Use of polarized light imaging and sensing in the clinical setting
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Transcript of 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
II Escuela de Optica Biomedica, Puebla, 2011
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
II Escuela de Optica Biomedica, Puebla, 2011
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
II Escuela de Optica Biomedica, Puebla, 2011
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
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64Polarized light in bio-photonics
•Filtering mechanism•Skin cancer imaging• Imaging of
superficial features•Vasculature•others
*JBO 2002
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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
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64
53% absorbed
~4% parallel surface glare
~2-4% parallel, sub surface
100% parallel incidence
unpolarized40%
Epidermis
papillary dermis
reticular dermis
Filtering mechanism-surface glare 64
x
y
II Escuela de Optica Biomedica, Puebla, 2011
64
53% absorbed
~4% parallel surface glare
~2-4% parallel, sub surface
100% parallel incidence
unpolarized40%
Epidermis
papillary dermis
reticular dermis
Filtering mechanism-single scatteringCopolarized
64
x
y
II Escuela de Optica Biomedica, Puebla, 2011
64
53% absorbed
~4% parallel surface glare
~2-4% parallel, sub surface
100% parallel incidence
unpolarized40%
Epidermis
papillary dermis
reticular dermis
Filtering mechanism-multiple scattering
Crosspolarized
64
x
y
II Escuela de Optica Biomedica, Puebla, 2011
64Polarized light imaging of skin cancer
H
H & V
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par per
par per
-
+Polarized image =
Par = Superficial + DeepPer = Deep
Enhance superficial structures such asskin cancer margins
II Escuela de Optica Biomedica, Puebla, 2011
64Polarized imaging: Basal-Cell Carcinoma
Unpolarized Polarized
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compound nevus
1-cm ruler
normal pol
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frecklenormal pol
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tattoo
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Imaging of superficial features
•Polarization signature of roughness •Cosmetic industry and
rendering community •Skin cancer
Fresnel Reflection
γαα
θi
θs
AirSkin top surface
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Vasculature enhancement
53% absorbed
~4% parallel surface glare
~2-4% parallel sub surface
100% parallel incidence
unpolarized40%
capillary
transillumination
II Escuela de Optica Biomedica, Puebla, 2011
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 • (….)
II Escuela de Optica Biomedica, Puebla, 2011
Polarization fundamentals
II Escuela de Optica Biomedica, Puebla, 2011
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
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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
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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
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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
II Escuela de Optica Biomedica, Puebla, 2011
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
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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
⎡
⎣
⎢ ⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥ ⎥
II Escuela de Optica Biomedica, Puebla, 2011
Stokes vector formalism
• 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
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
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Stokes vector formalism
• 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
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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
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Linearly polarized light
€
J 1 0
⎡ ⎣ ⎢
⎤ ⎦ ⎥
S
1 1 0 0
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
= E0x
= E0y
II Escuela de Optica Biomedica, Puebla, 2011
Linearly polarized light
€
J 0 1
⎡ ⎣ ⎢
⎤ ⎦ ⎥
S
1 −1 0 0
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
= E0x
= E0y
II Escuela de Optica Biomedica, Puebla, 2011
Linearly polarized light
€
J 1 1
⎡ ⎣ ⎢
⎤ ⎦ ⎥1
2
S
1 0 1 0
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
II Escuela de Optica Biomedica, Puebla, 2011
Linearly polarized light
€
J 1 −1
⎡ ⎣ ⎢
⎤ ⎦ ⎥1
2
S
1 0 −1 0
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
= -E0x
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Circularly polarized light
€
J 1 i
⎡ ⎣ ⎢
⎤ ⎦ ⎥1
2
S
1 0 0 1
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
II Escuela de Optica Biomedica, Puebla, 2011
Circularly polarized light
€
J 1 −i
⎡ ⎣ ⎢
⎤ ⎦ ⎥1
2
S
1 0 0 −1
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
II Escuela de Optica Biomedica, Puebla, 2011
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
⎡
⎣
⎢ ⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥ ⎥
II Escuela de Optica Biomedica, Puebla, 2011
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
II Escuela de Optica Biomedica, Puebla, 2011
Mueller matrix cnt.
€
So[ ] = Mi[ ] Mi−1[ ] ⋅⋅⋅⋅⋅M2[ ] M1[ ] Si[ ]
i, inputo, output
Multiple Mueller Matrices Mi
II Escuela de Optica Biomedica, Puebla, 2011
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
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Mueller Matrix from microspheres solutions
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*Cameron et al. JBO 2001
D= 2µm
m11
m44
II Escuela de Optica Biomedica, Puebla, 2011
Stokes polarimetry, metrics of interest
II Escuela de Optica Biomedica, Puebla, 2011
Net degree of polarization
€
DOP=Q2 +U 2 +V 2
I
€
0≤DOP≤1
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Unpolarized portion of the beam
€
1−Q2 +U 2 +V 2
I
€
0≤UNP≤1
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Degree of linear polarization
€
DOLP=Q2 +U 2
I
€
0≤DOLP≤1
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Degree of circular polarization
€
DOCP=VI
€
0≤DOCP≤1
II Escuela de Optica Biomedica, Puebla, 2011
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
II Escuela de Optica Biomedica, Puebla, 2011
Tomorrow
• Experimental application of polarimetry
• Introduction to a typical Stokes vector polarimeter
• Introduction to a typical Mueller Matrix polarimeter