Use of polarized light imaging and sensing in the clinical setting

II Escuela de Optica Biomedica, Puebla, 2011

Use of polarized light imaging and sensing in the clinical setting

Jessica C. Ramella-Roman, PhD


Short Bio

• Laura in Electrical Engineering, University of Pavia, Italy (93)

• MS and PhD in Electrical Engineering from Oregon Health & Science University (04)– Advisor Steve Jacques– Thesis on use of polarized light inbiophotonics

• Post doc at Johns Hopkins, APL (04,05)– Polarized light interaction with rough surfaces


Short Bio cnt.

• Associate Professor in Biomedical Engineering (05-present) at CUA

• Adjunct A. Prof. Johns Hopkins School of Medicine (06-present)

• Guest Researcher NIST (04- present)• Research – faculty.cua.edu/ramella– Tissue oximetry, retina, skin using reflectance

spectroscopy and MI– Small vessel Flowmetry and structural analysis– Polarized light imaging and sensing for the detection of

skin cancer, vascular abnormalities


Course outline

• Lecture 1- Introduction and fundamentals of polarimetry

• Lecture 2- Experimental Stokes and Mueller matrix polarimetry

• Lecture 3 – Modeling – Monte Carlo 1• Lecture 4 – Modeling – Monte Carlo 2• Lecture 5 – Clinical applications of polarized

light sensing


64Polarized light in bio-photonics

•Filtering mechanism•Skin cancer imaging• Imaging of

superficial features•Vasculature•others

*JBO 2002


53% absorbed

~4% parallel surface glare

~2-4% parallel, sub surface

100% parallel incidence

unpolarized40%

Epidermis

papillary dermis

reticular dermis

Filtering mechanism 64

x

y


64

53% absorbed




unpolarized40%

Epidermis

papillary dermis

reticular dermis

Filtering mechanism-surface glare 64

x

y


64

53% absorbed




unpolarized40%

Epidermis

papillary dermis

reticular dermis

Filtering mechanism-single scatteringCopolarized

64

x

y


64

53% absorbed




unpolarized40%

Epidermis

papillary dermis

reticular dermis

Filtering mechanism-multiple scattering

Crosspolarized

64

x

y


64Polarized light imaging of skin cancer

H

H & V


par per

par per

-

+Polarized image =

Par = Superficial + DeepPer = Deep

Enhance superficial structures such asskin cancer margins


64Polarized imaging: Basal-Cell Carcinoma

Unpolarized Polarized


compound nevus

1-cm ruler

normal pol


frecklenormal pol


tattoo


Imaging of superficial features

•Polarization signature of roughness •Cosmetic industry and

rendering community •Skin cancer

Fresnel Reflection

γαα

θi

θs

AirSkin top surface


Vasculature enhancement

53% absorbed


~2-4% parallel sub surface


unpolarized40%

capillary

transillumination


Other techniques that use polarization

• Mueller matrix imaging - colon cancer– De Martino et al. Opt. Exp. 2011

• Polarized light scattering spectroscopy – eliminate multiple scattering with co/cross polarized layout– V. Backman et al. Nature 2001

• PS OCT – birefringence / structural components– De Boer, Opt. Exp. 2005

• Particle sizing • (….)


Polarization fundamentals


Polarization basics

• Polarization is a property that arises out of the transverse (and vector) nature of the electromagnetic (EM) radiation

• It describes the shape and the orientation of the locus of the electric field vector (Ε) extremity as a function of time, at a given point of the space*.

*Ghosh et al. JBO 2011


Electric Field vector (EM)

€

Ex z,t( )=Eox cosωt−kz+δx( )

Ey z,t( )=Eoycosωt−kz+δ y( )

Eox

Eoy

X

Y

Z

Eδx, δy =phasesω =light frequencyk = 2p/lEox,Eoy, =magnitude of electric fieldl =wavelength of light in free space


Polarization Ellipse

2E0y

h x

y

2E0y

€

Ex z,t( )2

E0x2

+Ey z,t( )

2

E0y2

−2Ex z,t( )Ey z,t( )

E0xE0ycosδ =sin2δ


Jones vector formalism

€

E =Ex

Ey=Eoxe

iδ x

Eoyeiδ y

Advantages:- Measurement of coherence and time dependent phenomena- Speckle based techniques

Disadvantage-Cannot handle depolarization

δx, δy = phasesEox,Eoy, = magnitude of electric field


Jones matrix

• Polarized transfer of light – interaction with a medium

• J is a 2x2 complex matrix

€

′ E =JE′ E x′ E y=J11 J12J21 J22

Ex

Ey


Stokes vector formalism

• Intensity based representation• Characterize the polarization state of light• E0x, E0y, Cartesian electric field component• δ=δx-δy phase difference

€

S=

IQUV

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥=

ExEx* +EyEy

*

ExEx* −EyEy

*

ExEy* +EyEx

*

i ExEy* −EyEx

*( )

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥=

E0x2 +E0 y

2

E0x2 −E0 y

2

2E0xE0 ycosδ2E0xE0 ysinδ

⎡

⎣

⎢ ⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥ ⎥



• Four measurable quantities (intensities)• Characterize the polarization state of light• G.G. Stokes (1852)

Advantages:- Handles depolarization- Easy experimental application

Disadvantage- Cannot handle coherence

€

S=

IQUV

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥=

IH + IVIH −IVI 45 −I−45I R −IL

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥



• Four measurable quantities (intensities)• Characterize the polarization state of light• G.G. Stokes (1852)

• Restriction on the Stokes parameters

€

I ≥ Q2 +U 2 +V 2


Poincaré sphere

• A geometrical representation of Stokes vectors

• Sphere with unit radius• Linearly polarized states

are on the equator• Circularly polarized

states are at the poles• Partially polarized states

are inside the sphere


Linearly polarized light

€

J 1 0

⎡ ⎣ ⎢

⎤ ⎦ ⎥

S

1 1 0 0

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

= E0x

= E0y



€

J 0 1

⎡ ⎣ ⎢

⎤ ⎦ ⎥

S

1 −1 0 0

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

= E0x

= E0y



€

J 1 1

⎡ ⎣ ⎢

⎤ ⎦ ⎥1

2

S

1 0 1 0

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥



€

J 1 −1

⎡ ⎣ ⎢

⎤ ⎦ ⎥1

2

S

1 0 −1 0

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

= -E0x


Circularly polarized light

€

J 1 i

⎡ ⎣ ⎢

⎤ ⎦ ⎥1

2

S

1 0 0 1

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥


Circularly polarized light

€

J 1 −i

⎡ ⎣ ⎢

⎤ ⎦ ⎥1

2

S

1 0 0 −1

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥


Unpolarized light

• Unpolarized light cannot be described through a Jones vector

• Stokes vector and Mueller matrix formalism is mostly used in biophotonics

€

S

1 0 0 0

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥


Mueller matrix

€

I oQo

U o

V o

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥=

m11 m12 m13 m14

m 21 m22 m 23 m24

m 31 m32 m 32 m34

m 41 m 42 m 43 m 44

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

I iQi

U i

V i

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

€

So[ ] = M[ ] Si[ ]

i, inputo, output


Mueller matrix cnt.

€

So[ ] = Mi[ ] Mi−1[ ] ⋅⋅⋅⋅⋅M2[ ] M1[ ] Si[ ]

i, inputo, output

Multiple Mueller Matrices Mi


Scattering matrix

• Mie theory• Spheres, spheroids,cylinders

D=0.01µm

€

I oQo

U o

V o

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥=

s11 s12 0 0s12 s11 0 00 0 s33 s430 0 s−43 s33

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

I iQi

U i

V i

⎡

⎣

⎢ ⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥ ⎥

Scattering must be in reference plane If not Stokes vector must be rotatedonto that plane


Mueller Matrix from microspheres solutions

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

50 100150200

50100150200

*Cameron et al. JBO 2001

D= 2µm

m11

m44


Stokes polarimetry, metrics of interest


Net degree of polarization

€

DOP=Q2 +U 2 +V 2

I

€

0≤DOP≤1


Unpolarized portion of the beam

€

1−Q2 +U 2 +V 2

I

€

0≤UNP≤1


Degree of linear polarization

€

DOLP=Q2 +U 2

I

€

0≤DOLP≤1


Degree of circular polarization

€

DOCP=VI

€

0≤DOCP≤1


Principal angle of polarization

€

h=0.5αtαn S2S1

⎛ ⎝ ⎜

⎞ ⎠ ⎟

2E0y

h x

y

2E0y

Polarization Ellipse

€

Ex z,t( )2

E0x2

+Ey z,t( )

2

E0y2

−2Ex z,t( )Ey z,t( )

E0xE0ycosδ =sin2 δ


Tomorrow

• Experimental application of polarimetry

• Introduction to a typical Stokes vector polarimeter

• Introduction to a typical Mueller Matrix polarimeter

Documents

Use of polarized light imaging and sensing in the clinical setting