Mueller imaging polarimetry for biomedical research
Tatiana Novikova1, Jean Rehbinder1, Stanislas Deby1, Angelo Pierangelo1, Pierre Validire2, Abdelali Benali2, Brice Gayet3, Benjamin Teig4, Andr Nazac5, Franois
Moreau1 and R. Ossikovski1
1 LPICM, CNRS, Ecole polytechnique, Universit Paris-Saclay, Palaiseau France
2 Dpartement d'Anatomopathologie de l'Institut Mutualiste Montsouris, Paris, France
3 Dpartement mdico-chirurgical de pathologie digestive de lInstitut Mutualiste Montsouris, Paris, France
4 Service danatomie pathologique, CHU de Bictre, Le Kremlin-Bictre, France
5 Service de gyncologie et obsttrique, CHU de Bictre, Le Kremlin-Bictre, 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 Maxwells 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
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 SoutM
Sout=MSin
Linear optical system is characterized by the real
44 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
M = M MR MD 9
..
S. Y. Lu R. Chipman, JOSA A 13(5) 1106 (1996)
https://www.osapublishing.org/josaa/issue.cfm?volume=13&issue=5
Mueller matrix imaging polarimeter
Multi-spectral visible wavelength Mueller matrix imaging system installed and tested at IMM Anatomopathology Department, Paris, France
10
Cancer evolution
11
Source: http://www.ndhealthfacts.org/wiki/Oncology_%28Cancer%29
Epithelial cancer > 80%
Epithelial tissues line the cavities and surfaces of organs throughout the body
Epithelial layers contain no blood vessels, so they receive nourishment via
diffusion of substances from the underlying connective tissue
11
Colon specimens: early stage cancer
Colon
Cancer
Healthy
tissue
Mueller matrix images taken at 550 nm
Common features
Mueller matrices are diagonal :
tissues exhibit depolarization, wihout
signifiant retardation nor diattenuation
M22=M33>M44, meaning that circularly
polarized light is more depolarized
than linearly polarized light. This
behaviour is typical of small
scatterers (Rayleigh regime)
Depolarization increases with
wavelength in the visible, probably
due to decrease of absorption
Tumoral tissue is less depolarizing
than healthy tissue, at all wavelenghts
from 500 to 700 nm. T. Novikova et al., OPN, OSA, October 2012
12
5 c
m
htt
p:/
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/in
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Normal CIN I CIN II CIN III
Larger
and
more dense
nuclei!!
Histological
slides
of cervical
tissue
Cervical
Intraepithelial
Neoplasia
Diagnosis of cervical cancer
300 m
Cervical cancer is the second most frequent cancer affecting women, and causes 275 000 deaths per year worldwide mostly in developing countries
.
In the vast majority (95 to 98%) of cases the disease is due to infection by various types of Human Papillomavirus (HPV)
13
(Medical diagnostic procedure
to examine an illuminated,
magnified view of the cervix)
(Cytology) (Histology)
Diagnosis of cervical cancer
Colposcopy: Precancerous (CIN2+) lesions are very difficult to visualize. Results are very operator dependent.
Conization : the surgical margins are poorly defined
Screening : Systematic Pap smear cannot be implemented in low income countries.
14
15
Polaimetric images of cervical specimens 2 c
m
Intensity image
A. Pierangelo et al., Opt. Express 21 (12), 14120 (2013)
Mueller matrix images of uterine cervix
Pathology map
16
Lu Chipman product decomposition M = M MR MD
Ex vivo images of uterine cervix specimen
A. Pierangelo et al., Opt. Express 21 (12), 14120 (2013)
Depolarization @500nm Pathology map Scalar retardance @500nm
Healthy
CIN3
Healthy
CIN3
Healthy
CIN3
50
0
1
0
(a) (b) (c)
2 c
m
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
Birefringence disappears already at stage CIN1
Depolarization values: glandular < CIN3 < CIN2 < CIN1 <
healthy squamous epithelium
Ex-vivo s
