Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period
Determined in this work are analytical interrelations between orientations of optical axes and birefringence of biological crystals and characteristic values of Jonesmatrix elements corresponding to flat layers of polycrystalline networks, which set the conditions providing formation of polarization...
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irk-123456789-1177172017-05-27T03:05:55Z Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period Balanetska, V.O. Marchuk, Yu. Karachevtsev, A.V. Ushenko, V.O. Determined in this work are analytical interrelations between orientations of optical axes and birefringence of biological crystals and characteristic values of Jonesmatrix elements corresponding to flat layers of polycrystalline networks, which set the conditions providing formation of polarization singularities in laser images. Performed is the complex statistical, correlation and fractal analysis of distributions for the amount of characteristic values inherent to Jones-matrix elements corresponding to bile layers of healthy and sick patients. Also, offered are the objective criteria for differentiation of optical properties typical to polycrystalline networks of human bile in different physiological states, and realized is the Jones-matrix diagnostics of cholelithiasis. 2011 Article Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period / V.O. Balanetska, Yu. Marchuk, A.V. Karachevtsev, V.O. Ushenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 188-194. — Бібліогр.: 31 назв. — англ. 1560-8034 PACS 78.20.Fm, 87.64.-t http://dspace.nbuv.gov.ua/handle/123456789/117717 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Determined in this work are analytical interrelations between orientations of optical axes and birefringence of biological crystals and characteristic values of Jonesmatrix elements corresponding to flat layers of polycrystalline networks, which set the conditions providing formation of polarization singularities in laser images. Performed is the complex statistical, correlation and fractal analysis of distributions for the amount of characteristic values inherent to Jones-matrix elements corresponding to bile layers of healthy and sick patients. Also, offered are the objective criteria for differentiation of optical properties typical to polycrystalline networks of human bile in different physiological states, and realized is the Jones-matrix diagnostics of cholelithiasis. |
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Article |
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Balanetska, V.O. Marchuk, Yu. Karachevtsev, A.V. Ushenko, V.O. |
| spellingShingle |
Balanetska, V.O. Marchuk, Yu. Karachevtsev, A.V. Ushenko, V.O. Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Balanetska, V.O. Marchuk, Yu. Karachevtsev, A.V. Ushenko, V.O. |
| author_sort |
Balanetska, V.O. |
| title |
Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period |
| title_short |
Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period |
| title_full |
Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period |
| title_fullStr |
Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period |
| title_full_unstemmed |
Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period |
| title_sort |
singular analysis of jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2011 |
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http://dspace.nbuv.gov.ua/handle/123456789/117717 |
| citation_txt |
Singular analysis of Jones-matrix images describing polycrystalline networks of biological crystals in diagnostics of cholelithiasis in its latent period / V.O. Balanetska, Yu. Marchuk, A.V. Karachevtsev, V.O. Ushenko // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 2. — С. 188-194. — Бібліогр.: 31 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
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2025-07-08T12:40:51Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 188-194.
PACS 78.20.Fm, 87.64.-t
Singular analysis of Jones-matrix images describing polycrystalline
networks of biological crystals in diagnostics of cholelithiasis
in its latent period
V.O. Balanetska1, Yu. Marchuk2, A.V. Karachevtsev1, V.O. Ushenko1
1Chernivtsi National University, Department for Optics and Spectroscopy,
2, Kotsyubinsky str., 58012 Chernivtsi, Ukraine.
2Bukovina State Medical University, Department of Biophysics and
Medical Informatics, 2, Teatralnaya Sq., 58012 Chernivtsi, Ukraine.
Abstract. Determined in this work are analytical interrelations between orientations of
optical axes and birefringence of biological crystals and characteristic values of Jones-
matrix elements corresponding to flat layers of polycrystalline networks, which set the
conditions providing formation of polarization singularities in laser images. Performed is
the complex statistical, correlation and fractal analysis of distributions for the amount of
characteristic values inherent to Jones-matrix elements corresponding to bile layers of
healthy and sick patients. Also, offered are the objective criteria for differentiation of
optical properties typical to polycrystalline networks of human bile in different
physiological states, and realized is the Jones-matrix diagnostics of cholelithiasis.
Keywords: laser, polarization, birefringence, Jones matrix, statistical moment,
autocorrelation, power spectrum, bile.
Manuscript received 30.09.10; accepted for publication 16.03.11; published online 30.06.11.
1. Introduction
Among the methods for optical diagnostics of biological
layers, widely spread are those of laser polarimetric
diagnostics aimed at optical-anisotropic structure
inherent to human tissues [1 - 31]. The main
“information product” of these methods is obtaining the
coordinate distributions for elements of Mueller and
Jones matrixes corresponding to biological tissues (BT)
[1 - 5] with the following statistical (statistical moments
of the first to fourth orders [5, 6, 10, 14, 19, 25, 26, 30]),
correlation (auto- and mutual-correlation functions [12,
17, 18, 21, 26]), fractal (fractal dimensionalities [5, 6,
25]), singular (distributions of amounts of linear and
circularly polarized states), wavelet (sets of wavelet
coefficients for various scales of biological crystals [22,
28]) analyses. As a result, one can determine
interrelations between a set of these parameters and
distributions of optical axis directions as well as the
birefringence value inherent to networks of optically
uniaxial protein (myosin, collagen, elastin, etc.) fibrils in
optically-anisotropic component of BT layer. Being
based on this approach, a large amount of methods for
diagnostics and differentiation of pathological changes
in BT structure that are related with their degenerative-
dystrophic as well as oncological changes [4 - 6, 12, 19,
20-22, 27, 29, 31].
The above methods of studying the matrix images of
biological layers have been currently developed using the
new approach based on the analysis of coordinate
distributions for the so-called characteristic values that
describes conditions for formation of polarization
singularities [5]. The latter are pronounced as linearly
( −L − points) and circular ( C points) polarized states.
In the case of −L points, the direction of electric field
vector rotation is indeterminate. While for −C points,
indeterminate is the azimuth of electric field vector
polarization. Demonstrated in […] is the efficiency of this
approach for Mueller-matrix diagnostics of pathological
states observed for human biological tissues. At the same
time, there is a widely spread group of optically-
anisotropic biological objects that are not comprised yet
by the matrix methods of laser polarimetric diagnostics.
One can relate to these objects optically-thin (extinction
coefficient 1.0≤τ ) layers of diverse biological liquids
(bile, urine, liquor, synovial liquid, blood plasma, saliva,
etc.). These objects are considerably more accessible for
direct laboratory analyses as compared with traumatic
methods of biological tissue biopsy. Being based on that,
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
it seems topical to adapt the methods of laser polarimetric
188
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 188-194.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
ilities for
diagn
2. Main analytical relations
Our modeling the optical properties of polycrystalline
micel
ase
consistin
lline – solid crystalline phase that is
form
for studying the optical properties of
poly
are
optic
partial crystal is
exha iv
diagnostics to studying the optically-anisotropic structures
in polycrystalline networks of biological tissues.
Our work is aimed at searching the possib
ostics and differentiation of optical properties
inherent to polycrystalline networks of human bile by
determining the coordinate distributions of Jones-matrix
elements with the following statistical, correlation and
fractal analyses of distributions typical for their
characteristic (singular) values for diagnostics of
cholelithiasis in its latent period.
networks observed in human bile is based on the
following conceptions developed for optically-anisotropic
protein fibrils [1-4, 7, 9, 14, 16, 23-27, 30]. From the
optical viewpoint, bile is a multi-component phase-
inhomogeneous liquid consisting of three main fractions:
• optically isotropic – optically homogeneous
lar solution with a small amount of cylindrical
epithelium cells, leukocytes, leukocytoids, phlegm;
• optically anisotropic – liquid-crystalline ph
g of a set comprising liquid crystals of three
types, namely: needle-like crystals of fat acids, crystals
of cholesterol monohydrate, and those of calcium
bilirubinate;
• crysta
ed due to dendrite and disclination mechanisms of
crystallization.
As a base
crystalline networks corresponding to these main
fractions, we took the following conceptions developed
for optically-anisotropic biological liquids […….]:
• separate (partial) biological crystals
ally uniaxial and birefringent;
• optical properties of a
ust ely full described with the Jones operator [5]
{ }
( ) ( )[
( )[ ] ( )
] .
;expcossin;exp1sincos
;exp1sincos;expsincos
22
22
2221
1211 JJ
δ−ρ+ρδ−−ρρ
δ−−ρρδ−ρ+ρ
==
ii
ii
JJ
J
(1)
Here, ρ is the direction of the optical axis;
ndΔπ – phase shift between orthogonal
and of the amplitude of
illuminating laser wave with the wavelength
λ=δ 2
components xE yE
λ ; nΔ -
birefringence index for the crystal with g om c
dimension d .
Let us
e etri
consider the possibility to apply the singular
appr
is defined by the following conditions:
=
=
.0Im
;0Re
ik
ik
J
J (2)
With account of (2), the a sions
are transformed to the following relations:
=+ .0cossincos 22 δρρ
(3)
(4)
(5)
As it follows from (3) to (5), singula
complex matrix elements J are related with definite
ent
lyc
±=∗ .180;90;0 000δ
(6)
On the other hand, th ons (6) set cond
when optically uniaxial birefringent crystals form
polar
oach to the analysis of Jones-matrix images. From
the mathematical viewpoint, a singular value
corresponding to the complex value of a matrix element
( ) ( )⎧ =+ ;0ImRe 22
ikik JJ
ikJ
⎪
⎪
⎩
⎪⎪
⎨
nalytical expres (1)
⎪⎩
⎪
⎨
⎧ =
⇔
;0sinsin2
11
δρ
J ,
⎪⎩
⎪
⎨
⎧
=+
=
⇔
.0coscossin
;0sincos
22
2
22
δρρ
δρ
J
( )
( )⎪⎩
⎪
⎨
⎧
=+
=+
⇔=
.0cos12sin
;0cos1sincos2 22
2112 δρ
δρρJJ
rities of
∗
ik
(characteristic) values of ori ation ∗ρ and phase ∗δ
parameters of the studied po rystalline network:
⎪
⎨
⎧ ±=∗ ;90;45;0 000ρ
⎪⎩
e relati itions
ization singular states −L ( 00 180;0=δ ) and
−C ( 090±=δ ) of a laser beam. Bearing it in mind,
one can determine the characteristic values of Jones-
ix e ∗
ikJ that corresponds to −L and matr lements −C
states of polarization inherent to laser images of
polycrystalline ne rk:
• values 02211 =
two
= JJ correspond to −L
states of polarization;
• values 02112 == JJ correspond to −C
states of polarization.
It uld be nalytical approach ) sho noted that the a (1
to (6) is related to a partial optically uniaxial birefringent
crystal. Formed in real biological layers are complex
networks of these crystals. Therefore, application of the
singular analysis to the Jones matrix of this network
needs determination of coordinate distributions for the
characteristic values ( )yxJik ,∗ in the plane of a
biological liquid layer.
3. Optical setup for Jon
the optically anisotropi
es-matrix mapping
c biological liquids
olarimeter
of Jones-
matrix elements corresponding to birefringent layers.
Shown in Fig. 1 is the optical scheme of a p
r measuring the coordinate distributionsfo
189
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 188-194.
Fig. 1. Optical scheme of the polarimeter: 1 – He-Ne laser; 2 – collimator; 3 – stationary quarter-wave plate; 5, 8 –
mechanically movable quarter-wave plates; 4, 9 – polarizer and analyzer, respectively; 6 – object of inves ation; 7 – micro-
bjective; 10 – CCD camera; 11 – personal computer.
ing a
parallel beam (∅ = 104 µm) of He-Ne laser (λ = 0.6328
µm, W = 5.0 mW). The polarization illuminator consists
of q
Two-dimensional
array
era; 11 – personal computer.
ing a
parallel beam (∅ = 104 µm) of He-Ne laser (λ = 0.6328
µm, W = 5.0 mW). The polarization illuminator consists
of q
Two-dimensional
array
tig
o
Illumination of bile samples was performed usIllumination of bile samples was performed us
uarter-wave plates 3, 5 and polarizer 4, which
provides formation of the laser beam with an arbitrary
polarization state. Using the micro-objective 7
(magnification 4x), images of bile layers were projected
onto the plane of light-sensitive area (800x600 pixels) of
the CCD-camera 10 that provided the range for
measuring the structural elements from 2 to 2000 µm.
The analysis of laser images was carried out using the
polarizer 9 and quarter-wave plate 8.
In our experiments, distributions of characteristic
values for Jones-matrix images of bile layers were
determined in the following manner.
uarter-wave plates 3, 5 and polarizer 4, which
provides formation of the laser beam with an arbitrary
polarization state. Using the micro-objective 7
(magnification 4x), images of bile layers were projected
onto the plane of light-sensitive area (800x600 pixels) of
the CCD-camera 10 that provided the range for
measuring the structural elements from 2 to 2000 µm.
The analysis of laser images was carried out using the
polarizer 9 and quarter-wave plate 8.
In our experiments, distributions of characteristic
values for Jones-matrix images of bile layers were
determined in the following manner.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
s ( )nmJik × were scanned along horizontal direction
mx ...,,1≡ with the step pixx 1=
s ( )nmJik × were scanned along horizontal direction
mx ...,,1≡ with the step pixx 1=Δ . Within the limits
of every ampling (1local s pix×npix)(k = 1,2, …, m), we
calcula ount ( N ) of characteristic values
( ) 0=kJik , - ( ( )k
ikN ). Thus, we could determine the
dependences ( ) )...,,,( )()2( m
ikikikik NNNxN ≡ for
t of characteristic values corresponding to
ons of Jones-matrix elements
( )nmJik × fo gical
states.
for estimating the amount
of chara
ted the am
coordinate
r human bile layers in various physiolo
4. Criteria
cteristic values corresponding
to Jones-matrix images of bile layers
lues of Jones-
terized with the
)1(
the amoun
distributi
( )xNik distributions for characteristic va
matrix elements ( )nmJik × are charac
set of statistical moments of the 1-st to 4-th orders
EAM ;;; σ calcu using the following
relations [5, 6, 25, 30]:
lated
( ) ( )
( ) ( ) .11,11
1
1
4
4
1
3
3
1
∑∑
∑
==
=
σ
=
σ
=
=
D
j
jik
j
jik
j
ik
N
D
EN
D
A
NM
(7)
where D is the amount of characteristic values Nik
within the limits of coordinate distribution for Jones-
matrix images of elements.
To analyze the coordinate structure of
,1, 2
1
∑
=
=σ
D
D
jik
D
j
j N
DD
ikJ
( )xNik
distributions, we used the autocorrelation with
account of the following function [12, 21, 2
method
6]
( ) ( )[ ] ( )[ ]∫ Δ−=Δ
0
10X
Here, x
1
X
ikik dxxxNxNxG . (8)
Δ is the step for changing the coordinates
01 Xx ÷= .
As parameters characterizing
dependences
the
( )xG Δ , we chose the set of correlation
moments of the 1-st to 4-th orders 3;2;1=lK 4; that are
determined like to relations (7).
Estimating the degree of self-s ty and
repeatability for different geometric ( ) scales of the
structure inhere
values co ponding to the Jones matrix elements
imilari
d
nt to Nik(x) distributions of characteristic
rres
( )nmJik × of polycrystalline networks was performed
by calculatin logarithmic dependences for power
spectra
g the
( ) )log(log 1−− dNJ ik that we ximated
using the least-squares method t
re appro
o the curves ( )ηΦ . For
the straight parts of the curves ( )ηΦ , determined were
the slope angles iη and calculated were the values of
fractal dimensionalities for Nik distributions by using the
, 6, 11, 25]
ii tggD
relations [5
η−= 3)( . (9)
Classification of (x) distributions for
characte elements ( )nmJik
Nik
ristic values of matrix × was
carried out in accord with the criteria offered 5]. If
the value of the slope angle cons
in [
t=η in the
dependences ( )ηΦ for 2 or 3 decades of changing the
sizes d , then the distributions Nik(x) are fractal. Under
condition that several constant slope an ailable
in th
gles are av
e curve ( )ηΦ , the Nik(x) sets are multi-fractal. When
no s
ets Nik(x
table slope angles are available over the whole
interval of changing the sizes d, the s ) are
considered as random.
190
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 188-194.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Fig. 3. Coordinate (a), quantitative (b), correlation (c) and spectral (d) distributions for characteristic values of the Jones-matrix
elements J12;21 for the bile polycrystalline network of a healthy patient.
a
b
Fig. 2. Polarization-visualized images of polycrystalline
networks inherent to bile layers for patients in different
physiological states. See explanations in the text.
To make this comparative analysis of
dependences more objective, let us
tion of spectral mome ts from the
5. Jones-matrix diffe
As investigated objects, we used smears of bile taken
ithiasis
tropic
structures corresponding to samples of both types, which
s indicative of a higher level in birefringence
( ) )log(log 1−− dNJ ik
introduce the concep n
1-st to 4-th orders 4;3;2;1=jS he relation (7). - t
rentiation of polarization
properties inherent to the optically anisotropic
component of bile for healthy and sick patients
from healthy (18 samples) and sick with cholel
(17 samples) patients.
Fig. 2 shows laser images of optically aniso
were obtained in the case of crossed transmission planes
of the polarizer 4 and analyzer 9 in the laser polarimeter
(Fig. 1).
As follows from the comparative analysis of laser
images inherent to bile smears of both types, geometric
structures of optically anisotropic clusters are similar.
The higher level of bleaching in bile images for the sick
patients i
( )nm×δ of polycrystalline network. Therefore, we have
focused on investigation of diagnostic possibilities of the
complex statistical, correlation and phase analysis aimed
at distributions of the amount of characteristic values for
Jones-matrix elements J12;21(m×n) = 0 describing
-thin bile layers of both types.
Depicted in Figs 3 and 4 are the results of studying
the coordinate
optically
( ) 021;12 =× nmJ (fragments (a)),
quantitative ( )xN 21;12 (fragments (b)),
autocorrelation ( )xG Δ21;12 (fragments c)) and (
logarithmic ( ) 1
21; loglog −− dxN (fragments (d))
dependences that characterize the structure of
12
191
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 188-194.
Fig. 4. Coordinate (a), quantitative (b), correlation (c) and spectral (d) distributions for characteristic values of the Jones-
atrix elements J12;21 for the bile polycrystalline network of a patient with cholelithiasis.
m
distributions for characteristic values inherent to the
Jones-matrix elements 021;12 =J corresponding to bile
poly
ned data
on and frac
images 1
e owing to growth
of t
• Autocorrelation functions for the distri
21;1221;1221;12
ically (Figs 3
hom ncrystalline networks of healthy (Fig. 3) and sick
(Fig. 4) patients.
It follows from the obtai upon statistical,
correlati tal structures of the distribution for
the characteris
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Table 1. Statistical, correlation and spectral parameters for distributions of characteristic values in Jones-matrix
images of the element J12;21(m×n) corresponding to human bile in different physiological state.
Parameters Statistical Correlation Spectral
State norm pathology norm pathology norm pathology
1-st moment 0.18±0.038 0.51±0.11 0.48±0.092 0.41±0.083 0.17±0.036 0.19±0.043
2-nd moment 0.29±0.066 0.19±0.034 0.18±0.041 0.23±0.049 0.16±0.035 0.13±0.024
3-rd moment 0.47±0.099 0.84±0.189 0.16±0.029 0.21±0.041 0.11±0.023 0.17±0.035
4-th moment 0.38±0.075 0.65±0.15 0.25±0.053 0.32±0.065 0.18±0.041 0.25±0.054
tic sampling 021;12 =J in Jones-matrix
( )nm×21;2 of bile layers for both groups that:
• General amount of characteristic values
021;12 =J in the coordinate distribution J
J
12;21(m×n) for
the bile layer in the case of cholelithiasis is practically 2-
fold increased (Figs 3 and 4, fragments (a) and (b)). This
fact indicates increase in birefringenc
he concentration of the optically anisotropic
component in bile of the sick patient.
butions
of the amount of characteristic values
( ) )...,,,( )()2()1( mNNNxN ≡ for
bile samples of both types decay monoton
and 4, fragments (c)),
21;12
which is indicative of
oge eity in the coordinate distribution 021;12 =J .
values • Sets of
( ) )...,,,( )(
21;12
)2(
21;12
)1(
21;1221;12
mNNNxN ≡ are
fractal, since the Log –log dependenc wer
spectra (Figs 3 and 4, fragments (d)) c
the d
es for po
orresponding to
istribution of the amount of values 021;12 =J are
characterized with the only slope angle.
From the quantitative viewpoint, statistical,
correlation and self-similar structures of distributions for
the amount of characteristic values in Jones-matrix
images J12;21(m×n) corresponding to bile smears of both
types (Fig. 1) are illustrated by the set of moments from
e 1-st to 4-th orders, magnitudes and change ranges of
hich have been summarized in Table 1.
As it follows from the data summarized in Table 1,
main criteria for diagnostics of cholelithiasis in its latent
th
w
192
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 188-194.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
period can be based on statistical moments of the 1-st to
4-th orders that characterize distributions of the amount
of characteristic values 021;12 =J in Jones-matrix
images of ( )nmJ ×21;12 corresponding to
optically anis orks in human bile. Also
ascertained are the following differences between
EAM ;;;
elements
otropic netw
σ values (relations (7)) that
characterize dependences ( )xN 21;12 for Jones-matrix
images describing bile samples take from patients of
the reference group and from th cholelithiasis:
•
n
those wi
M - increase up to 3 times;
σ• - decrease down to 1.53 times;
• - increase up to 1.7 times; A
• E - increase up to 1.8 times.
The differences between values of correlation
7. Alexander G. Ushenko, “Polarizati
laser scatte
( K 4;3;2;1=i ) and mome
riz d s for b ples o
ious sign lie ang
to 40
oncl
e
characterist ributions of
Jones-matr n properties
of b frin orks in human
biolo
olarimetr holelithi
ng the statistical analy
1.
. Keijzer, S. L. Jacques, A. J. Welch,
tion of random electromagnetic beams ,”
Phys. Lett. A., Vol. 312, pp. 263-267, 2003.
der G. Ushenko and Vasilii P. Pishak,
“Laser Polarimetry of Biological Tissue: Principles
. Boston: Kluwer Academic
Publishers, 2004, pp. 93-138.
sky, Ed. Washington: Society of
6. henko,
Valery V. Tuchin, Ed. USA: CRC Press, 2010,
21-67.
on structure
ring fields,” Optical Engineering, vol.
34(4), pp. 1088-1093, November 1995.
8. A.G. Ushenko, iagnostics of biofractals,”
uantum tronics, ), pp. 1078–1084,
ecem
.V. A.G A.D. Arkhelyuk,
B. . ets, “Structure of
atri ans f laser radiation by
biofractals,” Quantum Electronics, vol. 29(12), pp.
1074-1077, December 1999.
10.
o, D. N. Burkovets, “Scattering of Laser
11.
ctober 2000.
13.
14. shenko, “Laser polarimetry of polarization-
, February
15.
gical tissues under the conditions
16.
l. 91(6), pp.932-936,
17.
78, June 2002.
spectral ( 4;3;2;1=iS ) nts that
characte e N ( )x21;12 istribution ile sam f Q
var types are in ificant and within the r e 9. O10 %.
6. C usions
1. ered is the method that all
c values for coordinate
Off ows estimating th
i dist
ix elements to describe polarizatio
ire gent polycrystalline netw
gical liquids.
Found and grounded are criteria for laser
p ic diagnostics of c asis in its latent
period by usi sis of distributions
typical for characteristic values of Jones-matrix images
corresponding to birefringent polycrystalline networks in
human bile.
References
W.-F. Cheong, S. A. Prahl, A. J. Welch, “A Review
of the Optical Properties of Biological Tissues,”
IEEE J. Quantum Electron, Vol. 26, pp. 2166-
2185, Dec. 1990.
2. S. A. Prahl, M
“A Monte Carlo model of light propagation in
tissue,” SPIE Proceedings of Dosimetry of Laser
Radiation in Medicine and Biology, Vol. IS 5, pp.
102-111, 1989.
3. E. Wolf, “Unified theory of coherence and
polariza
4. Alexan
and Applications”, in Handbook of Coherent-
Domain Optical Methods: Biomedical Diagnostics,
Environmental and Material Science, vol. I, Valery
V. Tuchin, Ed
5. O. V. Angelsky, A. G. Ushenko, Yu. A. Ushenko,
V. P. Pishak, “Statistical and Fractal Structure of
Biological Tissue Mueller Matrix Images”, in
Optical Correlation Techniques and Applications,
Oleg V. Angel
Photo-Optical Instrumentation Engineers , 2007,
pp. 213-266.
O.V. Angelsky, A.G. Ushenko, Yu.A. Us
V.P. Pishak, and A.P. Peresunko, “Statistical,
Correlation, and Topological Approaches in
Diagnostics of the Structure and Physiological
State of Birefringent Biological Tissues”, in
Handbook of Photonics for Biomedical Science,
pp.
of
O.V. Angel'skii, A.G. Ushenko A.D. Arheluk, S.B.
Ermolenk
“Laser d
Elec vol. 29(12
D ber 1999.
Angel'skii, . Ushenko,
S. Ermolenko, D N. Burkov
m ces for the tr formation o
Radiation by Multifractal Biological Structures,”
Optics and Spectroscopy, vol. 88(3), pp. 444-448,
March 2000.
A.G. Ushenko, “Polarization Structure of
Biospeckles and the Depolarization of Laser
Radiation,” Optics and Spectroscopy, vol. 89(4),
pp. 597-601, O
12. A.G. Ushenko, “Stokes-correlometry of
biotissues,” Laser Physics, vol. 10(5), pp.1286-
1292, May 2000.
A.G. Ushenko, “The Vector Structure of Laser
Biospeckle Fields and Polarization Diagnostics of
Collagen Skin Structures,” Laser Physics, vol.
10(5), pp. 1143-1149, May 2000.
A.G. U
phase statistical moments of the object field of
optically anisotropic scattering layers,” Optics and
Spectroscopy, vol. 91(2), pp. 313-316
2001.
A.G. Ushenko, “Polarization contrast enhancement
of images of biolo
of multiple scattering,” Optics and Spectroscopy,
vol. 91(6), pp. 937-940, August 2001.
A.G. Ushenko, “Laser probing of biological tissues
and the polarization selection of their images,”
Optics and Spectroscopy, vo
August 2001.
A.G. Ushenko, “Correlation processing and
wavelet analysis of polarization images of
biological tissues,” Optics and Spectroscopy, vol.
91(5), pp.773-7
193
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 2. P. 188-194.
18. A.G. Ushenko, “Polarization correlometry of
angular structure in the microrelief pattern or rough
surfaces,” Optics and spectroscopy, vol. 92(2), pp.
227-229, June 2002.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
agnostics of Their Pre-Cancer
20.
plex degree of
21. Angelsky, A. G. Ushenko, and Ye. G.
), pp. 4811-
22.
singularities of biological tissues
23.
blood plasma and
24. .G. Ushenko, I.P. Polyanskiy,
25. ergej Yermolenko,
of human bile secret,” Proceedings of the SPIE,
vol. 7368, Article ID 73681Q, July 2009.
27. A.G. Ushenko, Yu.Ya. Tomka, V.I. Istratiy,
“Polarization selection of two-dimensional phase-
inhomogeneous birefringence images of
biotissues,” Proceedings of the SPIE, vol. 7388,
Article ID 73881L, December 2009.
28. A.G. Ushenko, A.I. Fediv, Yu.F. Marchuk,
“Singular structure of polarization images of bile
secret in diagnostics of human physiological state,”
Proceedings of the SPIE, vol. 7368, Article ID
73681S, July 2009.
29. S.B. Yermolenko, A.G. Ushenko, P. Ivashko,
“Spectropolarimetry of cancer change of
biotissues,” Proceedings of the SPIE, vol. 7388,
Article ID 73881D, December 2009.
30. A.G. Ushenko, I. Z.Misevich, V. Istratiy, I.
Bachyns’ka, A. P. Peresunko, Omar Kamal
Numan, and T. G. Moiysuk, “Evolution of Statistic
Moments of 2D-Distributions of Biological Liquid
Crystal Net Mueller Matrix Elements in the Process
of Their Birefringent Structure
Changes,” Advances in Optical Technologies, vol.
2010, Article ID 423145, March 2010.
31. O.V. Dubolazov, A.G. Ushenko, V.T. Bachynsky,
A. P. Peresunko, and O. Ya. Vanchulyak, “On the
Feasibilities of Using the Wavelet Analysis of
Mueller Matrix Images of Biological
Crystals,” Advances in Optical Technologies, vol.
2010, Article ID 162832, March 2010.
19. O.V. Angelsky, A.G. Ushenko, Ye.G. Ushenko, “2-
D Stokes Polarimetry of Biospeckle Tissues Images
in Pre-Clinic Di
States,” Journal of Holography and Speckle, vol.
2(1), pp. 26-33, April 2005.
Oleg V. Angelsky, Alexander G. Ushenko, and
Yevheniya G. Ushenko, “Com
mutual polarization of biological tissue coherent
images for the diagnostics of their physiological
state,” J. Biomed. Opt., vol. 10(6), Article ID
060502, November 2005.
O. V.
Ushenko, “Investigation of the correlation structure
of biological tissue polarization images during the
diagnostics of their oncological changes,” Physics
in Medicine and Biology, vol. 50(20
4822, September 2005.
Oleg V. Angelsky, Alexander G. Ushenko,
Yevheniya G. Ushenko, Yuriy Y. Tomka,
“Polarization
images,” J. Biomed. Opt., vol. 11(5), Article ID
054030, September-October 2006.
O.G. Ushenko, S.G. Guminetsky, A.V. Motrich,
“Optical properties of urine,
pulmonary condensate of the patients with
pulmovnary form of tuberculosis,”
Photoelectronics, vol.16, pp. 133-139, June 2007.
S.H. Guminetskiy, O
A.V. Motrych, F.V. Grynchuk, “The optical
method for investigation of the peritonitis
progressing process,” Proceedings of the SPIE, vol.
7008, Article ID 700827, April 2008.
Alexander Ushenko, S
Alexander Prydij, Stepan Guminetsky, Ion Gruia,
Ovidiu Toma, Konstantin Vladychenko, “Statistical
and fractal approaches in laser polarimetry
diagnostics of the cancer prostate tissues,”
Proceedings of the SPIE, vol. 7008, Article ID
70082C, April 2008.
26. A.G. Ushenko, A.I. Fediv, Yu.F. Marchuk,
“Correlation and fractal structure of Jones matrices
194
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