Complex degree of coherency inherent to laser images of blood plasma polycrystalline networks
Given in this paper are theoretical basics for correlation-phase analysis of laser images inherent to human blood plasma. Also presented are comparative results of measurements aimed at coordinate distributions of the module of complex degree of coherency (CDC) and complex degree of mutual polari...
Збережено в:
| Дата: | 2010 |
|---|---|
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2010
|
| Назва видання: | Semiconductor Physics Quantum Electronics & Optoelectronics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/118548 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Complex degree of coherency inherent to laser images of blood plasma polycrystalline networks / Yu.A. Ushenko, V.V. Istratiy, A.V. Dubolazov, A.P. Angelsky // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 404-412. — Бібліогр.: 39 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-118548 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1185482017-05-31T03:05:03Z Complex degree of coherency inherent to laser images of blood plasma polycrystalline networks Ushenko, Yu.A. Istratiy, V.V. Dubolazov, A.V. Angelsky, A.P. Given in this paper are theoretical basics for correlation-phase analysis of laser images inherent to human blood plasma. Also presented are comparative results of measurements aimed at coordinate distributions of the module of complex degree of coherency (CDC) and complex degree of mutual polarization (CDMP) of laser images describing blood plasma of a healthy person as well as of a patient with prostate cancer of the first stage. The authors investigated both values and ranges of changing the statistical (moments of the first to fourth orders), correlation (coefficients of the GrammCharlie expansion for autocorrelation functions) and fractal (slopes and dispersion of extremes for logarithmic dependences of power spectra) parameters for coordinate distributions CDC and CDMP. Determined are objective criteria for diagnostics of cancer changes in blood plasma of a patient with cancer. 2010 Article Complex degree of coherency inherent to laser images of blood plasma polycrystalline networks / Yu.A. Ushenko, V.V. Istratiy, A.V. Dubolazov, A.P. Angelsky // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 404-412. — Бібліогр.: 39 назв. — англ. 1560-8034 PACS 78.20.Fm, 87.64.-t http://dspace.nbuv.gov.ua/handle/123456789/118548 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
Given in this paper are theoretical basics for correlation-phase analysis of laser
images inherent to human blood plasma. Also presented are comparative results of
measurements aimed at coordinate distributions of the module of complex degree of
coherency (CDC) and complex degree of mutual polarization (CDMP) of laser images
describing blood plasma of a healthy person as well as of a patient with prostate cancer
of the first stage. The authors investigated both values and ranges of changing the
statistical (moments of the first to fourth orders), correlation (coefficients of the GrammCharlie
expansion for autocorrelation functions) and fractal (slopes and dispersion of
extremes for logarithmic dependences of power spectra) parameters for coordinate
distributions CDC and CDMP. Determined are objective criteria for diagnostics of cancer
changes in blood plasma of a patient with cancer. |
| format |
Article |
| author |
Ushenko, Yu.A. Istratiy, V.V. Dubolazov, A.V. Angelsky, A.P. |
| spellingShingle |
Ushenko, Yu.A. Istratiy, V.V. Dubolazov, A.V. Angelsky, A.P. Complex degree of coherency inherent to laser images of blood plasma polycrystalline networks Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Ushenko, Yu.A. Istratiy, V.V. Dubolazov, A.V. Angelsky, A.P. |
| author_sort |
Ushenko, Yu.A. |
| title |
Complex degree of coherency inherent to laser images of blood plasma polycrystalline networks |
| title_short |
Complex degree of coherency inherent to laser images of blood plasma polycrystalline networks |
| title_full |
Complex degree of coherency inherent to laser images of blood plasma polycrystalline networks |
| title_fullStr |
Complex degree of coherency inherent to laser images of blood plasma polycrystalline networks |
| title_full_unstemmed |
Complex degree of coherency inherent to laser images of blood plasma polycrystalline networks |
| title_sort |
complex degree of coherency inherent to laser images of blood plasma polycrystalline networks |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/118548 |
| citation_txt |
Complex degree of coherency inherent to laser images
of blood plasma polycrystalline networks / Yu.A. Ushenko, V.V. Istratiy, A.V. Dubolazov, A.P. Angelsky // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2010. — Т. 13, № 4. — С. 404-412. — Бібліогр.: 39 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT ushenkoyua complexdegreeofcoherencyinherenttolaserimagesofbloodplasmapolycrystallinenetworks AT istratiyvv complexdegreeofcoherencyinherenttolaserimagesofbloodplasmapolycrystallinenetworks AT dubolazovav complexdegreeofcoherencyinherenttolaserimagesofbloodplasmapolycrystallinenetworks AT angelskyap complexdegreeofcoherencyinherenttolaserimagesofbloodplasmapolycrystallinenetworks |
| first_indexed |
2025-07-08T14:13:20Z |
| last_indexed |
2025-07-08T14:13:20Z |
| _version_ |
1837088378864009216 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 404-412.
PACS 78.20.Fm, 87.64.-t
Complex degree of coherency inherent to laser images
of blood plasma polycrystalline networks
Yu.A. Ushenko, V.V. Istratiy, A.V. Dubolazov, A.P. Angelsky
* Chernivtsi National University, Department for Correlation Optics,
2, vul. Kotsyubyns’kogo, 58012 Chernivtsi, Ukraine; yuriyu@gmail.com
** Chernivtsi National University, Department for Optics and Spectroscopy,
2, vul. Kotsyubyns’kogo, 58012 Chernivtsi, Ukraine
Abstract. Given in this paper are theoretical basics for correlation-phase analysis of laser
images inherent to human blood plasma. Also presented are comparative results of
measurements aimed at coordinate distributions of the module of complex degree of
coherency (CDC) and complex degree of mutual polarization (CDMP) of laser images
describing blood plasma of a healthy person as well as of a patient with prostate cancer
of the first stage. The authors investigated both values and ranges of changing the
statistical (moments of the first to fourth orders), correlation (coefficients of the Gramm-
Charlie expansion for autocorrelation functions) and fractal (slopes and dispersion of
extremes for logarithmic dependences of power spectra) parameters for coordinate
distributions CDC and CDMP. Determined are objective criteria for diagnostics of cancer
changes in blood plasma of a patient with cancer.
Keywords: laser, polarization, correlation, blood plasma, birefringence, crystal,
statistical moment, fractal.
Manuscript received 23.07.10; accepted for publication 02.12.10; published online 30.12.10.
1. Introduction
Among the diversity of directions for optical diagnostics
of biological objects, polarization methods are a most
popular [1 – 39]. The latter are based on such
fundamental conceptions as “matrix of coherency” and
“degree of polarization” that describe the field of
scattered radiation [1, 2]. These parameters characterize
correlation similarity of orthogonal components
of electromagnetic wave amplitudes in
separate points of optical field with coordinates
( ) ( )rErE yx ,
( )r [3].
In this sense, these analytical approaches will be
considered as the “one-point” ones. They serve as a base
for development of methods providing polarization
mapping biological tissues (BT) and diagnostics of their
pathological changes in structure (e.g., cancer of
women’s reproductive organs) [13 – 15].
Wide application of modern laser technique in
investigations of BT structures stimulates development
of essentially new approaches to analysis and description
of polarization-inhomogeneous fields of scattered
coherent radiation. One-point methods got their
development in a more general “two-point” approach
based on the analysis aimed at the degree of coherency
between polarization states of adjacent ( rrr Δ+11, )
points in the field of scattered radiation [4-11]. From the
quantitative viewpoint, this correlation may be
characterized with the value of module for complex
degree of mutual polarization (CDMP) ( )rrrV Δ+11,
[12]. In the works {13, 29], based on CDMP developed
was the method of polarization-correlation mapping
(PCM) for an optically-anisotropic BT structure. It was
based on the analysis of coordinate distributions
( )rrrV Δ+11, . As a result, the authors realized not only
diagnostics, but also differentiation of severity inherent
to oncological changes (precancer – cancer of the first to
fourth stages) in tissues of woman’s reproductive sphere
[18].
On the other hand, there is a wide circle of weakly
anisotropic biological liquids (BL) taken from a human
organism, which are considerably more accessible as
compared with BT samples that need a traumatic biopsy
operation. From the physical viewpoint, BL are matter
with a weak polarization modulation of laser radiation
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
404
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 404-412.
[33, 35, 37]. Thereof, the task of using phase
information contained in the field of radiation scattered
by BL is topical.
Our work is aimed at development and testing the
two-point correlation-phase method in investigations of
blood plasma in order to provide early diagnostics of
oncological changes in human organs (e.g., prostate).
2. Model conceptions
As a basis for the analysis of phase structure inherent to
the field of laser radiation transformed by blood plasma,
we used the following model [13, 17, 18, 21, 22, 25, 28,
32, 33, 35]:
- blood plasma is considered as a two-component
isotropic-anisotropic structure;
- optically isotropic component is the fraction
consisting of optically single-axis birefringent crystals of
albumin and globulin amino acids;
- phase properties of these biological crystals are
characterized with the Jones matrix
{ }
2221
1211
dd
dd
D = , (1)
where
( )
( ) ( ) ( )( )
( ) ( ) ( )( )(
( ) ( ) ( )( )⎪
⎩
⎪
⎨
⎧
δ−ρ+ρ=
δ−−ρρ==
δ−ρ+ρ=
=δρ
.expcossin
;exp1sincos
;expsincos
,,
22
22
2112
22
11
rirrd
rirrdd
rirrd
rdik
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
)
(2)
Here, is the direction of the optical axis; ρ
ndΔλ
π=δ 2 - phase shift between orthogonal
components of the amplitude; – wavelength; –
geometric distance; - birefringency coefficient.
λ d
nΔ
3. Brief theory of the correlation-phase method
As a basis for “two-point” correlation-phase method
providing investigation of blood plasma, we used the
conception of CDC for points of its laser image. The
parameter below characterizes correlation
between orthogonal components ( ) of the
amplitude of laser field in two points with coordinates 1r
d 2r
( 21, rrμ )
an
yx EE ,
( )
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⋅
=μ
◊
),(),(
),()r,(
)r,(
2211
2121
21 rrTrWrrWTr
rrWrWTr
r . (3)
Here is the transverse spectral density
matrix of the following form
)r,( 21rW
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
= ∗∗
∗∗
)()()()(
)()()()(
)r,(
2121
2121
21 rErErErE
rErErErE
rW
yyxy
yxxx , (4)
where is the Hermitian conjugate matrix to
; T
)r,( 21rW ◊
)r,( 21rW r - spur of the matrix.
Let us write the expression (3) for laser field
transformed by a biological crystal (relations (1) and (2))
in two its arbitrary points. In this case, the transverse
spectral matrix (relation (4)) for the density of this field
takes a look
)()r,()()r,( 221121 rDrWrDrW inout ⋅⋅= ◊ . (5)
Here and are Jones matrixes for the
biological crystal in the points and ; -
transverse spectral density matrix for the probing laser
beam
)( 1rD )( 2rD
1r 2r )( 21 xxWin ,
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
= ∗∗
∗∗
)()()()(
)()()()(
),(
2121
2121
21 rErErErE
rErErErE
rrW
yyxy
yxxx
in . (6)
With account of the expressions (1) to (6), the
expression ( )21, rrμ takes the following look
( ) .
))2exp(sin)(cos(
1,
1212
2
12
221
δΔ⋅−ρΔ+ρΔ+
=μ
iiba
rr
(7)
Here, ( ) ( )2112 rr ρ−ρ=ρΔ , ( ) ( )2112 rr δ−δ=δΔ ,
and ( iba + ) is the coefficient of proportionality.
The expression (7) shows a simultaneous
dependence of the CDC value for blood plasma image
both on the orientation ( ρΔ ) and phase ( ) structure
of its polycrystalline network. To eliminate this
ambiguity one can using laser probing beam with
circular polarization. In this case, Exp. (7) is transformed
into the only phase dependence
δΔ
( ) ( ) )12(exp
1,
12
21 +δΔ−
=μ
i
rr . (8)
In what follows (without losses in completeness of
analysis), let us confine ourselves by taking into account
the CDC module ( )21, rrμ
( ) ( ) 1
1221 2cos15.0, −δΔ+=μ rr . (9)
Thus, to determine the value of CDC module we
need information about the difference between phase
shifts ( ) ( )21 rr δ−δ inherent to orthogonal components of
amplitudes ( ) ( )11 , rErE yx and in the
points with coordinates .
( ) ( )22 , rErE yx
21, rr
To obtain this information, let us consider the
process of formation of the laser image
( ( )yxrEE ,0 ≡→ ) for the layer of blood plasma
( ( ){ }rD ) that is placed between two phase filters –
405
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 404-412.
quarter-wave plates ({ }, 1Φ { }2Φ ) and polarizers ({ }1P ,
), transmission planes of which make +45º and
–45 º angles with directions of maximum velocity axes.
{ }2P
This optical arrangement provides two functions
simultaneously:
- formation of the circular-polarized laser
beam that probes blood plasma; { }{ } 0110 EPE Φ=∗
- direct measurement of values for the phase
shift between orthogonal components of the laser
wave amplitudes
δ
( )yx EEE , in the points with
coordinates r .
Let us consider this phase-metric process in detail.
The amplitude in every point of polarization-
filtered laser image describing blood plasma can be
represented with the following matrix equation
( )rE
( ) { }{ } ( ){ }{ }{ } 0112225.0 EPrDPrE ΦΦ= . (10)
Here
( ) ( )
( )
( ) ( )( )
{ } { } { } { }⎪
⎪
⎩
⎪
⎪
⎨
⎧
=Φ=Φ
−
−
==
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
δ−
=⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
δ−
=
.
10
0
,
0
01
,
11
11
,
11
11
,
exp
,
exp
2121
00
0
0
i
i
PP
rirE
rE
rE
iE
E
E
y
x
y
x
(11)
In a particular case of linearly-polarized laser
radiation ( ) , Eq. (10) takes a look ⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
=
1
1
0E
( )
( ) ( ) ( )[ ] ( ) ( ) ( )[ ]{
( ) ( ) ( )[ ]{ } ( ) ( ) ( )[ ]
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Fig. 1. Optical scheme for measurements. 1 - He-Ne laser; 2 – collimator; 3, 5, 8 – quarter-wave plates; 4, 9 – polarizer and
analyzer, respectively; 6 – object; 7 – micro-objective (x4); 10 – CCD camera; 11 – personal computer.
}
.
1
1
11
11
0
01
expcossinexp1sincos
exp1sincosexpsincos
10
0
11
11
25.0
22
22
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
×
×
δ−ρ+ρδ−−ρρ
δ−−ρρδ−ρ+ρ
×
−
−
=
i
rirrrirr
rirrrirr
i
rE
(12)
Solution of the matrix equation (12) is values of
complex amplitudes that are exclusively
determined by the phase shift
( )rE
( )rδ and do not depend on
the orientation of the optical axis inherent to a
biological crystal.
( )rρ
Thus, the intensity ( )rI of every point in the
polarization-filtered laser image of blood plasma layer is
defined as
( ) ( ) ( ) ( )
⎥⎦
⎤
⎢⎣
⎡δ== ∗
δ 2sin 2
0
rIrErErI . (13)
Here, 10 ≡I is the intensity of a laser beam that
probes blood plasma. It is clear that the value of phase
shift ( )rδ can be determined using a direct measurement
of the intensity ( )rIδ in the given point of the laser
image
( )r
( ) ( )rIr δ=δ arcsin2 . (14)
Using the relations (10) to (14), one can obtain the
expression for the algorithm providing determination of
the CDC module describing the laser image of blood
plasma in the points and 1r 2r
( ) ( ) ( )( )( ) .arccosarccos2cos15.0,
1
2121
−
−+=μ rIrIrr
(15)
4. Method to measure the coordinate distribution
of the CDC module over the points of a laser image
Shown in Fig. 1 is the optical scheme to measure
coordinate distribution of the CDC module for laser
images of blood plasma [13, 32].
Illumination of blood plasma layers (smears) was
performed using a parallel beam (Ø= µm) from a
Hе-Nе laser 1 (λ = 0.6328 µm). The transmission plane
of the polarizer 4 and the axis of the maximum velocity
in the quarter-wave plate 5 made the angle .
The image of blood plasma samples 6 was projected
using the micro-objective 7 into the plane of a light-
sensitive area (
410
045=Θ
pixpixnmr 600800 ×=×≡ ) of
CCD camera 10.
The transmission plane of the analyzer 9 was
oriented at the angle °−=Θ 45 relatively to the axis of
the maximum velocity in the quarter-wave plate 8,
which provided formation of conditions for phase
filtration (relations (10) to (14)) for the laser image of a
blood plasma sample.
The CCD camera 10 provided measurements of
discrete two-dimensional ( )nm× distributions for the
intensity ( )nmI ×δ . Then, calculated in accord with
406
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 404-412.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
coordina
Δ+
↓↓
→→→→
↓↓
nmnn
m
rrrr ...11
of th ensional
array
sing the relation (15), for every pair of the points
rik ,
lood plasm
s a result, we obtained the coordinate distribution
( ) ( )⎟
⎟
⎟
⎠
⎜
⎜
⎜
⎝
⎛
Δ+Δ+
μ
−− rrrrrr
r
nmnmnn 1111 ,...,
......... that, in what
follows, we shall name as the correlation-phase map
5. Algorithms for the complex statistical,
(14) were te distributions ( )nm ×δ scanned
with the step pixr 1=Δ along the lines
⎛ Δ+ rrrr ... 11111
⎟
⎟
⎟
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎜
⎜
⎜
⎝
e two-dim
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
δ
nmn
m
rr
rr
,...
..........
,...
1
111
.
U
( rrik Δ+ ) in the polarization-filtered laser image of
b a, we determined the value of CDC
module ( )rrr ikik Δ+μ , .
A
( ) ( ) ⎞Δ+Δ+ −− rrrrr mm 11111111 ,...;
(CPM) for the blood plasma image.
correlation and fractal analysis of CPM
To objectively estimate the distributions
( )nymx ÷=−÷=μ 1,11 for blood plasma laser images,
atistical, correlation and fractal
analysis of their coordinate structure. The set of
statistical moments of the first to fourth orders μ
we used the complex st
=
, 15, 34
4,3,2,1jZ
was calculated using the following relations [14 ,
35, 39]
∑
=
μ μ=
N
i
iN
Z
1
1
1 , ∑
=
μ μ=
N
i
iN
Z
1
2
2
1 ,
( ) ∑
=
μ
μ μ=
N
i
iNZ
Z
1
3
3
2
3
11 ,
( ) ∑
=
μ
μ μ=
N
i
iNZ
Z
1
4
2
2
4
11 . (16)
Here, is the amount of pixels in the digital
came
orre
N
ra.
The c lation analysis of CPM is based on the
autocorrelation method with using the function [27, 30,
35]
( ) ( )[ ] ( )[ ]∫ Δ−μμ=Δ
→
μ
m
÷= mni dmmmm
m
mK
1
01
1lim . (17)
Here, is the “step” for changing
coordinates ( f CDC distribution for the
separate pixels in the digital camera.
using
( )pixm 1=Δ
mx ÷= 1 ) o
i - th line of
The net expression for the autocorrelation function
was obtained averaging the partial functions
(expression (17)) over all the lines ni ÷=1
( )
( )
n
mK
mK
n
i
i∑
= (18)
To quantitatively characterize the autocorrelation
dependence
μ
μ
Δ
=Δ 1 .
s ( )mK Δμ , we chose:
• “correlation area” S
(∫ Δ= μμ
m
KS
μ
) ;
1
dmm (19)
• “correlation moment” that defines the
excess for Gramm-C
μ
4Q
harlie expansion
( )( )
( )( )
;2
1
4Δ
=
∑
=i
imK
Q
1
2
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
Δ∑
=
N
i
i
N
mK
(20)
The fractal analysis of distributions
based on calculations of logarithmic dependences
)( nm×μ was
( ) 1loglog −−μ dJ for power spectra
where
( )μJ
( ) ∫
+∞
νπνμ=μ dJ 2cos , (21)
∞−
1−= dν are the spatial frequencies that are
etermined by geom sizes ) of stru
elements in laser images inherent to blood plasma layer.
sing the
d etrical ctural ( d
U least squares method, the dependences
( ) 1loglog −−μ dJ were approximated to the curves
( )ηV , the straight parts of which provided determination
of the slope angles η and fractal dimensions μF [34]
them
η− tg3 . (22)
Classification of the coordinate distr tions
)( nm
corresponding to
F
ibu
=μ
×μ was performed in accord with the following
criteria [13-1
•
5]:
fractal or self-similar, when the slope is constant
cons( t=η ) within the limits of 2 or 3 decades for
changing sizes ; d
• )( nm×μ - multi-fractal, when there are several
sl s ope angle ( )ηV ;
)( nm• ×μ - rand m, who en any stable slope angles
( )ηV are absent over the whole interval of
changing the dsizes .
All the distributions were
characterized with the dispersion
( ) 1loglog −−μ dJ
407
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 404-412.
( )[ ]∑
=
μ =
N
D 1
6. Di M and CPM
an blood plasma of
patients in different physiological state
Summarized in this Chapter are the data of comparative
investigation aimed at the structure of blood plasma by
30, 35,
y (group 1 -
hom
optical
the geo trical thickness of 7 to 10 μm.
−−μ
i
idJ
N 1
21loglog . (23)
agnostic efficiency of the PC
methods for laser images of hum
using the methods of polarization-correlation [27,
38] and correlation-phase [36] mapping its laser images.
We investigated blood plasma samples (Fig. 2)
taken from two group of patients – health
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
27=q ) and those with prostate cancer (group 2 -
25=q ).
Our technique of sample preparation involved
uniform applying the blood plasma smear on optically
ogeneous glass with the following drying it at room
temperature for 24 hours. As a result, we obtained
ly-thin (extinction coefficient 1.0≤τ ) layers with
me
Summarized in Fig. 3 is the series of coordinate
distributions for the CDMP module (fragments (1), (2))
and CPM (fragments (3), (4)); histograms ( )VH
(fragments (5), (6)) and ( )μH (fragments (7), (8));
autocorrelation functions ( )mKV Δ (fragm , (10)) ents (9)
and ( )mK Δμ (fragments (11), (12)), as well as
logarithmic dependences 1loglog −− dJ V (fragm
(13), (14)) and lolog −J μ (fragments (15), (16))
that characterize polarization-correlation ( )nmV
ents
1g −d
× and
corre e ( )nm×lation-phas μ maps of laser images
corresponding to blood p f a healthy
patient (fragments (1), (3), ( ), (13), (15))
and that with prostate ca ments (2), (4), (6), (8),
(10), (12), (14), (16)).
Our comparative analysis of
experimental data ical, correlation and fractal
structures of PCM (Fig. 3, fragments (1), (2), (5), (6),
(9), (10), (13), (14)) for laser images of blood plasma in
both groups (Fig. 2) shows:
1. The histograms )(VH (fragments (5), (6)) of
lasma layers o
5), (7), (9), (11
ncer (frag
this set of
on statist
distr
blood plasma laser images.
From oint,
om
ibutions for the CDMP value V in the
corresponding PCM (fragments (1), (2)) are
dependences with the clearly pronounced extreme
( 1=V ). This fact is indicative of a high degree of
polarization homogeneity in
the physical viewp it can be explained by
weakly pronounced polarization modulation of laser
radiation, which could be provided by protein
polycrystalline networks in blood plasma. As follows
fr relations (1) and (2), at low values
δ = 0.07…0.15 rad the values of elements in the Jones
matrix tend to their limiting meanings 122,11 →d ,
021,12 →d . In other words, the coordinate distribution
of polarization states in a blood plasma laser image is
close to polarization of the probing beam.
2. Autocorrelation functions ( )mKV Δ of CDMP
coordinate distributions ( )nmV × decay in a s
manner (fragments (9), (10)), which is also
indicative of polarization homogeneity in blood plasma
laser images of both groups.
mooth and
monotonic
3. Correlation consistency coordinate
distributions
of
( )nmV × is reflected in their fractal
structure. As seen, approximating curves to logarithmic
dependences 1loglog −− dJ V possess one stable slope
angle (fragments (13), (14)) over the whole range of
changing t
strated with stati
he geometrical sizes d .
Quantitatively, the PCM of laser images inherent to
blood plasma of healthy patients and those with cancer
have been illu stical ( V
iZ 41−= ), correlation
( VS , VQ ) and fractal ( VF , VD ) parameters (Table 1).
The comparative analysis of the obtained data set
(Tab
changing the statistical, correlation and fractal parameters
at har ina CD
“ove
le 1) did not reveal any reliable criteria for
differentiation of blood plasma laser images for both
groups. As can be seen, the values and ranges for
th c acterize coord te MP distributions are
rlapped” (see fragments (5) and (6)).
Fig. 2. Laser images ( ) of protein polycrystalline
networks inherent to blood plasma. Explanations are given in
the text.
090=Θ
408
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 404-412.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
409
(1) (2) (3) (4)
(5) (6) (7) (8)
(9) (10) (11) (12)
(13) (14) (15) (16)
Fig. 3. Coordinate, statistical, correlation and fractal structures of PCM and CPM of human blood plasma for patients in
different physiological states. Explanations are given in the text.
As to its diagnostic performance, the method of
correlation-ph mapping more sensitive to changes
in the structure of polycrystalline netwo human
blood plasma taken from the patient with prostate
cancer. Statistically, these differences can be observed in
transformation of CDC distributions (Fig. 3, fragments
(3) and (4)) of corresponding laser images.
The histograms are characterized with
availability of local extremes in a wider range of
changes in th rrelation-phase parame ragments
(7 (8)). This fact indicates growth in phase modulation,
w
Th
values of phase shifts δ = 07…0.15 rad, the CDC value
undergoes significant changes with the range ase is
rk in
( )μH
is co ter (f
),
hich is typical for blood plasma images in the group 2.
e analysis of Exp. (15) shows that, even for low
0.
in
. Autocorrelation functions ( )mK Δμ98.065.0 ≤μ≤ of
coordinate distributions ( )nm×μ
tive of
g blood
st pronounced is the
sharply drop (fragment
(12)), which is also indica phase inhomogeneity in
laser images describin plasma of patients with
cancer.
The mo change in coordinate
structure of ( )nm×μ distributions, which is caused by
pathological changes and is reflected in its
transformation from a fractal type (fragment (15)) to the
random one (fragment (16)).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 404-412.
Table 1. Statistical ( V correlation ( V V ) and fractal ( V
iZ 41−= ), S , Q F , V ) parameters of polarization-correlation
Parameters
D
maps for laser images of blood plasma
VZ1 VZ 2
V
3 VZ 4 VS VQ VF VD Z
Group 1
(27 samples)
7
±
0.02
0.05
±
0.007
0.08 0.9
±
0.009
0,73
±
0.26
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
0.87
±
0.21
0.011
±
2.42
±
0.18
±
0.032 0.011 0.021
Group 2
(25 samples)
0.96
±
0.01
0.06
±
0.008
0.1
±
0.017
0.67
±
0.075
0.24
±
0.013
0.27
±
0.036
2.49
±
0.012
0.23
±
0.027
Table 2. Statistical ( −= 41iZ ), correlation ( S Q and fractal ( Vμ V , )V F , VD arameters of correlation-phase maps for
blood plasma laser images
) p
Parameters μ
1Z μ
2Z μ
3Z μ
4Z μS μQ μF μD
Group 1
(27 samples)
0.91
±
0.009
0.07
±
0.009
0.09
±
0.011
0.27
±
0.031
0.24
±
0.01
0.23
±
0.032
1.952
±
0.014
0.21
±
0.026
Group 2
(25 samples)
0.79
±
0.08
0.15
±
0.018
0.325
±
0.017
1.39
±
0,017
0.17
±
0.012
0.86
±
0.091
-
0.28
±
0.036
From the phy ges in
CPM of blood plasma las
sical viewpoint, these chan
er images for the group 2 can
with growth o birefri ence i
polycrystalline networks due to increasing the
tion of albumin an ulin eins.
iochemical proc ses th of t
phase modulation f laser radi
ly, this effect manifests itself as spreadin
ges in the value of DC modu as well a
in loweri consistency ous
points and formation of the random distribution
be related f ng n
concentra d glob prot The
mentioned b ess cau
o
grow h
ation.
e
( )nm×δ
Statistical g the
range of chan
ng the correlation
C le s
of vari CPM
( )nm×μ .
Quantitatively, CPM of laser images corresponding to
blood plasma of patients both healthy and with cancer
are illustrated using the statistical ( μ
−= 41iZ ), correlation
( VS , VQ ) and fractal ( VF , VD ) parameters (Table 2).
7. Conclusions
The obtained results of studying the statistical,
correlation and fractal structures of correlation-phase
maps corresponding to blood plasma laser images for
both groups enabled us to formulate the following
objective criteria for their differentiation:
1. The values of statistical moments of d
and fourth orders, which characterize
the thir
( )nm×μ
distributions of laser images for the group 2 samples, are
3.45 and 4.17 times higher than e analogous
parame s μ
3Z , μ
4Z of b d p ma in the group 1.
th
ter loo las
2. The values of correlation area and
ents differ 1.4 and 3.6 times,
respectively, for both groups of blood plasma.
3. The fractal ( )nm×μ distribution of laser
images for samples of blood plasma in the group 1 is
transformed into the random one for t mples from
the p 2..
Thus, we have de rm t of obj ctive
criteria, using ch o f ate ate
distrib s he m com lex deg of
co y fo r im human blood ma.
Also, we have demonstrated he diagnostic sensitivity of
th red to logic states observed in
patients with cancer.
1. f
Press,
he sa
grou
te ined the se e
whi
of t
ne can di
odule of
ferenti
p
coordin
ree ution
herenc r lase ages of plas
t
e offe method patho
μS
correlation mom μQ
References
M. Born and E. Wolf, Principles o Optics
(Cambridge Univ. Cambridge), (1999).
2. E. Wolf, “Unified theory of coherence and
polarization of random electromagnetic beams,”
63-267
rum of random electromagnetic beams on
Phys. Lett. A. 312, 2 , (2003).
3. E. Wolf, “Correlation-induced changes in the
degree of polarization, the degree of coherence, and
the spect
propagation,” Opt. Lett. 28, 1078-1080, (2003).
4. J. M. Movilla, G. Piquero, R. Martínez-Herrero, P.
M. Mejías, “Parametric characterization of non-
uniformly polarized beams,” Opt. Commun. 149,
230-234, (1998).
5. Claudia Mujat and Aristide Dogariu, "Statistics of
partially coherent beams: a numerical analysis," J.
Opt. Soc. Am. A 21, 1000-1003 (2004).
“Matrix treatment for partially polarized,
partially coherent beams,” Opt. Lett. 23, 241-243
6. F.Gori,
(1998).
410
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 404-412.
7. E. Wolf, “Significance and measurability of the
phase of a spatially coherent optical field,” Opt.
Lett. 28, 5-6 (2003).
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
9. olf,
8. Mircea Mujat and Aristide Dogariu, "Polarimetric
and spectral changes in random electromagnetic
fields," Opt. Lett. 28, 2153-2155 (2003).
J. Ellis, A. Dogariu, S. Ponomarenko, E. W
“Interferometric measurement of the degree of
polarization and control of the contrast of intensity
fluctuations,” Opt. Lett. 29, 1536 - 1538 (2004).
M. Mujat, A. Dog10. ariu, G. S. Agarwal, “Correlation
5-237 (2004).
13. . Ushenko, Yu. A. Ushenko,
lications,
14. o,
ent Biological Tissues”, in
issue:
16.
o, “Polarization Microstructure of
17.
18.
the transformation of laser radiation by
19.
21. Ushenko, S.B. Ermolenko,
of
22.
ko, D.N. Burkovets, Yu.A. Ushenko,
23. er
24. o, S.B. Ermolenko, D.N. Burkovets,
25.
o,
26. D.N. Burkovets, and Yu.A.
27. .G. Ushenko, D.N. Burkovets,
28. henko, “Laser polarimetry of polarization-
matrix of a completely polarized, statistically
stationary electromagnetic field,” Opt. Lett., 29,
1539 -1541 (2004).
11. Adela Apostol and Aristide Dogariu, "First- and
second-order statistics of optical near fields," Opt.
Lett. 29, 23
12. J.Ellis and A.Dogariu, “Complex degree of mutual
polarization,” Opt.Lett., 29, 536-538 (2004).
O. V. Angelsky, A. G
V. P. Pishak, “Statistical and Fractal Structure of
Biological Tissue Mueller Matrix Images”, in
Optical Correlation Techniques and App
Oleg V. Angelsky, ed. (Washington: Society of
Photo-Optical Instrumentation Engineers), pp. 213-
266 (2007).
O.V. Angelsky, A.G. Ushenko, Yu.A. Ushenk
V.P. Pishak, and A.P. Peresunko, “Statistical,
Correlation, and Topological Approaches in
Diagnostics of the Structure and Physiological
State of Birefring
Handbook of Photonics for Biomedical Science,
Valery V. Tuchin, ed. (USA: CRC Press), pp. 21-
67 (2010).
15. Alexander G. Ushenko and Vasilii P. Pishak,
“Laser Polarimetry of Biological T
Principles and Applications”, in Handbook of
Coherent-Domain Optical Methods: Biomedical
Diagnostics, Environmental and Material Science,
Valery V. Tuchin, ed. (Boston: Kluwer Academic
Publishers), pp. 93-138 (2004).
A.G. Ushenko, S.B. Ermolenko, D.N. Burkovets,
Yu.A. Ushenk
Laser Radiation Scattered by Optically Active
Biotissues,” Optics and Spectroscopy 87(3), 434-
439 (1999).
A.G. Ushenko, “Laser diagnostics of biofractals,”
Quantum Electron. 29(12), 1078–1084 (1999).
O.V. Angel'skii, A.G. Ushenko, A.D. Arkhelyuk,
S.B. Ermolenko, D.N. Burkovets, “Structure of
matrices for
biofractals,” Quantum Electron. 29(12), 1074-1077
(1999).
O.V. Angel'skii, A.G. Ushenko, A.D. Arheluk, S.B.
Ermolenko, D.N. Burkovets, “Scattering of Laser
Radiation by Multifractal Biological Structures,”
Optics and Spectroscopy 88(3), 444-448 (2000).
20. A.G. Ushenko, “Polarization Structure of
Biospeckles and the Depolarization of Laser
Radiation,” Optics and Spectroscopy 89(4), 597-
601 (2000).
O.V. Angel'skii, A.G.
D.N. Burkovets, V.P. Pishak, Yu.A. Ushenko, O.V.
Pishak, “Polarization-Based Visualization
Multifractal Structures for the Diagnostics of
Pathological Changes in Biological Tissues,”
Optics and Spectroscopy 89(5), 799-805 (2000).
O.V. Angel'skii, A.G. Ushenko, A.D. Arheluk, S.B.
Ermolen
“Laser Polarimetry of Pathological Changes in
Biotissues,” Optics and Spectroscopy 89(6), 973-
979 (2000).
A.G. Ushenko, “The Vector Structure of Las
Biospeckle Fields and Polarization Diagnostics of
Collagen Skin Structures,” Laser Physics 10(5),
1143-1149 (2000).
A.G. Ushenk
Yu.A. Ushenko, “Laser polarimetry of the
orientation structure of bone tissue osteons,”
Journal of Applied Spectroscopy 67(1), 65-69
(2000).
O.V. Angel'skii, A.G. Ushenko, A.D. Arheluk, S.B.
Ermolenko, D.N. Burkovets, Yu.A. Ushenk
“Polarization-Phase Visualization and Processing
of Coherent Images of Fractal Structures of
Biotissues,” Journal of Applied Spectroscopy
67(5), 919-923 (2000).
A.G. Ushenko,
Ushenko, “Laser polarization visualization and
selection of biotissue images,” Laser Physics 11(5),
624-631 (2001).
O.V. Angel'skii, A
Yu.A. Ushenko, “Polarization-correlation analysis
of anisotropic structures in bone tissue for the
diagnostics of pathological changes,” Optics and
Spectroscopy 90(3), 458-462 (2001).
A.G. Us
phase statistical moments of the object field of
optically anisotropic scattering layers,” Optics and
Spectroscopy 91(2), 313-316 (2001).
A.G. Ushenko, “Polarization contrast enhancement
of images of biological tissues under the conditions
of multiple scattering,”
29.
Optics and Spectroscopy
30.
oscopy
91(6), 937-940 (2001).
A.G. Ushenko, “Laser probing of biological tissues
and the polarization selection of their images,”
Optics and Spectr 91(6), 932-936 (2001).
31. A.G. Ushenko, “Correlation processing and
wavelet analysis of polarization images of
biological tissues,” Optics and Spectroscopy 91(5),
773-778 (2002).
A.G. Ushenko, “Polarization corr32. elometry of
angular structure in the microrelief pattern or rough
surfaces,” Optics and spectroscopy 92(2), 227-229
(2002).
411
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVF-3WPXFKK-5&_user=3134091&_coverDate=04%2F15%2F1998&_rdoc=5&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235533%231998%23998509995%23102729%23FLA%23display%23Volume)&_cdi=5533&_sort=d&_docanchor=&_ct=34&_acct=C000059843&_version=1&_urlVersion=0&_userid=3134091&md5=e9d4f16e0f2eac1f565aaf6d14c15966&searchtype=a
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVF-3WPXFKK-5&_user=3134091&_coverDate=04%2F15%2F1998&_rdoc=5&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235533%231998%23998509995%23102729%23FLA%23display%23Volume)&_cdi=5533&_sort=d&_docanchor=&_ct=34&_acct=C000059843&_version=1&_urlVersion=0&_userid=3134091&md5=e9d4f16e0f2eac1f565aaf6d14c15966&searchtype=a
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6TVF-3WPXFKK-5&_user=3134091&_coverDate=04%2F15%2F1998&_rdoc=5&_fmt=high&_orig=browse&_origin=browse&_zone=rslt_list_item&_srch=doc-info(%23toc%235533%231998%23998509995%23102729%23FLA%23display%23Volume)&_cdi=5533&_sort=d&_docanchor=&_ct=34&_acct=C000059843&_version=1&_urlVersion=0&_userid=3134091&md5=e9d4f16e0f2eac1f565aaf6d14c15966&searchtype=a
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2010. V. 13, N 4. P. 404-412.
© 2010, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
cal Lesions,” Optics and
34.
er
35.
nstruction of orientation structure
33. A.G. Ushenko, D.N. Burkovets, Yu.A. Ushenko,
“Polarization-Phase Mapping and Reconstruction
of Biological Tissue Architectonics during
Diagnosis of Pathologi
Spectroscopy 93(3), 449-456 (2002).
Oleg V. Angelsky, Alexander G. Ushenko, Dimitry
N. Burkovets, Yuriy A. Ushenko, “Las
polarization visualization and selection of biotissue
images,” Optica Applicata 32(4), 591-602 (2002).
O.V. Angelsky, A.G. Ushenko, Yu.A. Ushenko,
“Polarization reco
of biological tissues birefringent architectonic nets
by using their Mueller-matrix speckle-images,”
Journal of Holography and Speckle 2(2), 72-79
(2002).
36. E.I. Olar, A.G. Ushenko, and Yu.A. Ushenko,
“Correlation Microstructure of the Jones Matrices
for Multifractal Networks of Biotissues,” Laser
Physics 14, 1012-1018 (2004).
37. O.V. Angelsky, A.G. Ushenko, Yu.A. Ushenko,
A.O. Angelskaya, “Fractal structure of 2D Mueller
matrix images of biotissues,” Ukrainian Journal of
Physical Optics 6(1), 13-23 (2004).
38. Oleg V. Angelsky, G.V. Demianovsky, A.G.
Ushenko, D.N. Burkovets, and Yu.A. Ushenko,
“Wavelet analysis of two-dimensional
birefringence images of architectonics in biotissues
for diagnosing pathological changes,” J. Biomed.
Opt. 9, 679-690 (2004).
39. Oleg V. Angelsky, Alexander G. Ushenko, Dimitry
N. Burcovets, Yuriy A. Ushenko, “Polarization
visualization and selection of biotissue image two-
layer scattering medium,” J. Biomed. Opt. 10(1),
014010 (2005).
412
http://bookstore.spie.org/index.cfm?fuseaction=detailpaper&cachedsearch=1&volume=9&fpage=679&coden=JBOPFO&producttype=pdf&CFID=4088041&CFTOKEN=43186825
http://bookstore.spie.org/index.cfm?fuseaction=detailpaper&cachedsearch=1&volume=9&fpage=679&coden=JBOPFO&producttype=pdf&CFID=4088041&CFTOKEN=43186825
http://bookstore.spie.org/index.cfm?fuseaction=detailpaper&cachedsearch=1&volume=9&fpage=679&coden=JBOPFO&producttype=pdf&CFID=4088041&CFTOKEN=43186825
|