Mueller Matrix: An approach to detect Abnormality in Human Brain Tissues

Indian Institute of Science Education & Research, Kolkata

1 | S u m m e r P r o j e c t R e p o r t

Mueller Abnormality i


S u m m e r P r o j e c t R e p o r t

Mueller Abnormality i

Indian Institute of Science Education & Research



Mueller ImagingAbnormality i

(

Under the humble guidance of

Indian Institute




Imaging: AAbnormality in

Project(13th May

Under the humble guidance ofDr. Asima PradhanAssociate Professor

Department of PhysicsCentre for Laser Technology

Indian Institute

Harsh Purwar

IInd Year Student



An approach Huma

Project Report May – 28th July 2009

Under the humble guidance ofDr. Asima PradhanAssociate Professor

Department of PhysicsCentre for Laser Technology

Indian Institute of Technology, Kanpur

Harsh Purwar

Year Student


Kolkata


n approach an Brain Tissues

Report July 2009)

Under the humble guidance ofDr. Asima Pradhan Associate Professor

Department of Physics Centre for Laser Technology

of Technology, Kanpur

Harsh Purwar

Year Student


Kolkata

n approach to Brain Tissues

Report )

Under the humble guidance of

Centre for Laser Technology of Technology, Kanpur


May

DetectBrain Tissues


May-July 2009

etect Brain Tissues

July 2009

Indian Institute of Science Education & Research, Kolkata May-July 2009


Certificate

It is certified that the work in this project report entitled “Mueller Imaging: An

approach to Detect Abnormality in Human Brain Tissues”, by Harsh Purwar has

been carried out under my supervision and is not submitted anywhere else for

publication till date.

Dated:

Place:

(Dr. Asima Pradhan)

Associate Professor

Centre for LASER Technology

Department of Physics

Indian Institute of Technology

Kanpur – 208016

Uttar Pradesh, India



Acknowledgement

I would like to express my gratitude to my mentor honorable Dr. Asima

Pradhan for her support, guidance and motivation throughout the project. I

would also like to thank Mr. Prashant Shukla (PhD. Scholar), Jaidip Jagtap (PhD.

Scholar) and Prabodh Pandey (Final Year Student, Int. M.Sc., IIT – Kanpur) for

their help and guiding me with their rich experience in the experiments and

data analysis. I would also like to thank for the co-operation extended by all

other graduate and post-graduate students in LASER Technology Laboratory,

SL - 111, Indian Institute of Technology, Kanpur for their help and support.

I thank my parents for their moral support.



Table of Contents

(The page numbers are indicated in the square brackets)

1. ABSTRACT [6]

2. KEYWORDS [6]

3. INTRODUCTION [6]

4. THEORY [7]

a. Stokes Vector & Mueller Matrix [7]

b. Polarization States [7]

c. Mueller Matrix [8]

d. Polarization Images [8]

e. Mueller Images [8]

f. Optical Parameters [9]

g. Decomposition Scheme [9]

5. APPARATUS & INSTRUMENTS [12]

6. DESIGNED EXPERIMENTS [14]

7. EXPERIMENTAL SETUP [14]

a. Back-scattering Mode [14]

b. Transmission Mode [15]

8. METHODOLOGY [16]

9. SAMPLE PREPARATION [17]



10. MICROSCOPIC IMAGES OF BRAIN TISSUES [18]

11. POLARIZATION IMAGES OF BRAIN TISSUE [20]

12. DATA ANALYSIS & RESULTS [23]

13. MUELLER IMAGES OF BRAIN TISSUE [28]

14. DECOMPOSITION PLOTS FOR BRAIN TISSUE [31]

15. DISCUSSIONS & CONCLUSIONS [32]

16. PRECAUTIONS [35]

17. BIBLIOGRAPHY [35]

18. REVISED MATLAB SCRIPT [37]



Abstract

It has been observed that in recent years, researchers have given much emphasis on exploring on

various tissues through polarized light imaging technique as a potential diagnostic tool for detecting

any kind of abnormality particularly chronic diseases such as Cancer, Tumor, etc. As we are aware

of the fact that tissues depolarize a large fraction of incident light so that the Mueller calculus lends

itself well to these applications. Cancerous tissues were well discriminated from normal tissues using

Mueller imaging. Analysis of 49 obtained Mueller images of samples via CCD by decomposition of 4 × 4 Mueller matrix, to give three independent parameters depolarization, diattenuation and

retardance in the form of three 4 × 4 matrices, containing information about the optical properties

of the tissues based on their morphology and various chemical changes that occur in cells during

different stages of chronic diseases. It was found that abnormal tissues can be identified and

distinguished from the normal tissues based on these Mueller images and various other

decomposition plots at different stages of abnormality.

Keywords: Mueller matrix, Mueller imaging, depolarization, diattenuation, birefringence, tissue optics,

polarization imaging, retardance, Mueller decomposition.

Introduction

In general, tissues are optically inhomogeneous and absorbing media whose average refractive index

is greater than that of air. This results in partial reflection of the radiations at the tissue/air interface,

while the remaining part penetrates the tissue. Bulk scattering of radiations in tissues is a major

cause of a large fraction of its dispersion in the backward direction, whereas multiple scattering and

absorption of radiations results in LASER beam broadening and its eventual decay as it travels

through them. Cellular organelles mitochondria, nucleus etc. are the major scatterers and blood is a

major absorber in the tissues. Scattering of radiations in tissues also depends on the water content

in them (1).

Biological tissues can be characterized by their optical properties, namely the absorbing coefficient ��, the scattering coefficient �� and the anisotropy factor ��. As a tissue becomes cancerous,

several morphological and chemical changes occur in them such as; uncontrolled growth of cells in

tissues causes the collagen fibers to breakdown, increased nucleus size & number of mitochondria

etc. These changes affect various optical properties of tissues mentioned above. Also due to

increased blood perfusion, cancerous tissue is typically higher in absorption of radiations than normal

tissue (2). In general, tissues are birefringent and therefore they randomize the incident polarized

light to a very large extent. This allows polarimetry to be used as a tool for studying the various

optical properties of tissues and distinguish them on this basis.



Theory

Stokes Vector and Mueller MatrixStokes vector is a 4 element column matrix

radiations. The elements of a Stokes vector are called Stokes parameters.

George Gabriel S

parameters are given by

Here , �And the intensity of light by

The polarization state of the scattered light in the far zone is described by the Stokes vector

connected with the Stokes vector of the incident light. If

is the Stokes vector describing the

Polarization StatesPolarization states are various orientations of a polarizer or analyzer. There can be infinitely many

orientations and so infinitely many states. These

states listed below.

example horizontal polarization state (H) should be

less from the vertical polarization state (

and -45 (M); Right circular (R) and left circular (L).

table lists different polarization states, and angles (in degrees) for

both the polarizers

polarizer and Polarizer (B

remember that these states depend on the polarizer and analyzer

being used.



Theory



George Gabriel Stokes in 1852.

parameters are given by

�, �, are the 4 elements of Stokes vector or Stokes parameters.

And the intensity of light by




where � is the normalized

Polarization StatesPolarization states are various orientations of a polarizer or analyzer. There can be infinitely many


listed below.



45 (M); Right circular (R) and left circular (L).


both the polarizers

polarizer and Polarizer (B


being used.





tokes in 1852.

parameters are given by (1):

are the 4 elements of Stokes vector or Stokes parameters.

And the intensity of light by




is the normalized

Polarization States Polarization states are various orientations of a polarizer or analyzer. There can be infinitely many


listed below. Important point to remember is the relative differences between the states.





used. Note that Polarizer (A) was used as a

polarizer and Polarizer (B) was used as an analyzer.






In terms of

��


� �The polarization state of the scattered light in the far zone is described by the Stokes vector


is the Stokes vector describing the scattered light then we have,

is the normalized 4 × 4 scattering matrix or Mueller matrix

Polarization states are various orientations of a polarizer or analyzer. There can be infinitely many


Important point to remember is the relative differences between the states.


less from the vertical polarization state (V). Same goes for +45 (P)



. Note that Polarizer (A) was used as a

) was used as an analyzer.



Stokes Vector and Mueller Matrix Stokes vector is a 4 element column matrix that describes the polarization state of electromagnetic


In terms of the components of

� ��


� �� The polarization state of the scattered light in the far zone is described by the Stokes vector


scattered light then we have,

� � � � � scattering matrix or Mueller matrix


orientations and so infinitely many states. These all experiments are


example horizontal polarization state (H) should be 90°V). Same goes for +45 (P)

45 (M); Right circular (R) and left circular (L). The following



) was used as an analyzer.



that describes the polarization state of electromagnetic


the components of electric field

��


� � The polarization state of the scattered light in the far zone is described by the Stokes vector

connected with the Stokes vector of the incident light. If � is the initial incident Stokes vector andscattered light then we have,

scattering matrix or Mueller matrix


experiments are

Important point to remember is the relative differences between the states. ° more or

V). Same goes for +45 (P)

The following



) was used as an analyzer. Also



radiations. The elements of a Stokes vector are called Stokes parameters. These were defined b

electric field (��



is the initial incident Stokes vector and

scattering matrix or Mueller matrix.


experiments are designed to use only seven such


Figure 1: Markings on Polarizer &

May


These were defined b

� and ��), the stokes


is the initial incident Stokes vector and


designed to use only seven such


: Markings on Polarizer & Analyzer

May-July 2009


These were defined by

, the stokes


is the initial incident Stokes vector and �


designed to use only seven such

Important point to remember is the relative differences between the states. For

: Markings on Polarizer &

July 2009



Table 1: Listing various polarization states & their corresponding angles

Polarization States Polarizer (A) Polarizer (B) Open (O) Removed Removed

Horizontal (H) 128 164 Vertical (V) 38 74 +45 (P) 353 29 -45 (M) 83 119

Right circular (R) 38 + QWP 74 + QWP Left circular (L) 128 + QWP 164 + QWP

These angles for the two polarizers were found out by fixing one polarizer’s orientation (analyzer)

and rotating the other to get a minimum intensity of the LASER beam.

It should be clear from the table that vertical polarization state and a quarter wave plate both of

them combine to give circular polarized and we call it right circular polarized light.

Mueller Matrix Mueller matrix is constructed as listed below. The different components of this matrix are made by

the combinations of different polarization states as stated above.

� ��

!! "! � ! #! � �! $! � %!!" � ! "" � � " � " #" � � � # � �" % � $" � %" � $ !# � !� "# � � � "� � # ## � �� #� � �# %� � $# � %# � $�!$ � !% "$ � % � "% � $ #$ � �% � #% � �$ %% � $$ � %$ � $% &

'(

The Mueller matrix can be calculated using 16, 36, or 49 polarization images, with 36 and 49 images

corresponding to an over determined system. Here it was necessary to use more than 16 images to

reduce the error due to noise associated with the Mueller matrix calculation (2). In this experiment,

49 polarization images based system is used.

Polarization Images – raw material for Mueller matrix In these experiments, polarization images are the images taken by the CCD for various polarization

states like HO, OO, VO, OV, RO, LR, etc. These polarization images may also be called as the

intensity images for various states. Basically these intensity images are 512 × 768 matrix, each

element storing the value of intensity falling at that particular location on the CCD’s chip. This

intensity can have values ranging from 0 to 12,000 in arbitrary units. While processing the images

and decomposing the matrix using a simple matlab script the value of each parameter is calculated

for each pixel of the images.

Mueller Images A Mueller image is an element of the Mueller matrix. Since Mueller matrix is being calculated for

each and every pixel of the polarization images obtained, therefore each element can be obtained as



an image of the same size i.e. 512 × 768 pixels. Each pixel of let’s say image, M11 stores the value of

the element M11 of the Mueller matrix – calculated for that pixel using the polarization images.

Optical Parameters (3) • Depolarization:

A process which couples polarized light into un-polarized light. Depolarization is intrinsically

associated with scattering and with diattenuation and retardance which vary in space, time,

and/or wavelength. Examples of depolarizers include tissues, polystyrene microspheres,

phantoms etc.

• Diattenuation:

The property of an optical element or system whereby the intensity transmittance of the

exiting beam depends on the polarization state of the incident beam. The intensity

transmittance is a maximum (Tmax) for one incident state, and a minimum (Tmin) for the

orthogonal state. The diattenuation is defined as (Tmax - Tmin) / (Tmax + Tmin).

Any homogeneous polarization element which displays significant diattenuation and minimal

retardance is called a diattenuator. Polarizers have a diattenuation close to one, but nearly

all optical interfaces are weak diattenuators. Examples of diattenuators include the following:

polarizers and di-chroic materials, as well as metal and dielectric interfaces with reflection

and transmission differences described by Fresnel equations; thin films (homogeneous and

isotropic); and diffraction gratings.

• Polarizance:

The property of an optical element or system whereby un-polarized light is transformed into

polarized light. The polarizance is described by its magnitude (equal to the degree of

polarization of light exiting the system when un-polarized light is input) and the Stokes

vector of the output light.

• Retardance:

A polarization-dependent phase change associated with a polarization element or system.

The phase (optical path length) of the output beam depends upon the polarization state of

the input beam. The transmitted phase is a maximum for one eigen polarization, and a

minimum for the other eigen polarization. Other states show polarization coupling and an

intermediate phase.

• Birefringence:

A material property, the retardance associated with propagation through an anisotropic

medium. For each propagation direction within a birefringent medium there are two modes

of propagation with different refractive indices /0 and /�. The birefringence is given by, |/0 � /�|. Decomposition Scheme for Mueller matrix An arbitrary 4 × 4 Mueller matrix can be decomposed into three basic optical parameters namely

decomposition, retardance and diattenuation discussed in the latter half of this section. It has been

shown that any Mueller matrix can be expressed as a product of three matrices called depolarizer,

diattenuator and retarder (4). So we have,

� � �∆�3�4 ⋯ ⋯ ⋯ ⋯ �1�



The three diattenuation components 6 7⁄ , 45 135⁄ and :;�ℎ=/?@A= provide its complete

description. The diattenuation of a Mueller matrix described above is given by

B � 1�00 C�0�� 0D� � �0E� ⋯ ⋯ ⋯ ⋯ �2� Similarly diattenuation vector is given by

BFFG� H BIBEJB3K � 1�00 H�0��0D�0E

K ⋯ ⋯ ⋯ ⋯ �3� And 4 × 4 diattenuation matrix is given by

�4 � L1 BFFGMBFFG N4O ⋯ ⋯ ⋯ ⋯ �4� where N4 is given by

N4 � P1 � B� H1 0 00 1 00 0 1K � Q1 � P1 � B�R BFFGBFFGM ⋯ ⋯ ⋯ ⋯ �5� The value of diattenuation (Eq. – 2), diattenuation vector (Eq. – 3) and diattenuator or diattenuation

matrix (Eq. – 4) was calculated for each pixel of cropped polarization images (100 × 100 pixels). The values of diattenuation for 10000 pixels are shown in the form of a figure (later). So, we are

now left with,

��4S0 � �∆�3 � �T ⋯ ⋯ ⋯ ⋯ �6� ⇒ NT � N∆N3 ⋯ ⋯ ⋯ ⋯ �7�

Let V0, V� and VDbe the eigenvalues of NT�NT�M . So from Eq. – 7, N∆ has PV0, PV� and PVD as eigenvalues. After calculating the eigenvalues of NT�NT�M we evaluate the following expression,

N∆ � ±XNT�NT�M � YPV0V� � PV�VD � PVDV0Z[S0× XYPV0 � PV� � PVDZNT�NT�M � PV0V�VD[ ⋯ ⋯ ⋯ ⋯ �8�

If the determinant of NT is negative then minus sign is applied otherwise positive. Now to get �∆ from N∆ we first calculate polarizance vector and polarizance matrix using,

#FG � 1�00 H��0�D0�E0K ⋯ ⋯ ⋯ ⋯ �9�

#FG∆ � #FG � NBFFG1 � B� ⋯ ⋯ ⋯ ⋯ �10� Now we write �∆ as a 4 × 4 matrix in terms of #FG∆ and N∆ as below,

�∆ � L 1 0FGM#FG∆ N∆O ⋯ ⋯ ⋯ ⋯ �11� The value of depolarization power or simple depolarization is also calculated and is shown as a figure

(later) using,



∆� 1 � |=:��∆� � 1|3 ⋯ ⋯ ⋯ ⋯ �12� Now again we pre-multiply �T (Eq. – 6) by �∆S0 to get,

�3 � �∆S0�T ⋯ ⋯ ⋯ ⋯ �13� The value of retardance was calculated as,

% � cosS0 L=:��3�2 � 1O ⋯ ⋯ ⋯ ⋯ �14� After calculating the values of all the parameters for each pixel of the cropped polarization images,

these values are plotted or represented in the form of images of the same size and orientation.



Apparatus & Instruments Required

•

•

•

•




He-Ne LASER (

Charge Coupled Device

pixels): A charge

analog shift register that enables the

transportation of analog signals (electri

charges) through successive stages

(capacitors), controlled by a clock signal.

Today, they are most widely used in arrays of

photoelectric light sensors to serialize parallel

analog signals. "CCD" refers to the way that

the image signal is read out from

capacitor can transfer its electric charge to one or another of its neighbors. CCDs are used

in digital photography, digital photogrammetry, astronomy (particularly in photometry),

converts the char

the entire semiconductor contents of the array to a sequence of voltages, which it samples,

digitizes and stores in some form of memory.

Computer:

or parallel port cable for recording various polarization images.

Lenses: Three lenses, two bi

around 5 cm and a plano

Figure 3: A 512 X 768 pixels Charge Coupled




Ne LASER (λ=632.8

Charge Coupled Device

A charge-coupled device (CCD) is an








the image signal is read out from



converts the charge into a voltage. By repeating this process, the controlling circuit converts



Computer: A computer is also required wh


Three lenses, two bi

around 5 cm and a plano

: A 512 X 768 pixels Charge Coupled Device (CCD)




632.8 nm, 20 mW

Charge Coupled Device (512coupled device (CCD) is an








the image signal is read out from the chip. Under the control of an external circuit, each



ge into a voltage. By repeating this process, the controlling circuit converts



A computer is also required wh


Three lenses, two bi-convex o

around 5 cm and a plano-convex lens of focal length 10

: A 512 X 768 pixels Charge Coupled Device (CCD)



, 20 mW)

512 × 768 coupled device (CCD) is an


transportation of analog signals (electric






the chip. Under the control of an external circuit, each



sensors, electron

fluoroscopy, optical and UV spectroscopy, and

high speed techniques such as lucky imaging.

a CCD for capturing images, there is a

photoactive region, and a transmission region.

An image is projected by a lens on the

capacitor array (the photoactive region),

causing each capacitor to accumulate an

electric charge proportional to the light

intensity at that location. A one

array, used in line

single slice of the image, while a two

dimensional array, used in video and still

cameras, captures a two

corresponding to the scene projected onto

focal plane of the sensor. Once the array has

been exposed to the image, a control circuit

causes each capacitor to transfer its contents

to its neighbor. The last capacitor in the array

dumps its charge into a charge amplifier, which




A computer is also required which is to be connected to the CCD by a serial


convex of focal lengths

convex lens of focal length 10

: A 512 X 768 pixels Charge Coupled






sensors, electron









ensity at that location. A one

array, used in line



cameras, captures a two









ich is to be connected to the CCD by a serial


f focal lengths 8 - 10 cm & 7

convex lens of focal length 10 – 15 cm having diameter 5

Figure





sensors, electron microscopy, medical









ensity at that location. A one

array, used in line-scan cameras, captures a



cameras, captures a two-











10 cm & 7 – 9 cm having diameter

15 cm having diameter 5

Figure 2: A He

May





microscopy, medical









ensity at that location. A one-dimensional

scan cameras, captures a



-dimensional picture










9 cm having diameter

15 cm having diameter 5 –

He - Ne LASER

May-July 2009




microscopy, medical


high speed techniques such as lucky imaging. In







dimensional

scan cameras, captures a

single slice of the image, while a two-


dimensional picture

corresponding to the scene projected onto the









9 cm having diameter

– 6 cm.

July 2009



• Polarizer & Analyzer

• Coherence Scrambler (or diffuser): A coherence scrambler is an optical instrument

that diffuses or spreads out or scatters light in some manner, to give soft light of nearly

uniform intensity. Optical diffusers use different methods to diffuse light and can include

ground glass diffusers, Teflon diffusers, holographic diffusers, opal glass diffusers, and greyed

glass diffusers. I used glass diffuser. Ideally a diffuser should not change the wavelength or

frequency of the light.

• Quarter Wave Plates (QWP): A wave plate or retarder is an optical device that alters

the polarization state of a light wave travelling through it. A wave plate works by shifting the

phase between two perpendicular polarization components of the light wave. A typical wave

plate is simply a birefringent crystal with a carefully chosen orientation and thickness. The

crystal is cut so that the extraordinary axis or "optic axis" is parallel to the surfaces of the

plate. Light polarized along this axis travels through the crystal at a different speed than light

with the perpendicular polarization, creating a phase difference. When the extraordinary

index is smaller than the ordinary index the extraordinary axis is called the "fast axis" and

the perpendicular direction in the plane of the surfaces is called the "slow axis". Depending

on the thickness of the crystal, light with polarization components along both axes will

emerge in a different polarization state. For instance a quarter-wave plate creates a quarter

wavelength phase shift and can change linearly polarized light to circular and vice versa. This

is done by adjusting the plane of the incident light so that it makes 45° angle with the fast

axis. This gives ordinary and extraordinary waves with equal amplitude.

• Mounts for lenses, polarizers, QWP, CCD, tissues etc.

• Polystyrene microsphere stock solution (Mean Diameter: 0.64 mm)

• Solid epoxy and titanium-oxide tissue phantom



Designed Experiments

Exp. – 1

• To compare the values of the optical parameters (depolarization, diattenuation and

retardance) obtained for a solid epoxy & titanium oxide phantom and determine the role of

a diffuser (coherence scrambler) in the experiments done using a LASER beam having

speckles in backscattering mode.

Exp. – 2

• To study the effect of scattering on optical parameters by taking various solutions of

polystyrene microspheres (scatterers) of different scattering coefficients and calculating

Mueller matrix for them from the polarization images obtained as data from the CCD and

decomposing it to give the values of the parameters.

• To determine whether this approach is sensitive for small changes in the concentration

(number) of scatterers in a medium. Is it possible to distinguish them using this approach?

Exp. – 3

• To distinguish between the various stages of abnormality in brain tissue slides obtained from

a local medical college by comparing the various parameters calculated from the polarization

images obtained from the CCD.

• To correlate the values of the optical parameters with the actual microscopic structures of

the tissues using Mueller imaging.

Experimental Setup

Back-scattering Mode (Exp – 1 and 2):

The setup for various experiments described above based on the backscattering mode

was laid out in the following manner-

• Helium Neon LASER was first aligned on an optical bread board and its beam was made

horizontal up to a distance of a few meters. The height of the LASER beam from the bread

board was adjusted according to the height of the other mounts and CCD.

• Then the LASER beam was expanded using an objective lens of a compound microscope.

• The expanded beam was then made parallel using a bi-convex lens (A) and a plano-convex

lens (B) of focal lengths 8 – 10 cm & 7 – 9 cm respectively. Lens (B) was placed at a distance

so that the image formed by the Lens (A) was at its focus and the rays emerging out of this

two lens system were parallel.



• This parallel beam was made to fall on the iris and its hole was adjusted according to the

need of the experiments.

• A polarizer and a quarter wave plate follows iris and were placed on the board such that the

beam falls at the center of them.

• Liquid samples were filled in a cuvette and mounted on adjustable stands in front of the

beam. The solid samples were mounted directly. The LASER beam was incident normally to

the samples.

• The light scattered from these samples was collected using a biconvex collecting lens of large

aperture (diameter) having short focal length. This collecting lens was placed as close to the

sample as possible so as to collect maximum scattered light. The sample should also be

oriented such that the speckles are reflected back and are not collected by the lens.

• The converged light (through lens) was focused on the CCD’s chip used to record intensity

profile.

• Another polarizer (as analyzer) and a quarter wave plate were placed between CCD and

collecting lens and their positions were marked on the board. These were used for

constructing various polarization states.

• The CCD was connected to the computer for recording the various polarization images for

analysis.

Lens BLens AHe-Ne LASER

QWP

QWP

Polarizer

Sample

CCD

DiffuserMirror

Polarizer

Collecting Lens

Transmission Mode (Exp. – 3):

The setup for various experiments described above based on the transmission mode

was laid out in the following manner-

• Helium Neon LASER was first aligned on an optical bread board and its beam was made

horizontal up to a distance of a few meters. The height of the LASER beam from the bread

board was adjusted according to the height of the other mounts and CCD.



• This aligned LASER beam was then made to fall on the iris and its hole was adjusted

according to the need of the experiments.

• A polarizer and a quarter wave plate follows iris and they are placed on the board such that

the beam falls at the center of both of them.

• The samples were mounted directly on an adjustable mount. The LASER beam was incident

normally on the samples.

• The transmitted light is allowed to fall on the CCD’s chip used to record intensity profile.

• In between the CCD and the collecting lens another polarizer (or analyzer) and a quarter

wave plate was placed and their positions were marked on the board. These polarizers and

QWP’s will be used for constructing various polarization states.

• The CCD was finally connected to the computer with a serial port cable provided with it.

Above basic setup was used for most of the experiments done in back-scattering and transmission

mode after desired modifications/adjustments such as adding an appropriate ND filter in front of the

LASER beam if the incoming intensity saturates the CCD.

A coherence scrambler (diffuser) was used and placed in front of the LASER to study its effect in

Exp. – 1.

He-Ne LASERND Filter

Polarizer

QWP QWP

Polarizer

Sample

CCD

Methodology

• Intensity of the source i.e. He – Ne LASER has to be made uniform as much as possible

before starting the experiments. A coherence scrambler (diffuser) may be used for this

purpose. Formation of any kind of patterns due to dust particles, scratches on the optical

instruments or due to the interference of the speckles (5; 6) produced by the LASER should

be avoided.

• A CCD controlled by a software called MaxImDL was used for measuring intensity profile

and it was cooled to -20° C before taking the images.

• The liquid/solid samples (according to the experiment) were mounted and illuminated.

• The exposure time of the CCD was adjusted before starting the experiment by recording

OO polarization images so that the maximum intensity in this state is below its saturation

level.

• A reference box (set wise) was drawn on the image window and its co-ordinates were

noted. This helps in monitoring even a small shift in the bright spot of the LASER beam

during the experiment. This reference box may be required to be changed in subsequent set

of images.

• The various polarization states like VO, HO, LO, MH, PV, etc were constructed manually by

rotating the polarization axis of polarizer and analyzer in specific angles mentioned above.

• The 49 polarization images of a set were recorded and saved in .tif format, maintaining the

same exposure time and its position marked by reference box.



• A background image was also recorded by blocking the main LASER source to correct the

intensity of OO polarization state later on, during image processing and cropping. Further

background correction also plays an important role in cropping the images by the algorithm

designed by me.

• These images were then processed and cropped by using a simple matlab script mentioned

at the end of this report.

• Images were then analyzed and decomposed according to the above mentioned

decomposition scheme to give the values of the three parameters – depolarization,

diattenuation and retardance for every pixel of the cropped images.

Sample Preparation

Solid Phantom (Exp. – 1) The epoxy and titanium oxide solid phantom was prepared in my laboratory by Mr. Prashant Shukla

(PhD. Scholar) under the guidance of Dr. Asima Pradhan (Associate Professor, Department of

Physics, IIT – Kanpur) and was used as a sample in this experiment. The main reason behind this was

that it was a solid phantom and could be mounted directly in front of the LASER beam. In

backscattering mode to study the effect of speckles produced by the LASER it was necessary to

collect the specular reflection. While in case of a liquid medium speckles are reflected by the

container’s surface (cuvette) and not from the sample placed inside it. Therefore it was essential to

use some solid as a sample and mount it directly in front of the beam. However, there is no specific

reason for using this same solid phantom and so it could be changed. (Results for different phantoms

might be different).

Polystyrene Microspheres (Exp. – 2) The polystyrene microspheres used were bought from Bangs Laboratories, Inc. and their detailed

specifications are –

• Mean diameter of microspheres: 0.64 mm

• Buffer: DI water

• Density of Solid Polymer: 1.05 g/ml

• Number of microspheres per ml: 6.972 × 1000 • Scattering coefficient (calculated from Mie Theory): 381 mm-1

Four samples of different scattering coefficients (�� 3, 4, 6, 10 mm-1) were made by diluting the

above stock solution according to the fundamental dilution formula (�0 0 � �� ).

Brain Tissue (Exp. – 3) The samples of brain tissues were obtained from a Sanjay Gandhi Postgraduate Institute of Medical

Sciences (SGPGIMS), Lucknow.



Microscopic Images of Brain Tissues

Brain Tissue (Exp. – 3) The microscopic images of these tissues were taken by a compound microscope at 5X zoom.

Slide ID Slide Picture

14 wks

Microscopic Image (5X)

P#: 1

P#: 2

P#: 3

P#: 4

17 wks


P#: 1

P#: 2

20 wks


P#: 1

P#: 2

P#: 3



24 wks


P#: 1

P#: 2

28 wks


P#: 1

P#: 2

P#: 3

P#: 4

33 wks


P#: 1

P#: 2

P#: 3

P#: 4

36 wks


P#: 1

P#: 2

P#: 3



Polarization Images of Brain Tissue





Figure 4: Polarization Images of Brain Tissues (Slide ID: 33 wks; Position # 2)

Above polarization images are centered and cropped to size 100 × 100 pixels using a small matlab

script. The depolarization scheme is then applied to all 10,000 pixels to give depolarization, retardance and diattenuation values for all 10,000 pixels. These values are then scaled properly and mapped to produce following plots.



Data Analysis & Results

The most critical part of any experiment is the analysis of its data and reaching to a definite

conclusion. Analysis of data in such bio-physical experiments is even more important as it may lead

to very important and significant conclusions. Data analysis in these experiments, where data is in

the form of images was done in the following manner.

• The obtained images were processed and cropped up to the bright spot’s size (100 × 100 pixels).

• These cropped images were then decomposed to give diattenuation, depolarization and

retardance values for each pixel.

• The values of these parameters were averaged over all the pixels and plotted against other

quantities.

• The Mueller images were also calculated and are compared. These images were normalized

in two different ways before comparing –

1. Normalized with respect to first element of Mueller matrix (M11)

2. Normalized with respect to the maximum intensity in that particular image.

• The decomposition plots were averaged either column wise or row wise and corresponding

values were plotted for comparison between two or more samples and distinguishing one

sample from the other. Similar treatment was also done with the Mueller images.

Solid Phantom (Exp. – 1)

Table 2: Listing average values of the three parameters, average being calculated over 100 X 100 pixels for the two sets.

Particulars Mean over àa × àa pixels

Depolarization Diattenuation Retardance With diffuser 0.8955 ± 0.018 0.1795 ± 0.004 2.0919 ± 0.042

Without diffuser 0.8256 ± 0.016 0.2138 ± 0.004 2.1514 ± 0.043

Figure 5: Depolarization Plots – without diffuser (left) & with diffuser (right)



Figure 6: Diattenuation plots – without diffuser (left) & with diffuser (right)

Figure 7: Retardance plots – without diffuser (left) & with diffuser (right)

Polystyrene microspheres (Exp. – 2)

Table 3: Listing average values of the three parameters, average being calculated over 100 X 100 pixels for various sets. Exposure time of CCD was 0.1 sec.

Solution ID Scattering Coeff. (bc) (mm-1)

Mean over àa × àa pixels Depolarization Diattenuation Retardance

Sol – 1 3.0 0.9114 ± 0.018 0.0271 ± 0.001 2.7613 ± 0.055 Sol – 2 4.0 0.9256 ± 0.019 0.0417 ± 0.001 2.5750 ± 0.052 Sol – 3 6.0 0.9373 ± 0.019 0.0220 ± 0.000 2.8883 ± 0.058 Sol – 4 10.0 0.9593 ± 0.019 0.0311 ± 0.001 2.6838 ± 0.054

Scattering coefficient was calculated using Mie calculator (7) based on the Mie Theory for scattering

of light in a highly turbid media.



Plot 1: Mean depolarization versus scattering coefficient

Plot 2: Mean diattenuation versus scattering coefficient

Plot 3: Mean retardance versus scattering coefficient

0.880.890.9

0.910.920.930.940.950.960.970.980.99

0 2 4 6 8 10 12

Mean over 100 X 100 pixels

Scattering Coefficient

Mean Depolarization

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0 2 4 6 8 10 12Mean over 100 X 100 pixels


Mean Diattenuation

2.2

2.3

2.4

2.5

2.6

2.7

2.8

2.9

3



Mean Retardance



Brain Tissues (Exp. – 3)

Table 4: Listing average values of the three parameters, average being calculated over 100 X 100 pixels for various sets. Exposure time of CCD was 1 sec.

Slide ID

Position #

Mean over àa × àa pixels Depolarization Error Diattenuation Error Retardance Error

14 wks

1 0.7313 0.007 0.0644 0.001 0.3384 0.015 2 1.1581 0.007 0.0651 0.001 0.3347 0.023 3 0.7497 0.007 0.0638 0.001 0.333 0.015 4 0.7496 0.007 0.063 0.001 0.3333 0.015

17 wks 1 0.6708 0.006 0.0558 0.001 0.2765 0.013

2 0.6714 0.006 0.0632 0.001 0.2782 0.013

20 wks

1 3.1036 0.007 0.0743 0.001 0.3426 0.062

2 3.0882 0.008 0.0673 0.001 0.3786 0.062

3 3.0754 0.005 0.0725 0.001 0.2620 0.062

24 wks 1 0.6245 0.006 0.0685 0.001 0.3038 0.012

2 0.6386 0.005 0.0931 0.002 0.2343 0.013

28 wks

1 0.7564 0.006 0.0647 0.001 0.3133 0.015

2 0.7739 0.006 0.0550 0.001 0.2890 0.015

3 3.1146 0.006 0.0641 0.001 0.3214 0.062

4 3.1085 0.006 0.0785 0.002 0.2871 0.062

33 wks

1 0.7248 0.006 0.0712 0.001 0.3106 0.014

2 0.6401 0.006 0.0527 0.001 0.2818 0.013

3 0.8756 0.006 0.0668 0.001 0.2858 0.018

4 0.6097 0.005 0.0517 0.001 0.2342 0.012

36 wks

1 3.1079 0.007 0.0667 0.001 0.3353 0.062

2 0.4284 0.007 0.0651 0.001 0.3485 0.009

3 0.5301 0.006 0.0408 0.001 0.2973 0.011



Plot 4: Mean depolarization versus Slide ID

Plot 5: Mean diattenuation versus Slide ID

Plot 6: Mean retardance versus Slide ID

0.2

0.25

0.3

0.35

0.4

10 15 20 25 30 35 40Mean over 100X100 pixels

Slide ID (wks)

Mean Depolarization

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

10 15 20 25 30 35 40Mean over 100X100 pixels

Slide ID (wks)

Mean Diattenuation

0

0.5

1

1.5

2

2.5

3

3.5


Slide ID (wks)

Mean Retardance



Mueller Images of Brain Tissue

Following are the normalized Mueller images (normalized with respect to M11) for the brain tissue.

(Slide ID 33 wks, position 2)

Figure 8: Normalized (with respect to M11) Mueller images for Brain tissue (Slide ID: 33 wks; Position # 2)



Table 5: For comparing the normalized (with respect to maximum intensity in that image) Mueller images M11 (only) for various sets.

Silde ID Normalized Mueller Image (M11)

Position 1 Position 2 Position 3 Position 4

14 wks

Avg. 0.4921 0.5053 0.4407 0.4876

17 wks

Avg. 0.5067 0.4509

20 wks

Avg. 0.3742 0.4396 0.4351

24 wks

Avg. 0.4327 0.4589

28 wks

Avg. 0.4898 0.4821 0.4795 0.4925

33 wks

Avg. 0.5002 0.5233 ± 0.15 0.4726 0.4918



36 wks

Avg. 0.6179 0.5903 0.5702

Plot 7: Average Intensity of M11 versus Slide ID

0.3

0.35

0.4

0.45

0.5

0.55

0.6

0.65

10 15 20 25 30 35 40

Mean over 100 X 100 pixels

Silde ID (wks)

Average M11 Intensity



Decomposition Plots for Brain Tissue

2-D decomposition plots of depolarization, diattenuation and retardance for a brain tissue slide

(Slide ID 33 wks, position 2) is shown below

Figure 9: Depolarization (top left), Retardance (top right) and Diattenuation (bottom) plots for brain tissue (Slide ID: 33 wks; Position # 2)

Note the common pattern in all the three plots. This common pattern is the diffraction pattern formed due to speckles of the LASER beam. This was confirmed after recording & analyzing the LASER spot (or oo polarization state’s image) and Mueller images (Figure 8).

Figure 10: LASER Spot (Non-uniform intensity distribution)



Discussions & Conclusions

• The use of diffuser (coherence scrambler or spinning ground glass) was found to be

important for the experiments done in the backscattering mode. Comparing the above plots

(Figure 5, Figure 6, Figure 7), it is very clear that there is more uniformity in the values of all

the three parameters when diffuser was used. This is only possible if the uniformity of the

initial LASER spot has changed. And a diffuser actually does that. As mentioned earlier that a

diffuser improves the uniformity in the intensity distribution of the LASER beam (from

Gaussian to uniform) and also by removing the speckles produced by the LASER. This is

even clearer from the following plot.

Figure 11: Average Depolarization – averaged through column

The above figure represents the average values of depolarization – calculated for the set of

data taken, without using a diffuser and using a diffuser. The spread in the average values of

depolarization is less using a diffuser. This is because the incident light is now more uniform

than the LASER beam.

• Different solutions of polystyrene microspheres of varying scattering coefficients are easily

distinguishable using this approach of decomposing the Mueller matrix to give complete

information about depolarization. The above plot (Plot 1) for mean depolarization verses

scattering coefficient shows an increase in the value of depolarization as the concentration

(or number) of scatterers in the solution increases (although not very sensitive). This is

because more the light scatters more is its depolarization. Diattenuation is also found to be

very sensitive but not consistent (Plot 2) whereas retardance (Plot 3) was neither very

sensitive nor did it gave consistent results in this case.

• Brain tissues can also be distinguished from each other on the basis of cell density or

scatterer density. More is the concentration of the cells in a particular region more are the



number of scatterers, absorbers, etc in that particular region. Talking simply if at a particular

location there is a very high density of scatterers like mitochondria, etc which happens in

cancer and other chronic diseases then a similar pattern should be shown by the values of

depolarization as well (concluded by Exp. – 2). From the plots (Plot 4, Plot 5 & Plot 6) it is

shown that these parameters are very sensitive and tissues can be distinguished on this basis.

Tissues can also be distinguished on the basis of the Mueller images. Following is a plot of

average of Mueller element (M43), average taken over each column of the Mueller image M43.

According to the above plot which shows a clear cut distinction in the values of the Mueller

element M43 compared between the various tissue slides. These can be divided into two

major groups based on this plot. Similar are the two following plots for M24 and M34, which

also shows that there is a range in which the values of these elements lie.



Any abnormality in the tissue’s morphology shows an abnormal increase or decrease in the

values of these parameters at that particular location. The curves for 36 wks (all positions)

all have the minimum value for this element (M24) and all lie close to each other. Similarly the

curves for 20 wks position 1 and 2 lie close to each other while the same for position

number 3 is quite high and might indicate some change in tissue morphology. This should be

compared with the histopathology report (yet to come) and then infer the final results.

Comparing the above graphs with the microscopic images of the tissues (shown above),

shows that the values being indicated by the above graphs for the various sets of data match

with them and hence, this approach can be used to detect severe abnormalities in the live

systems and should be further developed.



Precautions

• The background intensity and thermal noise of CCD should be lesser than the LASER

intensity (signal). It is strongly recommended to do the experiments in a completely dark

room.

• Before starting the experiment, initial spot’s size and its uniformity should be checked. There

should be no or very little variation in intensity.

• All optical instruments such as lenses, polarizers, quarter wave plate, CCD etc should be

free from any scratches or dust particles. Acetone or alcohol may be used for cleaning

purposes. Dust or scratch produces diffraction patterns due to which intensity varies.

• Don’t look at the LASER beam not even it reflection with the naked eyes.

• Wear gloves when dealing with cancerous tissues or toxic chemicals.

• In case of polystyrene microspheres solution (Exp. – 2) specular reflection in back-scattering

mode should not be taken into account. The speckles generally are of lesser intensity (than

main LASER beam) and get reflected from the walls of cuvette and so carry no information

about the sample filled inside it.

Bibliography

1. Tuchin, Valery. Optical properties of tissues with strong (multiple) scattering. Tissue Optics: Light

Scattering Methods and Instruments for Medical Diagnosis. Second. 1, pp. 3-108.

2. Gupta, Vivek. Mueller matrix in optical imaging for cervical cancer detection. Department of Physics,

Indian Institute of Technology. Kanpur : s.n., 2009. pp. 1-6.

3. Reference Page. Axometrics Web Site. [Online] http://www.axometrics.com/reference.htm.

4. Interpretation of Mueller matrices based on polar decomposition. Lu, Shih-Yau and Chipman,

Russell A. 5, Alabama : Optical Society of America, May 1996, Opt. Soc. Am. A, Vol. 13, pp. 1106-

1113.

5. Size determination by use of two-dimentional Mueller matrices backscattered by optically thick random

media. Dillet, Jerome, et al. 19, s.l. : Optical Society of America, February 23, 2006, APPLIED

OPTICS, Vol. 45, pp. 4669-4678.

6. Interpreting Mueller images of tissues. Smith, Matthew H. Alabama : SPIE, 2001, SPIE, pp. 82-89.

7. Prahl, Scott. Mie Scattering Calculator. [Online] Oregon Medical Laser Center, 2007.

http://omlc.ogi.edu/calc/mie_calc.html.

8. Measurement and calculation of the two-dimensional backscattering Mueller matrix of a turbid medium.

Cameron, Brent D., et al. 7, Texas : Optical Society of America, April 1, 1998, OPTICS

LETTERS, Vol. 23, pp. 485-487.



9. Diffuse backscattering Mueller matrices patterns from turbid media. Lian-Shun, ZHANG, et al. 6,

China : Chinese Physical Society and IOP Publishing Ltd., January 23, 2006, CHIN. PHYS. LETT., Vol.

23, pp. 1603-1606.

10. Bladwin, Angela M. Mueller matrix imaging for skin cancer detection. Biomedical Engineering,

Texas A & M University. Texas : s.n., 2004. pp. 1-135, Thesis.

11. Mueller decomposition images for cervical tissue: Potential for discriminating normal and dysplastic states.

Shukla, Prashant and Pradhan, Asima. 3, s.l. : Optical Society of America, February 2, 2009,

OPTICS EXPRESS, Vol. 17, pp. 1600-1609.

12. Hahn, Brian D. and Valentine, Daniel T. Essential Matlab for engineers and scientists. Second.

s.l. : Elsevier Ltd., 2007. p. 428. ISBN 13: 9-78-0-75-068417-0; ISBN 10: 0-75-068417-8.

13. Wikipedia. [Online] http://en.wikipedia.org.



Revised Matlab Script for better results: Add the following script/code to a new .m file and execute it. The depolarization, diattenuation and

retardance plots will be plotted and saved automatically. Remember to place the new .m file

containing the following script/code in the same directory in which finalchz_mod2.m file is saved and

you may have to change the directories accordingly. Appropriate changes were also made in the

finalchz_mod2.m script file.

close all clear wdir=input('Enter the location of original images: ','s'); fname=['oo';'oh';'ov';'op';'om';'ol';'or';'hh';'ho';'hp';'hm';'hr';'hl';'vv';'vo';'vp';'vm';'vr';'vl';'pp';'pl';'ph';'pr';'pv';'po';'mm';'mh';'mv';'mr';'ml';'mo';'rr';'rh';'rv';'ro';'rp';'rm';'rl';'ll';'lp';'lm';'lh';'lv';'lo';'lr';'hv';'vh';'mp';'pm']; [w,e]=size(fname); hlim=100; wlim=100; ch=input('Do you want to crop the images(Y/N)? ','s'); if ch=='Y' || ch=='y' fprintf('\nEnter the dimensions of the box...\n'); tl=input('Top left coordinates of the box: '); rb=input('Right bottom coordinates of the box: '); cd(wdir); mkdir new_data bg=imread('bkg.tif'); z=1; while z<=w-4 im=imread(fname(z,:),'tif'); I=im-bg; J=double(I); maxI=max(J(:)); M=(J/maxI)*255; M=uint8(M); thres=graythresh(M); bw=im2bw(M,thres); bw=bwareaopen(bw,5); bw=imfill(bw,'holes'); [B,L]=bwboundaries(bw); [p,q]=size(B); if p==0 fprintf('BAD IMAGE...%s.tif\n',fname(z,:)); else stats=regionprops(L,'Centroid','Area'); for t=1:p A(t)=stats(t).Area; end [val,ind]=max(A); cord=stats(ind).Centroid; I=imcrop(I,[round(cord(1,1)-wlim/2),round(cord(1,2)-hlim/2),wlim-1,hlim-1]); cd new_data imwrite(I,[fname(z,:),'.tif']); cd .. fprintf('%s.tif done...\n',fname(z,:));



clear A end z=z+1; end clear B z L t bw p q thres M maxI cord val ind e J im I stats cd(wdir) for z=w-3:w I=imread(fname(z,:),'tif'); I=I-bg; [u,v]=size(I); for i=1:u for j=1:v if I(i,j)<0 I(i,j)=0; end end end J=imcrop(I,[(tl(1)+(rb(1)-tl(1))/2),(tl(2)+(rb(2)-tl(2))/2),wlim-1,hlim-1]); cd new_data imwrite(J,[fname(z,:),'.tif']); cd .. fprintf('%s.tif done...\n',fname(z,:)); end clear tf rb I bg J z u v end ndir=[wdir,'\new_data']; ch=input('Do you want to check the images(Y/N)? ','s'); if ch=='y' || ch=='Y' cd(ndir); for i=1:w im=imread(fname(i,:),'tif'); if rem(i,12)==1 figure; end if rem(i,12)==0 j=12; else j=rem(i,12); end subplot(3,4,j);imagesc(im);axis off;colorbar; title(fname(i,:)); end end char=input('Do you want to decompose the Mueller images (Y/N)? ','s'); if char=='y' || char=='Y' cd 'C:\Users\Harsh Purwar\Documents\MATLAB' finalchz_mod2 end cd 'C:\Users\Harsh Purwar\Documents\MATLAB' clear