Mueller imaging polarimetry for biomedical research Tatiana Novikova 1 , Jean Rehbinder 1 , Stanislas Deby 1 , Angelo Pierangelo 1 , Pierre Validire 2 , Abdelali Benali 2 , Brice Gayet 3 , Benjamin Teig 4 , André Nazac 5 , François Moreau 1 and R. Ossikovski 1 1 LPICM, CNRS, Ecole polytechnique, Université Paris-Saclay, Palaiseau France 2 Département d'Anatomopathologie de l'Institut Mutualiste Montsouris, Paris, France 3 Département médico-chirurgical de pathologie digestive de l’Institut Mutualiste Montsouris, Paris, France 4 Service d’anatomie pathologique, CHU de Bicêtre, Le Kremlin-Bicêtre, France 5 Service de gynécologie et obstétrique, CHU de Bicêtre, Le Kremlin-Bicêtre, France June 1, 2017, Photonics Summer School, Oulu, Finland
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Mueller imaging polarimetry for biomedical research
Tatiana Novikova1, Jean Rehbinder1, Stanislas Deby1, Angelo Pierangelo1, Pierre Validire2, Abdelali Benali2, Brice Gayet3, Benjamin Teig4, André Nazac5, François
Moreau1 and R. Ossikovski1
1 LPICM, CNRS, Ecole polytechnique, Université Paris-Saclay, Palaiseau France
2 Département d'Anatomopathologie de l'Institut Mutualiste Montsouris, Paris, France
3 Département médico-chirurgical de pathologie digestive de l’Institut Mutualiste Montsouris, Paris, France
4 Service d’anatomie pathologique, CHU de Bicêtre, Le Kremlin-Bicêtre, France
5 Service de gynécologie et obstétrique, CHU de Bicêtre, Le Kremlin-Bicêtre, France
June 1, 2017, Photonics Summer School, Oulu, Finland
Outline
• Stokes-Mueller formalism
• Mueller matrix images of colon – Early cancer detection
• Mueller matrix images of uterine cervix – Mueller matrix images of fresh specimens
– Mueller matrix images of fixed specimens
• Conclusions
2
Polarization of light
The light propagation in time and space can be fully described by Maxwell’s equations. This varying spatio-temporal field has vectorial nature.
What kind of temporal evolution of the electric field vector E(r,t) occurs in a given point of space?
1. If the temporal evolution does not change in any fixed point of space => light is said to be polarized. NB: it is not necessarily the same in two different points in space.
2. Otherwise the light is said to be partially polarized or non-polarized
S. Huard, Polarization of Light (Wiley, New York, 1997). 3
4
Polarized monochromatic wave
0
)cos(~
)cos(~
0
),( yy
xx
y
x
kztE
kztE
E
E
tz
E
Linear
Circular
Elliptical
)exp(Re),( krErE tjt
Ellipse of
polarization
Monochromatic plane wave
Jones formalism We define the Jones vector E - field
complex amplitudes as:
y
x
yy
xx
E
E
jE
jE
)exp(~
)exp(~
E
Examples of Jones vectors of polarized light
e > 0 e < 0
Jones matrix J describes the transformation
of the Jones vector by the interaction of
the polarized light with an object
iny
inx
yyyx
xyxx
outy
outx
E
E
JJ
JJ
E
E
5
H V 45° -45° Left C Right C Elliptical
Correlation matrix of 2 complex components of electric field
Stokes formalism y
x
θ
ε
Partially polarized light
• « disordered » motion of the electric field vector
• only probability distribution of E can be defined
Linear optics (intensity measurements)
• only the second moments of the probability distribution of E are relevant
**
**
yyxy
yxxx
EEEE
EEEEC
Stokes vector
**
**
**
**
3
2
1
0
xyyx
xyyx
yyxx
yyxx
RL
4545
yx
yx
EEEEj
EEEE
EEEE
EEEE
II
II
II
II
V
U
Q
I
S
S
S
S
S
6
Degree of polarization
)10(
I
VUQ 222
Coherence vector
Tyyxyyxxx EEEEEEEE ),,,(' ****C
in
in
in
in
out
out
out
out
S
S
S
S
MMMM
MMMM
MMMM
MMMM
S
S
S
S
3
2
1
0
44434241
34333231
24232221
14131211
3
2
1
0
Sin Sout
M
Sout=M·Sin
Linear optical system is characterized by the real
4×4 matrix which is called Mueller matrix
Stokes formalism: Mueller matrix
Mueller matrix M
7
General principle of any polarimetric technique
Source
PSG
Sample
PSA Detector
• In order to determine optical properties of the sample one needs to measure
polarization changes occurring in the probing beam light after interaction with the
sample.
• Initial polarization state of the beam is defined by Polarization State Generator
(PSG). The output state is analyzed by Polarization State Analyzer (PSA)
followed by a detector, according to the general schema outlined above.
• Typically, the incident polarizations defined by the PSG and those detected by
the PSA may vary during a given experiment.
8
Interpretation of Mueller matrices
So what to do when a model is not readily available?
Experimental Mueller matrix
EM model relating the physical properties of measured structure to M
Classic physical approach
Phenomenological approach
Experimental Mueller matrix
M1 M2
M3
Lu-Chipman product decomposition represent any depolarizing M as a series combination of three basic blocks: diattenuator, retarder and depolarizer
• Intensity and polarimetric images of a healthy cervix (the positions of histological cuts, which confirmed that the sample was healthy, are shown with white lines)
Depolarization @550nm
Intensity image
Scalar birefringence @550nm
Ex vivo images of fresh cervical specimen
A. Pierangelo et al., Opt. Express 19 (2), (2011) 17
18
Typical experimental trends
• Healthy cervical tissue exhibits a significant birefringence