. McGraw-Hill:.

a —ch. 6, pp. 195 — 205 b - ch. 5, p. 116

SHULMAN , A.R. (1970 )_ Optical Data Processing. Wiley.

a - ch. 4

STILLWELL, D. (1969)

Directional Energy Spectra of the Sea, from Photographs..

Journal of Geophysical Research, 74, pp. 1974 - 1986

TAYLOR, C.A. and LIPSON, H. (1964)

Optical Transforms.. Bell..

TIPPETT, J.T-. et.ali. (1965)

Optical, and. Electra-Optical Information. Processing. MIT Press...

VAN DER.LUGT,.A (1964).

Signal Detection by Complex Spatial Filtering.

I.E.E.E. Trans. Inf. Theory, IT-10, pp.. 139 145

VON BIEREN, K. (1971)

Lens Design for Optical Fourier Transform Systems..

Applied Optics, 10, pp. 2739 — 2742

WHITMARSH,. R.B.. and LAUGHTON, A.S.. (1975)

The Fault Pattern of a Slow-Spreading Ridge near a Fracture Zone..

Nature, 258, pp. 509 - 510.

`4HITMARSH, R.B.. and LAUGHTON, A..S- (1976) A Long-Range Sonar Study of the Mid-Atlantic Ridge Crest

near 37°N. (FAMOUS Area) and its Tectonic Implications.

Deep Sea Research, 23, pp. 1005 — 1023

- 163 -

WOJTOWICZ, T. (1971); A. Study of some opticaa properties of photographic emulsionsi

with particular reference to rapid data processing.

PhD. Thesis, University of London..

WYNNE,. C.G. (1974). Simple Fourier Transform Lenses.-..

Optics Communications, 12, pp 266 —274

YASUHIRO SUGIMORI (1975): A study of the application of the holographic method to the

determination of the directional spectrum of ocean waves. Deep Sea Research, 22, pp 339 - 350

rn : Totally-Vignetted " it rt

CONTENTS

VOLUME I - TEXT

CONTENTS OF VOLUME II

VOLUME II -- FIGURES

CONVENTION: PART P

CHAPTER P.Q.. FIGURE FIG(P.Q)S

Optical Diffraction (Fourier Transform) Image Analysis

Showing Effect of Dominant Directionality

tr It r tr. Granularity."

Directional Filtering

FIG(2.1)1 One-Dimensional Fourier - Transform Pairs

2

3 Two- 4. tn

- 5 Diffraction from an infinite screen

6 Focussing of diffracted light by a lens

7 Basic Coherent Optical Fourier Transform Spatial Filtering Bench

8 Spatial Frequency Synthesis of a square wave

9 Illustrating Optical Fourier Analysis

10 .Infinite Aperture System: (Finite Object/Image Planes; Infinite Fourier Plane3)

Finite Aperture System: Nen-Vignetted Spatial Frequencies

ft tf:

" : Partially-Vignette& "

15 Aberration Correction Requirements for Transform Lenses

16 Typical Illumination System of a Coherent Spatial Filtering Bench

17 'Classical' Coherent Spatial Filtering Bench Arrangement

18 Optical Examples of Transform Pairs

19 Directional Filtering (Separation of particular direction)

2Q. Annular ft " frequency)

rn " ft

it

It

tt:

"'

it

ft "' " Fourier Plane Spatial Frequency StLP

tr

tr

FIG(2.2),1 Pilot Bench Layout

3 " if Display Functions

4

5 Display Requirements

6 CCTV Performance: Object/Image Plane

it s Fourier Plane Display

8 Sonar Image of Seabed off Hartland Point, Devon

9 Direct photography of diffraction pattern at

10 two exposure levels

11 Photography of diffraction pattern on CCTV monitor

12 at two contrast settings

13

14 Microdensitometer traces of a step-wedge

15 photographed directly and via a CCTV system

16

FIG(2.3);1 Diffraction Pattern of Oil-Immersed.(Gated.) Sonar Seabed Image

2 Diffraction Pattern of Sonar Seabed Image in Air

3 Video Processor 'Intensity-Slicing'

if LANDSAT Image of Grand Canyon Area

5 Sketch Map If' rr n n°

6 Unprocessed Diffraction Pattern

7 Intensity-S-liced: "

8 Relief Mode

9 Contour Mode

FIG(2.4)1 Diffraction Pattern Sampling - Schematic Diagram

2 Sector Specifications-

3 Sector Disc Construction

if Sector Sampling Unit - Schematic of Mechanical Aspectsr

5 rr - n• rr — It " Optical "'

6a " "' " - Master Assembly Diagram b

All Diffraction Patterns from LANDSAT Image

c rr n It — Dimensioned: Working Drawings

d..

7 Response to slit object: unaveraged linear plot

8 Illustrating effective 'imaging' of object onto photomultiplier diffusers

FIG(2.4)9 Photocathode Sensitivity Map (Unaveraged)

10 " " " (180°-Averaged)

11 Response to bar object: linear plots

12 Schematic Diagram of Semi-Automated Diffraction Pattern Sector Sampling System

13 Schematic Diagram of Control Box Operation in the Sector Sampling System

14 Sonar Seabed Image, Hartland Point, Devon

15 Linear Plot of Sector Sampling System Readings from Seabed Sonar Image.

Polar Plots (Rose Diagrams). of Sector Sampling System Readings from Seabed Sonar Image

18

19 Rose Diagrams from Seabed Sonar,Image.

20 illustrating the effeēt of omitting Oil'-Immersion

21 Rose Diagrams from Seabed Sonar Image?: Various Spatial Frequency Bands;- Absolute Values_

22_ Rose Diagrams from Seabed Sonar Image=: Various Spatial Frequency Bands - Normalised_Valuesj

23a- Sector Disc Centring Unit - O-verall Assembly Diagram

b in ri. ni " - Dimensioned. Workshop Drawings;

24 Aerial Photograph of Limestone Area, Yorkshire Penninesi

25 Rose Diagram for Pennine Limestone Area.: ' Unaveraged Plot - Miscentred Sector

26 Ross Diagram for Pennine Limestone Area: 180 — Averaged Plot - Miscentred Sector

27 Rose Diagram for Pennine Limestone Area: 180°— Averaged Plot - Centred,Sector

FIG(2.5)1 Directional Spatial Filter Types

2 Directional Inclusion Filtering of Seabed. Sonar Image ('Hartland Point')

3 .Directional Inclusion Filtering of Limestone?Area Aerial Image ('Yorkshire Pennines')

4 Directional Exclusion Filtering of ERTS. SatelMi.tee Image E1007 00362 (S.W . Angola)

5 Rose Diagram from portion of ERTS Image E1007 00362.

6 Directional Inclusion Filtering on Seabed Sonar Image ('Hartland Point')

16

17

FIG(3.1)1 Holographic Matched Filter Construction

2 Filtering Using the Holographic Matched Filter

3 Main Bench Layout - Display, Sampling,

Passive Filtering Modes

4 Main Bench Layout - Holographic Matched Filtering

Mode

FIG(3.2)1 Beam Expander and Collimator

2 " " Unit

3 " " and Reference Beam Mirrors

if C ol'l imat or " " "' "

5 'Through-the-Lena' Reference Beam System

6 'Beside-the-Lens' It ". "'

7 Practical " tr II

8a Traverse Table - Assembly Diagram

b. " "' - Full Workshop Drawings

9a Collimating Mirror Support --General View

b "' It "' - Detail of Adjustable=

Support Unit

10 Specification for Fourier-Transform Lenses

11a.. Transform Lens - Specification of Glass Elements

b m "- - Lens Barrel Construction

12a-- Lens Support Unit - Assembly Diagram

b It " " - Full Workshop Drawings

13a Sliding Base Plate --Assembly Diagram

b H rr "' _.Full Workshop Drawings

14 First Transform Lens and Supporting Units

15 Second " " II' II' tr.

16 Rotating Platform Assembly - Notes-

17 rr it it - Completed. Assembly Drawing

18a-c tr It It - Assembly Drawings

19a-g if II It - Full Workshop Drawings

20 Rotating Optical Bench: Bearing

21 It It 'r r Wheels

22 Liquid Gate:• Object Slide out

~3 It n. ; It m in

24 " "' : Full Workshop Drawings

25 Textural Spatial Filter Types

26 Filter Stage

27, Image Stage

FIG (3.2) 28 Mirror Mount - Full. Workshop Drawings

29 Beamsplitter Mount - Full Workshop Drawings,

30 Kinematic Mount - Main Assembly Drawings

31 Diffraction Pattern Display Path

32 " " Sampling Path

33 " " " Unit Front View

34 " It " " Top View

35 Imaging Display Path —Beamsplitter

36 rr rr 'r - Lens

37 " " " - Mirrors

38 rr '1; " - Images:

39 Auto/Cross-Correlation Display Path - Beamsplitter

4o m rr IT " " — Auto/Cross- Correlation Plane

41 General View of Bench from 'Image Plane' End.

42 " m " " " 'Object Plane' End

FIG(4.2)1 Fracture Trace Overlay

2 Diffraction Pattern from Overlay Area.A

3 Optical Rose Diagram " it " It

4 Aerial Photograph of Fracture Trace Overlay Area

5 Diffraction Pattern from Airphot a Area A-

6 Optical Rose Diagrams " rr I' rr

7 8 "' " Diagram " It " B

9 'GLORIA' Sonar Image of 'FAMOUS' Area. — Mid-Atlantic Ridge

10 Optical Rose Diagrams from Sonar Image

FIG(4.3):1 Botswana 'LANDSAT' Image - Unfiltered

a m m " -Filtered:

3 " "c " — Unfiltered (Enlargement)

4 "' tr "' Filteredi It

0 5 10 Directional Inclusion Filter (Zero-Order Pass)

with corresponding Diffraction Pattern

6 100 Directional Exclusion Filter (Zero-Order Pass) with corresponding Diffraction Pattern

7 Dartmoor 'LANDSAT' Unprocessed Images:

" Processed: "' 8 rn

[I Cr ( 1. 2) I

\ \ \ \

OPTICAL DIFFRACTION (FOURIER TRANSFORM) IMAG-E ANALYSIS I

o.B:JECT TRANSFoRM

,"" --- ............ ,

' .

' .....

/ / / v ~~ ' b,,,\e

I p \ \

'I r~ u. 1-'-

~/ I \ , p I ' , I V' /' ' // ......... ....__-""

Ft&-(1·2) 2 SHoWING'-- EFFEC.I OF OoMI NANT OIR.EC.IIONALfT'(

OB.:TE.c..T

FtG-(1·2)3 SHOWIN<r EFFEC..T OF DOMINANT G-R.A.NVLARITY

OS:TE:C:.T

TRANSFORM

FILTER BLocItS oFF ALL OF TRAAISFORM EXCEPT THAT WHICH CORRESPONDS TO NEAR-V R- mkt_ LINES

FIG- (1.2)4.

DIRECTIONAL FILTERING-

FILTERED IMAGE

61

O.

6.

e-7119 ae 9auss in rt 54u.ss io r1

ru - q

FIG (2.1) 1 ONE-DIMENSIONAL FOUR/ER--TRANSFORM PRmRS

f(x)

1 FCu)

'rect' func o4

i

I.0

q. 2

Co rlsf0.nt

i•0

>u

Ar x

-

FtW

•••

IL

+2 +4- -z ā -z -It -+ -L 0 +i 41 tit 4L tt:+;>-

0

x

F1G-C2 . I) 2 ONE -'DIMENSIONAL FOURIER-TRANSFORM PAIRS

COMB FUNCTION

+.500 e- A 664-1)

COMB FUNCTION

Y

(

coo

Fim) A

1 1,111111 1;z..-{-

1

RECTC'9 -I -. 3. ti 41

4 4

SQUARE +o0 WAVE L

+0r)REcTCx) @ M S(x_2J )1 1sINc. x 7 Sc,_ 2)] MCo LAAT EP

REcr(x).S(y)# SiNc(u) .

RECT(XĪ. I SINc(u) . S(v)

PILL (X,y) AIR y (u)v)

FF(G(2.1)3 Two-DIMENSIONAL FOURIER- TRANSFORM Pi IRS,

FIG-(2.1)4- Two-DIMENSIoNAL FoURIER—TRjNSFoRH PARS

f(x19 ailf RAW)

i

f R CT(x) SN —24]. 0LS ilk/ CC4) ao .coa(t- i )J • S(v)

9

got

re !

eivir

j> 1~ - / r 1 % it t,

<f ~

PILL (4y) Q-± g(x-n,y-m) e#- AIRY&Wv) ._Z S(Lk- n,v-m) .4 i - ■

COLLIMATED COHERENT 1.164-IT

COMPLEX AMPLITUDE A3

DIFFRACTING. SCREW ELEMENT AMPUTVpe TRANSMITTANCE ii(x)

F1G(2 •I)6 FOCUSSING OF DIFFRACTED LIGHT BY A LENS

I<

LENS DIFFRACTIWCr SCREEN

F1G(2.1) 5 DIFFRACTION FROM AN INFINITE SCREEN

Ix I

BACK FOCAL PLANE OF LENS

f 1.4 f -1• f

coL.LIMATD

COHERENT U4it T

WAVELENlrTH X

yz

T

°6TEGT PLANS

FIRST TRANSFORM LENS

FOURIER PLANE

f

FIG(2.I)7 BASIC COHERENT OPTICAL- FOURIER TRANSFORM SPATIAL FILTERING- BENCH

SQUARE WAVE

SOO

t', -1P,_ tk Cx

31

FIG C2.1)2 SPATIAL FREQUENCY SYNTHESIS OF A SQUARE WAVE,

CONSTANT iTC7)

1ST HARMONtC.

3Ro HARMoNLC

-11-WAAPAtobvt4(

SQtJARE WAVE= sum OF MoAuLATEP Carla = SUM or'

CogSTANT -- HA2wl0 $ c JTRAL -- StPE 6 FuNrc1 oKS

/

N. / 48- f u.nc bons /

fpo ints cf hi-h co r ipLe) ampLi twde strtn9 .h f wayeLen3tll o$ L jkt

A 5

Rn:

%A

NAk

FIG-(2.1)9 ILLusTRAT1NG OPTICAL FOURIER ANALYSIS

0T B- PLANE S afia~ crests i tromil

ratin9 ~of complex cutrtitucteI

TRANSFORM ~.,' ' LENS

FOUR(ER. PLANE

OBJECT PLANE

showing Q notionAL sinusoidal "5mtirg"

FOURIER PLANE

showing t msuLtant roc-functions

yr

S = spatial frejuertc5 of 5raten9 f = focal, lett6 of transform Lens

FIG (2. I) 1 0 INFINITE APERTURE SYSTEM : (FINITE OBTELT/IMAGE PLANES; INwNITE FOURIER PLANE)

f

A

FIG-(2.1)11 FINITE APERTURE SYSTEM : NON-VICrNETTED SPATIAL FREQUENCIES

FI Cr(2. I) 12 FI N I TE APERTURE SYSTEM ? PARTIALLY- VIGNETTED SPATIAL FREQUENCIES

L LZ

f f f

L, >i<

f >1

I.

Ft&(2.1)13 FINITE APERTURE SYSTEM : TOTALLY-VI&NE7TED SPATIAL FREQUENCIES

FIG-C2.1) 14- FINITE APERTURE SYSTEM : FouRIER PLANE SPATIAL FREQUENCY STOP

FlG (2.1) IS ABERRATION CoRRECTIoN REQUIREMENTS FOR TRANS FORM LENSES

f

IF j

ADERRA710N CORRECTION RE LHREP FOR: (LI) co -0'8AUC FOCAL PLANE (Li) FRoNT FOCAL PLANE-I~oo

[~.e. UNAI3ERRATEp POINT SPREAD FuNCTIoNS IN FOURIER PLANE]

• 0

V L, I F I 1..2.1..2.

ABERRATION CoRRE(TION REQUIRED FOR: (L,) FRONT FOCAL PLANE-Poo (L2) co -ar BACK FOCAL PLANE

jj.e.UNABR:RRATEP POINTSPREAp FuticrioNS IN 11 1#\GE PLANE]

0 fL,

T

t

a

FIG(2.I)17 CLASSICAL COHERENT SPATIAL FILTERING BENCH ARRANGEMENT ,

E BEAM EXPANDER LENS

P r PINHOLE FILTER

C = COLLIMATOR LENS

Li = FIRST TRANSFORM LENS

f2 = SECOND TRANSFORM LENS FocAL LENGTH aF TRANSFORM LENSES

O = Ol3ZECT PLANE. F = FOURIER PLANE I = IMA&-E PLANE

Fl&-(2 .J)I'i oPTlCA'- EXA.MPL£5 OF TR.AN.SFot<.t--1 PAIR-S

DIFFlt.A<.TlON PATTft'tN

ri&C2-I)l1 p,KECcc

(SEPARRTIoN of PMT1c0Lk1t PAC crroN)

OB 1EC7

FIGC2-1)2o ANN u(Aft F►c—TGf 1.J6.

(5'e/1W-07101V or PRftTi c uW rgo o wcy)

}

r-- TRANSF02M5 FIL7Ev it-1&G-ES

1

1a EN-is PLIT7ER.S RELR/ 3 LENS

M, oR

0 444

M I( c*, M2.

SEccr.l D Fou IER--rarNSFORM

LENS L2 ti IC(toS<oeE oa 3Ec-nVE

04A01 )FIER)

~ 5

- oBSevATI oN , Sc artni

FIc,-2.21 PILOT BENCH LAYOUT

.4

SCALE : * FULL SIZE 1

FIRST 7 Fou c a`T1I('4 f-oQM

LENS L ~

MI

LL

i

FIG. S•(2•2) 2-,I) If PILOT BENCH DISPLAY FUNCTIONS

FI Cr. (2.2) 2

Ls

FIG.C2.273 M1 ,.....

Ls

7 MAc,NIFIoe SECTION OF

FouRtIER PLANO

/ 1144NIFIED

!MAGI PLANA

•

0

SU BS ECTION MAGrNIF1CATION

S Dys - . REQUIREMENT

INFORMATION ----►--- QUANTITATIVE CONTROL FLOW PATH

• -1).-• -a SWITCH CONTROLQAN UTITATIVE}CONTROL ērQVAL1TATIVE

oB?ECT PLANE

FILTER FOURIER PLANE

IMAGE PLANE

O

0

0

0

SUBSECTION -$ MAGNIFICATION

VV

0

EVALUATION (HUMAN)

5 15 < 30 *

600 200 >100 t

F(42.2) 6 CCTV Performance: Object/Image Plane (f=25mm f/1.4 TV Lens)

i•.AGNIFICATION (Television Screen/Optical Bench)

FIELD SIZE (Optical Bench) mm

FIELD AREA (Percentage of 55mm x 55mm ERTS Frame)

RESOLUTION (Optical Bench) c/mm

RESOLUTION ('Ground') metres (Using 55mm x 55mm ERTS Frame)

x 5 x 15 x 30

Eo x 60 27 x 20 <13 x 10

160% 1 ū% < 4/

(* Over reduced field size; picture distortion caused by using TV lens at conjugates unsuited to its design makes Zone 2 of TV screen image unusable)

(t Resolution governed by input frame - not by TV system) All figures quoted are estimates for Main Bench extrapolated from Pilot Bench experimental measurements

FiG(..2)7 CCTV Performance: Fourier Plane Display (f=25r?m f/1.4 TV Lens;

Mt1GNIF IC ATION (Television Screen/Optical Bench) x 5 x 15 x 150 t

FIELD LIMIT c/mm 90 30 3 (Fourier plane spatial frequency at edge of TV field)

RESOLUTION (Optical Bench) c/mm 5 15 <150 *

RESOLUTION ('Fourier') c/mm 0.6 0.2 >0.02 (Spatial frequency discrimination)

Cr Using enlarger lens for primary magnification of x 10) (* Resolution losses due to TV lens - see FI_i(2.2)6 footnote) All figures quoted are estimates for Main :,ench extrapolated from Pilot Tench experimental rneasur.nents

FIG (2 2) g SoNAR IMAGE OF SEA3EP OFF HARTLAND POINT, PEVON _ (DIFFRACTION PATTER 4 5 BLOW ARE TAKEN FROM THE ErvCi2Li-EP RQ F/l)

FIG5(2.2)%I0 —0'

DIRECT PHo-coo-R1kPHY

oF pIFFRACTIo NJ PATTERN

Al- Two EXPosORE LEJELS

FIGs(2-2) 11) 12 —I•

PuoTOrr2APt-t7 of DIFF{1 CTDN

PAITERN oN CCTV rioNCTb2

RT -NJo Co ,J72P-sT sETrinf~S

• l•-•;. 1-717-1..,

.1

I. • _I_L..I._•.:.._.1.4.1.1.._- ILL:. t...4._ ,._-_. ._

! I .__1. L 17_-:•17-- .. L. __I . , I...•• i . - .

; • , ,

• . , , • i ) • : , . , , . . ...

• I , , I 1 .1 , - : : I .'

. : I 1 . 1 I - 1 i : • : ! i i • i ' i -: •• • 1 : • , , •• • : . -1111\11-iltAt1-1

_... .: .:; .. 1._.;. !_ • ,..... ._i : i • I i....; i.. i ..: I. : ' ..... .14• • _r--.0. TaftS1-__:

; • • e

.... i • ; I •7 j- . • -4-

micRoDENSIToteIETER TRACES OF A STEP- WE DG-E PHOTOGRAPHEDD DIRECTLY frIcr-C2-2.)13] ) AND VIA A CCTV SYSTEM frl &5.(2.2) ne, 15, . rtf VERTICAL SCALE REPRESENTS DENSITY IN AR51711ART UNITS

• • ; • ! ;; . ! _

2-

• • • I .. ,...i. : _ i . I._ . • . . , i

__EIG,42.2.1:15 .r-1-7- -:- --- •-'• -I. 1. 1 . • ' ; ! • 1 ; ; 1 _,._1.. i. _..... - --F.:-

-1---1.-I,--;- I_ _A ; , i i • ,...!‘tt - ; ..: . .. : I.. •

r-f . ! • : ! - ;

1-- : • • -1-- 1 r•-• . I . --1-

•

. • ..- . . .

I • : •

I : . ...

- - • - ----

;- - -

! ! _ • i

• • E.

; • I

I i 1 I • 1 .. I • • •

-1 I 71- 1:t Firl

I— • 7F:fl-RO !- '• 1. • • --

! •

TtTt

J.,.. • ; • .!., . !•11:.i,,1•• 1-.• : . i•--1-7.,::...i:..1.;.,, ., t r I • I : .1 i .I• . ! 1 ._.----17-, •• 11 .... ..:2:. .. . L 1 f-LL.L. '!: I ' !:' I I ' -.!:' -" ' .! ''' • • ' " • -.-a-014—,--, ; ,. • • •

, . . .

, . • ; ; ; i I ! f-o-,„,„,„....4

! ' -- • 1 I 'k

--71-71---f-- --;-- -;-- -4.-- -'• -- --'-t-- -----1-1. -

-1 -

i • It ---! - I

1 - , • I • -1- • . . )1,4....,/„" • ----!--!-- , 4

.; _I 1 _ . _- _':_.:1. ..I .. I-_-.7.- :_._. ...'L!. • . . . • - i-r-"T- 7-- ,

' - - - - ---1-- I- -- ! - - ' -r r - - •

-- 7 - A. • -Kas-auTE- - . L

I .

--1 •• • • :

....,.• 1... [ _ 1....L.._., _ i_.._. ......

i ,

. .,•___ 4 __I

i

• •

- 1'71 • 1419(c..otpithf÷.577.-_-

: : !

n6_0_3)1 Di FFscV J pA-r-rcnl of 0/L-1 rr r ats‘ o (6- OrED) so Weta SEA-Oki it'.

FI c. C2.3) 2 PI c ri o / PPrrr A of se rA-rt SEA-Q EJ' 4GL 1A1 Ala

>TI ME

VIDEO SIGNAL LEVEL A

pROCESSEV VIDEO SI AL

WINDOW

I

2

3 4

LEVEL

1

F1&(2.3)3 VIDEO PROCESSOR INTENS ITY-SLICING'

VIDEO SIGNAL LEVEL

PEAK WHITE

A A (TV SCREEN IMAGE INTENSITY)

UNPROCESSED VI CEO SI(rNAL

4

RANGE 1

WINDOW RANGE 2. RANGE 3 RANGE 4..

LEVEL BASE

aLACK >71 ME

r

`TV SCREEN IMAGE Po•S I TION) 1

Et&C2.3)6 UNPRocESSED

pIFFRA(TION PATTERN

F1 C-4 2 -3)6- sg.TcN rt& of G-4 4-Nlo c/MIY6.f PKAA

4110t

11

FIG- (2 3)7 INTcrvsrn'-sucEp

piFFRAC IoN PRTTc,RN

"PA 444,v F1G(2.3) $ RELIEF MODE

PIFFRACT1oN PriTTERN

LANDSRT 21R-cz oF (nfAnlo CANYo'.I / 42L

FiCr(2.3) 9 coNsYOug MopE

PiFFRAcrioN PATTERN

4

Ak g#41.1%

vsogi 401_,o.v 2o Km

11111111

CAL_ DIFFRAcrloN PaTTERNs r2o r1 L A Np s AT T H R{rE)

FlGC2•Li) I DIFFRAC-TIoN PR-TTERN SAMPLING SYSTEM — SCHEMATIC DtACrRAIh

CENTRIN6- ToLFRANcc_ =±o •o2S

Flff(2•4.)2 SECTOR SPECTFIL-ATIONS re = 30 men [eiuivale to 90 cycles/ m.1 (3= 1°— 15° (var•i0-1,Le)

2-5 TOP PISC BOTTohI DISC

GoLLEC.TING LENS

FIG (2.103 SECTOR DISC CoNtSTRUC_TL ON

DI&ITI L PAN EL METER

l SECTOR DISCS

r I pICr1TFIL-

OUTPUT

PHOTOMULTIPUER \.

FouRIER PLANE GIFPRACTlo '1 PATTERN / '

I vISuAI- PISPLAY

DIFFuSERS AND rILTERS

•

r I:

i

WFTCHt-IAtctRS SCREW

AN INDIVIOuAt_ PtSC

MANUAL ONVE

CONTftgTE GEAR

■ Y

r ,

sttRFT

ooU.FrrlNG LENS 'INNER

RACE

ouTER RACF.

SEC7bR 0►SCS

LoNGITUp{NFU- SEcTtoN END EL..EVATloN

piFFu5t s k FLI-TEtts LENS

SEcTo(Z CoLLEC-114 - MScS

A

FIG- (2.4-) 4- SEcToR SAPLPI.IN(r UIJLT- SCHEMATIC OF MECL1 NIcAL ABFECaS

FLG(2,L SECTofR SAMPLIN1.- urvtT - Sct4EjfcflL op OPTIOJL I~SPCGT$

F

FIU12 4)C-c

{.0C, a. :

SEc_TO(t PUC SuPPoC-T UH%T LENS Ri~TAINita (t:tn((-Sbao& pt ic ~TAtNIt~((r IC~iJG

GL-AR. g.Inf4 SuPPoirT uNJ-r -jia Ruw4

SLCTOF_ DISCS

SECTot- Disc ~ ~ SurrauuNIT LENS GtiSc- 5ECToR

p~~ REY~JNC, VISC$ gE Z144 NA Gq tS LENS ia&

SaCTGR 4(112 RenCr Su?PoRY uK IT

CoMp4 NTS: THE 4Ep2

RING, LENS AND NEEDLE.

RAcc RAzitaAR1 Au.

S uPPL. P BY .

-rrtl A5SEr40L UC%T

SHou1.0 oiPWE MSNIMA L

AXI/it. oR RA01Rt. woa4tE

1-4'71-4IN THE (f4IRlnf4

KEY To DirlENStoNNED woRtCtN4 P(4wId4S SEc.ToR SAMPLING. UNIT

MASTER AssefriaLY D/AGRAM

Au woRi%at- 0/244,4u46-3 ARE u/ITH DIMENStoNS IN WIS.

4QNVT NO:

AuT 1oRstEO S14n.ATt(RĒ

DtYr :

sev roa. DtS< 9£TAI4IPfL-RIn14

SEC_ToR Ot S4T

S \\ SEPRRItTF_1 DR.ANt0t(7.

LENS LENS

r. pE RErgIwrNG-

t. Su sir' R, us

SECToR DISC SoPeoRT uNtT

MATERJAL t DuRAL FiNista : HArr'r 13I_lVCIC PMNT

n 41 9 o

.13 03

•

•

I I

.......__._ - - Mar- - _.-- ~r-F,....,C\C ..o.4 a.. & • At-

95.0 1. 64.•0

to-0 7.0 9•o 4:0

2 •o — 4k-

!- w- -

t C

oC 1 ! J_ CCE –_ N BElaw•

c ome-IE.nn s

Di rum Seotv.s : C AR.E- To sz To rot..fRA WE. of 0.025,..,.(o•0oI .)

LENS 1?..E.TAtNING To jje. TECvRF? To SE.- OISC SsPP o2T

RING- CMecsEtI AD sek- nASiL2\

$GCToR OtSG UNtT S'r 6 £AAA eoLTS AS I.(E C6SS/ h2 (nsceHatYwl=

MTN Ni r2. • .4E.. %duo. u rv OEItTA ITE Ft n! P i -to CJ NTt ab- o F

RsIJZ' -ttiE LENS o.'RSEL.lE.1 .

T%4 . Dte1ENSto..S MA(LILES THus : IS RPPRoxgti, tF

LOEPEND. ON T4ttoc_NESS or secroe DISCS) ; TrcF

Rk-TA(Ntra- R.s•i(- S►tout„p CLAMP ME SEc.Tol. piscs FIKrtL1( oNro -tuE SuPeoLT uatT .

•

•

5-0 c o

&M2 21tI4 SON' 0(2..r UNIT

MATOLIfl(, CS PPon-rf rr) • DURA(,

FIN! SN r1 A17 $ tf -c . PAclOfT

C oMM6KT.S: THE “Pa. i.trar s v P Pl IED FAS PrN txT€R(s(Ai DlhKE162 of- q0 MM ANS AN 1N7FaWfil P1 Ar-t 7EE4 OF Ca. MM

( t'lcLu tR. 4-ER{L tEET4{) Tl- . r.1 7E2 Dc Alm.E-TER

I3 Zo t?E. In(c1L&,14SEQ To ( 7 r..n. )62..F-.1oi1cz- ,pl. re.t2 1_

of 44Al2 TEL-7H) AND TH+E- G-E_Aft. RAO,- SECV ~D

"to •'C1-tl- sop pacer uiNr+T 17Y 6 GA CHE63.£REliO 3oLTS

f~S N“...£SIACY ( CFP MA-3 TER 11-SSEr-i6tY Pt!}G-Mt1"1).

DIM&NSItoll MA•QV kP ml.'r = # IK1E: Ta ((L- -r.. Toc.[atAnycE oP 0• o2.5" C o •ool

Hot.E To CM 9Q,ct.E, ,N ckNTdtC, D,AME'1E2 0.5 r.. (Aff Ro$)

-?HE DiAME7E2 of 7(-(L. caructLF----14 1-6. fS

A PQo 1C, M fc7 īK od L-O n/ciT £?c c-S- . 1 0 r }

TE't N oCE_ r .0 i Y m AN; A e-L U a_P}tY mF 0 -02s r "' 0.0 0 rri

SEC.-ro2 E9CrE5 + CHA-Pt FE2EI)

MATER-1AI- : STEEL. CrAuErE. PL4TE

reNiSM HATT SLACK P4047

GIu/rk-rt-c'( - 2 0F'

510

400 —

200

0-

270°

I8o° 270° 36O°

T

,I—IG (2.0 7 RESPoN5E To SLIT 0BTECT: uNAVERAGED LINEAR PLOT

600

O87ECT FIEL-p LOOKING TOWARD

SOURCE

r O°

270

180

A

360

0°

SEC7of? AtlMuTH

1i60-------,- 40

200-

B

400—

200-,

SECTofl /k1.1HuThf fy0 °V

o°

180°

C 0 1 1800 270 ° 360°

600 - 5-65—

SEcroR Az r fc)7r-j 100 0

o 180

r

20o- 1803

0 I di'

sec-relit 1 014 O 270° 360° ° 610 180 Z70

It

U al .. f

TRflNSFOKN LENS COL,LEC-rvN6 LENS QAWot uL lPL-R

F ~l<

EFFEcTIvE MACGNIFICATIONI F WHERE :

F = FOCAL LE1VG'TH or TRANSFo211 1.-F-14S

C OLLS CT,44 FouR 1 ER PLANE

DASHED LIMPS 7NDICRTE'FILTEREP

MY PATHS

SEcToR p1SC DIFFUSER

087 E CT PIAN E

I

C !

t ( j

FIG (2.t) 8 11LOSTRfiTIN6- EFFECTIVE: 'jtl ING OF OWIECT ONTO rHoTaMUL_T1PLiaR DIFFUSERS,

90°

ecrai mows

TOWARP SOURCE TAN KE LooKthiC

0

0

Fl G (2 . 1) 9 PHOTOCATHODE SENSITIVITY MAP ( NAVERACrED)

0°

FIG-C2. 4)1 0 PH0TOCATi-4oDE SENS a tv (T Y MAP (180°- AVERAGED)

FIG42• 4.) II RESPONSE To BAR O 3YECT

— -,

Sso

400 -

LgKcPt2 PLOTS 013 EC_-r F1

h~LO LOOi.~ficE

~ 0°

276

Goo

°

20 0

9ō° 1$0° 2Zo°

(CO UNPIVE ZACrED S .TOR

360°. tuf{

60o - S5o S4O=

p

1

(00 -

270°

l8o0 Zoo

0 9 0°

555—

0

0°

iSoo-

(¢) UnIAVERA6-4

KEY:

IOOO -

Soo

4,„-k_44,491:112 OB7EGT(oPA0UE orlCLEAR)

NoN- IMMERSED

B a R 0137EL-7-00 0 e °iv cLF/12) OIL - Ir1r1ER.SEP

o131-Etztu c ON °Mav() OIL - t M r-t4.1z5 P

(e) AVERAG-EO co r1 PA R l so nl

0° Qō' (ōG °

TAPE PUNCH

—~j ZNFOR1 IgTlo.,1

CONTROL

BoX PAPER TAPE

—~' To COMPUTE,

Fri-n.45

---p CON-TfROL PATE-+S

H---

iSEcToR AnICS IWO RAPIL)

LIGHT FiD 1 TRANSFo ti LEMS

STEPPI 14G-MOTOR

SECTOR DISC

L

P1&IT 1- PANEL METER

PHo1b1,401-TiPLIER-- , COLLECTIN6 LENS

FIG- (2.z) 12 SCH~MATIC_ PIAG-R11÷1 oF g>:rtl- ROTOr1ATED DIFF(ACTLnN PATTERN SECTOR SHP'iPLIN(r S7ST -

FIG C2-4) 13 SCt-(EmPrTic. PIAL-Cul- 'i OF CONTROL Sox CPE2ATIOn( ITS! Tl-LE_ Sec-Fort SPM-jPLIt C- 5iSTI f1

PRIVE 5TEPPIr(G I'IOTOR TAKE (tEFjPING- FRor1 06-tr4E- PANEL t 7ElL

TRANSFE2 Rai40,n14 To TAPE PuNCF1 MONITbR SECTOR roSITJON RESET

F1cr-C2.L% )IL1. SoNR-rL SC&t3£D It-t , +-tāo_Tt p Poriri , Q V0"4

0 o~-----

0°

FI CT (2.14.) IS LINEAR PLOT OF SEc.To2 Sflt1Punl4 SYSTErI REAptn(t -S 1IG(24)I6 POLAR PLOT (RoSEPgAGgtNy) oF 3EC.ibrt: sArtPUWIG.

FROM SEAM() SONAR INA(rE.SPATrRt Fccqueaq' iCii'&:2•5-So 4.446.,

'SYSTEM REAOtn(-S Moil SEA-13E0 So,JA-2 IhAG£, SELTo2 ANG-UtJ & wIDTt-1 = (0° SPrMPLIt C- tweiVA.° 10°

(PARA!lErEas• M frillkr.f FOR FIG(2•Lt-) S) ,

P HrSoro E L.I(~

2000

FIG(2.4) I7 RosE Ou ntAH FR-011 SEAf3EO SoNArt lMA&. . SPATIAL FR Q tNCY RAK(TE IS-5o4MM SECTOR RNFLE=SAMPLitlr itoolVAL=,5°

0°

FIG-(2.4) (2 ROSE p/A-h F2ot-f sMi 0 so/vim. crr,4&c SPATIAL FRr:ruEAx_y RAN“ 2.5-So CJ4A4 SECrok AN6-L1= SAr1Pun4NT UAL= 2

O

00

30°

0 90

2 70 °

SPATIAL FREQ1)EJEY Rq'4GE = 2.5— So c/MM

SECToR ANGLE = SAIMINge I1'r(ERVAL = 2 °

OIL - IMhIERSEP

NON- IMMERSED

!Soo

FJ&C2 AO 19 ROSE D WI-RA-MS FROrt SEA' EO SoNAR IFIAG-E. ILIA/SMRATU* THc- EFFECT oF 01-ltTTING- — I M11 -i $tON

00

SPATIAL FREQUENCI RRNfrE = 2.5-So c/ -

5EcroR ANGLE = Sfq'PU4- tWTTRVAL = 2 °

OIL-IMMERSEp Wr(t- ADDED ' 13.C.1 LEVEL 330°

No/4 - I t 1t 1ERSEp

O°

1500

FIG-(2-1.020 ROSE DIA&2RI9$ FRoP1 SEABED SONAR IMAGE ILLUSTRATING- THE EFFECT OF ohtTT+ J( OILr t titiEi2SION

- r.

!·

\ -\ ---\ I

\ \ \ \

)

I ·, \

0 ~

c;)

"' ~ l: u 4: .J ~ < ~ ~ .. cr

~ ~ z ~ z ..; cr 7 :J ~

Q. !j 1: c:: z "' Ul d ~

~ ~ ~

~ "'Z cr .J ~ ct: 0 \= ~ <t a. \U V\ "'

'

! /

\

r ~ ....._,_

c.J

\/} f

\0 N

t

\

/ /"

; I· •. I , !

l I

\

\

\ \

\

\ .,

·o \

~: _,('(\ \

·.

\

\ \

\.,.

~ r t' t:. J "'J-

0 0 - \1\ I I

\tl 0

1 t

·, \

.,

'

\ \

'

·.

\

\

, · . .,// \ .

/ I

. -

"'\_

'

..

.... _.

- 4. ~.

·, /"

. I · ..

' '•

... . ·,

···;._ ..J·. ~---.. I .

I /'•

--...

':

. \

\

•.

l

/

" "

' --.

·-'

.._,_

0 ··.· gt·-· .. ?'·-

...............

,.-

~: ... ----7 -- -- ,

. ···-~- . - ... -

--·--·-·--:-- ..... .__ J

' , . I

/ " .... ~ ,· : .

.... .. -- f --~

--........ _!

.. --

·\

.I :

··./ - t,

_;' ... --. ·---.

~-- ,-

-·--.:

i

~~--

I ~--t- -~- ~. -

- -.----.

0·. g C'i"

-.... -t-------·

+-i--+ to -56

449(4k 2. 5 ofetM

c./ coA •.

ci

S ECTo AN G-LE Sa1PLA(46- (PSTEAVAL = 2°

5PR1iA1 FREQUEN CI RANG-ES =

33 o9

• •

•

, / i

i 1 / f I

FIG- (2 - 14-) 22 RosE 0016-RAMS FROM SEABED SONAR ttlAG-F : VARtoOs SPATIAL MEDUENC( BANDS - NoRMAuSEP VALUES

/Soo

Lr. t•f. Sch -4r pfAa- oN-ro Gl4,OV~ ON Grtt U:iIial_en%':L'

OF IN +J ea. SrcC'TI u nJ

Ov1E C. S'E c.-ri onJ

FIG- (2.4)23 SEC.To2 DISC. CENT2iC4G- UNIT

(a) OVERALL AssEMBL7 D1A6-i L/1

1

• -

1

FIG-(2.4.) 23 sEc_Torz. pisc_ cr,m-rRANG- Nrr

pi riFmsioNicp vaalcskoP PRALAJING-3 ALL DI t'In.f.S tonr.s

1.'44

r-l6r(2-4) Z4- A~2,Frt PHoTo62/1-00N oF -1111 5ro, 4-24 , YoR4Cr 2.E Prn11'JE.S

N

F,& (2.4)25 ROSE PoAll-RAti FoR

PaNNINe Lit1E5'10NEE (}REA

UNAVEMG-EP PL-or — MLSCENTRED SacroR

SECTo2 11N6-LE = Sfd'1PunfG inrcEQV4L = 2°

SPATIAL Fec_aoeNc t RANG-E = 2'S -Z5 c/ '1

C it- 25 — 250 c/km ' ont -rt-eE crgovrv0'

I 2.L4 26 ROSE DiAGRAf 1 FoR. PEt4NCNF L I t1 STon4E ftREA : 1$06- AVURA(-EP £LoT- MISC NITRED SECTOR . ALL SECToR PARAt1ETER5 les WVEN Fo2 FAG- (24) 25

N

FIG-(2.14-)27 ROSE p - iNr-1 roR PENNINE Ltl"ta=SToNaC ĪRi A: [SOD I: he-RAG-ED PLOT-CE N-f2gP SEC-To1 . ALL SecTaL PPr tAMTERS !kS 6-i.VEN foR F-16-(2.4)25 .

FIG- (2.5) I DIRECTIONAL SPATIAL. FILTER TYPES

KEY! u,v E SPATIAL FREQUENCY AXES T=- AMPLITUDE TRANSMiSSwMTY tp- At. ,uLRR BANDwtpTE

DIRECTIONAL INCLUSION FILRS ITE

IW 1Y

PIREC:Cl0NAL Exc u$t0N FILTERS

ZERO -ORDER E- PASSED --)P-

ZERO-ORDER .4E-- BLOCKED —~

a e. GEKTRE 1ot■s5

OF IN CL)S toN Fi L Q-

PR-SS ts I

OR P 2 oF F i i,TERED ir-tkcr£_<' 0,4 F C t4, PFtc-

(F u 1—TER. zrAo - o20kJ1 P A-CS 9

CI.) uNFtt_TE2ED i1MP-G--E

24.0° 120°

210° Igoe 150°

2NCLU.S1On!

F16-c 2 - 5) 2- P,REC Ti oNf/3LI FI LTE21il oF sE.A DEP So N,9it Z-P-i (Weal-1.4741P Pamir') )

(a) K E Y To Ftt.:MZEJ) CFI7g2 /46-u (AZPAII dAND Y=208)

c a

e f

9 k

F! (7- (2 • s )3 1)12EG?lo/4,0c- (N/:Lu S, on( Ft LTez, (16- O F 1-1/1E S ToAl& R2EA- if et.! t- Zr+A6 (' •lo t,citf l2E PEA4AIMJec )

(a) UNFILTEKED THA & E

A) F+L-rERC.0 Tr+AGL- : ( - 2o° EniLi-0 Sto FI L.-T6_%. (zKo - aaPet PASS) ALIG-NED AT 030° GFkITRE PiaLcTtflk.{

N. o-ri-. ENJ I'CA4CF-0 Feirra ks in1P Icfrt€ 0 (pi. fr{LQo.4S

FIC-(2-5-)14- Du -nonlRL ExcwStonl

F r Lzrrlr c t Erz TS s-r L, r - 16-4

E!007 00362 (S.w. AN-6-0L-4)

Ca.) O iJ F1 L"Tr O ZM G-E

(b)

(c) Ft t_-TF1 p rr11164-S-SEC KEY .7 J_ot.S

(1)

(a)

KEY To ni...TE-LES -tiGES

_> "Imol oF ExcLush:, Ai

F (UT 4R # 4C.. Jcli.t aLoU( Aflr (3A 0

(P=20° . z -o2.o4.A PhsT)

--- ► /at o 7 s TYPICAL FNKANG£mLWT PI/2f CT/aNS

(b)

(.b)

f/6(2 .5)5 RoSE OIAGRAM FRoM PORTION OF ERTS lMAGE ~1007 003'2.

SPATIAL fREQUENCY RANGE 0 .. 1,-4:40 cjkn

N

090°

f/&(2 ·5 )' Pt/U.c.:lto1114f....IN.l!WJt<>"' ftL7E/lJI{G-

Ot.J Sut<l~ SoN/!t(t 1H~('~~t'l71./+NP f<>14T')

(Cl) Uf'l pI'-Tf...R_£P IMITG-E

(b) FtL."P:..J?..f.p Tr-tA:v£. : IV~ 10° I~C..lV$101\1 F!LT£~ '

(-z::~ -oP-Pf.fi. f:SLo C.)C.) Au(,-HE...V f\-r l35 ° c{-AJ-rfU

0 11(£ c..-n o ...J (. I N (} l ~ l( '( M.JLo L.f.S)

pKoTOG.1 ft 7Htt oR

114.11K0 PC-AS-(1C- (tf c.) HOLD 641.4 "t R+EcaR.PMar r1TEL 4AL

tu,v)

o63.EcT PL14ui.

TRAN.$Fog. LkI Jf

FoU R1 ke. PLANE R 6F/ W'c (WI/4 604 (rtE

r gic

C+c,v)

V Trzornofo LkAgC

rouMER ru+tsE

-t•RA NS63 044nsAc E LES

02(x)€gct,y)

caoss- actEatrRN PLA4&-

Thus when the hologram is illuminated by 02(uA), the resultant

amplitude contains terms such as: 4(4,v)IO,(u,v)IZ~ Ot~~+V) RI1

02et1,00CN,v)R, 02(wv)0(4)v)R . The last of these transforms to i.e.02(X)40 Cai 0, (X,y) i.e. the cross-correlation of 0:0(13) and 01(x,5)

.c

F(G-(3.1) 1 Ho(.otRRPH(c. 74 rccH ? FILTER Co of.)

In the recording and development processes, the amplitude transmission

of the recording material is made proportional to the intensity of the

light falling on it and hence contains terms such as:

10, 64,012, 1R11) 01 (u.,v) R , a*ctL,v)R •

FIG- t) 2 Ft L-Tt.R(4.G- us 14t: T.-t -totrocr a Hkr -i-a.p

PEVW.oeep soc0(v44"

FIG(3.1)3 t-IgN BENCt{ LRjc OT — pis?Lfti, SAMPi.ra -, PflSSIVE FILTER..t - MoD-5

A

B1

B2 B3

C v E1 E2 F

c Ii

: L1 ,L2

I

J

M

LASER

OBJECT PLANE

TRANSFORM .PLANE BI AMSPLITTERS IMAGE PLANE , COLLIMATOR MASK LO'+r' P° ER HIGH POWERBEAM EXPANDERS

PASSIVE FILTER

LIQUID GATE HOLOGRAPHIC FILTER IMAGE PLANE

AUTO/CROSS-CORRELATION PLANE

SAMPLING CONTROL UNIT

FOU IER- ,'FA!tS CORM LENSES

L3 L4

M1,M2,i•13 MI+ ,M5 M6,M7 N 0 P Q

S

T1,T2

U V1,V2

It ;GING BEAM LENSES

SAMPLING BEAtI IMAGING BEAM: AMPLING FAM MIRRORS REFERENCE F.EAM STEPPING MOTOR OBJECT PLANE PHOTJi'1UI..TIP LT. ER DIGITAL PANEL METER TAPE PUNCH SAMPLING U11IT CLCS C1-CIi;CUIT TE12. IS ICN CAMERAS T;iE1 •:OPUS'=I% HOt):INL\N BEA TING UNIT ANALOGUE '1..D:;G i:; UNi'i'S . T!!:I:N,CPL ST1C aOLOI'.!:EId CHA.r.G.NG UNIT

FICr(3,1)4- MAIN 13-NCH CA•yooT — HOLOG-RA-PHIC NIATCI-IEP FILTER (NG- MopE

A B1 B2 B3 C D

LASER OBJECT PLANE TRANSFORM PLAN' BEA:•1SPLITTERS IMAGE PLANE COLLIMATOR

MASK

L3 L4

M1,M2,M3 M4, M5 M6,M7 N

IMAGING BEAM SAMPLING BEAM īFAGING BEAM l SAMPLING EEAM

J}

REFERENCE BEAM STEPPING MOTOR

LENSES

MIRRORS

El F.2

IA.J POWER} BEAM EXPANDERS

HIGiI POWER 0 P

OBJECT PLANE

PHOTCMULTIPLIER F PASSIVE FILTER Q DIGITAL PANEL METER G LIQUID GATE R TAPE PUNCH H HOLOSRAPUIC FILTER S SAMPLING [WIT .I IMAGE PLANE T1,T2 CLOSED-CIRCUIT TEL°':ISION CAMERAS

AUTO/CEO S-CORRE .ANON PLANE U TI1ERMOPL.ASPIC IiOLCM. i:F':TI :G UNIT K SAMPLING CONTROL UNIT V1,V2 ANALOGUE VIDEO-PR3C-SSi.iiG UNITS

L1, L2 P0UK1:R--TRANS RM LENSES THERMOPLASTIC HOLOGRAM CUA FG NG UNIT

.

..

G

-.z

F IG (3.2) I i BEAR EXPANDER br COLUMAT-R

A LASER C CoWMAToR

D MASK

E I LoW PbWER BEAN EXPANDER

G LIQUIP GATE

X BEM GUIPANCE rtt2aoR$

—+— LASER BEAN"(

•

,-r ,E1 or E2 oy.aY"•

FIG C3.2) 2

BEAr2 ExPANPER vr't1T

El

G

X

z

oR E2 LOW OR H14+4 Po4 & BEE --1 ExPA-NDER

LIQU19 CrAtTE

'BEAN GUIpRNCE MIRRoR

TRf\VERSE- TABLE_

Focal)OPTCAL 0E NUI

-~-- LRSER BEAM

L •

f

S

L

FIG-(3.2)3 Hirtte(IS

BEAM ExPA10EQ EFERENCE4EAN A

A LASER

E2. HI(N PoWER SFAtt ExPANKR

6- u a)10 G-FtTE

L I FIRST Fot)14ER TRAKI)FoiM L.1 N5

M } REFEC::P_Act:r Ntatuor~5

o OOTECT ?L E.

X 6t1 GoOI}e4c.E hit(tlto25

Y TQAVEiLIE TA-4(L

z FoLeo oPTtcAt 17c ck.i

~ — LASFR BER*1

FIG (3.2)4-

COI.UMAT02 L REFEREKCE BEAM n, 2¢o2S

A LASEX

C CaLL1MPrToa

P r-1136K

L: 13.0 pp (,-err

L I FIRST Amo ROPkT. V Osfofrr LiNSE.s

L 2 5E'c o

M6 RE ck. (3F + r-t,azaoas (17 FIXED PT: Oct_ 4ke.[CN

SCREEN : P(ACEP Fo0(14k.a pulkk

To s Now cou..0-1ATf40 REFERkP4C.E Br-kr1

—>- PATH oF osucx ē. RFFeQE140_ A S

L1

G

•

iM

a M"r° A I t

I tEEN11

L2 1. t:tw~ } ! i

1

k

+K

FouCZIE,R PLANE=

TRANSFoRM LENS

OB3c-r PLANE

FoouSc N![r LFi45 r-p2oV%OL 2EFEltE.xcr- QE/Ni

REFERENCE CSEf} i Ar4&-LL

TYPscau-Y < tO°

f

CO4F1tc. rT

Lt G H T _-__

o 67ELT P LA-

A-N5 Foa -t Lk-J5

FouQi ~(Z

P nrF

CONE RE

LtG-HT

a h M E 2rto (L

Q

F tG- C3.2)s 1TH ILO o 644-TKE-LE445 R~FER rc~ 43r t 5't5-71-P t

Ft Cr -a) 13G-s( DE_ - -L SD 2E EA- t ctrrEl

REFFI_E,.tcF a€AM AKrGLk-

T tPILA w 3o°

T(iAn1S l.AT0N AP4P Tip- APTofTNENCS Fo 2 AT4-t L. EN Cr-TH Eau A-LA S (CTI o N

G0r1E_(t.

Ll CrHT

FIRST R,~FEaFrac a CA tl f-ti &off

F l Cr C3.2) 7 PRA LT1CA1` REFERENCE 13,-1 S'( Tr -1

SEC ONO FF_ LiJ E (3k/M-1 i--{(R(LoR

•

(=lG-(3.2) 3 a TR11VF2s.e_ -Rif~,1c-~ Pil i

c.c:riirssrDIV SP12.01-S 7o M LO L, J tie) V •1&\r '

_, ..-R.-•tw-_n.,n,. - .! wr n..,R,rg,.,,..,,,,.~,.,.. ~”.--.

C U)j Re DS

Dif MST M.y PJ2ox. Sec JRED )1S, con./v iL,r-r.

■

/ Pk-7T LL---

i

/250

CrASE.

PL A7E

.Y

SL/OINtr

Put-rE. 0

BASE

'PLATE

0

0

plr-ICNS1ora5 IN t1'U.' TQES

MAYE(+AL: sL 0r/1 PLATE DoRA(- ,7ASE eL17E (,U.PE RODS - S-r-ELL

r'1c VC h&hr•r f'•'li,.J Ar c:,14(11.1 S(Iw rr•~~w4, }c..., ✓fN~Er+

SAnJOuYST00 LYCLOT

cN ,"01C-PTL1) c41CA(Xi

Gcho6 R.eO D'ANcTE,e AS NAIL II TQ, 5L) J-r 4r+r FNP°410".• 321S._ r0723Jc6

Avr11C21fLD f1EN.TTUrL

DATE 1312 175 EN:2,174 HACrrErr..ffria

FINISH

'7' NOTE

GRna-r No!

SEE n'ert EC to..., r;. o.n Nt+,C1 of TsC1t knLES

10 a

T

0 1n 1-‘

363sf OR cSA ~HRLA1

Ft G- C3.2) 8 6 ikilt -SE TR-0 LC_ - FJL.L_ wORKfHof' p21tw t'.J(rS

70.0

low ArKwc. I. -I<

r T\ 7-

4.13A TAPPCD HoLCS

2.0 ISO

O13A TAPPL.D HOLlci

-- i1111iū1'

+ . i

25 0 75.0

~±c 2S • 40 -ā

FlG-C3.2) 9 a. CoLLtr-loTit,* M(2202 SuPeo2T - G-E,I JZAL Vf .iv

I (l.uO(ffll S\lt~-r ~If

I . POSll"lON I

oF ~ M ,rut.D (Z_ I

I

FIG(3.2)10 Specification for Fourier-Transform Lenses

Transform Lens for Spatial Filtering Project for Department of Industry

Equivalent Focal Length: About 700mm, not critical.

Back Focal Length: Greater than 200mm.

Conjugates: Corrections as below for two sets of conjugates:- (a) image at infinity (object imagery) (b) object at infinity (transform imagery) Thus the design is probably symmetrical since both object and transform fields will be of equal sizes with 700mm equivalent focal length.

Object Format: 55mm x 55mm - applies to conjugates (a).

Object Field Angle: 10.058 radians (13.3°) - also for conjugates (a).

Transform Field: About 80mm diameter, depending on the exact value of the equivalent focal length.

Aperture: The aperture stop for conjugates (a) is at the transform plane, i.e. it is telecentric; the field stop for conjugates (a) is the aperture stop for conjugates (b); individual components must be large enough to ensure no vignetting of pencils for conjugates (a) at maximum field angle.

Wavelength Range: The system is to operate in monochromatic light, ultimately 0.488 microns wavelength. It would be useful if the design were also correct at 0.33 microns apart from changes in equivalent focal length and back focal length.

Aberrations: The system should be diffraction limited for both sets of conjugates for spherical aberration, coma, astigmatism and field curvature;distortion is not important for either conjugate. Coma is strictly not important for conjugates (a), since the complete optical system comprises two lenses with magnification -1 overall. However, if each lens is symmetrical, the correction of coma for conjugates (b) will ensure it is corrected for conjugates (a). If it is not possible to comply with diffraction limit correction for both conjugates, the lens could be made asymmetrical and the strict correction aimed at only for conjugates (a); however, we should very much prefer to have an aberration-free transform plane also.

. i

AIR SPACE AIR SPACE

2 1

3 6 f..

In the table below, bra~keted figures refer to optimisation using catalogue glasses; Plain figures refer to optimisation using melt glasses, made test plates and measured element thicknesses.

Surface Radius of Spacing mm Thickness mm Edge mm Glass Refractive InC.=x Humber Curvature mm Diameter Type !1el t/(Catalogue)

1 +162·2o8(+162·0CO) 19·2550(19·4978) 104 ·0CO EaLF4 1·58731(1·53711) 2 -1 68 · ~01 ( - 16~ · 71 1 ) 0·6237( 0 ·7370) 3 -1 66 ·7q;:;J _ .-::;;; . l•;c;~ 7 •1000( 6·6341) 102·000 S72 1·66209(1·66123) 4 +2522 · c63( + 2~-- 3 · ·J9i3 1~1·9803(110·6561) ') +1~~ · ub~( ~ 1?c; · ?~~\

6 +91 • ~97( +Y 1 · ~~~) 15·2400(17·0061) 80·000 BK1 1•51558(1•515t6)

7 - .) 1 . -:;::)C. ( - '-i • • -; 'l 130·4233(132·113u) 8 -17'5· 4,:: -.:.( - 17c; . 7'"''7':

15·2680(17·0061) 80·000 BK1 1·51558(1·515E6) _9 -25_2::> • ~G6( - 2c;: • ': 0 ·~

112·2271(110·6561) 10 + 166 · 7~2( ~ 1~6 · ~2))

7·1500( 6·6341) 102·0CO SF2 1·66209(1·66123) 11 + 16~ · LIJ!l -4 1 f-)~ · 'I ' 1 '1

0·5E05( 0·7370) 12 -162 ·298( -1 62 ·9CO) 19·2950(19·4978) 104·000 BaLF4 1·58731(1·58711)

Front Conjugate 181·65~m from Surface 1 Back Conjugate 205·60mm from Surface 12 Object Field Dianeter: 80mm Wavelength: 488nm Transform Field Diameter: 62mm Equivalent Focal Length: 700•00mm Object Field Angle: ±0•044 radians

ftG-(3.2)1\b T<t.AN5FoR.M L£N5 - LENS BARitE.L Cor-JS7RlJLTION

G(.3•2.) t2a LsA SoPPoit-r (wir - ASs-Lr-taLY PIA-G-(1_4-.64

7-0 Vr at il)

f

I Pus TI f

vu UlacKS

orf f ~

` _ s.

.s: ...

PZS •

~ F~ l.i Aedia

4.4

~ W

/ I • 75

/

•• •' 0 5 V 10 5. Crf o TS

1...-41 1--1 r ,r •t. •1

_ l_EJJS S U"PPo2T uNiT

MR MP. OA, . pccu/-ormiOrA- SMe..E_T

fait I' T(ILS uF ,NPI'1'D'101 PN271, Pur_Acr

fcP hPA-,,1Pn2 JNELT, •

Gft N T lo. 3311 So57o-7332us 11v7H.rtlsc0 5146,11-rv2J on-T5 r2/1477 FA) v,R.(S. M2- 440.0 TT , ,NT. 2 9 12.

OuA{i71TY ~ZL JIP. o: 2 °FF.

I t /

I Fl G 0-2-)t2 W'JS rOPPon_-r OWLT — FOU.— Wact<rkoe DR +t s

A

/ . 1 ' \

I. _ /

I

I

'

— —

1

■

1

I. — Pos 1T, oN

or 4/E.f

'4

J

I

—ij I

cr oiFs ■I

I

Ī I

\

\ ,

a

? C"

• mou---~i lrr••ō

• I.

1z•o'

10.0"

VIEW OF

TOPSIDE

VIEW OF

UNDERSIDE

~ Fk U--(3. 2) IS a- -So Orn!( BFtsk_ fAirr — f}sscr-w L.y Pi Pr , t },1 ~2

3.

SI L

3'loH TUbT1) 2

1 J1

ta7d1 UL

thSb 1

ZI h7 "1N2 :S9JU'n'.N ((l2I/Ī1 L 13'~L'Vn 'd

7).r':'9. )11, : Y1J(ltir9iS 01SI-dotilnj

3oZ 4.LL..L.S'51"t.1i :ON 1c41y- JJo ! tiLIJ fvy^~i

H:J \'311 it/1.1JcJdc c oy. COL %:i

10J1 , tJv91-411riub 15-v3WN911J Pno 'It/ °1 s_L-wn () ) Ny NtJ

T1r4 S J•6,0 r4 ou t-4 'mal __. 0703V'a.14) 3b ol SQlrl)) -3LGr1

O:-S 3')Nyvitol HLO'M 3G'n9

'9-315

9lb1d T1 -9N (l 11s

)Ic .. I ;4,N'

J '1 r Z. „i ā .4 Z

'111 4 ilAre 17'

N5

-r

S-9N►r-A vd dorls)Ive,01 --nrd - --3l d 3SV.O. I (7

r

FIG (3.2) ILf- P1R51 TRANSFORM LENS AND suPPo2-TIN.!(r UNITS vEE t3LOCKS LE45 SuPPo2T UNIT FIXiEp o' ticJt [3JCH QEAP-1. PiTt-15

O33-Ec-r Pt_!}NE $EAns et. t-rTE.2 PA 5S FILT~ Ft2ST -raA+4YF.R-H LE NIS

REFEi1 "JC. C€, -j r,trut.ons . s.

L1

tks-T427"7 / 1:1

! CN4 I

B1

1

nCrC3.2) I5 SECoND T2q4•1SFo2h-j LENS F\40 SuPPortTtN- UNrtTS

32 TRAN$FoR-I-t PLANfL UA-mset_crr-kk X 2 V f t3 Lo CK S

I ~Mq6-- PLANE I 2. LENS SUPPo(LT UNfl L2. S Er C-0 I TreANSV-OfLF1 LLP45 Z2 ROTPm Nar 0PTI(J t- 13E24c_H M3 riA-6 t N12,- 13 ra4e-t t-tt RRo —>-- (3F_A-f•t PPTH5

.. F1G-(? 2) /6 ATING- PLATFORM ASSEMBLY - NOTES The p'.iri.ose of this assembly is to provide a platform which will

sulpert a heavy lens and its mounting (about 50 kg weight), and is

capable of intermittent rotation about a distant bearing. The wheels on

which the platform is to be supported. will run on the surface of a cast-

iron table-top, to which the base of the bearing will be secured.. The

following description of the design accompanies. Figs(3.2)17,18, which

illustrate the method of construction..

Part :1 is the bearing base fixed plate, upon which rests part B,

the bearin.; base movable plate. It is desirable to have provision for

making occasional adjustments to the position of the axis of the bearing.

To acheivn this, the fixed plate is to support four horizontal translation

.,crews, which act on the sides of the movable plate. Between adjustments,

tt:!. movable plate can be clamped to the fixed plate by means of four bolts

e• ,:i)pcd with large diameter washers, running through large diameter clear

ho7.:s in tae movable plate and tapped into the fixed plate.

In plan, both thses plates are of an H-shape; this is dictated by the

fact that, when finally attatched to the table, they will occupy a confined,

~:nac:• between other parts of apparatus..

Part C is the bearing pin assembly, consisting of a pin, upper and

bushes, a ball-race bearing (supplied with these drawings), and a

loekin; nut.. To make provision for the possibility of future modifications.

to our apparatus, it is desirable that the bearing pin be detatchable from

the surrounding assembly.. In consequence, the pin should be a sliding fit

through the ball-race and both bushes, and should locate in the socket of

the bearing base movable plate (part B), in which it can be secured by a

::ircugh-bolt.

The lower bush rests on top of the socket, and the inner race of the

ball-race bearing is clamped between the two bushes by the locking nut

mounted on the threaded section of the bearing pin.

The outer race of the ball-race bearing is located between the

upper and lower parts of part D, the bearing head, and should be a

press fit into the recess of the lower part.

Part D is connected via part E, a connecting arm and spacer, to

part F, the platform; part F is provided with clear holes for the

attatchment of the lens mounting, 'and is supported by two wheel units,

part (3.

The design arranges for the points of contact between the wheels.

and the table-top to be directly beneath the centre of gravity of the

combined. lens/lens mounting/platform massa It is desired that the top

surface of the platform be about 1" above the table-top, so the wheel-

units have been designed to be bolted to the top surface and to project

through slots out in the platform; the sides of these slots are not

intended to act as guideways to the wheel units, whose location is

fixed by the positions of the securing bolt-holes; the units are angled,

such that the wheels run along the circumference of a circle centred at

the bearing axis..

Each unit consists of a ball-race bearing (supplied with these drawings)

whose outer race rests on the table-top, and whose inner race is a press

fit on a spindle, that/ is secured by a split-gin or grub-screw in the forks

of the unit.

Each of the parts A-l3 is the subject of a separate dimensioned

drawing shown as Figs(3.2)19a-g..

COMPLETED ASSEMBLY DRAW! NG

FIG-(3.2)17 ROTATING- PLATFORM ASSEMBLY

ffIG-(32)

A SS E. M SLY PR ALI I Cr

-

13aA MIN 0- 56AR346- 84.SE

PAk.--r5 A- - c)

gr-?A cz-;

NtWINts CLP;r t ii

- P19-11--r

Î c

F \

ftP JJ s-rts-tCr-ri

Cffr)

t i> • ASSEMBLY PRAWiNCr

SEARING. PIN — BEARK(r HEAD CONNECTINIG- ARTI

(PRR-rsc —p---- )

trQ.1

‘kail jOL Ora. St-u'.& et 1 ,-1

I

\\•••••••••••'.•••-.••••••••••,na,.p.•■••-.....-

1 . . -•,-r•-..r.- r....,--.......,..---• --/-. ...,,,,. ..-ar.,-,-------..,--•,..=.--,-,

L.):4

(2 0 FF)

DRAWING-

CONN EC 1. tisfCr MM ANP SffiCER

-- BASE PLATE — WHEEL UNITS

(PATS E F — G- C oaNecri kfte- nik-M

Pr E

if

------: — ,-.7,.■ ----- La 111 i-trzaS , soPPL i EV /,-------

' ,

o/ I

? sE /

I ' ..... ·., > .. ,;,;,.... d!w • t' t cto 't .. .!tbif't' d 'tf1 st¥· 'I '•'• ....,..t•4+i:•' I •••. t .... I dd '···-··. * ••• ~· .. ~tit.! 't J~ .......... h ,. ~' I

t I -

7" :;•

~ "lt. ·i ~ '4i. ~ "1 ,. I I C:"~1f YN'i'i/ I

s.· ! I• o-1 r<-..l!'. I c• " rf ;..• . 5" ~ {. Qsr H t Tllff/:..1 A ~ ~ ... ~~

I

I f I • I

2" '3" '2." I f ... 2t" ,~ zi' ... ~ ~ .. j .. .. ,. •1-4 .. 1• z. •I I• ~-

I :j'· -¢- t .I -- • I ~ .. • t

i I .. ~ f.

? I

j''1GSF ' ;. .

PART A I .. !'I I~ ("'\ Tl'lrfitll

.. ..u.s M'l78l•m...: 5"T££L

I I' f

i ··-$-· -$- I I I 1,1

F1&{3.22 '~ Q . , I

f: . ~ I -

• . 'I !

~r ~----fssF t I

~t i ,. I I

d l< •• hiii.U>• ~ ... t> AP~uS"rrt£NT

I ~ ! . I ~ I H~f!W (ft.ol'l")

} / !

-Ts T:

I

1

1r 4 ~u U

15,"3,u I U

.

SsF

/L

FIG-(3.2.) 19 6

1 E1\ NG 1ASE M oV IN'(r FLAT.-

PART B

MA-TULIPri-: S-TeaL -

N OTI;S : -nit S ?LAW- r S

SECL)11.0 r • TKE. EC?-nlr4 13rtsE coag A

FIxk.D ru!TCA al' 7-1G'1 (ra•r c

TutE. FoU<. 13c_-rS - r., irr,

SJpP1..,CP wiri1 4.J (E PI(\MC1 ,t

WFY3t4(.f11 — (L.;NN+ Z- Trt04.d frtrf

TPt& 7/1 PIM"irZC.t. t-

7It _ g4'i21 n/ (r pII4 Mil--T C S I40ULv 3E. A

SLAOtglr 1C1 IN T.t. I" plAraFTik cootx.-r. q-NO IS SE-cuct j r7

7rtk 1.6 " 7,,L-T. (f.,yavinflr i tf°u 44i ITE

•

t 1 v

C h11, CTā=D

ASS::N13l,3'

LoC IC. 1:4C., uuT Tc'P at,sti GALL IrhC _ p~,~~

w,-rt1 4fr4 e a)

1n

i p MW LP G ►t_ ūt E P1N

f 'r-ror-r

BEnA NI G- SSG M L

Fc C32.)19 c PART

N,r-A-T Lt Pvt.. STEL

N ct tr LLJC L

(t t..- (Vac- ,SJPG'(-1;n LJI14-J ?NESE_ n2A..rt,.1<<. ,,Jf-IIc-I

sei _121

g.1LL (IA- ....c..—

I . — p_i20N4 I } 56...1.4uco . . i I Pm..4Iv6S

i 1 I I .-.r -

' r

TAMP Sot=

` c15AR µa.ES

BARINIG HEAD

PFFgTD

MRTU:.AL: STE Ei

#NOTES : TNE j)NIT IVUUDES

A 17Au - (LACE c p (ti (.. , COMIC,

u1-r- T.{aiE Dnlh-..4L %,wa"w S14001,0 OF A flu- t1 rrr aft.rfe

'arte (1E.c-E v W -r>-1C C a.JEL

SG-CT-tarsi or ir{[- 4-1(-(9 Ai,fp

IS ' 1.o(f1W AwiALLY ArtourfD

Ir1F 0,r-rot (.-i IM Trt "-or

Se C1r.W of Tr{E rVtfl

F16-(3.2)19 d.

1/ Joi

~----------------------------------~r.' ~ ~>~ lj·jr.: . I' ! l

;~t .~~~~~~~~~~!~!:~ ---~-------- ·------·- ~.~, ~-----

2. ;I

" -3:Jr·-d ------------------··- -··· .............. _________ ..... lt'i !. -~~-·-· ------ ___ : ____________ ...... -~ ..... ·-·--------·-· i .,,1 1! ~I

t-------~+-~'--------------------------~----i:T~----------r--------.t~~~~j,~,~---------1

~ i

I i

!.'' i i" ~~~~ ----------------~----------------~·

l--~-1

.... .J . . .. . ----------------------- --------------.

-~r- . ,--~~r~--L_~·--~------------------------------~-4

II ,I . . AL-L f{oL. C.S ~ CL.£11~ 1>1/t'NIC.T£/l... ! · ,

1-------.--+--.~- -- . . . ----- ...... ·- . .. .. --- __ :_-. - ----·- ----- ···- - -·- ---··

(QNNE(.Tl~Jj_ AND SPFIC~f5

PARI· E ... --nl\ TE.P-.11\L .• STEE.L

' ~ ~ ~·

I

t t

i f.

t

! I

I

r. • r ,

' . '

N 5,*" trou 16

ca-ar- Hog-t-S 14

•

I I

1 I

I I I

5 2 2

• ii

Z.- A e.

•

C Aft HOLES

4-

'BASE FLR E PART

hicreft- AL- EE

FIG- (3.2) 19 f

1.'

1,,%••••*••••■■••■slpewe mn,,,••••••••••••••,••■••••• ••••••••■•••••*■••••0 1,1r•

1 1°

a" 11"

2,Z

4

N

1 e

i 1 I

si ornhzT

2 01RrtE144

(

FIG-(3.2) 19 ..

WHEEL UNIT

PART G-

PCTE AL

cou A ITi 2 cFF

NOTE S THS. UCJITs

INc:.nPcl'_(17E 2 13fiLL MpLe... •

13E-ARPn;Gs, SUP('(_IED wr ;H TH ES,C D 'tw+NG i, 17 is

Pi oPos,1D -THAT Gr1<-H of

f1-U-5E C ClotINTC) •+N A

SPIr4D(,L SL-cLR_L=A ū7 A

sr~l r r, v Na. u rl-IE.' ,...l ff) it./ Trill- Ft>(Lg. t-' J(T , .

(:AT: !1 17.4 L,C-c....() r

cc./N 1T Ut_-11. ! DF ū[; 12rv(r

Da•Tf11(-)

r 11

APPaco'. ji IL,i

/ — wPtsrftt.S

13~u. r-1y_C C JPLi ? ~+IT11 Coi\k /lN r

l G r'Ar e2

..

••

.

l

Fi&(3.2)20 -

RoTATIN4- OPTICAL }4 : $Eg21f /

52 TRR•4SFarte-1 PLANE

F PRSs+vE FtiTQ.R

Z I FIXED elcMC-AL

Z2 Rar-AT1fJ6- oeT►cAl.OFrJW

BE-A2in/(r 13A5E (3. Pfirai 'f i.- P i N (30 n, N1- KM-p

—•-0"—

BEAHSPUTTEQ

(?.FN41

Rrftn air p t_.PtTF-ofc

ASS4.MBL(

SEMI PATNS

(3.2)2I 4'

oT NG- OPTICAL t3ENLH : WHEEL.

L2 SECoNO TRA►15fofr-i

MS IMPCH . BEAM )(2 Vrs.._ QLocxs

YL LE NIS SUPP02T

Z2 Ro-PNTIN(t, opitc

C.Qt4N£L u4 NO-1

P Ltl'T F-02/4 i Wttir- -L VNIT

-9-- 3

LENS

F.—It/Lama

UNt"T

-A•LCE Jc.N

(207A-TtNAT Pt.fri F;Jru-t f}SSE~lrTL1

PP(TR5 E -P

c' f

T

Z2 1BEARINrG H EAD

.A

.1°Ik! MASE!l- --'4Y yR ak Ya,.y~4'3e

4. b.

•

FIGb•2)23 ~ ►

LIQUlP &ATE:

OQ3ECT SWOE Ii4

(r LIOIUI/ 6-ATL

LI Fla-31 īiveoFoo-1 1 LENS

O oe cx PtAME

Z FIXEQ

OPTI cfu BENCH

FIG(3.2)22 -•

LIQUID G-ATE:

oe3 cr SU* OUT

4

(T L i ). J (s-tifE

LI FIRST Taq#rir-04ry LENS

> BEAM PAflj

Z FI'EP oPTlcAt BeNLH

1. OQ1E LT

A

G

I

1

54

3sL 121 - Ito - 2 •

o i tp11111rtrprp•IrrriaNwPWEgairrAME474, ,eresern.7,1,214.".1P.1.▪ WINWIMPX

•

165

_ i3D 5 2L 51

i

' / ri ,..2-1------

------ — --_..,.. —"'"—• —......, _ ....„ , '', \ ---. -..,---=------- = Z,-,, '.- \ -.

/ s // / i f, i 1Iit! 1 Jt \ q■ \ A \ \ %\\ '‘

• - \ \

/x-

/

\ \ , \\■

\) \ I i 11,7-1 0

/ / / ,....

/ 1,J/ .,,,.., ,,,,

\ \\N, ,.//

.././ \ 1:. — ... ,....--:- ....., _ _......., . ....,

,• .

r-1, AR ipA cc, far.“1-Dit.

-P*4: "4 P

•

-oi.;.•;1'2:-r-28144. t.c..r U.1Š

T"'

—

?:$,? Pt 11jfarki►+ j:1912,,r19N3

nriAi,rr911 jitriQS'1

ao LEL0L.70.• - uL :orf J_J12f9 —

S-9NIM',MQ d(F-4soM -I-7 n~

~ alnc~l~ -~z(z-E)~r~

i

~l S i-- h c.

tn .1 e o 31I'd J9 ci

1.10 ,v 0 v7i3r6 19 0;11•4 1!

4 110 PA !' I:V,1

j\

N

{ •via ',6

r–

4 .via ot

541

4TOwaspy r»Nn •(S(1 hD C..7t1,.a

O i,) IiN»1-O 1iJ' -U

sr& (!r Al /J.iNIL,D

;n -_) rein Ir„ovJ p Avoi_Ltd

S7011i»41 £10475SV 'nrj 7m-1- :5-710N

1vvn0 ' I-V71.4W

'5L-G:w1/11W NI S140!51\13WId

1137 t(-;tin

TEXTURAL INCLVSIOti) FILTE.Q5

i Tavrort At E' c.LL s l a r1 FIL2VU

T= o T=

QAgp P Ass /

STOP \ QA '4 0

FIG-(3.2) 25 TEXTu2RL SPRTIPtL FIL__ TR TYPES

KEY = U, V = SPATIAL FREQUENCY AxE$ T_ Rn?LITUDE TRANShUsSIVITwl V =SPAT/AL FrEOULAC'I (SWNDWIP71

Low PASS \

I \

I HIG-H PASS

E \ /

44- I.

1-1

FiG(3.2)26 1=0.r'

FILTER_ STADE

Fib(3.2)27 i

62 T2AksfoRrl P LANL t .

eicf}ft CPI.11T42 r. lefet

itsitce s4

F PF S3i\( F 1L—TER

L, 2 5 ELcJ p T2fV(JFta.M LENS

r

I

7 Fi

DP-M tt ~, .~i 1 I s

Prrivt.S L2 :. 3 . "

I

f4-vlt +{< 9 9 Og

4a H o

EQO 2

a

1

_ D

()N

IS :

I

T`I

Nt A

-2

∎ A L ;

s

FIN

1.U

-1 1

If)

11

C 4 T I- r

0 0

F*Cs.2)2 E 11gR2oz Mounrr - FuL4- tJo2KSkop Pru ~nr&s

I

FIG- (3. 2? 21 f3...4?-0-Pc.4-r7-61'._ Moun..T — (...)0(144f14 o P Da.rft..11■16-3

I -

?

o

Z

z c.-

zl CI

: 3

. -

I

1 ,

47.1N.

5/ Pik

lorci L51 S 2Ci :oN L+de

C7/S{Il D

J i

a145,N✓ J

-7-73L5 _10Ii3 1 - 4

-1- J° L — D

_ —

: j 1Jlnw~O

311 ,-,:i:1114, 031- 11.15

•

7u'sur ldf∎1

SWH NI1

:SJe i iAr jiJIQ

C

or OE

it

Jr

7

Oct

F16-- (3- 2)30 KINIE mATtc_ t-AOLAIT

STE f+ANA pyt )146-

-1-0P "TeNStoni Spa,44,- sco_kv)

Post-n..4 oF crLA-Cr ftLocf-

_ uorrbel -7-6risforv sprikh/G-

+ • I I, I •

1-1A A- S E N tS PRSt- S

SrE -1

coMi'I.CTED A SSEi-'1 AJTyP._

7T11 s D P. G s;-rc s -rf k cor1 P ~

A s SF-r 16 vf Fox- , N E /1 RT, C. M o, NT

-t Y A (T yr'~ g ;SAS. u9rz6„6/L ZAC

'LAT~ A ND o,Mgic, ens s~ , 41. NI)

vas D‘._-r L_S oF M4- s i z. s or

S CAL. J S sea /46-f, £TC ., LiH 1 c4-+ A p.~

c vM r'-1 o ti To B~TF-1 YYPC A AND yc

?H~ s PP- i Aar c u P ,4 nro '--COS-E PN

SKo() 9 flCC0 MOOr- A crt.AiS / LA)C- --

-rN, c_wvfl O F 1 5-P"-M 02 -r yP+ A

AN ZO Fo2 rYPE s

S

• i27--- .:-,' ,.: .1

::. • s.= t ..;.,7,,..... .4 r i

1

-.... 11 IM•inKr. .2.-",-.41 I Wr. . . . . . , ' -' ..4 I I, • . .. , , 04-.11- ' "::; ' . :- - ' '

-.4 . • T . .7

L2-.

?LAKE- CS EA-MS PLAT T‘.12...

&ATE-

ir-Prni C--b 17-1-1 LEN -SE-5

•

131 .3

Cr L- Q-LAP

L I 1 na.sT 1 LZ.S 54.koly Lt4..SA rr■J

M.GRiG-

T

BEpir-j LE_.4 S

GE- A I-1 NS CZ-I2x1,

L4• '

M1

sq t-ipLAN/G-g:-Pt- r-AaRItoris

STE PPI e4(,- pH o t-tt.) t_7 if' LI EA S ANA P (,_ UNT (3 1--1 PINT l-t

m M5 N P 5

3 Ft CH 4 6- B 1N."4 r-t

2_ CL0.5ap cia-c-utT TELF_vi sconi C.-Arikaik

Dafre-t PPrrt-+.3

F M3 I- ' lc 41 ..... :,...

- -- -' u07z,...%. B2 , -.. ,.. ..,---,

•

15.4;11t4:7'. 'h.

... '' - CZ: ..e•

-

- Zb...i.

r •••■••■•■-.

2

YAP

62. R R.NisFoam PLI 13 F Pr15 SOX._ F1.1.-Tk..R.

Z C1-€- PUÆÑE LI nksr rui4.4 3 coap-t L,E.INS C. L2.j SEcorqo

N-4,1472-11t4. 7. I

? . T2

sr:A t-tfaxr-Tel _ .2:- 1

A Dorm) 6.1 At_ . . ".,, • --

4c.r 414.414;

- - -, ... 4.-

.„......0 ,cx, j*,io n will/f4.

ft 7 7. Ij ": , :

., -4.• . "!=.7'‘. '

•

•

4

FIG- (3.2) 32 PFACTIoÑ PPYTTif-LN S Pre-t P Nr- PT H

G- LS- 2 ) DI FFRA CTLo kJ PATTERN 0 IS PL Ay et-TH

I

N STEPPINA- MOTOR

S riPuNcr- u I-1

FI 6-C3 .2-) 33

yiFF/tAcnow rfrrrifim .54fleutglr U N tT

FRONT VIE W

- .....±L.,..i K. •

4 .•

,..,- ...2, ,...i;„_.,...„ ,..4... .., _ ..

PT ''T'"OtT$41 r . :{ .itt - r -•.;,;at.-•..:te .4 %.... . i

FIG (3-2-)34-

9IFFARCItoN1 Pft-TMAN JAlIPLA616 ()Nil

TOP I 1.0■1

Cr LI 0..■.) G-ftTL N STG_PP‘Kit. NOTorl_

P PHOTO

S SFt-NP1-41(r UNILT

GERM PIVT1-1

•

•

Il kcf. 4

.J

1;1444 „ , •A•

'a• 4

f,0 • r•' ;

ia,t44414:444,-

c.

41re, -

ii

I

S

. '

FIG- 3.2- 35 cs&Amrre.s.r7

Trqt1C--ING- '5PLA1PAj - B I OCI7ELT FtAiVE rigrAe150-rrrE.2 6 LIQUtP 6-1tvr-

L-1 Fs 2 -r Tr2Akis-Poftfy LL/■1 S MI tiktrleG t7kA-■■-i tattat_

S S/}1-4PL-4j(s.)

F (XL() 0 (?-PJ

(3F.Ail PPriltS MI "

G

•

FIG (.3.2)

?Melt-v.4 Pis PLA1 Perm - LENIS

132 Ta-41•15fT44-14 kM(70-/Ifflarria.

F PPI-TscvE. Fit.-Tot

L P CANE

o Lf i

5E-cohr F ittST

L2 IZA44Sicall S

13 1-flA-4.441- 602M-1 L re5

fl I P12. .1 13-f t4--a Airi4,kychAi Nia_rtA(u

f-t

ROP-t efrCKS

:F siviar.ft

-.141+1

...410-16491eittiNaiLammardlial. iiEj:

k......,...

I __ __- .L....-‹ 1 M3 _--.....„. _ ....J -

„,.,,P '--j-

...-., ..c...,_ _. , . .. • ...„.„ , - -. — -

,,,,-45; tr • ,

4.1.g Li 1 .....' ■ .......

..• '' f. • „Ai- 1.4 I

.....' .."; ■,.. .. ;,...t14'..",..411-1111*.*1.

4

M2

La 1

'

I-

,

M2

-r

z -.- I L2 • 4

._. •

I (3.2) 7

TM AGING- PISP 'Y PRTN -MIRMQS

PIANi

L2 5Ecfl T2PN SO) ark l...r,xs

M31 ZF+AG-Ie4&. t3EPr 1 r-tlrutio2s

-->-- i3 -c t PRTH5

a

•

FI6-C3.2)3g ■- ►

ItiAw14 ois'LRY PFYru — ZMI-64S

r-tA Pu I-

X I1&6-E Ft.0t1 TN RGi f•f f3 EA/1 (UH Fl LTE-2e_p)

Y z M FGH

TIZAA4s LS NS -

(F i tr cEp)

FIG-C3-2) 39 AuTo%Ross- CoRRELATfon/ 015PLAY PATH — (3F-RMSPc-('tTeR

a 133 It-1i 64- 8-isou =E _ ~-{ seTE or t{oi_o&-rttt '11c Ff1el2 Lf 25 T T(t~N1 FmRT-1 LF~S~S L2

} Ff sc~co,49

L3 Mf r2

MRC./ f■fir 6 41;-0 t c.~nt5 rt A'4t ar (3EA-+-1 I-t f t o 2S

SEA '-+ PaThS

F IF (3- 2) 4-0 A in ac - c' -- c v2.RZ.LA7t Alo P(sPLP-y

a3 z MAC P LANE Q .f PL TTER

S.1Tf= oF HcL.o(r{jWHtc. Fin-TE2 UTcjG2oSS - GW R.CEk.LATL0 PL/\

Pf — A0 To/tRc65-COgnAlA1oJ MANE

L2 5acorv0 TRAN i Ft) ti-f L-NS f"t Q 2r-t Q-tr+ C Nt f 2c1-0 2

geAfi1 PA-TH

to

w

F I G (3. 2) 144 GEJVEItAL view o &f'J G.. OLAN! E!J L() FI 5 3 TR s Ny U e.3 L2) SELONN V 3 S 1'1 (1 EA1 t.Er4S

L 4- SA-Ai ',cr., (! thM I ENt

H i 3 Zr(PrC 1 l S EAo-t ti A t. 45 M3

7ItAr(S+ i1 P~~~rE Qk+v~fvu-r-r c_rs L._1•-1ATC2 h;SIL PATs5tvL F-t~7F, . Li 0.007 c7-AT =Mf4GE PLA",E

r~t 7 s " r r rtndts

H7 RE,f./IENcL f7-01,1/2lto/t-S s SA-"01-(NG LAIrr TZ C1.41449 UO- vi-f T VII;.H .fitr(EIZA —> 364.-1 PcrIAS

FDG C3. 2-) 42 CrfNHL% v«k. 1 of Pt./{.14e E.JQ F(10I~{ ~Og-TF—T

GL1 NUT. ~-

F L2 _y4 it_ -

3 ī' f ~ 4 IV

TZ

fem,... y y~9y.M IrEtLlOI.~ rY MV'

A LASLA t z. VAN 5fo(Z. 1 PtAKE j3F,4n.(SpU rTE~ El lDi-/ Po fel1. 6E1ē•-∎ 4.4LPAa(OER. F Pk-sr i vi_ Ft LT IZ G LL v so c).ATE

Z FI)MiE al"((LPrisi QEE$CA

Li} S pair Tn •ufai-u-+ l4-N(sES 1.3 mir+ +rZ. OE14 Li N3 ik SA+14"4-4,41- OEAM Lh J'

ML ZmA-trortlt-6 MC(ZP4nl M3

earoi r

S 3 S f t'u'-4- r i QF At rZ L.2S

n b 3. REf rcL 06.A.m,-l+uwa-s M7 O o V 1F_L.4 PLEWE s sok,y071_, . Ncr T2 «oft; ut u,A (E1 1U i ICNfEAA

,))

si _ F A 'M4

J zL2' R_ -

-

L4

. .

Y ` i

44, r -

, 4 4

M2 -

Y

~nYb ~Ri a .ia+fr at41414+r M1 .r.:.x'~

a-

a.

F1c-. (4 .2) ! FRACTURE TRACE O\ERLAY

-1460O \ _

.A . rmr- -\

•

SCALE 0

KILOMETRES •

FICr(L .2) 2 DtFFRACTIon PATTERN FRor1 OVERLAY AREA A -

(CAL,tt3RfkTIoN MA2KS IN C7CLEStrnnt)

FIGCL•2)3 OPM-AL ROSE Pfgc,aAry FRot-1 OVeRLrnY

AREA A - Frchaegf4cy Sz.Ahr4-E 7.5 -2D 0'c11S/MM

(SuPE2u"tPoSe_p ont NANURLL-1 SL3MME.D t2.USE DI4Cr(LA11)

MA

Fl& 04-.2 )1 AEROL. PHoTDGRAPH OF FRAcru1 E TR/ICE OVERLAY AREa

FIG-04-2)5 DIFFRACTION Pil-TT -2

P Roi-i A I R PHOTo ((2EA A -

(CALI(32FtTloi\J (--i&i KS Irf CYCLES/M i)

FI Cr(.1-.z) 6 OPTICAL- RoSL D1A(rRAH FIZ.~r1

AQ A A - SAHPUK - U NC 2~NG6

[r5.5 -22 y,,-€3/ICM ON Tr1E (rAoJN0 3 , ( Tl-1

' 0e\\

e _ ' \ N\ \

f1ANUAC-

060°

FIC- L,.2)7 OPTICkL- RoS&- t71 +41 FR.ort 4i2PH07-o

r}2~A a - SA-Wog& Prt4Ac)E4YLY (,.& o•5-1 cYcLez Aim C2.2— 1l.•4 cYc.Les/kri ~o v 7rfE (s-(to JAW 'J . (wITH rI4'' .. QojE.

rlAKuRL of.TtcAL

Ft6(Lf.2) g oPTIC_At. (Los p r-t .'i F-acw-1 /}faPKoye,

A 2.E.A S - S PF-fl ' L1 F 1u £rjL Y (LAM L r b• 6- I c rcc.i=s

(2.2-4. L4 CYCL .5/KM ov Tvtf Cr2aJ40 1 . (WITr+ M /info At_ 2b5E).

AIRPko-ro

3-5 cy...mms/,..n

rAKUAt- (LOS~.

Fl c;- ( 4-. 2) 9 \ I

G-LORti\ SoNAR IMAG--E oF 'FAMOUS' AREA - MIP-- ATLANTIC.. RID(;-E

0

I KMS

·r I

250

I I

f<EY: LOc...A-rtoN AN.D .SCALE

o•S-1.5 M Ca

Lo•22- 0•44 . I (7) „ I — 4.

(b) (c)

(a)

FIC-614---2-)10 OPTICAL ROSE P,R6-42PMS FZai'-1 s0'4 M

'ON TNE CrftoVNp'

(0..) AREA I - 5AriPua6 RANG- 0.5- 7.5 cru-es/mm [0.22-3.3 cYCLL3/knil

Y a.

tt

INOIc-ATES PeQEc-TtoNI of NoQ1TN-SovTt-{ A>V5

S

(C) 2. -

(d) 3 -

FIG-(14--3) I BOTSWANA LANrOS err 11L--1P16-E. — ON FIL,TE_REP

FIG-(4-3)2 13o-rsMIN LRNDSPrr' rP-111-rr-E — r-tLTEREP _

LAR6-E ~ ) I Cr- (i-3)3 BoTSWcRR LA\DSRT' (M,G-E - UN FILT JEO

• ;vie .17 7 niet-%~~ ~ ~

.Z % ` .4.a !'

~.y; , 3~~ :. )\ tt_»f : : •

• 4 •

` «'.

mie.

1$7• irk‘

\'t; • \

, • .

•

rr a

•

M=

j

Ftc (4-.3) 5 100 p12ELT.o'JPtL 1►JLLUSION F1L"re2 (Zkao—oai'/t Piist) wl1N coR LkSPoNOIn - 01 RCTia PA7T&2&j

CLEa2 OPAQUE. (T I

10° T = TRr1NSNITTAntCE

FICT-C4 3)G 10° Pig5cTronrRL ExcLus,04 F+L3-E2 (z izo-e'PE PAsc) WtTN CoRR6sPoNPFnrL D,FFaAcYtan/ Pftrr(2v

CLi-F(Z- OPAQUE

(T=l) T=0)

1 a ~

1 11

4-4 10°

Ī = Tizilft5Mt7Aac_&

FIG-64-.3)g MR7r1oo2'LANO5ATI QROCE55EP Ill AGES

(0.) BAND 7 IMAGE Fa--re-2Ep

al- /-5-75 CYCLEsrmm [i•5-7•s c/km]

Cb) GAND 7 IMAGE FILTERED

AT i.5-7..5 crca..51..,, Ei- 5-7-S c /k,.,i

INTENSITY - SLIC ED' (I`/on(ocHRc7NE)

(C) DAN -7 ZMA(E FILTERED AT (5 -7-5 CYCLES/r,■-+ [1-'5-7'5 c/kn+j

INTENSITY-SLICD (-AL E colo z)