CHAPTER 4

DEVELOPMENT OF AN OPTICAL IMAGING SYSTEM FOR IMAGING THICK TISSUES - PEIASE I

4.1 NEED FOR AN OITICAL IMAGING SYSTEM

Medical imagng techn~ques currently in use like MRI, CT and Ultra

sound are costly and are out of reach of the majonty of ow population. The

need for a low ws1 but effective imaging technique can be a boon for the

depnved majority. Opbcal imaging presents several potential advantages over

existing radiological techniques being nonionic, inexpensive and providing

better spatial and temporal resolution.

The factors that limit this optical imaging technology are the scattering

property of the biological tissue and the thickness of the tissue. As light travels

through a tissue it is scattered by the numerous refractive index variations In

the tissue. Scattering plays an important role in limiting the imaging depth, as

it d e c m s the number of excited photons reaching the particular depth.

Consequently only few photons are able to reach greater depths without much

scattering. Therefore emct ion of the weakly scattered light from the highly

scattered light can yield images with increased contrast. In this work the

problem related to scattering of light is solved by polarization imaging and

image processing.

The research towards the development of an optical imaging system

capable of imaging tissues of thichess in the order of centimehes has been

camed out in three phases. The current chapter discusses the first phase of the

system development.

4.2 PRYSICS OF SCATTERIh'G AND ABSORPTION

4.2.1 Senttering and Absorption

Scattering of electromagnet~c waves by a system is related to the

heterogeneity of that system. If an obstacle which wuld be a single electron,

an atom or molecule, a solid or liquid panicle is illuminated by an

ele~omagnetic wave; electric charges in the obstacle an set into oscillatory

motion by the elwhic field of the incident wave. The accelerated electric

charges radiate e l~omagnet ic energy in all directions. This is the radiation

scattered by the obstacle. In addition to reradiating electromgneetic energy, the

excited elementary charge may transfonn part of the incident electromagnetic

energy into other forms and this called absorption.

In biomedical optics, absorption and scattering of photons are most

important events. Scattering and absorpt~on are u:d for both spectroscopic

and Imagng applications.

Absorption is the primary event that allows a laser or other light source

to cause a potentially therapeutic effect on a hsSUe. Wlthout

absorption, there 1s no energy transfer to the tissue and the tissue IS leA

unaffected by the light

Absorption of light prondes a diagnostic role such as the spectroscopy

of a tissue Absorption can provide a clue as to the chemtcal

composihon of a hssue, and serve as a mechanism of optical contrast

dunng imaging.

Scanering prov~des feedback durlng therapy For example, durlng

laser coagulabon of tissues, the onset of scattering 1s an observable

endpoint that correlates with a deslred therapeutic goal. Scanering also

strongly affects the dosimetry of light during therapeutic proccdurcs

that depend on absorpt~on.

Scattering has diagnostic value as well. Scattering depnds on the

smctlrre of a tissue. Scattering measurements are an important

diagnostic tool irrespective of whether one measures the wavelength

dependence of scattering, the polarization dependence of scattering, the

angular dependence of scattering or the scatferlng of coherent light

4.2.2 Single scattering

Consider an arbitrary particle that is conceptually subdivided into

small regions. An incident electromagnetic wave induces a dipole moment in

each region. These dipoles oscillate at the frequency of the applled field and

therefore scatter sewn* radiation in all directions. At a distant point, the

total scattered field is obmned by superposing the scattered wavelets and due

account is taken of their phase differences

In natural environments however, collections of very many pamcles

occur. Partrcles in collection are elecuo magnetically coupled The field

scattered by a particle depends on the total field to which it is exposed

Considerable simplificstion results if single scattering is assumed and the

proposed model makes this assumption.

4.2.3 Absorption and scattering coefficient

The absorption mef'licient p. [cm"] describes a medium contalnrng

many chromophores at a concentration described as a volume density P,

Icm3] The absorption coefficient is essentially the cross-sectional area per unlt

volume of medium

and m, [cm2] is called the effective cros&seetion.

A 0, = QaA geometrical ef fect ive

cross-section cross-section

A os = QsA geometrical ef fect ive

cross-section cross-section

Figure 4.1 Illustration of : (a) absorption ; (b) scattering

The scattering eafiicient 1, [cm"] describes a medium containing many

scattering particla at a concentration described as a volome density p, [cm".

'The scattermy wffrcient is given by

and 0. [cm2] is called the effective cross-section.

4.2.4 Anisotropy and Reduced scattering eoeficient

The aniaotropy, g [dimensionless], is a measure of the amount of

fonvard direction retained after a single scattering event. Imagine that a

photon is scattered by a prhcle. A scattering event causes a deflection at

angle 0 from the orignal forward trajectory, y, is the azimuthal angle of

scattering and is shown m the Figure 4.2. The component of the new trajectory

which is aligned in the fonvard direction is shown in red as cos(9). The

average deflection angle and the mean value of cos(8) is defined as the

anisotropy

Figure 4.2 lllustntion of scattering of a photon

The redud scattering coefficient is a lumped properly incorporaring

the scattering eameient and the maisotropy g and is given by

The purpose of p.' is to describe the diffusion of photons in a random walk of

step size of Ifp,' [cml where each step ~nvolves lsotroplc scattenng

In addjbon to ~ t s lrrad~ance and frequency, an clect~omagnebc wive

has a property called ~ t s state of polarlzat~on Cons~der a plane monochromat~c

wave w t h angular frequency m and wave number k, whch 1s propagahng In

the z d~rectlon In a nonabsorb~ng rned~um The electr~c field vector at any

polnt lies In a plane the normal to which 1s parallel to the &rechon of

propagat~on In a part~cular plane, say at z = 0, the t ~ p of the elecu~c vector

traces out a c w e

E ( z - 0 ) - A w s o t + B s ~ n o t (4 4)

Equation (4.4) describes an ellipse called the vibration ellipse and the

monochromatic wave 1s said to be elliptically polanmd If A = 0 or B = 0, the

vibration ellipse is just a straight line and the wave is linearly polarized. If

I A I = 1 B 1 and A . B = 0, the vibiation ellipse is a circle and the wave is

circularly polarized.

A vibration ellipse is characterized by its imdiance, handedness,

direction of rotstion of the el l ip , ellipticity (ratio of the length of its

semiminor axis to its semimajor axis), and its azimuth (the angle between the

semimajor axis and an arbitrary reference direction). These are called the

ell~psometric parameters of a plane wave.

42.6 Stoker Parameten

Although the ellipsometric parameters completely specify a

monochromatic wave of a gven Frequency, they are not conducive to

understanding the transformations of polanzed light. The Stokes parameters

[I421 are an equivalent description of polarized light and are particularly

useful in scattering problems.

The Stokes vector of a light beam IS p e n by

where [ 1' denotes transpose

Each element of the Stokes matrix can be written in terms of the Ilght

intensities as I = IH + lv

Q = IH - lv

u - I p - l u

V = l ~ - k

where In, Iv, IP, I& IR IL are the light ~ntensities measured with a

horizontal linear polanzer, a vertical linear polanzer, a +45" linear polarizer, a

-45" linear polarizer, a right circular analyzer and a left circular analyzer

respectively placed in front of the detector.

The Stokes elements of a single s~mple wave are related by

I~ 2 @+u2+v2

The equality holds if the light is polarid. If the light IS unpolan* Q = U =

V = 0. Natural sunlight is an example of completely unpolarized light and so it

is represented as [ I, 0.0.0 lT. Ln general, however, light is partially polarized

and so it consists of both polarized and unpolarized wmponenrs. This leads to

the concept of degree of polarization (DOP) Gven by (d + U' + v 2 ) lo 1 I ,

the deget of linear polarization @OLP) defined as ( Q' + U' ) l R / I and the

degee of c~rcular polarization (DOCP) equal to V I I.

The Stokes parameters for linearly polarized and circularly polarired

light are shown In Table 4.1.

Table 4.1 Stokes Parameters for Polarized ligbt

Linearly Polarized

0 " 1 90 ' 1 +45

Circularly Polarized

Rigbt Left

4.2.7 Mueller Matrices

The state of polarization of a beam 1s changed on interact~on w~th an

optical element. It is possible to represent such optical elements by a 4 x 4

matrix called the Mueller matrix. The Mueller matrix describes the relat~on

between "incident" and "transmitted" Stokes vectors and is witten as

S,=MS, (4.7)

where S, and S, are the Incident and the output Stokes vector

respectively.

Mueller matnx formulation IS very useful stnce it gives us a slmple

means of determin~ng the state of polarizahon of a beam wansmitted by an

opt~cal element for an arbitrarily polarized ~ncident beam Moreover, if a

serles of optical elements are interposed in a beam, the combined effect of all

these elements may be determined by merely multiplying their associated

Mueller mabices. The Mueller matrix can be obtained experimentally by

measurements with different combination of source polarizers and detection

analyms.

4.2.8 Absorption and SfPttering by a sphere

The most important exactly soluble problem in the theory of absorption

and scanering by small particles is that for a sphere of arbitrary radius and

refmhve lndm Gustav M e developed a formal soluhon to th~s problem,

whlch IS now called the Mte theory Mle theory of scanenng 1s a

stralghtforward appllcahon of Maxwell's equahons to an Isotropic,

homogenous, d~electnc sphere It 1s equally appl~cable to spheres of all slzes.

refrachve ~ndlces and for &ahon at all wavelengths

Mie's classical solution is described in terms of two parameters, n. and

a n, is the magnitude of refractive index mismatch between particle and

medium. Thls is expressed as the ratio of the refractive index for partlcle and

medium as

The size of the surface of refractive index mismatch is expressed as size

parameter a. This is the ratio of the meridional circumference of the sphere

(2na. where a is the radius) to the wavelength (hind) of light in the medium

It is given by

Consider a source, a spherical scattering particle and an observer

whose three positions define a plane called the scattering plane. Incident light

and scattered light can be reduced to the~r components, which an parallel or

perpendicular to the scattering plane. As shown in the F~gure 4.3, the +lei

polarizer

from source

event

Figure 4.3 Scattering of polarized light

and pnpendicular components can be experimentally selected by a linear

polarizer oriented pruallel or perpendicular to the mitering plane.

The Scanering matrix describes the relationship between incident and

scattered electric fi cld components perpendicular and parallel to the scanenng

plane as observed in the "far-field

The above expression simplifies In practical experiments.

The exponenual term, -exp(ik(r-z)yikr, is a transport factor that

depends on the distance between scatterer and observer. If one

measures scattered 11ght at a contant distance r from the scanerer, eg.,

as a function of angle or onentation of polarization, then the transport

factor becomes a constant.

The total field (E&) depends on the incident field (E,), the scattered

field 6) , and the interaction of these fields c,). If one observes the

scattering from a position which avoids Ei, then both E, and Em are

zero and only E, is observed

For "far-field observation of E, at a distance r from a particle of

diameter d such that ks >> a', k = Zdh, n, = &L, the scattering

elements & and S4 equal zero ( Eq. 4.75, Bohren and Huffman).

Hence for practical scanenng measurements, the above equation simplifies

to the following:

Maxwell's equahons are solved in spherical coordinates through

separation of variables. The inc~dent plane wave 1s expanded in Legendre

polynomials, so the solutions inside and outside the sphere can be matched at

the boundary. The far field solution is expressed In terms of two surtterlng

functions, [I421

" 2 n + l = -[a,rr, (cos8) +bar, (cos 8)]

r-1 n(n + 1) ( 4 12)

where 0 is the scattering angle

The functions n,, and 7, are given by

where P,' are associated Legendre Polynom~als of the first kind

and

a = h = 2xa 1 1 is the size parameter, m 1s the Index of rehaction, a is the

part~cle radi and y,, and S. are spherical Bessel functions

The Mle scattering matnx 1s oven by,

where the fow independent Mie scattering matrix elements are,

L pde) = &ls1(@)l1 +la(@)12i L pdel = K[ls(e)12 - IS1ce)ll %i

pa (el = g& lsd@)s: (el + $1 (el$ (ell

The Mie ext~nction, mttenng and absorpnon cross-sect~ons can all be

expressed in terms of the a. and b, coefficients as,

Another useful quantity is the asymmetry factor, g, which is the first

moment of the phase function and is given by.

The asymmetty factor describes the shape of the phase function; g>l

indtcates f o m d scattering, while g c l indicates backscattering. It is a useful

parameter for characterizing the phase function independent of scattering

angle. The Mie asymmetry factor can be expressed as,

4.3 POLARIZATION FILTERING TO ENHANCE VlSlBUITY OF

SUBSURFACE TISSUE IMAGES

Recently there has been a considerable interest in ustng the

polarization state of the hght as a discnminahon criterion. The polarization

d~scnmination techtque IS based on the assumphon that weakly scattered

light remns its miud polanmon whereas h~ghly scattered light does not

Consider a tlssue illuminated by a Itnearly polarized source. As photons

penetrate the tissue, they interact with various ttssue structures and some of

the Injected photons emerge from the tissue in the backscanering direct~on

Light that reflects from the surface (known as specml reflection) is polarized

but the light that backscanen from somewhere below the surface of the tissue

1s depolarizcd Therefore light viewed in the orthogonal state contains a large

proportion of the light that ~nteracted with the object than the copolarized

light. The use of this fact to discriminate between short and long path photons

in a scattering medium has been well explored theoretically and pract~cally

Studies clearly indicate that polarization discrimination [I 12 - 1271 can be

effective in extending the depth of visibility.

However even for this orthogonal state, as tissue thickness Incress ,

the loss of contrast is still the 11ght backscattered by the medium. So conbast

of the images obtained could be enhanced if this back scattered contribut~on

from the surrounding medium is removed. Hence if the copolarized image is

also recorded and a suitable fraction IS subtracted from the orthogonal

polanzed Image, sigmficant conbast wuld be achieved.

In th~s chapter, a Monte Carlo model for the proposed method is

simulated. Model Images are compared with the experimental images at

632nm for a scattering phantom.

4.4 MONTE CARL0 SIMULATION

The essential characteristic of Monte Carlo code is to study the

propagation of l~ght in biological tissue. The basic idea 1s that photons are

launched from an isotrop~c point source of unlt power within an infinite

homogeneous mubum with no boundaries The medium has optical properties

of absorption, scattering and auisotropy. N photons are launched, each w~th a

"photon weight" initially set to 1 The photon takes steps between interactions

wth the tissue. The steps are based on the probabil~ty of photon movement

before ~ntcraction by absorption and scattering. During each step as the photon

propagates, the photon deposits a fraction of its weight Into the local bin at its

position. The photon is assumed to be dead if the welght of the photon falls

below a f xed threshold. Now a new alive photon is launched.

Photons are launched as a beam from the ongn that initially

propagates parallel to the z-axis The lllwnlnanon 1s assumed to be linearly

polanzed. The biologcal tlssue IS modeled as a slab Infinlie in the x-y plane

containing randomly distributed sphencal Mle scatteren wth slze parameter

ka where k 1s the wave number and a 1s the particle radius [118.119] The

scattenng medium is assumed to be homogenous; hence the probability

density for the distance traveled by the ray before it encounten a particle 1s

determined by a negative exponential msmbution wth mean equal to the

mean free path Hence, in the simulat~on model the d~stance between two

successive scattenng points is a random number c h o m from this distribution.

After every scattering event In the tissue, the polarization state and the

direction of propagatton of the ray changes. The Stokes vector cames the full

polarilation information of the wave under simulafion. The scattering angle is

chosen randomly according to a probability law depending on the phase

function [117]. The scattering angle, 9 is generated by inversion and rejection

methods [1431. At each scattering position, the code randomly chooses the

azimuthal angle, w . Bruscaglioni et a1 [I 141 have proved that if the number

of effective scattering events were larger than a few wts and for pmiculates

that were not small in comparison Gth the wavelength , the angle wuld be

assumed to be equiprobable. Finally performing the local coordinate

transformation using the rotation matrix T [I 171, the modified Stokes vector

after scattering by the particle is

where M(0) is the Mie scattering matnx, and a IS the rotation angle with

respect to the ray direct~on [ I 171. Figure 4 4 illustrates the ray directions and

angles a, 8, for a ray hav~ng Initial d~rect~on d and scattered to a new

direction d' (0.0) and (9 ',@') are the spherical polar coordrnates of d and d'

To image an object located below the surface of the tissue, it IS

assumed that the object is placed at the boundary of the tissue i.e., at a distance

zl in the z direction The object is modeled as a depolarizing diffuse reflector.

The depolarization caused by the object can be modeled by generating random

numbers for the Stokes parameter. But this is equivalent to inducing random

rotation in Q,U,V and is modeled by the Mueller mamx [I441 given by,

Figure 4.4 nlustration of angles a ,8 and q~

* [ :3 z B , C , D J (4.27)

where R(B,C,D) is a Euler matrix of dimension 3x 3, OX is a zero three column

vector and B,CP are Euler angles

The photons after scanenng by the t~ssue medlum h ~ t the object and

ewt the tlssue For each photon backscattered and retumlng to the top surface,

!he coordinates (y,yd) at which ~t intersected the detector plane were

computed uslng geometrical ray traclng [62] uslng

where a, and a, are the exlt angles onto the xz and yz plane

rrspechvely and can be computed from the directional cosines

and f and h are the focal length and distance of the lens of the imaging system

from the surface of the tissue medium. The equation for y and yd takes into

account the refraction at the tissue-air interface.

A photon is counted as detected if its position falls within the area of

the imaging lens. which is assumed to be circular and is determined by

(a2 + ~ d ~ ) ~ ~ < dJ2 (4.32)

w3tere d, is the lens diameter.

The radiance components parallel to the reference plane i e ,

copolarized and perpendicular to the reference plane i.e., cross p o l 4

components can be expressed in terms of the Stokes parameten as

E = ( r + Q P and H = ( r - Q ) / 2 (4.33)

The first two rows of the Stokes vector of these photons impinging on

the lens yield the copolarized and the cross polarized components and these

are transformed to the image plane using paraxial optics. The image plane was

modeled as a grid with each pixel of size 0.04 x 0.04crn and yields an image of

size 60 x 60 pixels.

4.5 THE SIMULATION MODEL

A linearly polarized thin beam at 632 nm impinges on the scattering

tissue medium. The scattering medium was considered to be a homogenous

suspension of 2.02 pm diameter polystyrene spheres in water. The density of

scatteren is assumed to be O.0OI per cubic micron. The refractive index of the

medium (water) was assumed to be 1.33. At 632nm. the complex index of

refraction of the spheres was 1.589 -- i0.00113 and the sample's scanenng

coeffic~ent, reduced scattering coefhent, anisotropy and absorpt~on

coefficient were 100cm.', 8.9cm.'. 0.911 and 1.33cm.l respectively. These

values have been chosen so as to set to values obtalned from real muscle tissue

[371

The optical detector is a CCD camera wlth a circular lens of rad~us

0.05cm placed at a distance of 0 Icm from the surface of the tissue medium

The focal length IS also assumed to be O.lcm.

4.6 EXPERIMENTAL SET IIP

A schematic o i the experimental apparatus used for o b t a i ~ n g the

Images 1s shown in F~gure 4.5. A He Ne laser (Uniphase Inc, 1101P)

emitting approximately 4mW of 632nm light was firs! linearly polarized and

then focused onto the tissue phantom. The phantom that was utilized

in the study was a suspension of 2 . 0 2 ~ diameter

polystyrene spheres ( Polysciences Inc. 19814). The sample was

created by dilution with distilled water to 0.001 spheres per cubic mlcrons.

The index of refraction of the spheres was 1 589 - 10.00113 and the refractive

~ndex of the medium (water) IS 1.33. The sample had a scattering coefficient

(b) of lOOcm", reduced scattering coefic~ent (p,' ) of 8. 9cm.', anisotrop)

(g) of 0.91 1 and absorption coeficient (pa) of 1 33cm.' at 632~11, equal to

the values used in the simulation.

The sample was held in a glass container with flat walls. A 4mm

diameter and Imm thick object composed of chalk material was positioned at

the bottom of the sample. Light emerging from the sample and object was

collected though a camera lens and then ~nto the second polarizing element.

The image was then focused onto a digital CCD camem. The thickness of the

phantom sample was varied from 0 .5m to 2 cm and for each thickness two

Images, namely cross polarized image and copolarized image were acquired.

The obtained images were p r d

4.7 RESULTS AND DISCUSSION

4.7.1 Simulation results

The simulation for the imaging system illustrated in Figure 4.5 was run

by launch~ng a beam of photons from the origin. Random values were taken

for the scattering distance, scattering and the az~muth angles as described in

section 4 4 The &ptb of the object was incremented in steps of 0.5 cm, and

o b j d deptb Icm

o b j h deptb 1.5em

( 4 @) (c)

Figure 4.6 Images of abject from simuhtion for objeet depths of

I and 1.5em: (a) ortbogonrl polarized image; (b) a

pohrized image; ( c) image after polarintion filtcrhg

copolarizcd and cross polarized images were recorded at 632nm. The

simulation was run for a launch of 1x10' photons.

In Figurc 4.6, (a) and (b) shows the orthogonal and wpolarized images

of the object at 632 nm from the simulation. The images in the first and second

row are for the object at depth of Icm and 1.5cm respectively. Figure 4 6 (c) 1s

the ~mage after subtraction of orthogonal state and fraction of copolarized

state. In performing the subtraction [145,146], if the subtraction resulted In a

negative value, it was made equal to zero or a black pixel. Clearly the

improvement in contrast of the images in 4.qc) over 4.6(a) and @) is visible

provtng the merit of this model. The optimum subtraction fraction was chosen

as 0.5 based on best contrast ofthe final image.

4.7.2 Measurement of Conhmst

To validate the proposed technique, image contrast as a function of

depth for the images obtained was computed. The contrast is defined as

where A1 is the average intensity from the light returning from the object

calculated from the central 3 x 3 pixels and Aa is that from light returning

from the background calculated from the c e n d 21 x 21 pixels The image

contrasts are listed in Table 4.2 for three different depths. The values in last

column show the improvement of wnbnst by the proposed method.

Table 4.2 Conhpst for the simahted images of the object obtainecl

a t depths of 0.5,l.O and 1.5 em in the tissue.

1.7.3 Experimental Reaulta

' ~ e ? h of ob~cct

0 5

1 0

I 5

The experiment was carned out using the expenmental set up and

cross and copolarized images of the object at varying depths were recorded

Figure 4,7(a) and 4.8(a) shows the orthogonal image from the experimental set

up for the object at a depth of 0.5 and lcm. Figure 4.7(b) and 4.Yb) IS the

image after subtraction of orthogonal state and fraction of wpolanzed state for

the respctive depths.

Cross polarized image at 632nm

0.901

0.6293

0 5300

Proposed method

1 0000

0 7287

0 651 1

@)

F i i m r e 4.7 Inugcs of tbe object from experime~tatiom

8t 8 dcptb of Okm: (8) C m pd.rizcd ia%c;

@) iaugc after p o h r b h

@)

Figure 4.8 Images of the object fmm experimentation

at a depth of I em: (a) cross pohriud image;

@) image after polariution filtering

4.7.4 Intensity Profile

The intensity profile of the experimental images along the line

contain~ng the object for varying depths 1s shown in Figure 4.9. It can be seen

that the profile is narrow for the object when it is at a depth of Ian from the

surface and the profile wdens as depth is ~ncreased to I .5cm. When the depth

of object is further increased, the object 1s no longer visible even by the

proposed method

P d

Figure 4.9 Intensity profile of experimentally obtained images

after polarization filtering at varying deptha

4.8 SUMMARY

In this chapter the first phase in the development of an optical imagng

system is discussed. This phase termed polarization filtering enhances the

contrast of tissue images at deeper depths using image-processing tools. Image

subhaction is done to detect changes in the tissue composition. Computer

simulations based on Monte Carlo model have been carried out and

experimentation done to check the validity of the method. Resultant images

indicate the merit of the proposed method for depths up to lcm