DEVELOPMENT OF AN OPTICAL IMAGING SYSTEM FOR IMAGING THICK TISSUES
Transcript of DEVELOPMENT OF AN OPTICAL IMAGING SYSTEM FOR IMAGING THICK TISSUES
CHAPTER 4
DEVELOPMENT OF AN OPTICAL IMAGING SYSTEM FOR IMAGING THICK TISSUES - PEIASE I
4.1 NEED FOR AN OITICAL IMAGING SYSTEM
Medical imagng techn~ques currently in use like MRI, CT and Ultra
sound are costly and are out of reach of the majonty of ow population. The
need for a low ws1 but effective imaging technique can be a boon for the
depnved majority. Opbcal imaging presents several potential advantages over
existing radiological techniques being nonionic, inexpensive and providing
better spatial and temporal resolution.
The factors that limit this optical imaging technology are the scattering
property of the biological tissue and the thickness of the tissue. As light travels
through a tissue it is scattered by the numerous refractive index variations In
the tissue. Scattering plays an important role in limiting the imaging depth, as
it d e c m s the number of excited photons reaching the particular depth.
Consequently only few photons are able to reach greater depths without much
scattering. Therefore emct ion of the weakly scattered light from the highly
scattered light can yield images with increased contrast. In this work the
problem related to scattering of light is solved by polarization imaging and
image processing.
The research towards the development of an optical imaging system
capable of imaging tissues of thichess in the order of centimehes has been
camed out in three phases. The current chapter discusses the first phase of the
system development.
4.2 PRYSICS OF SCATTERIh'G AND ABSORPTION
4.2.1 Senttering and Absorption
Scattering of electromagnet~c waves by a system is related to the
heterogeneity of that system. If an obstacle which wuld be a single electron,
an atom or molecule, a solid or liquid panicle is illuminated by an
ele~omagnetic wave; electric charges in the obstacle an set into oscillatory
motion by the elwhic field of the incident wave. The accelerated electric
charges radiate e l~omagnet ic energy in all directions. This is the radiation
scattered by the obstacle. In addition to reradiating electromgneetic energy, the
excited elementary charge may transfonn part of the incident electromagnetic
energy into other forms and this called absorption.
In biomedical optics, absorption and scattering of photons are most
important events. Scattering and absorpt~on are u:d for both spectroscopic
and Imagng applications.
Absorption is the primary event that allows a laser or other light source
to cause a potentially therapeutic effect on a hsSUe. Wlthout
absorption, there 1s no energy transfer to the tissue and the tissue IS leA
unaffected by the light
Absorption of light prondes a diagnostic role such as the spectroscopy
of a tissue Absorption can provide a clue as to the chemtcal
composihon of a hssue, and serve as a mechanism of optical contrast
dunng imaging.
Scanering prov~des feedback durlng therapy For example, durlng
laser coagulabon of tissues, the onset of scattering 1s an observable
endpoint that correlates with a deslred therapeutic goal. Scanering also
strongly affects the dosimetry of light during therapeutic proccdurcs
that depend on absorpt~on.
Scattering has diagnostic value as well. Scattering depnds on the
smctlrre of a tissue. Scattering measurements are an important
diagnostic tool irrespective of whether one measures the wavelength
dependence of scattering, the polarization dependence of scattering, the
angular dependence of scattering or the scatferlng of coherent light
4.2.2 Single scattering
Consider an arbitrary particle that is conceptually subdivided into
small regions. An incident electromagnetic wave induces a dipole moment in
each region. These dipoles oscillate at the frequency of the applled field and
therefore scatter sewn* radiation in all directions. At a distant point, the
total scattered field is obmned by superposing the scattered wavelets and due
account is taken of their phase differences
In natural environments however, collections of very many pamcles
occur. Partrcles in collection are elecuo magnetically coupled The field
scattered by a particle depends on the total field to which it is exposed
Considerable simplificstion results if single scattering is assumed and the
proposed model makes this assumption.
4.2.3 Absorption and scattering coefficient
The absorption mef'licient p. [cm"] describes a medium contalnrng
many chromophores at a concentration described as a volume density P,
Icm3] The absorption coefficient is essentially the cross-sectional area per unlt
volume of medium
and m, [cm2] is called the effective cros&seetion.
A 0, = QaA geometrical ef fect ive
cross-section cross-section
A os = QsA geometrical ef fect ive
cross-section cross-section
Figure 4.1 Illustration of : (a) absorption ; (b) scattering
The scattering eafiicient 1, [cm"] describes a medium containing many
scattering particla at a concentration described as a volome density p, [cm".
'The scattermy wffrcient is given by
and 0. [cm2] is called the effective cross-section.
4.2.4 Anisotropy and Reduced scattering eoeficient
The aniaotropy, g [dimensionless], is a measure of the amount of
fonvard direction retained after a single scattering event. Imagine that a
photon is scattered by a prhcle. A scattering event causes a deflection at
angle 0 from the orignal forward trajectory, y, is the azimuthal angle of
scattering and is shown m the Figure 4.2. The component of the new trajectory
which is aligned in the fonvard direction is shown in red as cos(9). The
average deflection angle and the mean value of cos(8) is defined as the
anisotropy
Figure 4.2 lllustntion of scattering of a photon
The redud scattering coefficient is a lumped properly incorporaring
the scattering eameient and the maisotropy g and is given by
The purpose of p.' is to describe the diffusion of photons in a random walk of
step size of Ifp,' [cml where each step ~nvolves lsotroplc scattenng
In addjbon to ~ t s lrrad~ance and frequency, an clect~omagnebc wive
has a property called ~ t s state of polarlzat~on Cons~der a plane monochromat~c
wave w t h angular frequency m and wave number k, whch 1s propagahng In
the z d~rectlon In a nonabsorb~ng rned~um The electr~c field vector at any
polnt lies In a plane the normal to which 1s parallel to the &rechon of
propagat~on In a part~cular plane, say at z = 0, the t ~ p of the elecu~c vector
traces out a c w e
E ( z - 0 ) - A w s o t + B s ~ n o t (4 4)
Equation (4.4) describes an ellipse called the vibration ellipse and the
monochromatic wave 1s said to be elliptically polanmd If A = 0 or B = 0, the
vibration ellipse is just a straight line and the wave is linearly polarized. If
I A I = 1 B 1 and A . B = 0, the vibiation ellipse is a circle and the wave is
circularly polarized.
A vibration ellipse is characterized by its imdiance, handedness,
direction of rotstion of the el l ip , ellipticity (ratio of the length of its
semiminor axis to its semimajor axis), and its azimuth (the angle between the
semimajor axis and an arbitrary reference direction). These are called the
ell~psometric parameters of a plane wave.
42.6 Stoker Parameten
Although the ellipsometric parameters completely specify a
monochromatic wave of a gven Frequency, they are not conducive to
understanding the transformations of polanzed light. The Stokes parameters
[I421 are an equivalent description of polarized light and are particularly
useful in scattering problems.
The Stokes vector of a light beam IS p e n by
where [ 1' denotes transpose
Each element of the Stokes matrix can be written in terms of the Ilght
intensities as I = IH + lv
Q = IH - lv
u - I p - l u
V = l ~ - k
where In, Iv, IP, I& IR IL are the light ~ntensities measured with a
horizontal linear polanzer, a vertical linear polanzer, a +45" linear polarizer, a
-45" linear polarizer, a right circular analyzer and a left circular analyzer
respectively placed in front of the detector.
The Stokes elements of a single s~mple wave are related by
I~ 2 @+u2+v2
The equality holds if the light is polarid. If the light IS unpolan* Q = U =
V = 0. Natural sunlight is an example of completely unpolarized light and so it
is represented as [ I, 0.0.0 lT. Ln general, however, light is partially polarized
and so it consists of both polarized and unpolarized wmponenrs. This leads to
the concept of degree of polarization (DOP) Gven by (d + U' + v 2 ) lo 1 I ,
the deget of linear polarization @OLP) defined as ( Q' + U' ) l R / I and the
degee of c~rcular polarization (DOCP) equal to V I I.
The Stokes parameters for linearly polarized and circularly polarired
light are shown In Table 4.1.
Table 4.1 Stokes Parameters for Polarized ligbt
Linearly Polarized
0 " 1 90 ' 1 +45
Circularly Polarized
Rigbt Left
4.2.7 Mueller Matrices
The state of polarization of a beam 1s changed on interact~on w~th an
optical element. It is possible to represent such optical elements by a 4 x 4
matrix called the Mueller matrix. The Mueller matrix describes the relat~on
between "incident" and "transmitted" Stokes vectors and is witten as
S,=MS, (4.7)
where S, and S, are the Incident and the output Stokes vector
respectively.
Mueller matnx formulation IS very useful stnce it gives us a slmple
means of determin~ng the state of polarizahon of a beam wansmitted by an
opt~cal element for an arbitrarily polarized ~ncident beam Moreover, if a
serles of optical elements are interposed in a beam, the combined effect of all
these elements may be determined by merely multiplying their associated
Mueller mabices. The Mueller matrix can be obtained experimentally by
measurements with different combination of source polarizers and detection
analyms.
4.2.8 Absorption and SfPttering by a sphere
The most important exactly soluble problem in the theory of absorption
and scanering by small particles is that for a sphere of arbitrary radius and
refmhve lndm Gustav M e developed a formal soluhon to th~s problem,
whlch IS now called the Mte theory Mle theory of scanenng 1s a
stralghtforward appllcahon of Maxwell's equahons to an Isotropic,
homogenous, d~electnc sphere It 1s equally appl~cable to spheres of all slzes.
refrachve ~ndlces and for &ahon at all wavelengths
Mie's classical solution is described in terms of two parameters, n. and
a n, is the magnitude of refractive index mismatch between particle and
medium. Thls is expressed as the ratio of the refractive index for partlcle and
medium as
The size of the surface of refractive index mismatch is expressed as size
parameter a. This is the ratio of the meridional circumference of the sphere
(2na. where a is the radius) to the wavelength (hind) of light in the medium
It is given by
Consider a source, a spherical scattering particle and an observer
whose three positions define a plane called the scattering plane. Incident light
and scattered light can be reduced to the~r components, which an parallel or
perpendicular to the scattering plane. As shown in the F~gure 4.3, the +lei
polarizer
from source
event
Figure 4.3 Scattering of polarized light
and pnpendicular components can be experimentally selected by a linear
polarizer oriented pruallel or perpendicular to the mitering plane.
The Scanering matrix describes the relationship between incident and
scattered electric fi cld components perpendicular and parallel to the scanenng
plane as observed in the "far-field
The above expression simplifies In practical experiments.
The exponenual term, -exp(ik(r-z)yikr, is a transport factor that
depends on the distance between scatterer and observer. If one
measures scattered 11ght at a contant distance r from the scanerer, eg.,
as a function of angle or onentation of polarization, then the transport
factor becomes a constant.
The total field (E&) depends on the incident field (E,), the scattered
field 6) , and the interaction of these fields c,). If one observes the
scattering from a position which avoids Ei, then both E, and Em are
zero and only E, is observed
For "far-field observation of E, at a distance r from a particle of
diameter d such that ks >> a', k = Zdh, n, = &L, the scattering
elements & and S4 equal zero ( Eq. 4.75, Bohren and Huffman).
Hence for practical scanenng measurements, the above equation simplifies
to the following:
Maxwell's equahons are solved in spherical coordinates through
separation of variables. The inc~dent plane wave 1s expanded in Legendre
polynomials, so the solutions inside and outside the sphere can be matched at
the boundary. The far field solution is expressed In terms of two surtterlng
functions, [I421
" 2 n + l = -[a,rr, (cos8) +bar, (cos 8)]
r-1 n(n + 1) ( 4 12)
where 0 is the scattering angle
The functions n,, and 7, are given by
where P,' are associated Legendre Polynom~als of the first kind
and
a = h = 2xa 1 1 is the size parameter, m 1s the Index of rehaction, a is the
part~cle radi and y,, and S. are spherical Bessel functions
The Mle scattering matnx 1s oven by,
where the fow independent Mie scattering matrix elements are,
L pde) = &ls1(@)l1 +la(@)12i L pdel = K[ls(e)12 - IS1ce)ll %i
pa (el = g& lsd@)s: (el + $1 (el$ (ell
The Mie ext~nction, mttenng and absorpnon cross-sect~ons can all be
expressed in terms of the a. and b, coefficients as,
Another useful quantity is the asymmetry factor, g, which is the first
moment of the phase function and is given by.
The asymmetty factor describes the shape of the phase function; g>l
indtcates f o m d scattering, while g c l indicates backscattering. It is a useful
parameter for characterizing the phase function independent of scattering
angle. The Mie asymmetry factor can be expressed as,
4.3 POLARIZATION FILTERING TO ENHANCE VlSlBUITY OF
SUBSURFACE TISSUE IMAGES
Recently there has been a considerable interest in ustng the
polarization state of the hght as a discnminahon criterion. The polarization
d~scnmination techtque IS based on the assumphon that weakly scattered
light remns its miud polanmon whereas h~ghly scattered light does not
Consider a tlssue illuminated by a Itnearly polarized source. As photons
penetrate the tissue, they interact with various ttssue structures and some of
the Injected photons emerge from the tissue in the backscanering direct~on
Light that reflects from the surface (known as specml reflection) is polarized
but the light that backscanen from somewhere below the surface of the tissue
1s depolarizcd Therefore light viewed in the orthogonal state contains a large
proportion of the light that ~nteracted with the object than the copolarized
light. The use of this fact to discriminate between short and long path photons
in a scattering medium has been well explored theoretically and pract~cally
Studies clearly indicate that polarization discrimination [I 12 - 1271 can be
effective in extending the depth of visibility.
However even for this orthogonal state, as tissue thickness Incress ,
the loss of contrast is still the 11ght backscattered by the medium. So conbast
of the images obtained could be enhanced if this back scattered contribut~on
from the surrounding medium is removed. Hence if the copolarized image is
also recorded and a suitable fraction IS subtracted from the orthogonal
polanzed Image, sigmficant conbast wuld be achieved.
In th~s chapter, a Monte Carlo model for the proposed method is
simulated. Model Images are compared with the experimental images at
632nm for a scattering phantom.
4.4 MONTE CARL0 SIMULATION
The essential characteristic of Monte Carlo code is to study the
propagation of l~ght in biological tissue. The basic idea 1s that photons are
launched from an isotrop~c point source of unlt power within an infinite
homogeneous mubum with no boundaries The medium has optical properties
of absorption, scattering and auisotropy. N photons are launched, each w~th a
"photon weight" initially set to 1 The photon takes steps between interactions
wth the tissue. The steps are based on the probabil~ty of photon movement
before ~ntcraction by absorption and scattering. During each step as the photon
propagates, the photon deposits a fraction of its weight Into the local bin at its
position. The photon is assumed to be dead if the welght of the photon falls
below a f xed threshold. Now a new alive photon is launched.
Photons are launched as a beam from the ongn that initially
propagates parallel to the z-axis The lllwnlnanon 1s assumed to be linearly
polanzed. The biologcal tlssue IS modeled as a slab Infinlie in the x-y plane
containing randomly distributed sphencal Mle scatteren wth slze parameter
ka where k 1s the wave number and a 1s the particle radius [118.119] The
scattenng medium is assumed to be homogenous; hence the probability
density for the distance traveled by the ray before it encounten a particle 1s
determined by a negative exponential msmbution wth mean equal to the
mean free path Hence, in the simulat~on model the d~stance between two
successive scattenng points is a random number c h o m from this distribution.
After every scattering event In the tissue, the polarization state and the
direction of propagatton of the ray changes. The Stokes vector cames the full
polarilation information of the wave under simulafion. The scattering angle is
chosen randomly according to a probability law depending on the phase
function [117]. The scattering angle, 9 is generated by inversion and rejection
methods [1431. At each scattering position, the code randomly chooses the
azimuthal angle, w . Bruscaglioni et a1 [I 141 have proved that if the number
of effective scattering events were larger than a few wts and for pmiculates
that were not small in comparison Gth the wavelength , the angle wuld be
assumed to be equiprobable. Finally performing the local coordinate
transformation using the rotation matrix T [I 171, the modified Stokes vector
after scattering by the particle is
where M(0) is the Mie scattering matnx, and a IS the rotation angle with
respect to the ray direct~on [ I 171. Figure 4 4 illustrates the ray directions and
angles a, 8, for a ray hav~ng Initial d~rect~on d and scattered to a new
direction d' (0.0) and (9 ',@') are the spherical polar coordrnates of d and d'
To image an object located below the surface of the tissue, it IS
assumed that the object is placed at the boundary of the tissue i.e., at a distance
zl in the z direction The object is modeled as a depolarizing diffuse reflector.
The depolarization caused by the object can be modeled by generating random
numbers for the Stokes parameter. But this is equivalent to inducing random
rotation in Q,U,V and is modeled by the Mueller mamx [I441 given by,
Figure 4.4 nlustration of angles a ,8 and q~
* [ :3 z B , C , D J (4.27)
where R(B,C,D) is a Euler matrix of dimension 3x 3, OX is a zero three column
vector and B,CP are Euler angles
The photons after scanenng by the t~ssue medlum h ~ t the object and
ewt the tlssue For each photon backscattered and retumlng to the top surface,
!he coordinates (y,yd) at which ~t intersected the detector plane were
computed uslng geometrical ray traclng [62] uslng
where a, and a, are the exlt angles onto the xz and yz plane
rrspechvely and can be computed from the directional cosines
and f and h are the focal length and distance of the lens of the imaging system
from the surface of the tissue medium. The equation for y and yd takes into
account the refraction at the tissue-air interface.
A photon is counted as detected if its position falls within the area of
the imaging lens. which is assumed to be circular and is determined by
(a2 + ~ d ~ ) ~ ~ < dJ2 (4.32)
w3tere d, is the lens diameter.
The radiance components parallel to the reference plane i e ,
copolarized and perpendicular to the reference plane i.e., cross p o l 4
components can be expressed in terms of the Stokes parameten as
E = ( r + Q P and H = ( r - Q ) / 2 (4.33)
The first two rows of the Stokes vector of these photons impinging on
the lens yield the copolarized and the cross polarized components and these
are transformed to the image plane using paraxial optics. The image plane was
modeled as a grid with each pixel of size 0.04 x 0.04crn and yields an image of
size 60 x 60 pixels.
4.5 THE SIMULATION MODEL
A linearly polarized thin beam at 632 nm impinges on the scattering
tissue medium. The scattering medium was considered to be a homogenous
suspension of 2.02 pm diameter polystyrene spheres in water. The density of
scatteren is assumed to be O.0OI per cubic micron. The refractive index of the
medium (water) was assumed to be 1.33. At 632nm. the complex index of
refraction of the spheres was 1.589 -- i0.00113 and the sample's scanenng
coeffic~ent, reduced scattering coefhent, anisotropy and absorpt~on
coefficient were 100cm.', 8.9cm.'. 0.911 and 1.33cm.l respectively. These
values have been chosen so as to set to values obtalned from real muscle tissue
[371
The optical detector is a CCD camera wlth a circular lens of rad~us
0.05cm placed at a distance of 0 Icm from the surface of the tissue medium
The focal length IS also assumed to be O.lcm.
4.6 EXPERIMENTAL SET IIP
A schematic o i the experimental apparatus used for o b t a i ~ n g the
Images 1s shown in F~gure 4.5. A He Ne laser (Uniphase Inc, 1101P)
emitting approximately 4mW of 632nm light was firs! linearly polarized and
then focused onto the tissue phantom. The phantom that was utilized
in the study was a suspension of 2 . 0 2 ~ diameter
polystyrene spheres ( Polysciences Inc. 19814). The sample was
created by dilution with distilled water to 0.001 spheres per cubic mlcrons.
The index of refraction of the spheres was 1 589 - 10.00113 and the refractive
~ndex of the medium (water) IS 1.33. The sample had a scattering coefficient
(b) of lOOcm", reduced scattering coefic~ent (p,' ) of 8. 9cm.', anisotrop)
(g) of 0.91 1 and absorption coeficient (pa) of 1 33cm.' at 632~11, equal to
the values used in the simulation.
The sample was held in a glass container with flat walls. A 4mm
diameter and Imm thick object composed of chalk material was positioned at
the bottom of the sample. Light emerging from the sample and object was
collected though a camera lens and then ~nto the second polarizing element.
The image was then focused onto a digital CCD camem. The thickness of the
phantom sample was varied from 0 .5m to 2 cm and for each thickness two
Images, namely cross polarized image and copolarized image were acquired.
The obtained images were p r d
4.7 RESULTS AND DISCUSSION
4.7.1 Simulation results
The simulation for the imaging system illustrated in Figure 4.5 was run
by launch~ng a beam of photons from the origin. Random values were taken
for the scattering distance, scattering and the az~muth angles as described in
section 4 4 The &ptb of the object was incremented in steps of 0.5 cm, and
o b j d deptb Icm
o b j h deptb 1.5em
( 4 @) (c)
Figure 4.6 Images of abject from simuhtion for objeet depths of
I and 1.5em: (a) ortbogonrl polarized image; (b) a
pohrized image; ( c) image after polarintion filtcrhg
copolarizcd and cross polarized images were recorded at 632nm. The
simulation was run for a launch of 1x10' photons.
In Figurc 4.6, (a) and (b) shows the orthogonal and wpolarized images
of the object at 632 nm from the simulation. The images in the first and second
row are for the object at depth of Icm and 1.5cm respectively. Figure 4 6 (c) 1s
the ~mage after subtraction of orthogonal state and fraction of copolarized
state. In performing the subtraction [145,146], if the subtraction resulted In a
negative value, it was made equal to zero or a black pixel. Clearly the
improvement in contrast of the images in 4.qc) over 4.6(a) and @) is visible
provtng the merit of this model. The optimum subtraction fraction was chosen
as 0.5 based on best contrast ofthe final image.
4.7.2 Measurement of Conhmst
To validate the proposed technique, image contrast as a function of
depth for the images obtained was computed. The contrast is defined as
where A1 is the average intensity from the light returning from the object
calculated from the central 3 x 3 pixels and Aa is that from light returning
from the background calculated from the c e n d 21 x 21 pixels The image
contrasts are listed in Table 4.2 for three different depths. The values in last
column show the improvement of wnbnst by the proposed method.
Table 4.2 Conhpst for the simahted images of the object obtainecl
a t depths of 0.5,l.O and 1.5 em in the tissue.
1.7.3 Experimental Reaulta
' ~ e ? h of ob~cct
0 5
1 0
I 5
The experiment was carned out using the expenmental set up and
cross and copolarized images of the object at varying depths were recorded
Figure 4,7(a) and 4.8(a) shows the orthogonal image from the experimental set
up for the object at a depth of 0.5 and lcm. Figure 4.7(b) and 4.Yb) IS the
image after subtraction of orthogonal state and fraction of wpolanzed state for
the respctive depths.
Cross polarized image at 632nm
0.901
0.6293
0 5300
Proposed method
1 0000
0 7287
0 651 1
@)
F i i m r e 4.7 Inugcs of tbe object from experime~tatiom
8t 8 dcptb of Okm: (8) C m pd.rizcd ia%c;
@) iaugc after p o h r b h
@)
Figure 4.8 Images of the object fmm experimentation
at a depth of I em: (a) cross pohriud image;
@) image after polariution filtering
4.7.4 Intensity Profile
The intensity profile of the experimental images along the line
contain~ng the object for varying depths 1s shown in Figure 4.9. It can be seen
that the profile is narrow for the object when it is at a depth of Ian from the
surface and the profile wdens as depth is ~ncreased to I .5cm. When the depth
of object is further increased, the object 1s no longer visible even by the
proposed method
P d
Figure 4.9 Intensity profile of experimentally obtained images
after polarization filtering at varying deptha
4.8 SUMMARY
In this chapter the first phase in the development of an optical imagng
system is discussed. This phase termed polarization filtering enhances the
contrast of tissue images at deeper depths using image-processing tools. Image
subhaction is done to detect changes in the tissue composition. Computer
simulations based on Monte Carlo model have been carried out and
experimentation done to check the validity of the method. Resultant images
indicate the merit of the proposed method for depths up to lcm