P OLARIZATION MICROSCOPY : BIOMEDICAL IMAGING AND DIAGNOSTICS Yuriy - - PowerPoint PPT Presentation

POLARIZATION MICROSCOPY: BIOMEDICAL

IMAGING AND DIAGNOSTICS Yuriy A. Ushenko Chernivtsi National University Ukraine

1

Winter College on Optics: Advanced Optical Techniques for Bio-imaging Date & time:

(Lecture) February 17, 2017 (Friday), 15.30 (Experiment) February 23 , 2017 (Thursday), 14.00 Room: Leonardo Building - Budinich Lecture Hall

LIST OF LECTURES

Introduction. Lecture 1. Basic concepts. Polarization. Stokes

vector. Mueller matrix. Basics

• f

laser polarimetry.

Lecture 2. Basics of model description of structure

and optical anisotropy of biological tissues.

Lecture 3. Methods and resources of analysis and

processing

• f

biological tissues polarization- inhomogeneous images.

Lecture 4. Principles and methods of polarization

and Mueller-matrix mapping.

2

3

4

5

6

INTRODUCTION

Optical methods of diagnostics of biological objects and visualization of

their structures occupy a leading position thanks to their high information content, multi-functional capabilities (photometric, spectral, and polarization correlation).

It should be stated that new scientific direction - optics of biological

tissues and fluids was finally formed and rapidly developing. The main areas of basic research are the results of theoretical and experimental studies of photon transport in biological tissues and fluids.

A separate direction in optics of biological tissues formed polarimetric

• investigations. Analysis of polarization characteristics of the scattered

radiation allows to obtain qualitatively new results on morphological and physiological state of biological tissues.

A new step in the development of methods of optical diagnostics of

biological tissues was successful unification of polarimetric and fluorescent techniques.

7

LECTURE 1. BASIC CONCEPTS. POLARIZATION. STOKES VECTOR. MUELLER

• MATRIX. BASICS OF LASER POLARIMETRY.

8

Light as transverse electromagnetic wave

y ) t

• kz

cos( E ) t z, ( E x t)

• kz

cos( E ) t z, ( E

0y y 0x x

• The electric and magnetic fields of an

electromagnetic wave are perpendicular to each other and transverse to the direction

• f propagation. An electromagnetic wave is

propagating along z-axis. Its electric field is aligned to the x-axis and magnetic field along the y-axis.

ω = 2πν – angular frequency k = 2π/λ – wave number Parameters:

• 1. Amplitude
• 2. Frequency
• 3. Phase
• 4. Polarization

– phase (initial)

LECTURE 1. BASIC CONCEPTS. POLARIZATION. STOKES VECTOR. MUELLER

• MATRIX. BASICS OF LASER POLARIMETRY.

9

Polarization of electromagnetic wave Polarization is a important property

• f

electromagnetic waves. In communications, completely polarized waves are used. In radio astronomy un- polarized components exist. The techniques to analyze polarization known as polarimetry. The complete polarization types of electromagnetic waves are: (i) Linear Polarization. (ii) Circular Polarization. (iii) Elliptical Polarization. Electromagnetic waves from of radio astronomical sources may posses: (i) Random polarization (also known as un-polarized waves). (ii) Partial polarization (completely polarized + un-polarized)

LECTURE 1. BASIC CONCEPTS. POLARIZATION. STOKES VECTOR. MUELLER

• MATRIX. BASICS OF LASER POLARIMETRY.

10

Polarization of electromagnetic wave. Graphical representation. Polarization ellipse y ) t

• kz

cos( E ) t z, ( E x t)

• kz

cos( E ) t z, ( E

0y y 0x x

• 2

0y y 0x x 2 0y y 2 0x x

sin cos E E E E 2 E E E E

• Some algebra

equation of an ellipse

An ellipse can be characterized by: 1. size of minor axis 2. size of major axis 3.

• rientation (tilt angle, azimuth)

4. Axial ratio (ellipticity) 5. sense (CW, CCW)

Axial ratio - is a ratio of length of minor to the length of major axis.

) arctan(OA OB

• ellipticity (angle)

LECTURE 1. BASIC CONCEPTS. POLARIZATION. STOKES VECTOR. MUELLER

• MATRIX. BASICS OF LASER POLARIMETRY.

11

Polarization of electromagnetic wave. Types of polarization. Linear polarization

Any form of complete polarization resulting from a coherent source can be analyzed using polarization ellipse !!!

• 90
• 45
• If there is no amplitude in x (E0x = 0), there is
• nly one component, in y (horizontal).

If there is no amplitude in y (E0y = 0), there is

• nly one component, in x (vertical).

Phase difference ( )) and E0x = E0y, then Ex = Ey

• ;
• y

) t

• kz

cos( E ) t z, ( E x t)

• kz

cos( E ) t z, ( E

0y y 0x x

LECTURE 1. BASIC CONCEPTS. POLARIZATION. STOKES VECTOR. MUELLER

• MATRIX. BASICS OF LASER POLARIMETRY.

12

Polarization of electromagnetic wave. Types of polarization. Circular polarization

y ) t

• kz

cos( E ) t z, ( E x t)

• kz

cos( E ) t z, ( E

0y y 0x x

• 1

sin cos E E E E

2 2 2 0y y 2 0x x

• If the phase difference is and E0x = E0y

then: Ex / E0x = cos, Ey / E0y = sin and we get the equation of a circle with CW or CCW rotation and wave is said to be circularly polarized:

90

LECTURE 1. BASIC CONCEPTS. POLARIZATION. STOKES VECTOR. MUELLER

• MATRIX. BASICS OF LASER POLARIMETRY.

13

Polarization of electromagnetic wave. Types of polarization. Elliptical polarization. If the magnitudes of Ex and Ey are not equal, and there exists a phase difference between the two, the tip of the electric field vector describes an ellipse and wave is said to be elliptically polarized. Linear + circular polarization = elliptical polarization

ANIMATIONS

Any wave may be written as a superposition of the two polarizations

LECTURE 1. BASIC CONCEPTS. POLARIZATION. STOKES VECTOR. MUELLER

• MATRIX. BASICS OF LASER POLARIMETRY.

14

Stokes parameters 1852: Sir George Gabriel Stokes took a very different approach and discovered that polarization can be described in terms of observables using an experimental definition. The polarization ellipse is only valid at a given instant of time (function of time)!!!

• 2

0y y 0x x 2 0y y 2 0x x

sin cos E E E E 2 E E E E

• To get the Stokes parameters, do a time average (integral over time) and a

little bit of algebra...

• 2

0y 0x 2 0y 0x 2 2 0y 2 0x 2 2 0y 2 0x

sin E E 2 cos E E 2 E E E E

• sin

E E 2 V cos E E 2 U E E Q E E I

0y 0x 3 0y 0x 2 2 0y 2 0x 1 2 0y 2 0x

• S

S S S

The 4 Stokes parameters are:

LECTURE 1. BASIC CONCEPTS. POLARIZATION. STOKES VECTOR. MUELLER

• MATRIX. BASICS OF LASER POLARIMETRY.

15

Stokes parameters described in geometrical terms. Stokes vector

• 2

sin 2 sin 2 cos 2 cos 2 cos 1 V U Q I

The Stokes parameters can be arranged in a Stokes vector:

• LCP

I RCP I 135 I 45 I 90 I I intensity sin E E 2 cos E E 2 E E E E V U Q I

0y 0x 0y 0x 2 0y 2 0x 2 0y 2 0x

• Linear polarization
• Circular polarization
• Fully polarized light

2 2 2 2

V U Q I V 0, U 0, Q V 0, U 0, Q

LECTURE 1. BASIC CONCEPTS. POLARIZATION. STOKES VECTOR. MUELLER

• MATRIX. BASICS OF LASER POLARIMETRY.

16

Mueller matrices If light is represented by Stokes vectors, optical components are then described with Mueller matrices: [output light] = [Muller matrix] [input light]

• V

U Q I V' U' Q' I'

44 43 42 41 34 33 32 31 24 23 22 21 14 13 12 11

m m m m m m m m m m m m m m m m

Element 1 Element 2 Element 3

1

M

2

M

3

M

S’ = M3 M2 M1 S

LECTURE 1. BASIC CONCEPTS. POLARIZATION. STOKES VECTOR. MUELLER

• MATRIX. BASICS OF LASER POLARIMETRY.

17

Basics of laser polarimetry

• m

n m m n m

r r r r I r r r r I ,... .......... ,... ; ,... .......... ,...

1 max 1 min

• min

,... .......... ,... ,... .......... ,...

1 1 m n m m n m

r r r r I r r r r

• .

,... .......... ,... ; 2 min ,... .......... ,...

max min 1 1 i i m n m i m n m

r I r I arctg r r r r r I r r r r

• Polarization maps (calculation)

Need to be measured

LIST OF LECTURES

Introduction. Lecture 1. Basic concepts. Polarization. Stokes

• vector. Mueller matrix. Basics of laser polarimetry.

Lecture 2. Basics of model description of

structure and optical anisotropy of biological tissues.

Lecture 3. Methods and resources of analysis and

processing

• f

biological tissues polarization- inhomogeneous images.

Lecture 4. Principles and methods of polarization

and Mueller-matrix mapping.

18

LECTURE 2. BASICS OF MODEL DESCRIPTION OF STRUCTURE AND OPTICAL

ANISOTROPY OF BIOLOGICAL TISSUES. 19

Optical anisotropy Optical anisotropy - difference in the optical properties of a medium as a function of the direction of propagation of optical radiation (light) in the medium and of the state of polarization of the radiation.

Amplitude anisotropy (dichroism) Phase anisotropy (birefringence)

• 1. Linear dichroism
• 2. Circular dichroism
• 1. Linear birefringence
• 2. Circular birefringence

(optical activity)

• asymmetry in crystal structure causes two different

refractive indices;

• pposite polarizations follow different paths through

crystal.

• crystals may similarly show absorption which

depends upon polarization.

ANIMATIONS

LECTURE 2. BASICS OF MODEL DESCRIPTION OF STRUCTURE AND OPTICAL

ANISOTROPY OF BIOLOGICAL TISSUES. 20

Mueller-matrix approach for description of biological layers with amplitude and phase anisotropies Soft tissue structure

Transmission electron micrograph of human skin (dermis), showing collagen fibers sectioned both longitudinally and transversely. Magnification 4900x.

Biological tissues reveal self- similar (fractal) structure as a result of growth processes

LECTURE 2. BASICS OF MODEL DESCRIPTION OF STRUCTURE AND OPTICAL

ANISOTROPY OF BIOLOGICAL TISSUES. 21

Mueller-matrix approach for description of biological layers with amplitude and phase anisotropies

Optically anisotropic biological layer Phase anisotropy Amplitude anisotropy Optical activity Linear birefringence Circular dichroism Linear dichroism Parameters Polarization plane rotation angle - Phase shift between the orthogonal components of amplitude - Circular dichroism index - Linear dichroism index - Partial Mueller matrix - Partial Mueller matrix - Partial Mueller matrix - Partial Mueller matrix - Mueller matrix of generalized anisotropy Azimuthally independent Mueller-matrix elements and invariants ; Algorithms of Mueller-matrix reconstruction of parameters of optical anisotropy

• g
• D
• D

M

const M ik

• const

M ik

• ik

ik

M M w ,

• ik

ik

M M u ,

• ik

ik

M M h g ,

• ik

ik

M M v ,

• Algorithm of Mueller-matrix modeling of biological layer anisotropy

LECTURE 2. BASICS OF MODEL DESCRIPTION OF STRUCTURE AND OPTICAL

ANISOTROPY OF BIOLOGICAL TISSUES. 22

Mueller-matrix operators of mechanisms of phase and amplitude anisotropy

1 1

33 32 23 22

• .

2 sin , 2 cos

32 23 33 22

• ik

44 43 42 34 33 32 24 23 22

1 d d d d d d d d d D

• .

cos , sin 2 cos , sin 2 sin , cos 2 cos 2 sin , cos 1 2 sin 2 cos , cos 2 sin 2 cos

44 43 34 24 42 2 2 33 32 23 2 2 22

• d

d d d d d d d d dik 1 1

41 33 22 14

• .

1 2 , 1 1

2 41 14 2 2 33 22

g g g g

ik

• .

2 ; 2 cos 2 2 sin 1 ; 2 sin 2 cos 1 ; 2 sin 2 2 cos 1 ; 2 sin 1 ; 2 cos 1 1 1

44 2 2 33 2 32 23 2 2 22 31 13 21 12

• ik

44 33 32 31 23 22 21 13 12

1

• D

M

44 43 42 41 34 33 32 31 24 23 22 21 14 13 12 1 11

1 M M M M M M M M M M M M M M M M M

• Circular birefringence

Linear birefringence Circular dichroism Linear dichroism Generalized Mueller matrix of biological tissue optical anisotropy

LECTURE 2. BASICS OF MODEL DESCRIPTION OF STRUCTURE AND OPTICAL

ANISOTROPY OF BIOLOGICAL TISSUES. 23

Mueller-matrix approach for description of biological layers with amplitude and phase anisotropies

• ik

M

Mueller-matrix images of skeletal muscle

LECTURE 2. BASICS OF MODEL DESCRIPTION OF STRUCTURE AND OPTICAL

ANISOTROPY OF BIOLOGICAL TISSUES. 24

Information content of Mueller-matrix elements

4 ; 3 ; 2 ; 1 ; 1

• k

i

M

• Mechanisms of optically anisotropic absorption

4 ; 3 ; 2 ; 1 ; 3 ; 2

• k

i

M

• Phase modulation ( ) of laser radiation on the

background of optically anisotropic absorption ( )

• ,
• ,

g

4 ; 3 ; 2 ; 1 ; 4

• k

i

M

• Complex information about superposition of mechanisms
• f linear birefringence and dichroism

Mueller-matrix invariants

• cos

44

M

. 2 tg M

• ,

; , ;

44 41 14 11

const M const M const M const M

const M M M M M

• 33

22 32 23

• 14

M g M

• 41

LECTURE 2. BASICS OF MODEL DESCRIPTION OF STRUCTURE AND OPTICAL

ANISOTROPY OF BIOLOGICAL TISSUES. 25

Samples structure (histological sections)

• 1. Tissue with ordered and disordered structure

Myocardium tissue in coaxial and crossed polarizer-analyzer Brain tissue in coaxial and crossed polarizer-analyzer

LECTURE 2. BASICS OF MODEL DESCRIPTION OF STRUCTURE AND OPTICAL

ANISOTROPY OF BIOLOGICAL TISSUES. 26

• 2. Parenchymatous tissue with cluster (disordered)

structure Benign tumor (adenoma) of prostate gland tissue in coaxial and crossed polarizer-analyzer Samples structure (histological sections)

LECTURE 2. BASICS OF MODEL DESCRIPTION OF STRUCTURE AND OPTICAL

ANISOTROPY OF BIOLOGICAL TISSUES. 27

• 3. Tissues with benign and malignant formations

Samples structure (histological sections) Precancer (dysplasia) of cervix uteri tissue Malignant formation (adenocarcinopma)

• f cervix uteri tissue

LECTURE 2. BASICS OF MODEL DESCRIPTION OF STRUCTURE AND OPTICAL

ANISOTROPY OF BIOLOGICAL TISSUES. 28

Samples structure (dried smears of biological fluids) Donor blood plasma in coaxial and crossed polarizer-analyzer Synovial fluid of joint with rheumatoid arthritis in coaxial and crossed polarizer-analyzer

LIST OF LECTURES

Introduction. Lecture 1. Basic concepts. Polarization. Stokes

• vector. Mueller matrix. Basics of laser polarimetry.

Lecture 2. Basics of model description of structure

and optical anisotropy of biological tissues.

Lecture 3. Methods and resources of analysis

and processing

• f

biological tissues polarization-inhomogeneous images.

Lecture 4. Principles and methods of polarization

and Mueller-matrix mapping.

29

LECTURE 3. METHODS AND RESOURCES OF ANALYSIS AND PROCESSING OF

BIOLOGICAL TISSUES POLARIZATION-INHOMOGENEOUS IMAGES. 30

Objective criteria

All the data and parameters (q) presented in previous lectures need to be quantitatively analyzed!!! It was proposed to use:

• 1. Statistic analysis
• N

i i

q N Z

1 1

) ( 1

• N

i i

Z q N Z

1 2 1 2

) ( 1

• N

i i

Z q N M Z

1 3 1 3 2 3

) ( 1 1

• N

i i

Z q N M Z

1 4 1 4 2 4

) ( 1 1

Leptokurtic Mesokurtic Platykurtic

Negatively Skewed Mode Median Mean Symmetric (Not Skewed) Mean Median Mode Positively Skewed Mode Median Mean

• Mean value
• Standard deviation
• Skewness
• Kurtosis

A moment is a quantitative measure

• f the shape of a set of points.

LECTURE 3. METHODS AND RESOURCES OF ANALYSIS AND PROCESSING OF

BIOLOGICAL TISSUES POLARIZATION-INHOMOGENEOUS IMAGES. 31

All the data and parameters (q) presented in previous lectures need to be quantitatively analyzed!!! It was proposed to use:

• 2. Correlation analysis

Objective criteria Correlation plays a central role in the study of time series. In general, correlation gives a quantitative estimate of the degree of similarity between two

• functions. The correlation of functions g and f both with N samples is defined

as:

1 , , 2 , 1 , 1

1

• N

k f g N r

k N i i k i k

• Auto-correlation – correlation of a signal with

itself.

LECTURE 3. METHODS AND RESOURCES OF ANALYSIS AND PROCESSING OF

BIOLOGICAL TISSUES POLARIZATION-INHOMOGENEOUS IMAGES. 32

All the data and parameters (q) presented in previous lectures need to be quantitatively analyzed!!! It was proposed to use:

• 2. Correlation analysis

Objective criteria

Any azimuthally asymmetric distribution can be evaluated by correlation analysis in two perpendicular directions. Based on this, we used the following methodology of autocorrelation processing of the distribution of values q:

min max

• n

i i m y x n i i n y y

y K m y K n y y K n y y K Y x W K x K n x K m x x K m x x K y X W K

1 1 1 1

. 1 ,..., 1 ; .......... .......... .......... ,..., 1 ; , , ; 1 ,..., 1 ; .......... .......... .......... ,..., 1 ; , ,

• Asymmetry coefficient

Half-width of autocorrelation dependency is an important diagnostical characteristic!!!

LECTURE 3. METHODS AND RESOURCES OF ANALYSIS AND PROCESSING OF

BIOLOGICAL TISSUES POLARIZATION-INHOMOGENEOUS IMAGES. 33

All the data and parameters (q) presented in previous lectures need to be quantitatively analyzed!!! It was proposed to use:

• 3. Fractal (self-similarity) analysis

Objective criteria Fractal anlysis is based on the calculation of logarithmic dependencies of power spectra of values q: . Further mentioned dependecies are approximated by least squares method in a curves . Due to the form of curves one can classify:

• 1. Distributions q are fractal when there is one stable inclination angle

within 2-3 decades of sizes changes.

• 2. Distributions q are multifractal when there is several stable inclination angles

exist.

• 3. Distributions q are random when there is no stable inclination angles.

) lg( lg

1

• d

q L

• const

LIST OF LECTURES

Introduction. Lecture 1. Basic concepts. Polarization. Stokes

• vector. Mueller matrix. Basics of laser polarimetry.

Lecture 2. Basics of model description of structure

and optical anisotropy of biological tissues.

Lecture 3. Methods and resources of analysis and

processing

• f

biological tissues polarization- inhomogeneous images.

Lecture

4. Principles and methods

• f

polarization and Mueller-matrix mapping.

34

LECTURE 4. PRINCIPLES AND METHODS OF POLARIZATION AND MUELLER-MATRIX

MAPPING. 35

Experimental setup and measuring technique Right circular polarization Illumination Analysis

LECTURE 4. PRINCIPLES AND METHODS OF POLARIZATION AND MUELLER-MATRIX

MAPPING. 36

Experimental setup and measuring technique Let the probing beam will be linearly polarized with azimuth .

• First step: set transmission plane of analyzer 9 at an angle of and measure

set transmission plane of analyzer 9 at an angle of and measure

• n

m I

• 90
• n

m I

• 90

90 1

I I S

• 1

90 2

/ ) ( S I I S

• Second step: set transmission plane of analyzer 9 at an angle of and measure

set transmission plane of analyzer 9 at an angle of and measure

45

• n

m I

• 45

135

• n

m I

• 135

1 135 45 3

/ ) ( S I I S

• n

m I

• n

m I

• 90

1

S

2

S

• n

m I

• 45
• n

m I

• 135

3

S

LECTURE 4. PRINCIPLES AND METHODS OF POLARIZATION AND MUELLER-MATRIX

MAPPING. 37

Experimental setup and measuring technique

Third step: insert quarter-wave plate 8 set transmission plane of analyzer 9 at an angle of and measure set transmission plane of analyzer 9 at an angle of and measure

45

• n

m I

• 135
• n

m I

• n

m I

• n

m I

• I

I S4

4

S

Similarly one can calculate other Stokes vectors:

• n

m Si

• ,

90 , 45 4 ; 3 ; 2 ; 1

. ; ; ;

; 90 ; 45 ; ; 90 ; 45 ; ; 90 ; 45 ; 4 ; 90 ; 45 ; 135 ; 90 ; 45 ; 45 ; 90 ; 45 ; 3 ; 90 ; 45 ; 90 ; 90 ; 45 ; ; 90 ; 45 ; 2 ; 90 ; 45 ; 90 ; 90 ; 45 ; ; 90 ; 45 ; 1

• I

I S I I S I I S I I S

i i i i

; ; ); ( 5 . ); ( 5 .

11 1 14 11 45 1 13 90 1 1 12 90 1 1 11

f S M f S M S S M S S M

• ;

; ); ( 5 . ); ( 5 .

21 2 24 21 45 2 23 90 2 2 22 90 2 2 21

f S M f S M S S M S S M

• ;

; ); ( 5 . ); ( 5 .

31 3 34 31 45 3 33 90 3 3 32 90 3 3 31

f S M f S M S S M S S M

• .

; ); ( 5 . ); ( 5 .

41 4 44 41 45 4 43 90 4 4 42 90 4 4 41

f S M f S M S S M S S M

• Algorithm for Mueller matrix calculation

. arcsin 5 . ; arctan 5 .

1 4 2 3

• i

i i i

S S S S

• Polarization parameters

Mueller-matrix elements Stokes vector parameters

LECTURE 4. PRINCIPLES AND METHODS OF POLARIZATION AND MUELLER-MATRIX

MAPPING. 38

Mueller-matrix invariants and optical anisotropy parameters Linear birefringence Circular birefringence

LECTURE 4. PRINCIPLES AND METHODS OF POLARIZATION AND MUELLER-MATRIX

MAPPING. 39

Mueller-matrix invariants and optical anisotropy parameters Linear dichroism Circular dichroism

LECTURE 4. PRINCIPLES AND METHODS OF POLARIZATION AND MUELLER-MATRIX

MAPPING. 40

Mueller-matrix invariants and optical anisotropy parameters

Parameters 0.46 0.12 0.73 0.16 0.29 0.13 0.19 0.11 0.48 0.23 0.57 1.14 0.47 0.61 0.41 0.93 0.23 0.29 0.26 0.22

44

M

M

• 14

M

41

M

1

Z

2

Z

3

Z

4

Z D