Table Of ContentJessica C. Ramella-Roman
Tatiana Novikova Editors
Polarized Light in
Biomedical Imaging
and Sensing
Clinical and Preclinical Applications
Polarized Light in Biomedical Imaging and Sensing
Jessica C. Ramella-Roman • Tatiana Novikova
Editors
Polarized Light in
Biomedical Imaging and
Sensing
Clinical and Preclinical Applications
Editors
JessicaC.Ramella-Roman TatianaNovikova
DepartmentofBiomedicalEngineering LPICM,CNRS
HerbertWertheimCollegeofMedicine, ÉcolePolytechnique,IPParis
FloridaInternationalUniversity Palaiseau,France
Miami,FL,USA
ISBN978-3-031-04740-4 ISBN978-3-031-04741-1 (eBook)
https://doi.org/10.1007/978-3-031-04741-1
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Contents
PolarizedLight................................................................... 1
TatianaNovikovaandJessicaC.Ramella-Roman
Mueller Matrix Analysis, Decompositions, and Novel
QuantitativeApproachestoProcessingComplexPolarimetricData ...... 25
OriolArteagaandRazvigorOssikovski
Mueller Matrix Polarimetry in Biomedicine: Enabling
Technology,BiomedicalApplications,andFutureProspects ............... 61
MichaelD.Singh,NirmalyaGhosh,andI.AlexVitkin
Polarization-SensitiveMonteCarlo............................................ 105
TatianaNovikovaandJessicaC.Ramella-Roman
PolarizedLightImagingoftheSub-diffuseRegimeofTissues............. 133
StevenL.Jacques
Mueller Polarimetric Imaging for Cervical Intraepithelial
NeoplasiaDetection.............................................................. 149
AngeloPierangelo,TatianaNovikova,JeanRehbinder,AndréNazac,
andJérémyVizet
PolarimetricEndoscopy......................................................... 179
JiQiandDanielS.Elson
MuellerPolarimetryofBrainTissues ......................................... 205
TatianaNovikova,AngeloPierangelo,PhilippeSchucht,IgorMeglinski,
OmarRodríguez-Núñez,andHeeRyungLee
ClinicalApplicationsofPolarization-SensitiveOpticalCoherence
Tomography ...................................................................... 231
MartinVilligerandBrettE.Bouma
v
vi Contents
Tractography Using Polarization-Sensitive Optical
CoherenceTomography......................................................... 263
GangYao
MuellerMatrixMicroscopy..................................................... 281
HuiMa,HonghuiHe,andJessicaC.Ramella-Roman
ConfocalLaserScanningPolarimetry......................................... 321
MariacarlaGonzalez,V. N.DuLe,andJessicaC.Ramella-Roman
Improvement of Resolution and Polarisation Measurement
PrecisioninBiomedicalImagingThroughAdaptiveOptics ................ 345
ChaoHeandMartinJ.Booth
Index............................................................................... 361
Polarized Light
TatianaNovikovaandJessicaC.Ramella-Roman
1 Introduction
Humanvisionisnotsensitivetothepolarizationofthelight.Wedetecttheintensity
of the visible light and its wavelengths (as a color), but the vector nature of the
light—polarization—escapeshumaneyes,contrarytosomeanimalsandinsects[1].
When polarized probing light interacts with a sample, the polarization of
reflected,transmitted,andscatteredlightwillchange,andanysample’spolarimetric
properties can be investigated through specialized instrumentation. The polarized
lightmicroscope,introducedintheearly1800[2],isanexampleofpolarizedlight
applicationtowardtheinvestigationofmaterialproperties.
Recently, new focus has been given to polarized light imaging and sensing
for biomedical applications, with studies that go beyond microscopy and include
measurements in bulk tissue; this is the focus of our book. Although early work
introduced the use of polarized light in imaging of cells, bacteria, and other small
biologicalparticles,[3–5]Andersonin1991[6]wasthefirsttofocusonbulktissue
reporting on the use of polarized sunglasses and cross-polarization imaging for
dermatological applications, particularly for enhancement of vascular contrast in
thestudyofrosaceaandtominimizesurfaceglare.Jacquesetal.[7]continuedthis
effortdevelopingaclinic-readytoolandfocusingonskincancerimagingenhancing
T.Novikova
LPICM,CNRS,ÉcolePolytechnique,IPParis,Palaiseau,France
FloridaInternationalUniversity,BiomedicalEngineeringDepartment,Miami,USA
J.C.Ramella-Roman((cid:2))
FloridaInternationalUniversity,BiomedicalEngineeringDepartment,Miami,FL,USA
FloridaInternationalUniversity,HerbertWertheimCollegeofMedicineCellularBiologyand
Pharmacology,DepartmentofOphthalmology,Miami,FL,USA
e-mail:Jramella@fiu.edu
©SpringerNatureSwitzerlandAG2023 1
J.C.Ramella-Roman,T.Novikova(eds.),PolarizedLightinBiomedicalImaging
andSensing,https://doi.org/10.1007/978-3-031-04741-1_1
2 T.NovikovaandJ.C.Ramella-Roman
thebordersofthelesionthatwerenotvisibletothenakedeye,sodidMorganetal.
[8,9]investigatingcircularpolarizationratherthanlinearstates.
Demos et al. [10, 11] investigated the spectral dependence of polarized light
penetration in biological media; spectral polarization difference imaging was
utilized todemonstrate subsurface imaging atdifferent depths. Intravital polarized
microscopyformeasurementofperfusionwasstudiedbyGroneretal.[12–17].
The expansion of research in the use of polarized light for biomedical applica-
tionsinthelast30yearshasbeentremendousandhasbeenpropelledbyadvances
inbothinstrumentationandmethodologies.Severalarticleshaverecentlyreviewed
the state of the field [18–22]. Here we hope to expand on this work by covering
in-depthsomeofthemostinterestingapplicationsofpolarizedlights.
In this chapter, we briefly review the theoretical descriptions of the light
polarizationproperties,namely,theJonesformalismfortotallypolarizedlightand
theStokes–Mueller formalism,which ismoregeneral and canadequately account
foranypolarizationstate.
1.1 JonesFormalism
Theelectromagneticfieldpropagatingasawaveindifferentmediaisaspatiotempo-
ralfieldwhichisvectorialbyitsnature,couplingthevectorofelectricfieldstrength
E(r, t) and the vector of magnetic field strength H(r, t). r is the vector of spatial
position,andtisthetime.Sometimesonecanignorethevectornatureofthelight
and treat it within the frame of scalar theory, like it is done in the geometrical ray
opticstheory.
Nevertheless, the study of polarization of light requires the full vector descrip-
tion.Ifthetemporalevolutionofavectorofelectromagneticfieldatthegivenpoint
of a space is identical for all the space points, we call this electromagnetic field
polarized.Otherwise,wedealwithapartiallyorevencompletelydepolarizedstate
ofanelectromagneticfield.
The light propagation in time and space can be fully described by Maxwell’s
equations[23]:
∂B(r,t)
∇·D(r,t)=ρ, ∇×E(r,t)=− (1)
∂t
∂D(r,t)
∇·B(r,t)=0, ∇×H(r,t)=J+ (2)
∂t
D=εE, B=μH, J=σ E (3)
PolarizedLight 3
wheret-time,D-dielectricdisplacementvector,ρ-chargedensity,E-vectorofelec-
tric field strength, B-magnetic induction or magnetic flux density vector, H-vector
of magnetic field strength, J-current density, ε-dielectric constant (or dielectric
permittivity) of the medium, μ-magnetic permeability of the medium (in the most
generalcase,εandμarethetensors),σ-electricalconductivityofthemedium.
The values of ε and μ are constant in a homogeneous medium. Moreover, for
a homogeneous linear optical material without any charge and current densities,
ρ =0;J=0;σ =0.Equations(1),(2),and(3)canbewrittenas
∂B(r,t)
∇·D(r,t)=0, ∇×E(r,t)=− (4)
∂t
∂D(r,t)
∇·B(r,t)=0, ∇×H(r,t)= (5)
∂t
D=εE, B=μH (6)
Maxwell’s equations can be further simplified and formulated for electric and
magneticfieldsseparatelybytakingthecurl(∇×)of(4)and(5).Theelectricand
magneticfieldsthenobeythewell-knownwaveequations:
∂2E(r,t)
∇2E(r,t)−με =0 (7)
∂t2
∂2H(r,t)
∇2H(r,t)−με =0 (8)
∂t2
Solving the problem for a propagation of the electric wave E, one can further
findthesolutionforthemagneticwaveH,andfinallyobtainthecompletesolution
ofMaxwell’sequations.
Itwasshownthatanyelectromagneticfieldmaybedecomposedintoaninfinite
number of monochromatic waves with angular frequency ω, any of which in turn
i
canbedecomposedintoaninfinitenumberofplanewaveswiththewavevectork
j
[24].Fourierintegraltheorydescribesthisbythefollowingequation:
(cid:2) (cid:2)
D(r,t)= dω D(k,ω)exp[j(ωt −kr)] dk (9)
ω k
Hence, for the studies of light polarization properties, we can consider an
elementarycomponentofthisdecomposition,namely,aplanemonochromaticwave
characterized by itsangular frequency ω and wavevector k. Iftheelectromagnetic
fieldsassociatedwiththeelementarycomponentshavethesamevectorialbehavior,
theproblemcanbeeasilysolved.
4 T.NovikovaandJ.C.Ramella-Roman
When a plane homogeneous optical wave travels through an infinite isotropic
medium,theelectricfieldEisconfinedtooscillateintheplaneofthewave,which
isorthogonaltothewavevectork.Withoutthelossofgenerality,wecandefinethe
Ozaxisasthedirectionofwavepropagation(k=kz,z-unitvectorsalongOzaxis).
TheoscillationofelectricfieldEintheplaneorthogonaltoOzaxisandintersecting
Oz axis at point (0, 0, z) is the superposition of two independent simple harmonic
oscillationsE ’andE ’[25].
x y
(cid:3) (cid:6) (cid:3) (cid:6)
E(z,t)= EE˜˜xccooss(cid:4)(ωωtt −−kkzz++δδx)(cid:5) = EEx(cid:3)(cid:3) (10)
y y y
˜
where E and δ are the amplitude and the phase of the oscillation along the i-
i i
axis, respectively, ω–angular frequency of temporal harmonic oscillations of the
components of monochromatic field. Using a complex number representation, a
monochromatic wave propagating through an infinite isotropic medium can be
writteninaform:
E(z,t)=Re{E(z)exp(jωt)} (11)
where
(cid:3) (cid:6)
˜
E(z)=exp(−jkz) E˜xexp(cid:4)(jδx)(cid:5) (12)
E exp jδ
y y
Toexcludethespatialdependenceonz,wedefinethevectorE(0)as
(cid:3) (cid:6) (cid:3) (cid:6)
˜
E(0)= E˜xexp(cid:4)(jδx)(cid:5) = Ex (13)
E exp jδ E
y y y
It follows from (11), (12), and (13) that if we know the oscillations of electric
field at time t = 0 and plane z = 0, we can reconstruct the electromagnetic field
at any time and any point of the space just by multiplying E(0) by the factor
exp(−j(kz−ωt))andtakingtherealpartoftheresultingexpression.
E(z,t)=Re{E(0)exp(−j(kz−ωt))} (14)
The vector E(0) (see Eq. 13) is called the Jones vector. It provides a compact
descriptionofahomogeneousmonochromaticharmonicwave.Itisworthmention-
ingthattheelementsE andE ofJonesvectorarecomplexnumbers;hence,Jones
x y
vectorisnotavectorinarealspace.
