22-09-2014

1

INTERFEROMETRY

CONTENTS

• Introduction

• Interference of 2 rays

• Optical flats – description, evaluation of flatness using optical flat NPL flatness interferometer

• Simple numerical on absolute length measurement.

• Optical Projectors: Bausch & Lomb projector.

PRINCIPLE

• Interferometry makes use of the principle of superposition to combine waves in a way that will cause the result of their combination to have some meaningful property that is diagnostic of the original state of the waves.

• This works because when two waves with the same frequency combine, the resulting pattern is determined by the phase difference between the two waves—waves that are in phase will undergo constructive interference while waves that are out of phase will undergo destructive interference.

• Most interferometers use light or some other form of electromagnetic wave.

• For understanding the phenomenon associated with interferometry, let us first study the nature of light. According to Huygens Theory, light is considered as wave motion propagated in the ether.

• The light, therefore, can be considered as an electro-magnetic wave of sinusoidal form. The high point of the wave is called the crest and the low point is called the trough. The distance between two troughs or two crests is called the wavelength λ.

INTR

OD

UC

TIO

N

22-09-2014

2

• Generically, an interferometer is a device for producing interference between two or more waves. There are numerous types with various features, but only two distinctly different strategies.

• The other approach is to use some sort of partial reflector to divide the amplitude of the incident wave into separate beams which are eventually rejoined.

• Either method can make use of multiple beams.

• light travels along the OX-axis and the time taken for travelling one wave length λ is called the time period (T).

• The maximum disturbance of the wave is called the amplitude (A) and velocity of transmission is λ/T , 1/T being called the frequency

• A ray of ordinary light can be considered as composed of an infinite number of wave lengths, the value of which determines the color of light. The amplitude defines the intensity.

• White light is a combination of all the colours of the visible spectrum, red, orange, yellow, green, blue, indigo and violet, each colour band consisting of a group of similar wavelengths.

• The advantage and peculiar property of the monochromatic light source is that the above characteristics are virtually independent of any ambient conditions such as temperature and pressure etc.

INTERFERENCE OF LIGHT • To understand the formation of interference fringes we must consider

what happens when two rays of the same wavelength are combined.

• two monochromatic rays A and B of identical wavelength but of unequal intensity; the wavelength is denoted by the symbol λ and the intensity measured by the square of the amplitudes a and b.

• The rays are exactly in phase and their combined effect is equal to the sum of the two curves A and B and is represented by the resultant ray R

• Ray R, which has the same phase as the component rays and an amplitude r equal to the sum of a and b.

22-09-2014

3

• the rays are shown out of phase by 180 degrees, i.e., by half a wavelength; the combined result, R, is now very small and would obviously reduce to zero if the amplitudes a and b were equal.

• if two rays of equal intensity are in phase they augment each other and produce increased brightness while if they are out of phase, i.e., differ in phase by λ/2 , they nullify each other and result in darkness.

If we have two rays of equal intensity then the resultant wave will have zero amplitude and complete interference will be produced. At this condition, no sensation of light is registered by the eye and the zero amplitude (intensity) of light produces darkness.

• For interference to occur, the two conditions are necessary, i.e. the light rays are obtained by division from a single source and the rays before being combined at the eye must travel paths whose lengths differ by an odd number of half wavelengths

when light from a single monochromatic source is split optically, made to travel along two different paths and then recombined at a screen.

Light from monochromatic source A is split into two beams by passing it through two splits Band C which are close together.

two separate beams of light are formed which for the purpose of this explanation may be assumed to be in phase.

• If the path BO & CO are exactly equal, the waves on these path are in phase, producing maximum intensity at O.

• At point M the CM-BM=λ/2 resulting in the waves to be out of face producing a total darkness at M and similarly at N.

• At point P, the ray path difference is 1λ and waves again in phase producing maximum intensity at P & Q.

• Thus a series of light and dark bands are produced called as interference fringes.

22-09-2014

4

• Whenever CM-BM is odd multiplier of λ/2, two waves arriving at M are opposite phase.

• Thus for max intensity at P CP-BP= (2n)λ/2

• For total darkness at M CM-BM= (2n+1) λ/2

CONDITIONS FOR INTERFERENCE OF LIGHT WAVES

• The two sources should continuously emit waves of the same wavelength or frequency.

• For obtaining interference fringes, the amplitudes of the two interfering wave trains should be equal or very nearly equal.

• The two sets of wave-trains. from the two sources should either have the same phase or a constant difference in phase.

• The two sources should be very narrow.

• The sources emitting a set of interfering beams should be very close to each other.

• The surface must be reflective

FLATNESS

• Flatness is one of the most important aspect of a part's geometry.

• Before length can be measured, for example, the two planes that include the length must be defined, and an important of that definition is flatness.

• And as the dimensional tolerances for length grow tighter, so do these for flatness.

22-09-2014

5

DEFINITION OF FLATNESS

• Flatness is the minimum distance between two parallel planes that contain all the irregularities of the surface under examination.

• Flatness tolerance zone is the area between these two parallel planes Figure shows the flatness value and the symbol used to represent the flatness on the drawing.

GENERAL DESCRIPTION OF OPTICAL FLAT [O.F]

• Application of interface – OF

• Transparent Material

• Glass or Quartz with two highly polished surface

• The OF is never a perfect plane

• Made to flatness error of 25 to 100 micromillimeter from edge to edge

• Appropriate for 1/10 th of typical flatness work tolerance.

• Any slight imperfection is in OF a calibrated values should be considered.

FOR GREATER ACCURACY OF OPTICAL FLAT

• Must be used in constant temperature

• The surface of work & flat must be thoroughly clean and free from dust.

• The surface should be wiped with solvent such as Benzine or Methylated spirit.

• Clean with soft cloth, brushed.

• Flat must be laid on the work not slide across the surface – causes wringing false pattern of interference band.

• Fine scratches will not affect the accuracy

22-09-2014

6

FLATNESS TESTING

• Flat plate placed upon a flat metal surface so that a thin wedge film of air is entrapped between them.

• This wedge is stable enough for bands reading because of the presence of minute dust particles or lint after grease and soil have been removed.

• When suitably illuminated interference fringes are visible when the deviation from the planarity are of order 0.001mm or less.

• Part of ray is reflected to follow the path AB

• Remainder continues along the path AC

• Reflected from the metal surface C along the path CDE

• Both rays [AB & CDE] are combined at eye having traversed unequal distance.

• For small values of θ, AC=DC=λ/4.

• Therefore, the change in separation between the optical flat and the surface between two similar adjacent fringes is difference between

AC and FH= 3λ/4- λ/4= λ/2

RECALL

• For interference to occur, the two conditions are necessary, i.e. the light rays are obtained by division from a single source and the rays before being combined at the eye must travel paths whose lengths differ by an odd number of half wavelengths

22-09-2014

7

• Thus it is obvious that each adjacent fringe represents a change in elevation of the work surface relative to the optical flat of λ/2 and total change in elevation from point of contact to the outermost fringe will be n x λ/2 if it contains n number of adjacent fringes.

Each band indicating a path of constant separation between optical flat and surface under examination

Now there are four possible cases when the contact between the optical flat and the work surface occurs at one point only. (i) If the surfaces are perfectly wrung together, then no air gap exists

and no fringe pattern will be observable. (ii) If angle θ is increased, then points C and H will be closer together

and fringes are brought closer together. (iii) If angle θ is reduced, then fringes spacing increases as the points C

and H will occur at greater distances. (iv) If θ is made too large, then fringes will be closely spaced as to be

indistinguishable and no observable pattern will be visible. It may be necessary to perform a number of trial placing with optical flat before satisfactory result are obtained.

• If the surface is curved then the band will follow the line of constant separation and curvature in one plane reproduced by the fringes.

• Concave and Convex

• Will not be clear from the simple usual observation .

• Some other methods are used to detect the surfaces.

Each band indicating a path of constant separation between optical flat and surface under examination • Change in the elevation between the optical flat and surface can

be calculated by counting the number of fringes and multiplying by half the wave length.

where 3 fringes are seen with an incident light having A of 0.5µm, the separation will be

22-09-2014

8

• While checking the flat surface

• first inspection – flat fringes

• Advised – rotate the air wedge to 90deg, if the second test also shows the flat fringes

• Then the surface is flat surface.

• If the other surface is curved bands – workpiece is cylindrical

• The degree of accuracy also depends upon • Support of the optical flat

• Viewing angle

• If only the surface counter being checked- mounting arrangement not important.

• If measurement involves comparison of two surface- the surface support become the deciding factor.

• Steel flats, Granite flats and even optical flats are used as the supporting the work.

In-case of spherically concave surface, the flat is resting on a line passing around the surface and on lightly pressing the edge of the optical flat, the edge line does not move as the pressure is varied. Rather, light pressure at the centre will cause the optical flat to be deflected and will become more nearly parallel to the concave surface, thus reducing the number of fringes observed

Thus if by light pressure, the centre of fringes is displaced and the fringes are brought closer, it is convex (hill) surface and the level at that place must be lowered down to form a flat surface. If by light pressure the number of fringes is reduced and the fringes move apart, It is (valley) concave surface

Fringe pattern

22-09-2014

9

SURFACE CONTOUR TEST

• In the study of the surface contours it is important to know as to where the optical flat is in contact with the surface being tested.

• In mono-chromatic light, the bands are sharper near the point of contact; and in daylight the point of contact can be seen as the colour of the surface being tested.

Let XX be the line of contact in Fig. Contour BAB shows that all the points on it are at equal height from the surface of the optical flat. Points A and C are at the centre of two contours BAB and DCD. It is obvious in Fig. that edge at B is λ/2 higher or lower than C. The air gap will keep on increasing as we move away from XX. As BAB represents points at equal height, it means that B is actually higher than C. This means that edges of this surface are higher and central portion is lower, thus, it is concave surface. If the bands curve in opposite direction, the surface in convex

concave surface convex surface

Band due to scratch

D – distance between two dark bands d- distance due to scratch Depth of scratch= (d/D)X(λ/2)

High or low spots Surface in the middle is flat

22-09-2014

10

N.P.L. FLATNESS INTERFEROMETER

• This interferometer, as the name suggests, is used for checking the flatness of the surfaces.

• The interferometer was designed by N.P.L. and is commercially manufactured by Hilger and Watts ltd.

• The flatness of the surface is measured by comparing it with an optically flat surface which is generally the base plate of the interferometer.

interferometer in its simplest form consists of a

mercury vapor lamp whose radiations are

passed through a green-filter, this is giving less

fatiguing green monochromatic light.

This light is focused on to a pinhole, giving an

intense point source of monochromatic light

which is in the focal plane of a collimating lens

and is thus projected as a parallel beam of light.

22-09-2014

11

This beam is directed on to the gauge to be

tested via an optical flat so that interference

fringes are formed across the face of the gauge,

the fringes being viewed from directly above by

means of a thick glass plate semi-reflector set at

45° to the optical axis.

The gauge base plate is so designed that it can

be rotated and the fringes can be oriented to the

best advantage. Further, the optical flat is

mounted on an adjustable tripod, independent of

the gauge base plate, so that its angle can be

adjusted.

The gauge to be tested is wrung on the base platen

whose surface is finished to a degree comparable to

that of the highest quality gauge face.

the optical flat is placed above it in a little tilted

position, interference fringes are formed; one between

rays reflected from the under surface of the optical flat

and those reflected from the surface of the gauge, and

the other between rays reflected from the under

surface of the optical flat and those reflected' from the

base plate.

The gauge to be tested is wrung on the base

platen whose surface is finished to a degree comparable

to that of the highest quality gauge face. As

22-09-2014

12

• indicates that the upper surface of a gauge block is both flat and parallel to the base platen.

• The fringes are straight, parallel to the base.

• The fringes are straight, parallel to the base fringes, and equi-spaced, and their spacing is the same as the base fringe spacing.

• Thus the angle θ is the same for both the gauge and the base.

• The displacement of the gauge fringes relative to the base fringes is entirely a function of the gauge length and wavelength of the light used and is of no concern in flatness testing.

• The fields of view in Fig. indicate that the gauge face is flat but not parallel to the base in the direction X-Y as the pitch of the fringes on base plate and the gauge surface is different.

• The difference between the number of gauge and base fringes multiplied by 1/2 λ will give the amount of taper present.

When the gauge surfaces are more than

about 25 mm apart, the fringes from the

platen are not bright enough to be used

for comparison purposes, and so a

method must be used whereby only

those from the top surface of the gauge

are used.

However, if only the number of fringes from the top surface of the gauge are

considered, the method must eliminate the effect of the inclination of the optical

flat, and the inclination of the platen axis (causing the platen surfaces to be

inclined).

• The procedure for checking the parallelism (or taper) of the gauge surface using this, is as follows:

1. With the slip gauge in position '1' on the platen, count the number of fringes or bands from its surface (N1).

2. With the slip gauge still on the platen, rotate the platen through an angle of 180. (i.e. position 2) and count the number of fringes from the surface of the slip gauge (N2).

3. Half the difference between the two counts, i.e. 1/2 (N1 - N2) multiplied by 1/2λ will give the error (e) or taper is

22-09-2014

13

OPTICAL PROJECTORS

• The adaptation of optical principles to the practical needs of workshop inspection has given rise to the construction of toolmaker’s microscope and projectors.

• These apparatuses incorporate every feature of accuracy and refinement in their design, and hence they are known as precision inspection apparatuses.

• The inspection operation and dimensional measurement that can be carried out with optical projector are similar to engineering microscope

• Microscopes are intended primarily for tool room and gauge room applications and require certain degree of skill in operation.

• On the other hand, projectors are basically production-oriented instruments in shop floor by machine tool operators.

• Optical projectors are not adaptable to various types of special accessories designed for microscope. But they provide application advantages in many other respects in comparison to the capabilities of engineering microscopes.

PRINCIPLES OF OPTICAL PROJECTORS

• The need of observing a magnified image of an object from a convenient distance has given rise to the construction of projectors.

• Unlike microscope where observation and measurement of objects with the aid of optical magnification are limited to viewing through an ocular, projector uses project magnified image of the object on a glass screen.

• As a result visual impressions become a physical reality as the dimensions and forms can be directly compared to the physical master components

22-09-2014

14

PARTS OF A PROJECTOR 1. SOURCE OF LIGHT • Light source is usually a powerful lamp up to 1000 watts or more.

• Generally, tungsten filament lamp is used for illumination.

• it is replaced by high-pressure mercury lamp when specific measurement has to be made. It produces steady light without flickering.

• The light source has to be designed with consideration of several factors to avoid harmful heat transfer to the optical system and operating elements of the projector. Therefore, the lamp house is usually mounted externally with a powerful blower fan.

• It also has special heat absorbing glass filters to keep back the heat rays that might affect the dimensional stability of the object.

SHADOW PROJECTION LIGHT SOURCE SYSTEM • In this system, light source illuminate

the front side of the object, which faces the lens system.

• The lens system receives reflected light, which is magnified and projected on the screen as the object image.

• Modern optical projectors are equipped with light switches with a provision to regulate the light intensity.

• This enables the production of best level of illumination for any particular magnification

• In this system, light rays originating from the light source hit the object, whose physical body creates a shadow bounded by the actual contour of the object when viewed in the direction of light rays.

• This shadow is then magnified by the lens system and projected on the viewing screen.

• a relay lens is used to transfer the shadow on the projecting lenses.

REFLECTION PROJECTION LIGHT SOURCE SYSTEM 2. COLLIMATING OR CONDENSING LENS

• These lenses are the parts of a projector, which refract the light into a beam with parallel rays of almost uniform intensity on the entire area of object illumination.

• They are fixed in the lens housing and are situated nearest to the light source.

• The glass used for collimating lens must be heat resistant.

• For special applications of projectors, like photo-elastic stress analysis provisions are made in the collimators to mounting of polarizing filters.

22-09-2014

15

3. PROJECTION LENS

• The projection lens system magnifies and transmits the object contour or image resulting from the collimated parallel light rays.

• The image formed on the screen should be unreversed.

• Different types of lens arrangement are possible according to need and application.

• For plainer type of optical projectors, the magnifying lens system is interchangeable lens system. For complicated application like in measuring machine, the lens system consists of several lenses with different magnification.

• They can be adjusted manually or with power drives. The lens system must be capable of giving clear definition of the object. Therefore it is coated for extra light transmission

4. SCREEN

• The projected image of the object appears and is displayed on the screen for inspection.

• It is made of ground glass, with finely grained texture, to provide a bright, glare-free image. The screen must present an image easy to measure with accuracy without causing fatigue to the operator.

• The brightness of the image must be uniform over the full area of the screen. It must permit observation of the image without distortion, when viewed by a group at different angles.

CABINET PROJECTOR

• The various advantages and conveniences of projection as a method of inspection have led to the development of a self-contained type of projector.

Bausch and Lomb Projector

Bausch and Lomb Projector

22-09-2014

16

• The various parts of a Bausch and Lomb projector is shown in Figure.

• The eliminating system consists of a light source, a tungsten arc lamp.

• The glowing element in the lamp is a small cylinder of tungsten, which is heated to incandescent by electron bombardment. It is enclosed in a ventilated lamp house.

• The light from the lamp passes to a system of lenses called achromatic condenser. With a single lens condenser, the screen image consists of various colors. So to get rid of them, each lens assembly is composed of two kinds of glasses. The parallel beam of light from the condenser is then transmitted to the illumination mirror, which sends them vertically upward, through the glass stage plate in the worktable, past the object.

• The projection system consists of projection lens, roof prism, a pair of image reflectors and screen.

• The magnification of the projector can be adjusted by changing the projection lens assembly. The adjustment for changing the lens assembly is very easy and accurate. It is done by merely placing the assembly into the bracket.

• The light travels past the object to the projection lens from which it passes upward to the roof prism.

• The function of the roof prism is to direct the beam of light horizontally towards the back of the projector to assist in the projections of the image so that its aspects presented to the observer are correct.

• From the roof prism, light passes to two optically flat reflectors that change the direction of the beam of light and direct it horizontally to the screen.

22-09-2014

17

• When an observer looks at the image, he will find the image as erect and its aspects same as that of the object, i.e. movement of an object in any direction on the worktable will cause a corresponding travel of the image.

• If the object is moved to right or back, a corresponding movement of image to the right or up will be observed.

APPLICATIONS OF PROJECTOR

• A variety of inspection can be made with the help of projectors.

Image Inspection

This is the primary use of projectors. Shadow outline of the image to be inspected is

formed on the screen. The image is magnified by projection, reflection or the

combination of both.

Inspection by Observation

Surface properties like texture, finish, surface conditions; general contour

straightness, consistency of curvature; contact patterns with mating parts are

observed by projectors.

Inspection by Comparison to Master Charts

Projected images are compared with the help of screen charts for the inspection of

standard forms, e.g. angles, radii, screw threads, gear forms, etc.

Inspection by Direct Measurement on the Screen Image

Linear measurements using graduated rulers or glass scales, angular measurements

using drafting or toolmaker’s protractor, radii using transparent templates are also

done with projectors.

Inspection with Measuring Devices Built into the Optical Projectors

Projectors can be used for measuring the Coordinate table movement (along X and Y

axes) by reading the displacement distance on the micrometer heads. For angular

measurement, graduated protractors provided in the instruments are used.

Inspection with the Aid of Fixtures and Special Attachments

Adjustment of helix angle to project thread form, transferring dimensions by means

of work holding devices and charts with reference points, optical sectioning with

special illumination can also be done.

22-09-2014

18

ADVANTAGES OF OPTICAL PROJECTORS

A single setting of the specimen provides observation, comparison and inspection of

several dimensions and form characteristics in a projector.

Several people can observe the projected image simultaneously. Thus, projectors are

handy tools when images are to be inspected by a group of people.

The image can be magnified according to requirement. Thus, dimensions to be

inspected individually or their interrelation with other dimensions of the same part

can be observed without any additional instruments

Projector provides direct measurements of various lengths and angles. Lengths are

measured by graduated rulers and angles by drafting protractors.

There is no physical contact between the specimen and the measuring instruments in

projectors. Thus, specimen to be inspected is free from mechanical distortion or

defects. This increases the accuracy in measurement

Unlike the mechanical gauges, which undergo wear and tear due to prolong uses,

measurements by optical projectors are free from wear.

Optically obstructed surface elements can be traced by means of projectors.

Application of cross-sectioning provides means for the accurate measurement of

dimensions, whose inspection by any method other than optical projection is

extremely difficult

Greater range of inspection is possible in projectors. For example, the observation of

surface characteristics by light reflection, using either normal or oblique illumination,

substantially widens the scope of inspection procedure.

The open screen, commonly at eye level, permits the observation of the image in

unrestricted position under more natural conditions than viewing through a

microscope eyepiece

The contour of the inspected part can be traced with a pencil by mounting a vellum

paper on the glass screen. This serves for future recording.