OCT Monte Carlo & Deep Learning

OCT
Monte Carlo
For synthesizing new
OCT volumes for
ophthalmologic
deep learning
Petteri Teikari, PhD
Singapore Eye Research Institute (SERI)
Visual Neurosciences group
http://petteri-teikari.com/
Version “Thu 11 October 2018“

Binary foreground Synthesizebackgroundaroundit
http://doi.org/10.1167/iovs.15-17210
Givenabinary groundtruth,
synthesizebackground
(“physicaldataaugmentation”)
Blur+Noise
Noise
Baseline
quality
CreateOCT
volumevia
MonteCarlo
model

Thebettermodel themorerealisticsamples
Create imaging artifacts Leahy et al.(2015)
(De)blurwith synthetic AO SinaFarsiu
Cross-modality
transfer Kaizuet al. (2017)
Pathology-specifc
OCTmodelling Apostolopoulo et al. (2017)
Rathkeetal. (2017)
Voxeleron RPEBaseline
Polarization
properties of retina
Schütze et al. (2015)

CombineGenerativeAdversarialNetworks(GANs)
with Physics-basedmodeling
Physics-baseddataaugmentationforhigh
frequency3Dradarsystems
MilesCrosskey;PatrickWang;Rayn Sakaguchi;Kenneth D.
Mortonhttps://doi.org/10.1117/12.2304018
“...For other types of sensors, such as radar, the physics
governing the sensing phenomenology must be
understood and leveraged to expand the existing training data.
Our previous work has developed and leveraged physically
motivated augmentation techniques for ground
penetrating radar data to improve detection of explosive threats [
Goodfellow etal. 2014].”
Shrivastavaetal. (2016):
Learning from Simulated and Unsupervised
Images through Adversarial Training
https://github.com/wayaai/SimGAN
We use a simple 3D model of the binary marker to generate an idealistic image of the
marker. The generator network then learns to add the missing image detail such as
lighting, background,andimagenoisesothat theresultingimageslookstrikinglyreal.
Sixtetal.(2018):
RenderGAN: Generating Realistic Labeled Data

Cross-modelstyletransfer OCTtoPAT,etc.
GeneratingsyntheticCTsfrommagnetic
resonanceimagesusinggenerative
adversarialnetworks
Hajar Emami MingDong SiamakP. Nejad Davarani CarriK.‐Davarani Carri K.
Glide Hurst. Medical Physics(14June 2018)‐Davarani Carri K.
https://doi.org/10.1002/mp.13047
“We developed and validated a GAN model using a single T1‐Davarani Carri K.
weighted MR image as the input that generates robust, high
quality synthetic CTs (synCTs) in seconds. Our method
offers strong potential for supporting near real time MR only‐Davarani Carri K. ‐Davarani Carri K.
treatmentplanningin the brain.”

Multimodalmodel improvelowqualitywithhigherqualitymodality
Amultimodalimagingplatformwith
integratedsimultaneousphotoacoustic
microscopy,opticalcoherencetomography,
opticalDopplertomographyand
fluorescencemicroscopy
Arash Dadkhah;Jun Zhou;Nusrat Yeasmin;ShuliangJiao
PhotonsPlusUltrasound:Imagingand Sensing2018
https://doi.org/10.1117/12.2289211
“Integrating all the aforementioned imaging
modalities for simultaneous multimodal imaging has
promising potential for preclinical research and
clinicalpracticeinthenear future.”
For example use differentvasculatureimagingmodalities
●
4channelsfrom multiphotonmicroscopy with4different
dye for vasculature {Green fluorescein [FITC], quantum dot [QTracker], Alexa
Fluor633,andthirdharmonicgeneration[THG] label-freevasculatureimaging}
●
4 clinical modalities {OCT-A, photoacoustic, doppler OCT and confocal in
microscopy}
Simultaneously acquired PAM, FLM and OCT images of a human eye ex vivo. (a) PA
image (average contrast-to-noise ratio 31 dB); (b) FLM image (average contrast-to-
noise ratio 30 dB); (c) OCT B-scan at the location marked in panel (a) by the solid line
(displayeddynamicrange,45dB);LF:Lipofuscin;SL:Sclera;bar,200μm.m.
SimultaneouslyacquiredPAM,FLM,OCTandODTimagesofamouseear.
(a)PAimage(averagecontrast-to-noiseratio34 dB); (b)OCT B-scanatthe
locationmarkedinpanel(e)bythesolidline(displayeddynamicrange,40
dB); (c)ODTB-scanatthelocationmarkedinpanel(e)bythesolidline;(d)
FLMimage(averagecontrast-to-noiseratio14 dB);(e)OCT2Dprojection
imagesgeneratedfromtheacquired3DOCTdatasets;SG:Sebaceous
glands;bar,100μm.m.

MonteCarloOCT
”GoldStandardformodelling”comeswithlimitationsthough

MonteCarloIntrofor Light Propagationmodelling
AdvancesinMonteCarlo Simulation
for LightPropagation in Tissue
VijithaPeriyasamy; Manojit Pramanik
IEEE Reviewsin Biomedical Engineering( Volume:10 )
https://doi.org/10.1109/RBME.2017.2739801
Thefuturedirectionof MCsimulationsistoimprovethesimulationspeed,use
moreanatomicallyrealisticsimulationgeometry,andtodevelopamoreuser-
friendly simulationtoolbox[Lou etal.2017].
For better performance, individual photons were
tracked in parallel. With use of field-programmable
gate arrays (FPGA) and GPU, 21x and 64x speed
enhancement was reported for platforms such as
core i7, GTS 450, and stratix V, which is shown in
TableIforconventionalmultilayermodel

MonteCarlo vsWaveoptics
PawełOssowskietal.(2018):
Existing models tend to fall into one of two
categories[Munro 2016, Munro et al.2015]
:
Wave optics and Monte Carlo-based. Up until
now, wave optics models have not been full wave
and have thus been unable to treat phenomena like
multiple scattering, the change in coherence of light
due to propagation in tissue and the explicit
interference of sample and reference light for
deterministicsamples.
Monte-Carlo models are also not applicable to
deterministic refractive index distributions and
do not naturally include phenomena such as
polarisation,coherenceandinterference.
We have developed our full wave model to
address questions which these existing models
areunabletoanswer.
Munro(2016):
There are several models of OCT image
formation (for example [11–16]) based upon the
Monte Carlo method for modelling light
propagation in biological tissue [17]. These
models have revealed much about OCT image
formation and Monte Carlo modelling is considered
to be the gold standard technique in some
branchesofbiomedicaloptics.
Despite this, Monte Carlo based models possess
some limitations when used to model image
formation in OCT. Monte Carlo methods represent
tissuebyitsspatiallyresolved,statisticallyaveraged,
properties, which are assumed to “extend uniformly
oversmallunitsoftissuevolume”[17].
Furthermore, although some effort has been made
along these lines, wave properties such as
polarisation, coherence and interference are not
naturally treated using the particle formalism
intrinsictotheMonteCarlomethod.
Munroetal.(2015)
A range of phenomena arising from OCT imaging can
now be examined. For example, in the future, we plan to
consider applications such as displacement
measurement using phase sensitive detection [11],
parametricimaging [46],the use of non-Gaussian
beams, such as Bessel beams [47, 48], and to test
hypotheses regarding unresolved features
observed in a variety of medical and biomedical OCT
images[15].
The capability of modern desktop (and superior)
computers, along with the emergence of open
source finite-difference time-domain (FDTD)
implementations [44, 45] mean that this kind of
simulation will eventually be accessible to non-
specialists. Access to institutional computer clusters
willenablevolumescanstobeevaluatedinontheorder
of a day, which is a time short enough to be of practical
use.

MonteCarlo vsWaveoptics
MonteCarlosimulationof abiological objectwith optical coherenttomography structural
imagesusinga voxel-basedgeometryof amedium
S.V.Frolov,A.Yu.Potlov,D.A.PetrovandS.G.Proskurin
QuantumElectronics(2017) http://dx.doi.org/10.1070/QEL16204
"We describe a Monte Carlo
algorithm for simulating an
interference signal and
constructing a structural image of
a biological object using optical
coherenttomography(OCT).
The geometry of the simulated
object is reconstructed based on
the structure of real biological
tissuesobtainedbyOCT"
Especially interesting in biomedical
investigations is visualisation of
subcutaneous structures in vivo, such as
saphenous blood vessels. Possible
visualisation of such structures was
demonstrated in previous works [
ProskurinandVang2004, Proskurin2012]
. Since blood has a
high index of scattering, which is several
times that of epidermis and dermis, the
test for adequacy of the voxel-based OCT
modelling is of particular interest in this
case.

Beyond MonteCarlo
Realistic simulation andexperimentrevealsthe importance of scatterer microstructure
in optical coherencetomography image formation
PawełOssowski,AndreaCuratolo,DavidD.Sampson,andPeter R.T.Munro
BiomedicalOpticsExpressVol.9,Issue7,pp.3122-3136(2018) https://doi.org/10.1364/BOE.9.003122
Schematic diagram of the modelled OCT system and the model itself. Sill
and Sdet
represent the
planar surfaces upon which the illumination is introduced and the scattered field is detected, respectively.
Scattering in free space is simulated by using a perfectly matched layer (PML) which absorbs incident
radiation with verylow reflection.
Comparison between experimental (left) and simulated (right) images
of the OBEL phantom. The lower image in each column is an expanded view
of the region bounded by a red rectangle in the full image of the same column.
The white right-angle in each image denotes 50μm.m. The blue rectangle in the
expanded images denotes the region used to calculate the autocovariance
plots in Fig.10. The axial dimension is scaled to physical distance in both
cases.
Weanticipatethatthiswork will enable highly
realisticsimulation inarangeof OCT
applications.Forexample,biological tissuesare
oftencharacterisedexperimentallyintermsof
scattering coefficientandasymmetry parameter.

MonteCarlo/FDTD Implementations#1
B-CALM:Anopen-sourceGPU-based
3D-FDTD with multi-poledispersion
for plasmonics
Pierre Wahl, Dany-SebastienLy-Gagnon, ChristofDebaes, David A. B. Miller, HugoThienpont
OpticalandQuantumElectronics
June2012,Volume44,Issue3–5,pp285–290)
https://doi.org/10.1007/s11082-012-9558-z | Citedby21
https://sourceforge.net/projects/b-calm/ (CUDA,Matlab)
“As an example, we use B-CALM to simulate the absorption cross
section of a gold nanosphere and compare the results with Mie
theory. Compared with Mie theory, we obtain an error of less than
5% on a broad spectral range and an overall 40X speedup
comparedtoMeep,awidelyspreadCPU-asedFDTDsimulator”
Multiple-GPU-BasedFrequency-
DependentFinite-DifferenceTime
DomainFormulationUsing MATLAB
Parallel ComputingToolbox
WenyiShaoand WilliamMcCollough
ProgressInElectromagneticsResearchM,Vol.60,93–100,2017
http://doi.org/10.2528/PIERM17071704
http://www.celadon-inc.com/ |Celadon
Matlabimplementationnnotavailable[“Showoff”article]
“The results provide recommendations for partitioning data from a 3-D
computationalmodeltoachievethebestGPUperformance.”
A Z-X cross plane of
the knee model. The
3-D knee model is
partitioned along the
Z direction and
evenly allocated to
eightGPUs.

MonteCarlo/FDTD Implementations#2
Massively parallel simulator of optical
coherence tomography of
inhomogeneousturbidmedia
ComputerMethodsandProgramsinBiomedicine
Volume150,October2017,Pages97-105
https://doi.org/10.1016/j.cmpb.2017.08.001 |Relatedarticles
https://github.com/SiavashMT/OCT-MPS OCT-MPSOCTMPS
NVIDIACUDAwithPythonwrappers(cpython)
“We developed a massively parallel simulator of OCT of inhomogeneous
turbid media that obtains both Class I diffusive reflectivity, due to ballistic
and quasi-ballistic scattered photons, and Class II diffusive reflectivity due
tomultiplyscatteredphotons.
This new simulator speeds up simulations of OCT of inhomogeneous
turbid media by about two orders of magnitude. We have shown that our
parallel implementation reduced simulation time of OCT of the first
sample medium from 407min to 92min by using a single GPU card, to
12minbyusing8GPUcardsandto7minbyusing16GPUcards”

MonteCarlo/FDTD Implementations Python GPU
Massively parallel simulator of optical
coherence tomography of
inhomogeneousturbidmedia
ComputerMethodsandProgramsinBiomedicine
Volume150,October2017,Pages97-105
https://doi.org/10.1016/j.cmpb.2017.08.001 |Relatedarticles
https://github.com/SiavashMT/OCT-MPS OCT-MPSOCTMPS
NVIDIACUDAwithPythonwrappers(cpython)
“We developed a massively parallel simulator of OCT of inhomogeneous
turbid media that obtains both Class I diffusive reflectivity, due to ballistic
and quasi-ballistic scattered photons, and Class II diffusive reflectivity due
tomultiplyscatteredphotons.
This new simulator speeds up simulations of OCT of inhomogeneous
turbid media by about two orders of magnitude. We have shown that our
parallel implementation reduced simulation time of OCT of the first
sample medium from 407min to 92min by using a single GPU card, to
12minbyusing8GPUcardsandto7minbyusing16GPUcards”

MonteCarloResources
MonteCarlo LightScattering Programs byScottPrahl
mcxyz.c
byStevenJacques,TingLi,
ScottPrahl
mcxyz.c,a3DMonteCarlo
simulationofheterogeneou
stissues
mcxyz.cisacomputer
simulationoflighttransport
inaheterogenousmedium
withvaryingabsorptionand
scattering properties.
PolarizedLight
Monte Carlo
byJessicaRamella-Roman,
ScottPrahl,StevenJacques
PolarizedLightMonteCarlosoft
ware.
Themovementofpolarizedlight
istreatedasthepropagationofa
StokesVector ofintensity,
[I Q U V]T,foreachof4 sources
oflight,H,V,P,andR(H=linearly
polarizedparalleltoscattering
plane,V=linearlypolarized
perpendiculartoscattering
plane,P=linearlypolarizedat
+45°,R=rightcircularpolarized).
Hence,16outputfilesare
generates,HI,HQ,HU,HV,PI,
PQ,PU,PV,etc.,whereeachis
thex-ymapofescaping
reflectancefromaplanar slabof
tissueofspecifiedthickness.
(MCML)Monte Carlofor
Multi-Layeredmedia
by LihongWang (TexasA&M)and
StevenL.Jacques
MCMLisasteady-stateMonteCarlo
simulationprogramfor multi-layered
turbidmediawithaninfinitelynarrow
photonbeamasthelightsource.Each
layerhasitsownopticalpropertiesof
absorption,scattering,anisotropy,and
refractiveindex.Thesimulationis3D,
buttheresultsarestoredinanr-zarray
incylindricalcoordinatesdenoting
radialanddepthpositions.Outputs
includetheradialpositionandangular
dependenceoflocalreflectanceand
transmittance,andtheinternal
distributionofenergydepositionand
fluenceratewithinthemultilayered
medium.Theprogramcanbeeasily
modified.
GPUMonteCarlofor
GraphicsCards
byE.Alerstam,T.Svensson,
andS.Andersson-Engels
CUDAMCMLisanexcellent
implementationofMCML
thattakesadvantageofthe
presenceofNVIDIAgraphics
cardstorunmuchfaster.
Thedetailsofthelight
propagationmodelaregiven
inE.Alerstam,T.Svensson,
andS.Andersson-Engels J.
BiomedicalOpticsLetters 13,
060504(2008).
YoucandownloadtheGPU
MCMLsourcecodefromthe
LundUniversityBiophotonics
site

MonteCarloandDeepLearning
OptimizetheMonteCarloitself

Self-learningMonte Carlo
Self-learning Monte Carlowith deep
neural networks
HuitaoShen, JunweiLiu, and Liang Fu
Department ofPhysics, Massachusetts Institute ofTechnology, Cambridge, Massachusetts
Phys.Rev.B97,205140–(Vol.97,Iss.20—15May2018)
https://doi.org/10.1103/PhysRevB.97.205140
The self-learning Monte Carlo (SLMC)
method is a general algorithm to speedup
MC simulations. Its efficiency has been
demonstrated in various systems by
introducing an effective model to propose
global moves in the configuration
space. In this paper, we show that deep
neural networks can be naturally
incorporated into SLMC, and without any
prior knowledge can learn the original model
accuratelyandefficiently.
There are still many interesting systems that are practically beyond the
capability of conventional MC methods, due to the strong
autocorrelation of local updatesordue to the heavycomputationalcostof
a single local update. In the midst of recent developments of machine
learning techniques in physics [e.g. Cristoforetti etal.2017], a general method
called selflearning Monte Carlo (SLMC) was introduced to reduce or solve
theseproblems [TanakaandTomiya2017],
The advantage of SLMC is two-fold. First, simulating the effective model
is much faster, which enables the machine to propose global moves to
accelerate MC simulations on the original model. Second, the effective
modelcan directly revealthe underlyingphysics.
The efficiency of SLMC depends on the accuracy of the effective
model, which is usually invented basedonthehumanunderstanding
of the originalsystem[Huang etal.2017].
In this paper, we showed how to integrate neural networks into the
framework of SLMC. Both the architecture of the networks and the way we
design these networks are general and not restricted to impurity models.
This work can help design neural networks as effective models in more
complicated systems, thereby introducing the state-of-the-art deep
learninghardware intothe fieldofcomputational physics.

“Amazon”toMonte Carlo RecommenderEngine
Recommender engine for continuous-
timequantumMonte Carlo methods
LiHuang, Yi-fengYangand Lei Wang
Phys.Rev.E95,031301(R)(2017)
https://doi.org/10.1103/PhysRevE.95.031301
The idea of a “recommender
system” points to a general route to
accelerate the quantum Monte Carlo
simulations. The recommender system
is a broad and active research field [
Aggarwal 2016]in machine learning.
One can build a probabilistic model
based on the users’ past behavior and
suggest favorable products back
with highacceptance rates.
To collect the training data, we perform CT-QMC simulations with
conventional random insertion and removal updates [Rubtsov etal.2005].
For each update whether it is accepted and rejected we extract the features
and compute the log weight as the regression target. After collecting around
20 000 samples we perform the ridge regression [Hastieetal.2009] for the
fitting parameters, where we use an L2 regularization of the strength 10−3
for
thecoefficientstopreventoverfitting.
There are various ways that the CT-QMC simulation can benefit from
the recommender system [Huang andWang 2017]. First, the updates
can be nonlocal. even without the luxury of performing global updates for the
reference system, one can still afford to accumulate many local
updates before recommending a nonlocal update to the CT-QMC
simulation.
Finally, as long as the classical molecular gas model captures correlations in
the CT-QMC configurations, it is already beneficial since it suggests better
update proposals by exploiting the correlations. The recommended
update can be local, but has an improved acceptance rate and enjoys the
advantage of the O(k2
) fast update schemes in the CT-QMC [Gull etal. 2011].
Using therecommenderengineinthisway, onecanalwaysspeedup the
simulation comparedto the originalcase.

Appendix#1
OcularOCTImageformation

OphthalmicOptics
Wide-fieldoptical model of the human
eye withasymmetrically tilted and
decenteredlensthatreproduces
measuredocular aberrations
James Polans, Bart Jaeken, Ryan P. McNabb, PabloArtal, and JosephA. Izatt
OpticaVol.2,Issue2,pp.124-134 (2015)
https://doi.org/10.1364/OPTICA.2.000124
We propose an optically accurate wide-field
schematic eye that reproduces the complete
aberration profile of the human eye across a wide
visual field.
Our proposed model may aid in the design of wide-
field imaging instrumentation, including optical
coherence tomography, scanning laser
ophthalmoscopy, fluorescence imaging, and fundus
photography, and it has the potential to provide
further insights in the study and understanding of
the peripheral optics of thehuman eye.
Zemax 2Draytrace of the
sagittal cutof our eye model.
The colored linesrepresent
thoseraysthat originated
from acommon point source
on the retina. The chief rayof
each setof raysformed an
angle of incidence withthe
pupil stop ranging
from ±40°±40° in 10°
increments. It isapparent
that there isasmall tilt and
displacement of the
crystalline lens, which was
required inorder tosatisfy
the known asymmetriesof
the eye’s aberrations

OphthalmicOptics#2
https://doi.org/10.1364/OPTICA.2.000124 -Citedby22

OCT TheEyeBasics
Opticalcoherencetomography
A.F. Fercher and C.K. Hitzenberger
ProgressinOpticsVolume44,2002,Pages215-302
https://doi.org/10.1016/S0079-6638(02)80017-8
Basic components of an OCT system and some of its functions
and variations. ASE, amplified spontaneous emission fiber light source;
CCD, CCD detector array; MML, multimode laser; PC, PC/monitor; PCE
photonic crystal fiber; PIN, PIN photodiode; SLD, superluminescent
diode; SPDA,smartpixel detectorarray.
Basic OCT interferometer schemes. The open
double arrow indicates the rapid (or "priority") scan. (a)
Reflectometer: based on Michelson LCI; this is the
dominating optical scheme. (b) Dual beam: this
configuration is not sensitive to longitudinal movements
between sample and interferometer. (c) En face: the fast
scan is performed transversally; a separate modulator can
be used to generate the carrier frequency. (d) Parallel
OCT: The sample is illuminated with an extended beam
and imaged on anarray of photodetectors.
Macroscopic
OCTtechnique
implementedin
fiberoptics
Opticalcoherence
microscopy(OCM)
implementedas
parallelOCTinbulk
optics.PC,PC
monitor.

OCT TheEyeBasics: Variants
Fourier-domainOCT(FD-OCT)
SS-OCT, alsoknown asoptical frequency domain imaging(OFDI)
In 2003 it was recognized that FD-OCT has a fundamental signal-to-noise ratio (SNR)
advantage over TD-OCT with a typical sensitivity improvement of 2 to 3 orders of magnitude
[13-15]. The SNRimprovement ofFD-OCT arisesfrom the distribution ofthe photonic shotnoise over
multiple separately detected spectral bands, instead of a single detection over the full spectral width
asdoneinTDOCT.
The principles of Optical Coherence Tomography for posterior eye imaging | Boy Braaf, PhD Thesis (2015)
OCTSelectionGuide
https://www.thorlabs.com/newgrouppage9.cfm?objectgroup_id=5702

OCT TheEyeBasics: Resolution
The human eye is an
integrated part of the
OCT system and its
optics should therefore
be considered when
evaluating the lateral
resolution and FOV.
Although the axial
resolution for OCT is
determined by the
spectral bandwidth
of the light source, the
lateral resolution is
purely depending on the
optical system.
https://www.retinalphysician.com/issues/2008/jan-feb/oct-imaging-a
dvances-over-the-past-5-years-and-be

OCT TheEyeBasics: OCTWavelengths
The wavelength ranges that can be used for OCT
imaging of the posterior eye are mainly restricted by
three parameters: the available broadband light
sources, light absorption by water in the ocular media,
and the maximum permissible exposure (MPE) that
ensuresasafeleveloflaserradiation.
The principles of Optical Coherence Tomography for posterior eye imaging | Boy Braaf, PhD Thesis (2015)

OCT PolarizationSensitive(PS-OCT)
Polarization sensitiveoptical coherence
tomography – areview
Johannes F. deBoer, Christoph K. Hitzenberger, and YoshiakiYasuno
BiomedicalOpticsExpressVol.8,Issue3,pp.1838-1873(2017)
https://doi.org/10.1364/BOE.8.001838
Electricfieldscomponentsforvariouspolarizationstates
correspondingtothedifferentStokesparameters.
Birefringent materials are characterized by a refractive index that
depends on the polarization orientation and on the propagation direction of
light within the material. If polarized light enters a birefringent material, it is
decomposed into two orthogonally polarized beam components that travel
at different speeds. After transiting through a sheet of birefringent material, one
polarization state of the light beam is retarded with respect to the other,
depending on the amount of birefringence Δnn (refractive index difference for the
two orthogonal polarization states) and on the thickness of the sheet. This effect
can be found in anisotropic crystals or in fibrous materials that consist of
long, parallel fibrils embedded in a matrix of different refractive index (form
birefringence). Form birefringence can be observed in several fibrous tissues like
muscle,nervefiber tissue,and tissuesthatcontain collagen.
Diattenuation(or
dichroism) describesthe
propertyofsomematerialsto
absorblightofdifferent
polarizationstatesdifferently.
Depolarization can be caused by
multiple scattering or scattering at
non-spherical particles. It is observed
in pigmented tissue, where the
depolarizing effect was shown to be
caused bymelanin granules
Sketch of basic
PS-OCT system.
BS, beam splitter;
Det, detector;P,
polarizer;PBS,
polarizingbeam
splitter;QWP,
quarter wave plate;
RM, reference
mirror;SLD, super
luminescent diode.
WidefieldRNFLretardation
mapsobtainedinhuman
eyes.
(a)Healthyeye;
(b)glaucomatouseye.

OCTNoise Model
Statisticalmodelfor OCT image
denoising
MuxingziLi, RamziIdoughi, Biswarup Choudhury, and WolfgangHeidrich
KingAbdullah Universityofscience and Technology, Thuwal 23955-6900, SaudiArabia
http://vccimaging.org
BiomedicalOpticsExpressVol.8,Issue9,pp.3903-3917(2017)
https://doi.org/10.1364/BOE.8.003903
Illustration of the relationship between the local standard deviation and the local
mean in OCT images. (a,b) Masks used for this computation for the images of
phantom structure and biofilm sample respectively. For each pixel, the mean
and standard deviation are computed over a local 9-by-9 window. Pixels lying
between 2 different clusters (represented in red) are not considered in this
computation. (c,d) Graphics showing the local standard deviation against the
local mean, respectivelyfor thephantom image and biofilm image.
a) A selected homogeneous region of a 3D-printed phantom sample with layered structure. (b) Empirical probability
distribution functionsof intensity values in the selected region before (blue) and after (red) asquare-root transformation,
and the fitted Gaussian distribution (black) to the transformed distribution. (c) The Q-Q plot of the transformed
distribution and the fitted Gaussian distribution. The dashed red line corresponds to quantiles of the fitted Gaussian
distribution.
ComparisonofOCTretinallayer
segmentationresultsondenoised
retinalimagesusing:
(a)Gaussianfilter.
(b)Log-spaceBM3D.
(c)K-SVD.
(d)GeneralBayesian.
(e)TGVdecomposition.
(f)Proposed.

OCTSignalProcessing
MathematicalMethodsof Optical
Coherence Tomography
PeterElbau,LeonidasMindrinosandOtmarScherzer
HandbookofMathematicalMethodsin Imaging pp1169-1204(2015)
https://doi.org/10.1007/978-1-4939-0790-8_44

OCTSignalProcessing Discretization
How tooptimize OCT image
KaiYu,LiangJi,LeiWang,andPingXue
OpticsExpressVol.9,Issue1,pp.24-35(2001)
https://doi.org/10.1364/OE.9.000024
Resulting imagesofthe femoralisofrabbit. (a) Direct
Logarithm, (b)Truncation Logarithm, (c) Minimum
Distortion, (d) Truncation Minimum Distortion, (e)
Information Expansion, (f) Information Hyperbolized
Expansion (g) Maximum Entropy(h) Equal Interval
Resulting images of capillary with milk. (a) Direct Logarithm, (b)
Truncation Logarithm, (c) Minimum Distortion, (d) Truncation Minimum
Distortion, (e) Information Expansion, (f) Information Hyperbolized
Expansion(g)Maximum Entropy(h)EqualInterval
Quantization, which maps real values of
raw data to a series of fixed gray levels, is an
inevitable step in OCT image formation.
Image quantization is usually used for three
purposes. The first is for image
compression, transmission, storage, etc [3].
The second purpose is to enhance images
by adaptation to the visual properties of the
human eyes [3, 4]. In this situation, visual
effect is more important than absolute
distortion. For example, for an image that has
few gray levels, the dithering technique can
make the image look smooth by adding
random noise without changing the number
of gray levels [3]. This kind of quantization
does not concern any real information of
images but the human psychological visual
impression. It is indeed a “visual perceptional
deceit”. The third purpose is for data
visualization or pixel level transformation [5].
For example, quantization methods that map
raw data to image scale levels are employed
toobtain imagesfrom FFT transformation,X-
ray, MRI, ultra-sound and OCT. In this case, a
distortion function, which is related to real
information of raw data, should be kept to a
minimum.
“ We investigate standard 8-bit
gray images in this paper. “
Petteri: “One might to deep learningfy
raw to 8-bit quantization with “deep
OCT ISP”

Appendix#2
ParametersfortheEye

Lightpropagationmodelofretina#1
Model ofopticalreflectanceofthefovea, with pathways through the receptorlayerand
reflections fromtheILM, the receptordiscs and thesclera. Reflectors areindicated by horizontal
lines. Absorbing pigments aredrawnas horizontal boxes. Cones are depicted as funnel-shaped
objects. Inthe dark-adapted conditionthe cones are filled with visual pigment. Light enters the eye
fromthe top, as indicated by the downward pointing arrow. Upward pointingarrows representlight
detected by the instrument, emerging from theeyeafterreflectionfrom the different layers.
Secondaryreflectionsare assumedtobelost elsewhere. Onlythereflection fromthe
cone receptor discs is directional
van deKraatsetal. (1996)
Several origins of the retinal reflections
have been proposed in previous studies.
Polarization, spectral decomposition,
image quality of reflected light and visual
pigment bleaching have been used as
tools to discriminate between different
layers
The model also yields estimates of the optical properties of
otherimportant absorbers. In spiteofincludingthereceptor
layer with inherent refracting aspects, for the non-
directional reflection from the deeper layers in bleached
conditions it can still be ignored. As we simplified the
modeling of these deeper layers, more complex modeling
would be needed to arrive at physiologically relevant
estimatesfortheparametersin the choroidalspace.

Lightpropagationmodelofretina#2
van deKraatsandvan Norren (2008)
"An earlier version ofthemodelwithanextensivediscussionwaspublishedby vandeKraats etal. (1996)
The maindeviationsinthepresentmodelconcern theregainingofscatteredlightofthe
nondirectionalcomponent,awavelength-dependentreflectionfromthecones,theuseofataperedblood
layer thickness,andnewtemplatesfor theeyemediaandthemacular pigment."

Lightpath-lengthdistributions withintheretina
; Stephen P. Morgan

RetinaRefractiveIndices
Chen,OphthalmicRes1993;25:65–68
http://doi.org/10.1159/000267223 | Citedby10
Thurin2008
Thurin2008: "Computation. The physical
dimensions of many cells are available in the
literature [Hoganetal.1971]. The refractive index
values, however, are difficult to find. The
reason for this lack of data is two-fold. The living cell
reacts to changes in its environment and the
refractive index varies accordingly [Barer 1957].
There is a large variation of the refractive
indexes of the different cell components within a
given population [BrunstingandMullaney1974]. An
approximationoftheopticalpathdifferenceinduced
by a cell can nevertheless be obtained. The neural
cells of the retina are closely spaced and therefore
the principal phase structure is probably due to
the difference between the refractive index of the
nucleus and the refractive index of the cytoplasm—
which is mainly the liquid of the cell body and small
membrane components. ... It is difficult to estimate
the magnitude of the phase structures of the retina.
All the figures given in this section are
approximations using a very simple model of the
neuraltissue.The realrefractiveindexdistributionfor
a single cell or its components probably varies in an
irregular manner as shown by Choietal.2007 for a
HeLacell."

Retinasomeauthorshaveusedone
refractiveindexforwholeretina
Zhanget al.(2006), https://dx.doi.org/10.1364%2FOE.14.004380
●
"an aggregate refractiveindex of1.38"
https://dx.doi.org/10.1136%2Fbjo.2009.163501
●
"assumedrefractiveindex of thetissue, 1.333."
http://doi.org/10.1167/iovs.07-0838
●
"assuming anindexofrefractionof1.4."
Andasafunctionof light (bleached)/darkadaptation in cows (Ajo 1947):
●
Asarule therefractiveindex for dark adaptedretinaeofcowswas1.358.
●
321 casesthelightadaptedretina'sindex was 1.3610
van deKraatsetal. (1996)

Anisotropy inreflectionhttps://doi-org/10.1117/12.2288739 (18March2018)
Ratheesh K. Meleppat;MyeongJinJu; PengfeiZhang;Yifan Jian; Suman Manna;Daniel J. Wahl;Marinko V. Sarunic;Edward N. Pugh;RobertJ. Zawadzki
The imaging probe of our OCT system was mounted on a X-Y-Z
translation stage. This allows controlled positioning of the entrance
pupil with respect to the dilated mouse pupil by translating the
micrometer screw.
(a) OCT fundus image of WT pigmented mouse (b),(c) and (d): Directional OCT B-scans acquired at -12.5,
0 and +12.5 Degrees along X-direction. (e): Angular reflectivity Profiles. The dark blue shaded circle
showsthe mouse pupil. The white and colored dotsrepresent differentbeam entrypositions.
(a) OCT fundus image of Albino (b), (c) and (d): Directional OCT B-scans acquired at -12.5, 0 and
+12.5 Degrees along X-direction. (e): Angular reflectivity Profiles. The dark blue shaded circle
showsthe mouse pupil. The whiteand colored dotsrepresentdifferent beam entrypositions.
RepresentativeOCTB-
scansandcorresponding
A-Scanprofilesfrom
retinallayersfor (a)Albino
(BALB/c)(b)WT
Pigmented.

PhotoreceptorLayer Directionality
Asevidentfromthe width ofthe curvesand the corresponding octvalueslistedinTable 1,theρoct values listed in Table 1, the
reflectionsfromtheIS/OSandPTOSarehighlysensitive tothe aperturepositioninthepupil.In
contrast,thereflectionfromtheRPEwaslargelyinsensitive.
Gaoetal. (2008)fordirectionalityparameters https://doi.org/10.1364/OE.16.006486 OpticalStiles-Crawfordstartingtohaveaneffect
especiallythenfor AO-correctedOCT
Miloudietal.(2015): “In32eyes(64%),off-axisFIAOimagesof
theretinalperiphery( 15–20°fromthefovea)showedvariably∼15–20° from the fovea) showed variably
sizedpatchesof hyporeflectivedots(calledherenegative
mosaic)coexistingwith hyperreflective (positive)cones.
Inninecases,shiftingtheentrypupiltowardtheopticalaxis
restoredthepositiveconemosaic,withapoint-by-point
correspondencebetweenpositiveandnegativemosaics.
Rodsremainedhyperreflectivearoundnegativeandpositive
cones.Thesechangeswereparalleledbychangesofthe OCT
reflectanceoftheconeoutersegmenttips and,toa
lesser extent,oftheinner/outer segmentlimit.
Vohnsen(2014)

RetinaDiffuseReflection#1
Methodfor Calculatingthe Optical
DiffuseReflectionCoefficientfor the
Ocular Fundus
S. A. Lisenko, M. M. Kugeiko
Journal ofApplied SpectroscopyJuly 2016, Volume 83, Issue 3, pp 412–421
https://doi.org/10.1007/s10812-016-0303-4
Wehavedeveloped amethodfor calculatingtheopticaldiffuse
reflection coefficient for the ocular fundus, taking into account
multiple scattering oflight in itslayers(retina, epithelium, choroid)
andmultiplereflectionoflightbetweenlayers.Themethodis
based on the formulas for optical “combination” of the layers of the
medium, in which the optical parameters of the layers (absorption
and scattering coefficients) are replaced by some effective values,
different for cases of directional and diffuse illumination of the
layer. Coefficients relating the effective optical parameters of the
layersandtheactual valueswereestablished basedon theresultsof
a Monte Carlo numerical simulation of radiation transport in the
medium.
We estimate the uncertainties in retrieval of the structural and
morphological parameters for the fundus from its diffuse reflectance
spectrum using our method. We show that the simulated spectra
correspond to the experimental data and that the estimates of the
fundus parameters obtained as a result of solving the inverse
problemarereasonable.
absorptioncoefficientscatteringcoefficient scatteringcoefficient

RetinaDiffuseReflection #2
Methodfor Calculatingthe Optical Diffuse Reflection Coefficientfor theOcular Fundus
S. A. Lisenko, M. M. Kugeiko
Journal ofApplied SpectroscopyJuly 2016, Volume 83, Issue 3, pp 412–421
https://doi.org/10.1007/s10812-016-0303-4
absorptioncoefficientscatteringcoefficient βi
?
gi
average cosines of the scattering indicatrix
ki
depth (or asymptotic) attenuation coefficient
retina
epithelium
choroid
Due to the small thicknessofthe funduslayers(the total thicknessofthe retina,epithelium, and choroidis
~0.5 mm) compared with the diameter of the eyeball (~24 mm) and the strong absorption of light by the
epithelium, the curvature of the eyeball has practically no effect on the light conditions in the
layersofthefundus[Guoet al.2008]
.
Thus the diffuse reflection coefficient of the eye measured in the experiment depends on the transmission and
reflection coefficients for directional and diffuse light transmitted and reflected by the layers of the fundus. At the
moment, there is no analytical method for calculating these coefficients for layers of finite thickness with
arbitrary optical parameters, and the familiar formulas relate to semi-infinite media [Farrelletal.1992, ZoniosandDimou2006]
or to
special cases of weak absorption [EganandHilgerman1979]
and scattering [Sokoletskyetal.2013]
of light in a homogeneous layer.
None of the familiar formulas are applicable to layers of the fundus, the optical characteristics of which,
depending on the anatomical section of the fundus and the wavelength of the light, vary from weak absorption
and scattering (typical for theretina beyond the macula)to very strong absorption andscattering (typicalforthethin
epithelium)[Hammeretal.1995]
.

RetinaSpectralReflection
Spectral behavior of the directional
reflection from the foveal cones thin
solid curve, the nondirectional reflection
dashed curve from the background,
originating from pre- and post-receptor
layers, and the sum of both thick solid
line.
Continuous curves connecting the data points
are presented for clarity. The data points in the
lower half of the figure represent scale on the
right. Because of the noisy appearance and to
avoid overlap with the amplitude curves,
directionality ρ is not plotted below 420 nm.
vande KraatsandvanNorren(2008)

SpectralReflection Scintillation whenbleached
Invivofunctionalimagingofhumancone
photoreceptors
R. S. Jonnal, J. Rha, Y. Zhang, B. Cense, W. Gao, and D. T. Miller.
OpticsExpress, 15(24):16141–16160, Nov. 2007.
http://dx.doi.org/10.1364/OE.15.016141 | Cited by115
“The cone signal scintillation (reflectance originating
from the inner and outer segment refractive index
transition, see Gaoetal.2008) in the study by Jonnal
et al. 2007 was shown to occur quickly after the
stimulus onset (5 to 10 ms) with high stimuli strength,
the scintillation lasting roughly 300 to 400 ms. This
observed time course was in accordance with
human cone electroretinography (ERG) data (
HoodandBirch1995), supporting the claim that the
observed scintillation was linked to the cone
phototransduction.”
Representativevideoshowing
conescintillationafter asingle
briefstimulusof8ms(or
1.35×106Td·s).Center panelshows
aregisteredconemosaicvideoof
90frames(.45s),with20frames
beforestimulusand70framesafter
stimulus.
Reflectanceof thesamecone beforeandaftera
singleflashof670nmlightofvaryingstrength.
StimuluslevelisshownoneachplotinunitsofTd·s,as
wellasthecorrespondingstimulusdurationinms.
Theamplitudeofthescintillationisshownasa
proportionoftheflatfield.Thevariationininitial
directionofscintillationsupportsthehypothesisthat
interference,withrandominitialphase,underlies
thescintillationphenomenon.
in vivostudiesof phototransduction benefitfrom
OCT model thataccountsfor interference?

SpectralReflection MonteCarlo
MonteCarlomodellingofthespectral
reflectanceofthehumaneye
Preece SJ& Claridge E.
PhysMed Biol 2002;47:2863–2877.
https://doi.org/10.1088/0031-9155/47/16/303
“In this paper the results of a Monte Carlo simulation
are presented. Three histological variables are
considered: the RPE melanin concentration, the
choriodal haemoglobin concentration and the
choroidal melanin concentrcrate model spectra
which agree well with in vivo experimental
measurements of the nasal fundus. The model has
implications for the problem of extracting histological
parameters from spectral reflectance
measurements.”

Müllercells ”allover thelayers”
https://doi.org/10.1073/pnas.0611180104
Müllercellshape,refractive
properties,andlight-guiding
capability.(a) Nomarski
differentialinterferencecontrast
microscopyimageof
a dissociatedguineapigMüller
cell withseveraladherent
photoreceptor cells,including
their outer segments(ROS)and
adissociatedretinalneuron
(bipolar cell)totheleft.The
refractiveindicesofthedifferent
cellsectionsaregiven.
(b) Schematicillustrationofa
Müllercell insitu.The lighter the
coloring oftheMüller cell,the
lowertherefractiveindex.Typical
diametersandthe
calculated V parametersfor700
nm(red)and500nm(blue)
areindicatedattheendfoot,the
inner process,andtheouter
process.Althoughdiametersand
refractiveindiceschangealong
thecell,itslight-guidingcapability
remainsfairlyconstant.(Scale
bar,25μm.m.)
Labinetal.(2014)
LabinandRibak(2010)

RetinaAbsorbers: Melanin
MonteCarlomodel for studyingthe
effectsof melanin concentrationson
retina lightabsorption
Ya Guo, Gang Yao, BoLei, and JingluTan
Journal of theOpticalSocietyof AmericaA Vol. 25,Issue2,pp. 304-311 (2008)
https://doi.org/10.1364/JOSAA.25.000304 |Citedby22
We developed a Monte Carlo model to calculate light
absorption in human and mouse retinas. The retina
was modeled as a five-layer spherical structure. The
effects of melanin concentrations in the retinal pigment
epithelium (RPE) and choroid layer were studied.
Variations of blood content in choroid were also
considered in the simulation. Our simulation results
indicated that light absorption in neural retina was at least
20% higher in albino subjects than in pigmented subjects
under both photobleaching and dark-adapted
conditions. It can be four times higher at optical
wavelengths corresponding to minimal hemoglobin
absorption. The elevated absorption at neural
retina was attributed to the light backscattered from
the choroid and sclera layers. This simulation model
may provide useful information in studying light-induced
retina damage.

RetinaAbsorbers: Melanin
MonteCarloinvestigation on
quantifying theretinal pigment
epitheliummelanin concentrationby
photoacoustic ophthalmoscopy
XiaoShu;WenzhongLiu;HaoFeng Zhang
J. of Biomedical Optics, 20(10),106005 (2015). https://doi.org/10.1117/1.JBO.20.10.106005
Simulateddepth-resolvedprofilesofenergydepositionin VRandRPE region(RR).
Simulation results with different RPE melanin concentrations are shown in the
same plot. (a) Vessel region (VR) and RR. It is a top–down view of simulation field.
The redsquareisthe retinalbloodvesselwhilethegraybackgroundrepresentsthe
RPE. (b) Depth-resolved profiles of energy deposition in VR. (c) A magnified view
ofthedashedsquare(b).(d) Depth-resolvedprofilesofenergydepositioninRR.

RetinaMelanininOCTimageformation
Theeffectof retinalmelanin on
optical coherencetomography
images
Melissa A. Wilk;Alison L. Huckenpahler;Ross F. Collery;BrianA. Link;JosephCarroll
Translational Vision Science&TechnologyApril 2017, Vol.6, 8. doi: 10.1167/tvst.6.2.8
Conclusions: Thehyperreflectiveouterretinal bandsin OCTimagesarehighly
variablein appearance. Weshowed thatmelanin isamajor contributor to theintensity
andwidth of theRPE band on OCT.Oneshould use caution in extrapolating
findingsfromOCTimagesofoneorevenafew individualstodefinethe
absolute anatomic correlates of thehyperreflectiveouterretinal bandsinOCT
images.
Translational Relevance: Melaninaffectstheappearanceof theouterretinal bands
inOCTimages. Useof animalmodelsmayhelp dissecttheanatomic correlates ofthe
complex reflectivesignalsin OCT retinalimages.
While little work has been done to examine changes in normal human RPE
with dark adaptation, several groups have used OCT to examine photoreceptor
changes with dark adaptation in patients with Oguchi disease, a form of
congenital night blindness due to defects in arrestin or rhodopsin kinase. In these
subjects, the peripheral outer segments appear normal (hyporeflective) when
dark-adapted butincreases in reflectance withlight adaptation.
In addition to Oguchi disease, the presence of a tapetal-like reflex (TLR) in carriers
of X-linked retinitis pigmentosa (XLRP) results in focal disruptions of the
EZ, which resemble the patterns of outer segment disruption noted in Oguchi
patients. Examination of the underlying mechanisms and processes affected in
patients with Oguchi disease and carriers of XLRP, as well as the changes
associated with adaptation state, could provide key insight into the specific
cellularstructuresregulating the reflectance ofthe outerretina.
To provide a thorough analysis of the anatomic correlates of OCT, all
factors contributing to this variable appearance of these bands should be explored
systematically, and controlled for when possible. As illustrated here, this could be
accomplished using either animal models or by leveraging experiments of nature in
human patients. Use of independent methods, such as near-infrared
autofluorescence, polarization sensitive OCT, and photoacoustic
ophthalmoscopy, to measure retinal melanin may be worthwhile in future studies.
Combined,
thesesubjects
highlightthe
variabilityin
melaninand
OCT
appearance
acrossnormal
subjectsaswell
aspatientswith
albinism.

RetinaAbsorptionandscatter ininfants
MonteCarlosimulationof retinal
lightabsorption by infants
Ya Guoand Jinglu Tan
Journal of theOpticalSocietyof AmericaA Vol. 32,Issue2,pp. 271-276 (2015)
https://doi.org/10.1364/JOSAA.32.000271
Retinal damage can occur in normal ambient lighting conditions. Infants
are particularly vulnerable to retinal damage, and thousands of preterm
infants sustain vision damage each year. The size of the ocular fundus
affects retinal light absorption, but there is a lack of understanding of this
effect forinfants.
In this work, retinal light absorption is simulated for different ocular
fundus sizes, wavelengths, and pigment concentrations by
using the Monte Carlo method. The results indicate that the neural retina
light absorption per volume for infants can be two or more times
that foradults.

RetinaSpectralAbsorbanceandScatter
Opticalabsorption andscatteringof
bovine cornea,lens,andretina inthe
near-infraredregion
BrianG. Yust, LawrenceC. Mimun, and DhirajK. Sardar
LasersMedSci.2012Mar;27(2):413–422
https://dx.doi.org/10.1007%2Fs10103-011-0927-9|Citedby24
The actual values of the absorption and scattering
coefficients for the retinal tissues reported in this study
have importance for practical applications requiring
the prediction of light transport through tissue, e.g., in
the design of treatment modalities for
photodynamic therapy in the eye where the degree
of interactionwith lightatthe targetsitesmayvary.
Variable concentrations of photopigments
obviously complicates the laser dosimetry for such
treatment modes, because the amount of light
delivered will have to be adjustedbasedon the amount
of absorbing chromophores in order to achieve some
standard clinical effect. Values in this region are of
particular importance because of the recent interest in
laser andscanningtechnologiesintheinfrared.
https://dx.doi.org/10.1007/s10103-009-0677-0
RetinaScattering coefficient
RetinaAbsorptioncoefficient

RetinalScatter
Thurin2008:
"Comparedtotheinnerretina,
the outerretina,thechoroid,andthe
sclera are more efficientscatterers.
Hammeretal.[1995] usedthe
double integrating-spheretechnique
toobtainthe optical propertiesof
bovinetissues.Ata wavelengthof550
nm,thescatteringcoefficientµs
—whichistheinverseofthemean
opticalpathlengthbetweentwo
scatteringeventsinanhomogeneous
tissuewithoutabsorption—is
●
30mm−1
forthe retina;
●
120mm−1
fortheRPE;
●
60mm−1
forthechoroid,
●
80mm−1
forthesclera"
Directional sensitivity of the retina: A layered scattering modelof outer-segment
photoreceptor pigments
Brian Vohnsen |Biomed Opt Express. 2014 May1;5(5):1569–1587.https://dx.doi.org/10.1364%2FBOE.5.001569
“Photoreceptor outer segments have been modeled as stacked arrays of discs or membrane infoldings containing
visual pigments with light-induced dipole moments. Two models have been introduced: one a macroscopic model
that assumes a uniform pigment density across each layer and another microscopic model that includes the
spatial location of each pigment molecule within each layer. Both models result in highly similar directionality at the pupil
planewhichprovesto beinsensitivetotheexactdetailsoftheouter-segment packing being predominantlydetermined
bythefirstandlastcontributinglayers asset by thefraction ofbleaching.”
Radiativefar-field componentof scatteredlightintensitiesforanisolatedouter segment(OS) propagated fromthemiddleinsideof theOS (left)
towards the inner segment (IS) and pupil (right) when including N = 1 (top), 100 (middle) and 1000 (bottom) equally contributing layers containing 740
dipoles in each. The molecular arrangement of dipolar pigments within a single layer is shown in the top-left corner. OS: outer segment and IS: inner
segment.

Appendix#3
Howtomeasure the retinalparameters

RetinaRefractiveIndexmeasurement
Błaszczaketal.(2014)
Therefractiveindexofthesilica
microspheresusedinthecalibrationtest was
determined by:1)immersionrefractometry;2)
digitalholographicmicroscopy(DHM);and3)a
novelapproachusingwidefieldmicroscopy.
Briefly, immersion refractometry, first
introduced for biological specimens by Barer [26
] is a technique where the object of unknown
refractive index is immersed in media with a
known refractive index (we have used Cargille
Labs refractive index matching liquids,combined
set nD= 1.400 – 1.700, cat. no. 18005) and
inspected with a phase microscope. The
behaviour of the halo around the sample
changes as the ratio between the refractive
index of the sample and the medium changes. A
plot of the number of beads exhibiting one
behaviour against the refractive index of the
suspension medium can be plottedand the point
of inflection gives the refractive index of the
sample (see right )→) . The precision of the
method depends on the ability to create
suspension media with a sufficiently small
incrementinrefractiveindex.
Anothermethodofmeasuring
refractiveindicesistousetheDHM.
TheDHMisaninterferencemicroscope
whereanoff-axishologramiscapturedona
CCDcamera.Thehologramretains
informationaboutthephaseofthe
illuminaatingwaveasitpropagatesthrough
thesample.Thewaveundergoesaphase
changethatdependsexplicitlyonthe
differenceinrefractiveindexbetweenthe
sphereandthesurroundingmedium.The
phasechangeiscapturedintheimageand
therefractiveindexcanbedetermined
providedthesizeofthesampleisknown.
For moredetailsonthetechniquesee[25].
Thethirdmethod ofmeasuringthe
refractiveindexwasbasedonthewide
fieldmicroscopesetup.Imagestacks
werecollectedfor microspheresimmersed
indifferentrefractiveindexoils(asin
immersionrefractometry)and xz viewswere
created.Thecrosssectionsofbeads
suspendedinamediumwitharefractive
indexlowerthanthebeadshowanormal
focusbutimmersioninahigher refractive
indexoilresultsinaformationofavirtual
focus.

Refraction Microspheresinwidefield microscopy
(a) The light distribution for a silica microsphere suspended in water and
illuminated from above; the focus point is clearly below the bead whose
positionisindicatedby thegreencircle.
(b) Similar bead, but suspended in an oil with a refractive index of 1.51. Here
the focus point is above the microsphere. The refractive index of the
immersionmediumisincreaseduntil thefocusbecomesavirtualfocus.
Błaszczaketal.(2014)
All three measurementsof the refractive
index of silica beads used as mimics of the
photoreceptor nuclei agree. Immersion
refractometry measurements gave a value
of n = 1.420±0.002 where the error is the
standard deviation extracted from an
integrated Gauss fit to the graph (Fig.8). A
virtual focus was seen when beads were
immersed in medium with n=1.43 and a real
focus was observed in suspension with
refractive index n=1.42. The most precise
measurement was obatined by digital
holographic microscopy and the measured
refractive index n = 1.423±0.001 was used
throughout (error is standard error of the
mean).

RetinalScatter
Analysisof the scattering performance of humanretinal tissue layers
Dan Zhu; Zhisan Gao; HaishuiYe; Qun Yuan
International Conference on Optical and PhotonicsEngineering(icOPEN 2016);1025007 (2017) https://doi.org/10.1117/12.2266646
“Human retina is different from other ocular tissues, such as cornea, crystalline lens and vitreous because of high
scattering performance. Asan anisotropic tissue, we cannot neglectits impact on thepolarization state of the scattered
light.
In this paper, Mie scattering and radiative transfer theory are applied to analyze the polarization state of backscattered
lightfromfourtypesof retinaltissues, includingneuralretina,retinalpigmentepithelial(RPE),choroidandsclera.
The results show that the most backscattered zones in different depths have almost the same electrical fields of Jones
vector, which represents the polarization state of light, whether neural retina layer is under normal incidence or oblique
incidence. Very little change occurs in the polarization of backscattered light compared to that of the incident light.
Polarization distribution of backward scattered light from neural retina layer doesn’t make apparent effects on
polarization phase shifting in spectral domain OCT because its thickness is far less than photon mean free path, while
otherretinaltissuesdonotmeetthisrule.

(2016) https://doi.org/10.1364/BOE.7.004595

IntraocularScatter Wavelengthdependence
WavelengthDependenceoftheOcular
Straylight
HarilaosS. Ginis;GuillermoM. Perez; Juan M. Bueno;Alexandros
Pennos;PabloArtal. Investigative Ophthalmology& Visual
Science May2013, Vol.54, 3702-3708.
https://doi.org/10.1002/mp.13047 | Citedby27
“For small angles, the wavelength dependence of
straylight matches the transmittance spectrum of
hemoglobin, which suggests that diffuse light from
the fundus contributes significantly to the total
straylight for wavelengths longer than 600 nm.
Eyes with lighter pigmentation exhibited higher
straylight at all wavelengths. For larger angles,
straylight was less dependent on wavelength and
eyepigmentation.”
Straylight parameter at 0.5° (average of all
subjects) and other spectral properties of the
fundus. Oxyhemoglobin density is from
Berendschot al., fundus reflectance from
Delori and Pflibsen, and the standard
deviation (width) of the PSF from Hodgkinson
etal.
Ratio of the PSF at “red”
wavelengths to the PSF at
“green” wavelengths. Gray
areacorresponds to 2
standard deviations (across
subjects).

IntraocularScatter MonteCarloSimulation
Scatteringcontributiontothedouble passPSF‐pass PSF
usingMonteCarlosimulations
DimitriosChristaras, HarilaosGinis, AlexandrosPennos, PabloArtal
Ophthalmic and Physiological OpticsVolume37, Issue3May2017
https://doi.org/10.1111/opo.12375
“The objective of this work was to determine the
domain of contribution at the double pass PSF of light‐Davarani Carri K.
scattered in the ocular media and the ocular fundus,
using simulated and experimental data for two different
wavelengthsandfor twodifferentpigmentations.”
The simulations showed that at 560 nm, diffusion in the
fundus causes light to extend to a radius of 2°,
independently of the choroidal pigmentation, whereas at
650 nm it extends to radii of 4.5° and 4° for low and high
choroidal pigmentation respectively. Experimental data
showed a similar behaviour at low angles where light
diffusion in the fundus is dominant, but different at higher
anglesduetoscatteringintheocularmedia.
The spatial contribution of light diffused in the ocular
fundustothe PSF wasfound tobe limitedtonarrower
anglescomparedtothatofscattering atthe ocular media.
The comparison ofsimulatedandopticaldatashowedthat
beyond 2° at 560 nm and 4–4.5° at 650 nm the only
phenomenon contributing to the PSF is scattering in the
ocular media, whereas the fundus contribution can be
assumedasnegligible.”
“A fundus model for Monte Carlo
simulation was considered and
diffuse light in the fundus at two
different wavelengths and for
two different choroidal
absorptions was simulated. The
simulated data were,
subsequently, compared against
experimental data from fundus
reflectance values collected from
two different melanin groups
at the above wavelengths from a
previous study. The objective of
the study was the analysis of the
spatial characteristics of the
reflected fundus light. More
specifically, the study aimed to
determine, using simulations, the
spatial domain of contribution for
fundus diffusion and compare it to
that of scattering in the optical
media observed in experimental
fundusreflectiondata.”

OcularAbsorbers
vandeKraatsandvanNorren(2008)
Quantitativeanalysisofmulti-spectralfundusimages
I.B.Styles,A.Calcagni,E.Claridge,F.Orihuela-Espina,J.M.Gibson
Medical ImageAnalysisVolume10, Issue4, August2006,Pages578-597
https://doi.org/10.1016/j.media.2006.05.007

OcularMedia SpectralCharacteristics
LaserBiologicalHazards-Eyes
https://ehs.oregonstate.edu/laser/training/laser-biologic
al-hazards-eyes
Lasersin Ophthalmology.DrRashmi Amarnath.
https://slideplayer.com/slide/10510747/
vandeKraatsandvanNorren(2008)
Parameter 10. Lensaging part (Dlens-a
)
Theythemselvesupdated this(https://doi.org/10.1364/JOSAA.24.001842),
you can usethe agedLensFilter.m inMatlab to correctforaverage
attenuation with ageasa parameter.
And you could experimentallymeasurethewholething spectroscopically
extending thisanteriorsegmentOCT (
https://doi.org/10.1364/BOE.9.003821)
Parameter 8. Densityof macularpigment(Dmac
)
andlikewiseestimatethewholespatial distribution (
http://doi.org/10.1167/iovs.15-17532, dual auto-fluorescence) with spectral
characteristicsfor macular pigmentaswell?As theyused a global macular
pigmentoptical density(calc_macularPigment_walraven2003.m)

Ocular
Media
Crystalline lens
and cornea
vandeKraats and vanNorren(2007): “Optical densityof the aging human ocular media in
the visible and theUV”. J. Opt. Soc. Am. A/ Vol. 24, No. 7/ July2007
https://doi.org/10.1364/JOSAA.24.001842 | Cited by124 articles
Petteri Teikari, Raymond P. Najjar, Kenneth Knoblauch, DominiqueDumortier, Pierre-
Loïc Cornut, PhilippeDenis, Howard M. Cooper and Claude Gronfier "Refined flicker
photometrytechniqueto measure ocularlens density" J. Opt. Soc. Am. A Vol. 29, Issue
11, pp. 2469-2478 (2012) https://doi.org/10.1364/JOSAA.29.002469
Human crystalline
lensgetsmore
yellow with age

OcularMedia near-infrared(NIR)characteristics
Opticalabsorption andscatteringof
bovine cornea,lens,andretina inthe
near-infraredregion
BrianG. Yust, LawrenceC. Mimun, and DhirajK. Sardar
LasersMedSci.2012Mar;27(2):413–422
https://dx.doi.org/10.1007%2Fs10103-011-0927-9|Citedby24
“Previously, the characterization of bovine ocular tissues in the visible
region was performed; here, we extend the scope of that study into the
near-infrared (NIR) using the three models: (a)inverse adding doubling
(IAD), (b) inverse Monte Carlo (IMC), and (c) Kubelka–Munk (KM).
Through a comparison of the three models, a clearer sense of the optical
propertiesmaybeobtained. “
The corneas and lenses of both samples proved to be much more
scattering than absorbing in the region of interest, which is expected per
theirbiologicalfunction in thenearbyvisiblespectrum.
Despite the small disagreements between the differently computed
values, the general trends for interaction with light are clear for each
tissue type. The cornea becomes slightly more absorbent and less
scattering occurs as the wavelength reaches out into the infrared. The
lens absorbs very weakly throughout the whole region, only becoming
slightly more absorbent at 950 and 1,000 nm. There is an almost inverse
correlation between the absorption and scattering influence of the lens,
as the scattering coefficients remained rather constant until 950 and
1,000nm, wherethey decreased.
CorneaScattering coefficient Lens Scattering coefficient
Lens AbsorptioncoefficientCorneaAbsorptioncoefficient

Changeofproperties from intervention?
Opticalcharacteristicsof the cornea and
sclera andtheir alterationsunder the
effectof nondestructive1.56-μm laser mlaser
radiation
AlekseyV. Yuzhakov;Alexander P. Sviridov;OlgaI. Baum; EvgeniiM. Shcherbakov;Emil N. Sobol
J.ofBiomedicalOptics,18(5),058003(2013).
https://doi.org/10.1117/1.JBO.18.5.058003
“Optical properties of cornea and sclera of the eye and
their alterations under the effect of 1.56-μm laser m laser
radiation are studied. The laser settings corresponded to
the laser treatment regimens used (1) to correct the
shape of the cornea and change the refraction of the eye
and (2) to improve the hydraulic permeability of the
sclera in glaucoma cases. A fiber-optical system to
investigate the dynamics of the reflected and transmitted
scattered laser radiation and a setup with a double
integrating sphere to determine the optical properties of the
ocular tissues on the basis of the Monte-Carlo simulation
of thepropagationoflight wasused.“
This setup consists of two spheres with their internal surfaces coated with fine-dispersed
barium sulfate, ensuring practically a 100% reflection of IR radiation. As a result, a uniform light field
is produced within the spheres irrespective of the radiation direction, and the signal of interest can be
recorded at any point therein.

CornealMeasurement qualityofdonorlenses
Evaluation of BroadbandSpectral
TransmissionCharacteristicsof Fresh
andGamma-IrradiatedCorneal Tissues
Calhoun, WilliamR. MPH;Akpek, Esen K. MD;Weiblinger, Richard MPH;Ilev, IlkoK. PhD
Cornea:February2015-Volume34-Issue2-p228–234
doi:10.1097/ICO.0000000000000323
Spectral transmission
measurements for (A) fresh, full-
thickness, (B) irradiated full-thickness,
and (C) irradiated, partialthickness
corneas
The major light attenuating
structures of the cornea are the
epithelium, Bowman layer, and stroma.
Although the epithelium and Bowman
layer have absorption coefficients
approximately 2 and 3 times higher than
stroma, respectively, the stroma is
significantly thicker andprovidesmostof
the attenuation in the 300 to 400 nm
range. Therefore, the high transmission
seen in the 100-mm irradiated cornea is
expected.
In this study, we demonstrated that
gamma-irradiated sterile corneal tissues
have spectral transmission
characteristics as good as or better than
fresh corneas in the visible spectral
range, with both tissue types having
better transmission than a standard IOL
implant.

Macular
Pigment
Across the macula, macular protective pigment (MPP) distribution
takes the form of a mountain, peaking centrally at the foveola and
declining to nil at an eccentricity of 7°. L – lutein, Z – zeaxanthin.
optometricmanagement.com
Recovered spectra for one normal subject. The four spectra recovered by NMF. The
fourth spectrum denotes the MP spectrum (solid line). The two peaks between 450
and 500 nm are the classic bifid spectrum previously reported (Hammond etal.2005) in
vitro.Thesecondarypeaksat425 nmhavealso been reported invitro. -Fawzi etal. (2011)
Clinicalimagingof macular pigment opticaldensityand
spatial distribution
Christopher M Putnam | College of Optometry,Universityof Missouri-St Louis
Clin Exp Optom, 100: 333–340. doi: 10.1111/cxo.12500
Spectralis optical coherence tomography (OCT)
provides a cross-section of the central retina of a
healthy human subject. The layers of the retina have
been identified with arrows. The vertical
distribution pattern of macular pigment (MP) is
identified primarily within the photoreceptor
axons that comprise the outer plexiform layer (OPL),
the inner plexiform layer (IPL) and Henle fibre layer
within the macula. Lesser concentrations of macular
pigment have also been identified at the level of the
retinal pigment epithelium (RPE) and photoreceptor
outer segments.
Macular pigment is deposited preferentially in the fovea in the Henle fiber layer which
consists of the foveal cones’ axons, and in the parafovea, macular pigment is also located in
the inner plexiform layers of the retina (Snodderly, Auran &Delori,1984;
Trieschmann,etal.,2008).
Macular pigment optical densitymap ofone eyeincluded in
the study. - VerônicaCastroLimaet al. (2013)

Sclera
Vogel etal. (1991):Optical Properties ofHuman Sclera, andTheir Consequences for
Transscleral LaserApplications. Lasersin Surgeryand Medicine 11:331340(1991)

Irisand
Ocular
Wall
“In special cases such as with intraocular straylight measuruments (
Ijspeertetal.1990; vanden Berg etal.2009; Michael etal.2009), the
transmural (ocular wall) and iris transmittance need to be explicitly
addressed in contrast of assuming them to be light-tight structures (
vanden Berg etal.1990). The translucency of iris and the ocular wall are
exploited by ophthalmologists when performing diaphanoscopy (cf
Greenwood 1913), in which a light guide is positioned against the sclera
andthepupil isseento glowfromwithin(La Heyetal. 1993).
Van denBerg etal. 1991 estimated the irises of blue-eyed individuals to
attenuate the red light only 0.72 log units and the green for 1.48 log units,
whereas the corresponding attenuation values were 2.27 for red and 2.64
log unitsforgreen lightin brown-eyed individuals.
In addition to the translucency of the iris and the surrounding ocular wall,
fundal reflections (Vos1963; vandeKraatsand vanNorren2008) might
contribute to the pigmentation-related differences. Furthermore, the iris
pigmentation have been shown to correlate directly with choroidal
pigmentation (Weiter et al. 1985) and to be reduced with aging (
Schmidtand Peisch 1986).”
SPEED:SPectraleyevidEo database
AnaGebejes,Pauli Fält,Roman Bednarik,MarkkuHauta-Kasari
University ofEastern Finland,Joensuu,Finland
UbiComp '16 https://doi.org/10.1145/2968219.2968335
Ahyperspectralimagingsystemfor the
evaluation ofthehumanirisspectralreflectance
Luca Di Cecilia; FrancescoMarazzi;Luigi Rovati
Univ. ofModenaandReggioEmilia, Italy
SPIE BiOS,2017,doi: 10.1117/12.2252184
Hyperspectral optical imaging of
human irisin vivo: characteristicsof
reflectance spectra
JoseM.Medina, LuísM. Pereira,Helder T.Correia, and Sérgio M.
C. Nascimento, UniversityofMinho,Portugal
Journal of Biomedical Optics 16(7), 076001 (July 2011)
Reflectance factor as a function of the wavelength
measured with the hyperspectral system. Reflectance
data correspond to (a) dark (orange), (b) light
pigmented iris (cyan)
Our study provides evidence for hyperspectral imaging
being suitable for the characterization of melanin and the
noninvasivediagnosis ofocular diseases and iris color.
Iris reflectances in the visible/near-infrared spectral
region. Light blue iris (blue line), hazelnut-green iris
(green line) and darkbrown iris (brown line).
(right) RGB image generated form the liquid crystal
tunable filter (LCTF) spectral image; Bottom – spectral
signatures of the points selected from the spectral image.
These are mean spectra from a 10x10 pixel areas sampled
fromthe features ofinterest marked ontheRGB image.

Eyelid
M. J. Moseley, S. C. Baylissand A. R. Fielder (1988) Light transmission
through the eyelid:doi:10.1111/j.1475-1313.1988.tb01043.x
Spectral transmittance of arbitrary unit amounts of hemoglobin,
melanin, and bilirubin used for predicting the spectral transmittance of
eyelid skin.
Bierman etal.(2011): Measuring and predicting eyelid spectral
transmittance. J.of BiomedicalOptics,16(6),
MillisecondFlashesofLightPhaseDelay the HumanCircadian
Clockduring Sleep JamieM.Zeitzer, Ryan A.Fisicaro, Norman F. Ruby, H.
Craig Heller.StanfordUniversity.Journal of Biological Rhythms201429(5):
370-376. doi: 10.1177/0748730414546532
“Confirmation that the flashes penetrated the
eyelids is presented by the occurrence of an
evokedresponseintheEEG.“

OCT Monte Carlo & Deep Learning

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