anisotropic materials using Stokes

Decoupling six effective parameters of anisotropic materials using Stokes

polarimetry

National Cheng Kung University Mechanical Engineering Department

PhD student: PHAM, THI-THU-HIEN Advisor: Prof. LO, YU-LUNG

National Cheng Kung University

Department of Mechanical Engineering

Contents

Introduction 1

Method of measurement 2

Analytical simulation 3

Experimental setup & results 4

Conclusions

5

Introduction

Random scattering on a rough surface Scattering on impurities in the volume

Tissues

(turbid media) Light

scattering

Potential applications

(medical diagnosis) Major role

Optics

Depolarization

Polarized light Unpolarized light

Polarization & Depolarization

Associate

Scattering Retardance Diattenuation

Introduction

Some current techniques

Polyacrylamide phantoms Polystyrene microspheres

Sucrose

•Linear retardance (β)

•Optical rotation angle (γ)

•Diattenuation (D)

•Depolarization coefficient (∆) The system

Monte Carlo

measure Simulate

3 bio-samples Optical properties

Their study did not show enough nine parameters of characteristics of a bio-sample.

One famous group is from Canada (Ghosh et al or Wood et al)

Some current techniques

Other famous group is from Portland and USA (Prahl et al): many papers

Tissue chromophores (water, dry tissue and blood) Polystyrene microspheres

Bovine muscle

•The absorption coefficient(μ_a)

•The scattering coefficient (μ_s)

•The anisotropy factor (g)

The system

Integrating sphere

measure enhance

Bio-samples

Optical properties

Their study did not show enough nine parameters of characteristics of a bio-sample.

Some current techniques

Other famous group is from USA (Cameron et al): many papers had published

Polystyrene microspheres (different diameter)

Melanoma Rat skin

•The scattering coefficient (μ_s)

•The image of Mueller matrix

The system

Mueller matrix &

Stokes polarimeter

measure

Bio-samples

Optical properties

Their study did not show enough nine

parameters of characteristics of a bio-sample.

The image of Mueller matrix for a complex polystyrence mixture.

 The Stokes vector of the output light:

0 1

2 45 45

3

o o

x y

x y

rcp lcp

I I S

I I S S

S I I

S I I



  

   

    

       

   

  

   

• S₀: the total light intensity;

• S₁: the intensity difference between horizontally and vertically polarized components

• S₂: the intensity difference between +45° and -45°

polarized components

• S₃: the intensity difference between right- and left- circularly polarized components

0 11 12 13 14 0

1 21 22 23 24 1

2 31 32 33 34 2

3 41 42 43 44

3

ˆ

ˆ ˆ

ˆ ˆ S m m m m S

S m m m m S

S MS

S m m m m S

S m m m m S

        

     

                        

Stokes vectors

Mueller matrices

The polarization

state of the light (optical sample)

Stokes and Mueller matrix

Purposes

 Principal axis angle (α)

 Retardance (β)

 Optical rotation angle (γ)

 Diattenuation axis angle (θ

)

 Diattenuation (D)

 Circular diattenuation (R)

Measuring six parameters of characteristics in materials:

Linear birefringence (LB)

Circular birefringence (CB)

Linear diattenuation (LD)

Circular diattenuation (CD)

Mueller matrix of six parameters

[M_D] : diattenuation Mueller matrix [M_R] : retardance Mueller matrix

The six effective optical parameters of an anisotropic material:

 Principal axis angle & retardance of LB,

 Optical rotation of CB,

 Diattenuation axis angle & diattenuation of LD,

 Circular diattenuation of CD

He-Ne Laser

Q Stokes

Polarimeter P

CD LD CB LB

Sample

Ŝc S_c

] ][

[

D

M M

M 

] ][

[ M

M

M 

] ][

[

R

M M

M 

c c

cd ld

cb lb

c c

S S S S

m m

m m

m m

m m

m m

m m

m m

m m

S M M

M M

S S S S S































































3 2 1 0

44 43

42 41

34 33

32 31

24 23

22 21

14 13

12 11

3 2 1 0

ˆ ˆ ˆ ˆ ] ˆ

][

][

][

[

2 2 2

2 2 2

1 0 0 0

0 cos(4 )sin ( / 2) cos ( / 2) sin(4 )sin ( / 2) sin(2 ) sin( ) 0 sin(4 )sin ( / 2) cos(4 )sin ( / 2) cos ( / 2) cos(2 ) sin( )

0 sin(2 )sin( ) cos(2 )sin( ) cos( )

Mlb       

      

    

 

  

 

     

 

  

 





















 

1 0

0 0

0 ) 2 cos(

) 2 sin(

0

0 ) 2 sin(

) 2 cos(

0

0 0

0 1







 Mcb

2 2 2

2 2 2

1 1 1

(1 ) cos(2 )(1 ) sin(2 )(1 )

1 1 1 0

2 2 2

1 1 1

1 (1 ) cos(4 )(1 ) sin(4 )(1 )

cos(2 )(1 )

1 1 1

1 0

2 4 4 4

1 1 1

1 sin(4 )(1 ) (1 ) cos(4 )(1 )

sin(2 )(1 )

1 1 1

1 0

2 4 4 4

d d

d d

d

ld

d d

d

D D D

D D D

D D D

D

D D D

D M

D D D

D

D D D

D

 

 



 



  

  

  

  

   

     



  

   

     

0 0 0 1

1 D D

 

 

 

 

 

 

 

 

 

 

 

 

 

  

 

  

 































2 2

2 2

1 0

0 2

0 1

0 0

0 0

1 0

2 0

0 1

R R

R R

R R

M_cd

Mueller matrices of six parameters





S₀0  ₁₁  ₁₂, ₂₁  ₂₂, ₃₁  ₃₂, ₄₁  ₄₂





S _{11 13 21 23 31 33 41 43}

450   ,  ,  , 





S₉₀0  ₁₁  ₁₂, ₂₁  ₂₂, ₃₁  ₃₂, ₄₁  ₄₂





S _{11 13 21 23 31 33 41 43}

1350   ,  ,  

 

RHC m m m m m m m m

S  ₁₁  ₁₄, ₂₁  ₂₄, ₃₁  _{34 41}  ₄₄

 

LHC m m m m m m m m

S  ₁₁  ₁₄, ₂₁  ₂₄, ₃₁  _{34 41}  ₄₄

The output Stokes vectors can be obtained as:

0 11 12 13 14 0

1 21 22 23 24 1

2 31 32 33 34 2

3 41 42 43 44

3

ˆ

ˆ ˆ

ˆ ˆ S m m m m S

S m m m m S

S MS

S m m m m S

S m m m m S

        

     

                        

Known Find Known

(

Measurement of LB/CB and LD/CD

Six input vectors

Six output vectors

Find

α, β, γ, θ_d, D, and R Input

Stokes vectors

Output Stokes vectors

Diattenuation axis angle: _^













 ^ 

) ( )

(

) ( )

tan ( 2

90 0 0 0

135 0 45 0

1

0 0

0 0

S S S

S

S S S

S

d

Diattenuation: ^{cos(2 )[}





)]

( )

( [

2 0 0

2 90 0

0 0

90 0 0 0

0 0

0 0

S S S S S

S S S

S S S D S

LHC RHC

d   

 



Circular diattenuation:

  ^{ }

)]

( )

( [

] ) ( )

( )

( )

( [

)]

( )

( [

0 0

2 0 0

2 90 0

0 0 90 0

0⁰ 0 ^{0 0 0}

S S S S

S S S S S

S S S S

S S R S

LHC RHC

LHC RHC











 



 





 ^

34 1 24

2tan 1

A

 A



 



 ^ 

44 1 34

) 2 tan cos(

A A

  Linear birefringence axis angle:

Retardance:

Circular birefringence: _



 









 ^ 

33 1 23 2

33 2 23 1 3

2tan 1

A C A

C

A C A

 C























44 43

42

34 33

32

24 23

22

0 0 0

0 0

0 1 ] ][

[

A A

A

A A

A

A A

M A M_{lb cb}

Measurement of LB/CB and LD/CD

The analytical model enables the full-range measurement of the principal axis angle, optical rotation angle, diattenuation axis angle, diattenuation and circular diattenuation. However, the measurable range of the phase retardance is limited to 0 ~ 180°.

 

0

ˆ 1, 1, 0, 0 S 

 

45

ˆ 1, 0, 1, 0 S 

 

90

ˆ 1, -1, 0, 0 S 

 

135

ˆ 1, 0, -1, 0 S 

 

ˆ_RHC 1, 0, 0, 1

S  S^ˆ_LHC 





The six input polarization states:

• Four linear polarization lights

• Two circular polarization lights right/left handed

Experimental setup for measurement of six parameters

Stokes Polarimeter He-Ne Laser

Q45⁰,-45⁰ Neutral

Density Filter

Power meter detector LP

RHC or LHC

P

LP

0⁰,45⁰, 90⁰,135⁰

CD LD CB LB

Sample

0⁰,30⁰, 60⁰,90⁰, 120⁰,150⁰

Measurement of LB, CB, LD, & CD samples

Experimental results for (a) LB of quarter- wave plate, (b) LD of polarizer (c) CB of half-wave plate, and (d) CD of polarization controller.

 The experimental results show that a good agreement is obtained between the experimental and actual values of the LB, CB, LD and CD sample.

Measurement of baked polarizer

 The experimental results show that a good agreement

is obtained

between the

experimental and actual values of a baked polarizer at 150⁰C for 100 minutes (LB and LD properties) .

(a) (b)

(c) (d)

0 30 60 90 120 150 180

0 30 60 90 120 150 180

Measured principal axis (deg.)

Known diattenuation axis (deg.)

0 30 60 90 120 150 18014

15 16 17 18 19 20

Measured phase retardation (deg.)

S

S

0 30 60 90 120 150 180

0 30 60 90 120 150 180

Measured diattenuation axis (deg.)

Known diattenuation axis (deg.)

0 30 60 90 120 150 1800.7

0.8 0.9 1 1.1 1.2 1.3

Measured diattenuation

_dS DS

0 30 60 90 120 150 180

0 1 2 3 4 5 6

Measured optical rotation angle (deg.)

Known diattenuation axis (deg.)

S

0 30 60 90 120 150 180

0 0.1 0.2 0.3 0.4 0.5 0.6

Measured circular diattenuation

Known diattenuation axis (deg.) RS

Measurement of composite samples

 The experimental results show that a good agreement is obtained between the experimental and actual values of the composite sample comprising quarter-wave plate, half-wave plate and polarizer (LB, CB, and LD properties) .

0 30 60 90 120 150 180

0 30 60 90 120 150 180 210

Measured principal axis(deg.)

Known principal axis(deg.)

0 30 60 90 120 150 18060

70 80 90 100 110 120 130

Measured phase retardation(deg.)

S

_S

0 30 60 90 120 150 180

0 30 60 90 120 150 180 210

Measured diattenuation axis(deg.)

Known diattenuation axis(deg.)

0 30 60 90 120 150 1800.6

0.7 0.8 0.9 1 1.1 1.2 1.3

Measured diattenuation

_dS DS

0 30 60 90 120 150 180

-1.5 -1 -0.5 0 0.5 1 1.5

Measured circular diattenuation (R)

Known principal axis angle(deg.) RS

0 15 30 45 60 75 90

0 30 60 90 120 150 180 210

Measured optical rotation angle ( deg.)

Input optical rotation angle(deg.)

S

Measured effective parameters

Shape No.

#1 #2 #3 #4

Principal axis angle α

(deg.) 126.27⁰ 112.82⁰ 114.81⁰ 122.24⁰

Retardance β (deg.) 19.69⁰ 24.02⁰ 25.67⁰ 132.07⁰

Diattenuation axis angle θ_d

(deg.) 8.25⁰ 55.41⁰ 109.5⁰ 46.03⁰

Diattenuation D 0.06 0.07 0.07 0.1

Optical rotation γ (deg.) -22.71⁰ -22.28⁰ -23.55⁰ -62.04⁰

Measuring effective parameters in a single mode optical fiber

He-Ne Laser

Q45⁰,-45⁰ Neutral

Density Filter

Power meter detector

Fiber-coupler

Stokes Polarimeter

Fiber LP

RHC (for the four-parameter case) RHC and LHC (for the five-parameter case)

P

LP

0⁰,45⁰, 90⁰,135⁰

The schematic diagram used to measure the parameters of a

LB/LD sample using a fiber-type polarimeter.

Experimental results for (a) birefringence of quarter-wave plate and (b) diattenuation of polarizer obtained using the common-path interferometer with a polarization-insensitive fiber probe.

0 30 60 90 120 150 180

0 30 60 90 120 150 180 210

Measured principal axis(deg.)

Known principal axis(deg.)

0 30 60 90 120 150 18060

70 80 90 100 110 120 130

Measured phase retardation(deg.)

_S

_S

0 30 60 90 120 150 180

0 30 60 90 120 150 180 210

Measured diattenuation axis(deg.)

Known diattenuation axis(deg.)

0 30 60 90 120 150 1800.6

0.7 0.8 0.9 1 1.1 1.2 1.3

Measured diattenuation(deg.)

_dS D_S

Measuring effective parameters in a

single mode optical fiber

Nine parameters

R

γ β

θ

D

Extract bio-sample

e

e

e

α

Current work on measurement of nine parameters

• e₁: the degrees of linear depolarization

• e₂: the degrees of linear depolarization

• e₃: the degree of circular depolarization

 High potential for practical applications, especially in noninvasive medical diagnosis.

 The recent studies did not show enough six parameters of characteristics of a bio-sample.

 Most of them did not decouple linear depolarization and circular depolarization in the scattering events.

 The new proposed technique is proposed with all decoupling characteristics in six parameters which other studies do not mention before.

Conclusions

Applications & Development of the study

Some important applications:

(1) LB measurements for LCD’s compensator films…….

(2) LB measurements for photoelasticity, tumors……..

(2) CB measurements for diabetics………

(3) CD measurements for protein structures………..

(4) LD measurements for tumors………..

(5) L-Dep, and C-Dep measurements for tumors……..

(6) L-Dep, and C-Dep measurements for surface measurements………

Universal Measuring System: All parameters are decoupling

(pretreatment in samples is not needed)

1. P. C. Chen, *Y. L. Lo, T. C. Yu, J. F. Lin, and T. T. Yang,

“Measurement of linear birefringence and diattenuation properties of optical samples using polarimeter and Stokes parameters,” Optics Express, Vol. 17, No. 18, 15860-15884, (2009).

2. *Y. L. Lo, T. T. H. Pham, and P. C. Chen, “Characterization on five effective parameters of anisotropic optical material using Stokes

parameters- Demonstration by a fiber-type polarimeter,” Optics Express, Vol. 18, No. 9, 9133-9150, (2010).

3. T. T. H. Pham, *Y. L. Lo, P. C. Chen, “Designing a polarization- insensitive optical fiber probe based on effective parameters,”

IEEE/OSA Journal of Light wave Technology, Vol. 29, 1127-1135, (2011)

4. T. T. H. Pham and *Y. L. Lo, “Extraction of effective parameters of anisotropic optical materials using decoupled analytical method,”

Revising for Optics Express, (2011).

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