Jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues
Performed in this work is the complex statistical, correlation and fractal analysis of coordinate distributions of Jones-matrix elements corresponding to birefringent networks of liquid crystals in human biological liquids (saliva, blood plasma, bile). The authors have determined the values and r...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2011
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| Цитувати: | Jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues / O.G. Ushenko, V.O. Balanetska, N.I. Zabolotna // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 4. — С. 403-410. — Бібліогр.: 31 назв. — англ. |
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irk-123456789-1177852017-05-27T03:04:36Z Jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues Ushenko, O.G. Balanetska, V.O. Zabolotna, N.I. Performed in this work is the complex statistical, correlation and fractal analysis of coordinate distributions of Jones-matrix elements corresponding to birefringent networks of liquid crystals in human biological liquids (saliva, blood plasma, bile). The authors have determined the values and ranges for changing statistical, correlation and spectral moments of the 1-st to 4-th orders that characterize Jones-matrix images of these objects. Ascertained are objective criteria for classification and differentiation of optical properties inherent to polycrystalline networks of biological crystals with various kinds of spatial symmetry: dendrite, spherolite and cluster ones. 2011 Article Jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues / O.G. Ushenko, V.O. Balanetska, N.I. Zabolotna // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 4. — С. 403-410. — Бібліогр.: 31 назв. — англ. 1560-8034 PACS 33.50.-j, 34.35.+a, 73.20.Mf, 78.30.-j http://dspace.nbuv.gov.ua/handle/123456789/117785 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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English |
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Performed in this work is the complex statistical, correlation and fractal
analysis of coordinate distributions of Jones-matrix elements corresponding to
birefringent networks of liquid crystals in human biological liquids (saliva, blood plasma,
bile). The authors have determined the values and ranges for changing statistical,
correlation and spectral moments of the 1-st to 4-th orders that characterize Jones-matrix
images of these objects. Ascertained are objective criteria for classification and
differentiation of optical properties inherent to polycrystalline networks of biological
crystals with various kinds of spatial symmetry: dendrite, spherolite and cluster ones. |
| format |
Article |
| author |
Ushenko, O.G. Balanetska, V.O. Zabolotna, N.I. |
| spellingShingle |
Ushenko, O.G. Balanetska, V.O. Zabolotna, N.I. Jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Ushenko, O.G. Balanetska, V.O. Zabolotna, N.I. |
| author_sort |
Ushenko, O.G. |
| title |
Jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues |
| title_short |
Jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues |
| title_full |
Jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues |
| title_fullStr |
Jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues |
| title_full_unstemmed |
Jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues |
| title_sort |
jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/117785 |
| citation_txt |
Jones-matrix diagnostics of the structure and classification of optical properties inherent to birefringent polycrystalline networks of human biological tissues / O.G. Ushenko, V.O. Balanetska, N.I. Zabolotna // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2011. — Т. 14, № 4. — С. 403-410. — Бібліогр.: 31 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT ushenkoog jonesmatrixdiagnosticsofthestructureandclassificationofopticalpropertiesinherenttobirefringentpolycrystallinenetworksofhumanbiologicaltissues AT balanetskavo jonesmatrixdiagnosticsofthestructureandclassificationofopticalpropertiesinherenttobirefringentpolycrystallinenetworksofhumanbiologicaltissues AT zabolotnani jonesmatrixdiagnosticsofthestructureandclassificationofopticalpropertiesinherenttobirefringentpolycrystallinenetworksofhumanbiologicaltissues |
| first_indexed |
2025-07-08T12:47:47Z |
| last_indexed |
2025-07-08T12:47:47Z |
| _version_ |
1837082995350044672 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 4. P. 403-410.
PACS 33.50.-j, 34.35.+a, 73.20.Mf, 78.30.-j
Jones-matrix diagnostics of the structure
and classification of optical properties inherent to birefringent
polycrystalline networks of human biological tissues
O.G. Ushenko, V.O. Balanetska, N.I. Zabolotna
Chernivtsi National University
2, Kotsyubinsky vul., 58012 Chernivtsi, Ukraine
Abstract. Performed in this work is the complex statistical, correlation and fractal
analysis of coordinate distributions of Jones-matrix elements corresponding to
birefringent networks of liquid crystals in human biological liquids (saliva, blood plasma,
bile). The authors have determined the values and ranges for changing statistical,
correlation and spectral moments of the 1-st to 4-th orders that characterize Jones-matrix
images of these objects. Ascertained are objective criteria for classification and
differentiation of optical properties inherent to polycrystalline networks of biological
crystals with various kinds of spatial symmetry: dendrite, spherolite and cluster ones.
Keywords: laser, polarization, birefringence, Jones matrix, biological liquids, statistical
moments, autocorrelation, power spectrum, fractal.
Manuscript received 30.07.11; revised manuscript received 10.08.11; accepted for
publication 14.09.11; published online 30.11.11.
1. Introduction
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
1.0≤Among the methods for optical diagnostics of biological
layers, the most 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
single-axis 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].
It should be noted that there is a widely spread
group of optically anisotropic biological objects, for
which the methods of laser polarimetric diagnostics did
not acquire wide application yet. Related to these objects
are optically-thin (extinction coefficientτ ) layers
of various 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 BT
biopsy. Being based on these reasons, it seems topical to
adapt the methods of laser polarimetric diagnostics for
studying the optically-anisotropic structure of BT
polycrystalline networks.
Our work is aimed at searching the possibilities for
diagnostics and classification of optical properties of
human biological liquids with various spatial symmetry
of polycrystalline networks. With this purpose, we offer
to determine coordinate distributions corresponding to
Jones-matrix elements with the following statistical,
correlation and fractal analyses of these distributions.
2. Main analytical relations
Our analysis of experimental results is based on the
following conceptions developed for optically
anisotropic protein fibrils [1 - 4, 7, 9, 14, 16, 23-27, 30]:
• separate (partial) amino acid crystals are optically
uniaxial and birefringent;
• optical properties of a partial crystal are exhaustively
full described with the Jones operator [5]
403
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 4. P. 403-410.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
Here, is the direction of the optical axis; ρ
ndΔλ
π=δ 2 – phase shift between orthogonal
components and of the amplitude of
illuminating laser wave with the wavelength
xE yE
λ ; nΔ -
birefringence index for the crystal with geometric
dimension . d
The Jones matrix of a flat layer corresponding
to polycrystalline network can be defined as a sum of
operators {J}
{ }ℑ
l for K separate amino acid crystal [5, 11, 30]
{ } { }∑
=
=ℑ
K
l
lJ
1
, (2)
It can be shown that for Q sequentially placed flat
layers the net Jones matrix is defined with the expression
{ } { } { } { } { } { }121
1
... ℑ×ℑ××ℑ×ℑ=ℑ=ℵ −
=
∏ QQ
Q
q
q . (3)
In an expanded version, the matrix elements ikℵ
possess a cumbersome analytical look. Therefore, to
consider the structure of generalized Jones matrix { }ℵ
in more convenient manner, we limit ourselves (without
losses in fullness of analysis) by the case of bilayer
( ) polycrystalline network. With account of this
approximation as well as an evident look of dependences
(relation (1)) for matrix elements
2=Q
( δ)ρ,ikJ , it is possible
to show that the elements of generalized Jones matrix
can be expressed with the following dependences
( ) ( ) ( )
( ) ( ) .2exp
exp
δ−ρ+
+δ−ρ+ρ=ℵ
iU
iTR
ik
ikikik (4)
Here, are the coefficients
expressed via quasi-harmonic functionals
( ) from coordinate changes in
orientations of optical axis
ikikik UTR ;;
sin"cos";"sin";"cos~" 22 −
( )yx,ρ
Our comparative analysis of relations (1), (2) and
(3)–(7) has shown that the coordinate distributions of
ikℵ elements in Jones matrixes describing multi-layer
polycrystalline networks of optically birefringent
crystals simultaneously possess various properties:
{ } ( ) ( )[ ]
( )[ ] ( );expcossin;exp1sincos
;exp1sincos;expsincos
22
22
2221
1211
δ−ρ+ρδ−−ρρ
δ−−ρρδ−ρ+ρ
==
ii
ii
JJ
JJ
J . (1)
• complex multi-parametric dependences of ( )δρℵ ,ik
values on specificity of distributions inherent to
orientation ( )ρf and phase parameters; ( )δg
• ikℵ distributions are superposition of various
harmonic components ( sin"cos";"sin";"cos~" 22 − );
d em• ependences of matrix el ents are scale-
hus, an objective analysis of coordinate
distr
3. Criteria for estimation of Jones-matrix images
Distributions of values inherent to elements
ikℵ
repeated.
T
ibutions for elements of the Jones matrixes
corresponding to polycrystalline networks needs the
complex (statistical, correlation and fractal) analytical
approach.
corresponding to polycrystalline networks
ikℵ of the
e Jones matrix can be characterized with th set of
statistical moments of the 1-st to 4-th orders M; σ; A; E
calculated using the following relations [5, 6, 25, 30]:
( ) ( )
( ) ( ) .11,
,1,1
1
4
4
1
3
3
1
2
1
∑∑
∑∑
==
==
ℵ
σ
=ℵ
σ
=
ℵ=σℵ=
N
j
jik
N
j
jik
j
jik
j
jik
N
E
N
A
NN
M
(8)
ere is the amount of local values within
its
11
NN
wh N ( ) jikℵ
the lim of coordinate distribution corresponding to the
Jones-matrix image.
( ) ( ) ( )
( ) ( ) ( )[ ] ( )
( ) ( )[ ]⎪⎩ −ρΔ+ρρ+ρΔ+ρρ= 2exp2sin2sin2sinsin 22
11U ( )⎪
⎪⎪
⎨
⎧
δ
δ−ρΔ+ρρ−ρΔ+ρρ+ρΔ+ρρ=
ρΔ+ρρ+ρΔ+ρρ=
.
;exp2sin2sin2cossinsincos
;2sin2sin5,0coscos
2222
11
422
11
i
iT
R
(5)
( ) ( )[ ]
( ) ( )[ ] ( )
( )[ ] ( )⎪
⎪
⎩
⎪⎪
⎨
⎧
δ−ρρ+ρΔ+ρρ=
δ−ρΔ+ρρ+ρΔ+ρρ=
ρΔ+ρρ+ρΔ+ρρ=
.2expcos2sin2sinsin25,0
;exp2sinsincos2sin25,0
;cos2sin2sincos25,0
22
21;12
22
21;12
22
21;12
iU
iT
R
(6)
( ) ( ) ( )
( ) ( ) ( )[ ] ( )
( ) ( )[ ] ( )⎪
⎩
⎪
⎨
⎧
−Δ++Δ+=
−Δ+−Δ++Δ+=
Δ++Δ+=
.2exp2sin2sin2coscos
;exp2sin2sin2sincoscossin
;2sin2sin5,0sinsin
22
22
2222
22
422
22
δρρρρρρ
δρρρρρρρρρ
ρρρρρρ
iU
iT
R
(7)
404
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 4. P. 403-410.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
alyzing the coordinate structure of
with usin
As a base for an
( ) jikℵ distributions, we took the autocorrelation method
g the function [12, 21, 26]
( ) ( )[ ] ( )[ ]∫ Δ−ℵℵ=Δ
01
X
10
ikik dxxxx
X
xG (9)
Here, is the “step” of changing the coordinates
x =
As p meters that characterize the dependences
G Δ
1-st to
g the degree of self-similarity and
repea
xΔ
0X÷ .
ara
1
( )x , we chose the set of correlation moments of the
4-th orders 4;3;2;1=lK that are defined like to
relations (8).
Estimatin
tability for different geometric ( d ) scales of the
structure inherent to coordinate distributions of elements
ikℵ corresponding to the Jones matrix of polycrystalline
orks was performed by calculation of logarithmic
dependences for power spectra ( ) )log(log 1−−ℵ dJ that
were approximated using the lea o the
curves ( )
netw
ik
st-squares method t
ηΦ . For the straight parts of the curves ( )ηΦ ,
determi re the slope angles ined a η and calculated are the
values of fractal dimensionalitie for the sets of iks ℵ
values by using the relations [5, 6, 11, 25]
tggD η−= 3)( . ii (10)
Classification of coordinate distributions for m
elem
atrix
ents ( )yxik ,ℵ was carried out in accord with the
criteria offe [5]. If the value of the slope angle
const=η in the dependences ( )η
red in
Φ for 2 or 3 decades of
the sizes d , then the ributionschanging dist ( )yxik ,ℵ are
fractal. Under co ition that several constant lope
angles are available in the curve ( )ηΦ , the sets
nd s
( )yxik ,ℵ
are multi-fractal. When no stable slope an
available over the whole interval of changing the
sizes d , the sets ( )yxik ,ℵ are considered as random.
make comparative analysis
gles are
To this of
J ik
( ) )log( 1−−ℵ d dependences more objective, let
us introduce the conception of spectral moments from
the 1-st to 4-th orders - the relation (8).
log
4;3;2;1=jS
4. Brief characterization of the studied objects
As the studied objects, we used smears of biological
liquids taken from healthy patients:
• saliva (21 samples) – group 1;
• blood plasma (21 samples) – group 2;
• bile (21 samples) – group 3.
This choice of biological liquids was related with
the following factors:
• they comprise a wide circle of physiological
functions in a human organism;
• diverse biochemical structure of these liquids, as
well as others no less important from the
physiological viewpoint (transudate, exudate,
………., liquor, ….), possesses common optical
properties that are related with birefringent liquid-
crystalline networks of amino acids, calcium
bilirubinate, fat acids, cholesterol monohydrate,
etc.
Fig. 1 shows polarization-visualized images of
polycrystalline networks inherent to birefringent
biological crystals of the liquid samples in all the groups.
These images were obtained for crossed transmission
planes of the polarizer and analyzer.
The comparative analysis of laser images
corresponding to smears of human liquids enabled us to
ascertain:
• availability of optically-anisotropic polycrystalline
networks inherent to biological crystals in all the
groups of liquids;
• dependence of optical anisotropy parameters
(distribution of orientation directions for biological
crystals and the value of their birefringence) on the
type of liquid (Fig. 1, fragments a, b, c);
• in the geometrical structure of polycrystalline
networks typical for saliva (a) and blood plasma
(b), there predominant are needle-like or dendrite-
like structures, while for bile (c) – spherolitic
creations.
(a) (b) (c)
Fig. 1. Polarization-visualized laser images corresponding to polycrystalline networks of saliva (a), blood plasma (b) and bile
(c).
405
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 4. P. 403-410.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
5. O tup for Jones-matrix mapping
the optically-anisotropic biological liquids
polarimeter
for measuring the coordinate distributions of Jones-
W
= 5.0
elements within the range 2 to 2000 µm. The analysis of
laser images was performed using the polarizer 9 and
quarter-wave plate 8.
Conditions of our experiments were chosen in such
a manner that enabled to practically eliminate spatial-
angle aperture filtration when forming the images of
biological liquids. It was provided by coincidence of
angular characteristics for indicatrixes of light scattering
by samples of biological liquids ( and angular
aperture of the used micro-objective ). Here,
is the angular cone of indicatrixes where 98% of all
the scattered radiation energy is concentra
ptical se
Shown in Fig. 2 is the optical scheme of a
matrix elements corresponding to birefringent layers.
Illumination was provided with a parallel
(∅ = 104 µm) beam of a He-Ne laser (λ = 0.6328 µm,
mW). The polarization illuminator consists of the
quarter-wave plates 3, 5 and polarizer 4, which provides
formation of a laser beam with an arbitrary polarization
state. Using the micro-objective 7 (magnification 4x),
images of biological layers were projected onto the plane
of light-sensitive area (800x600 pixels) of the CCD-
camera 10 that provided measurements of structural
Adduced in Fig. 3 are coordinate (a, b, c), probability (d,
e, f), autocorrelation (g, h, i), spectral (k, l, m)
dependences that characterize Jones-matrix images of
ℵ
016≈Ω )
( 020=Δω
Ω
ted.
6. Analysis of experimental results
and their discussion
11(m × n). elements for optically-thin (extinction
coefficient 01.0≤τ ) layers of saliva (a, d, g, k), blood
plasma (b, e, h, l) and bile (c, f, i, m).
Performing the model analysis (relations (1) to (7)),
we have shown that our choice of elements ( )δρℵ ,11 in
the Jones matrix allows estimating (without lowering the
fullness of this analysis) the contribution f orientation-
phase (
o
ρ , δ ) structure of polycrys etworks with talline n
ine networks (Fig.
1) o
nt level
different symmetry (Fig. 1) to formation of their
polarization properties.
The results obtained in the course of studying the
Jones-matrix images of ℵ11(m × n). element, which
characterize polarization properties of the orientation-
phase structure inherent to polycrystall
f optically-thin layers for biological liquids of
different types, are indicative of a sufficie of
birefringence in these liquid crystals. This fact is
confirmed by a wide range of changes ( 10 11 ≤ℵΔ≤ ) in
intrinsic values of the given matrix element ( )δρ ,11ℵ .
On the other hand, different spatial symmetry of
distributions for optical axis directions ( nm( )×ρ ) is
pronounced in individual dependences for the series of
histograms ( )11ℵH corresponding to the probability of
ragments (d,
etwork of
ram
element values in the Jones matrix (Fig. 3
e, f). For instance, in the case of dendrite
biological crystals in saliva layer, the histog
, f
n
( )11ℵH
e, the value
other
ℵ
is asymmetric relatively to the main extrem
of which is 2 – 7 times higher than those of
extremes in the probability of local values
(Fig. 3, fragment (d)). This fact is in a goo
with model notions about the influence of
describing the directions of optical axes
crystals that form birefringent netwo k (re
7), Fig. 1, fragment ) on the coo nate
the Jones-matrix image 11(m × n).
dire
partial crystals in spherolite polycrystalline
of changes i
t (e)).
mponen
pressed
ution
11(ρ, δ)
d correlation
distributions
for partial
lations (1) to
structure of
ctions for
network of
albumin and globulin in optically-thin layer of blood
plasma (Fig. 1, fragment (b)) is pronounced in more
uniform distribution for extreme values in the
histogram H(ℵ
r
rdi( (a)
ℵ
Azimuth symmetry of optical axis
11) over the whole range n
local values of the matrix element ℵ11(ρ, δ) (Fig. 3,
fragmen
Polarization properties of cluster polycrystalline
co t in the bile layer (Fig. 1, fragment (c)) are
ex in rather symmetrical, close to the level of
probabilistic one, distrib for extremes of the
histogram H(ℵ11) describing probabilities of random
values ℵ11(ρ, δ) (Fig. 3, fragment (f)).
Fig. 2. 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 under
investigation; 7 – micro-objective; 10 – CCD camera; 11 – personal computer.
406
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 4. P. 403-410.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
analytical data
(rela
The correlation approach (relation (9)) to analyses
of ( )nm×ℵ11 elements in Jones-matrix images for
various types of biological liquids has shown that, in the
case of dendrite and spherolite birefringent networks, the
autocorrelation functions ( )xG Δ11 are decaying
dependences with clearly pronounced fluctuations of
intrinsic values (Fig. 3, fragments (g, h)). The
experimentally found fact on availability of harmonic
modulation is in good accordance with
tion (1) to (7)) for the influence of orientation-phase
( ρ ,δ ) parameters corresponding to optically uniaxial
birefringent crystals on distributions ℵ11(ρ, δ) that are
superposition of various harmonic components
( sin"cos";"sin";"cos~" 22 − ). The autocorrelation
(a) (b) (c)
(d) (e) (f)
(g) (h) (i)
(k) (l) (m)
Fig. 3. Statistical, correlation and fractal parameters of Jones-matrix images ℵ11(m × n). for optically-thin layers of saliva (a, d,
g, k), blood plasma (b, e, h, l) and bile (c, f, i, m). See explanations in the text.
407
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 4. P. 403-410.
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
rrespon e cluster
om the
functions ( )xG Δ11 for Jones-matrix images ℵ11(m × n)
co birefringent network of bile
samples fr group 3 are monotonous decaying
dependences without any fluctuations of intrinsic values
(Fig. 3, fragment (i)), which can be related with
practically full disordering the directions of optical axes
in optically anisotropic structures.
Discrete scale-repeated changes in orientations of
optical axes of partial biological crystals (Fig. 1,
fragm
ding to th
ignifica of (b .3
es) and
ents (a, b, c)) with simultaneous multiple changes
in the phase δ period (relations (4) to (7)) is
pronounced as formation of self-similar coordinate
distributions of Jones-matrix elements ℵ11(ρ, δ) in the
plane of biological liquid layers in all the groups. It is
seen from the analysis of logarithmic dependences
( ) )log(log 1
11
−−ℵ dJ (Fig. 3, fragments (k, l, m)) that
the approximating curves ( )ηΦ are broken lines with
In other words, distributions of
matrix element values ℵ
three slope angles.
× n
E), correlation (Ki = 1; 2; 3; 4)
nd spectral (Si = 1; 2; 3; 4) parameters of Jones-matrix
orks o
11(m ) are multi-fractal.
The results of our quantitative analysis concerning
values and ranges for changing the statistical, correlation
and spectral moments in coordinate distributions of
ℵ11(m × n) that characterize polarization properties of
birefringent networks corresponding to biological liquids
of various types (Fig. 1) are summarized in Table 1.
The analysis of the obtained data enabled us to find
satisfactory correlation with the results of computer
modeling, and it shows that the whole set of statistical,
correlation and spectral moments of the 1-st to 4-th
orders characterizing coordinate distributions of Jones-
matrix elements possesses individual sets of values
dependent on optical-and-geometrical parameters
corresponding to amino acid polycrystalline networks.
For instance, changes in spatial symmetry of partial
amino acid crystals, in accord with the scenario
“dendrite network – spherolitic network – cluster
ensemble”, is pronounced as:
able 1. Statistical (M; σ; A; T
a
images ℵ11(m × n) inherent to polycrystalline netw f
biological liquids
Parameters Saliva (21
samples)
Blood
plasma (21
Bile (21
samples)
samples)
M 0.41±0.19 0.49±0.14 0.54±0.12
σ 0 .24±0.092 0.28±0.089 0.34±0.12
A 1.26±0.41 0.77±0.072 0.45±0.097
E 3.17±0.075 1.89±0.48 0.89±0.13
K1 0.41±0.086 0.44±0.098 0.47±0.105
K2 0.09±0.0082 0.15±0.029 0.25±0.062
K3 3.28±0.71 1.91±0.46 0.89±0.23
K4 5.88±1.44 3.08±0.57 1.86±0.32
S1 0.51±0.13 0.44±0.072 0.38±0.16
S2 0.27±0.061 0.14±0.031 0.11±0.014
S3 0.69±0.11 0.34±0.067 0.18±0.11
S4 1.25±0.24 0.64±0.17 0.29±0.08
• ins nt growth the mean M y 1.2 – 1
tim dispersion σ (by 1.2 – 1.4 d, times) an
contrary, considerable decrease in values of
statistical moments of the 3-rd ( A - by 1.6 – 2.8
times) and 4-th orders ( E - by 1.7 – 3.6 times) of
coordinate distributions for ( )nmℵ11 elements;
decaying oscillations of autocorrelation functions
corresponding to Jones-matr
×
•
ix images as well as in
•
to 4-th orders
decrease in respective values of correlation
moments of higher orders (K3 - by 1.7 – 3.7 times
and K4 - by 1.9 – 3.1 times) for these dependences,
while the correlation moment of the 2-nd order K2
is 1.7 – 2.8 times increased;
decrease by 1.3 – 4.3 times in the whole set of
spectral moments of the 1-st 4;3;2;1=i
that characterize logarithmic dependences
S
( ) )log(log 1
11
−−ℵ dJ .
Fig. 4 shows circle diagrams for the values of
ranges ( )iZΔ corresponding to changes in values of the
set
a
comprising statistical (M; σ; A; E), correlation
( 4;3;2;1=iK nd spectral ( 4;3;2;1=iS ) parameters of Jones-
matrix images
)
( )nm×ℵ11 inherent to polycrystalline
ne of human biolog ids.
tworks ical liqu
Fig. On the analysis of capabilities typical for Jones-
matrix classification of polarization properties inherent to
the
follo ing manner. In the Cartesian coordinate system,
the
4.
polycrystalline networks in human biological liquids.
Classification dependences were plotted in
w
abscissa corresponds to values of ranges
( ) ( ) ( )i
msn
ii ZZZ −=Δ max , while the ordinate – to the values of
parameters 4;3Z . For every group of human
biological liq we determined the dispersion
;2;1=i
uids,
( ) ZZ Δ=2 t d as a radius of the circle diagram hat serve
( )( )ZZ i Δ of random values related to parameters
characterizing the Jones-matrix images
n) of biological liquid polycrystalline networks.
er of this circle diagram was determined as the
cross-point of two normals to axes of the chosen
coordinate system, which were plotted from the middles
of the segments
4;3;2;1=iZ
ℵ11(m ×
The cent
( )iZ and ZΔ .
It is seen from the results adduced in Fig. 4 that the
ranges for chang ing ZΔ values for statistical moments
of various orders M , σ , A , E possess individual
character, and can be d in various ways to classify the
studied types of ica li ids. For example,
geometrical areas of the circles M(ΔZ) and σ(ΔZ)
determined for Jones-matrix images ℵ
use
biolog l qu
11(m × n) within
the limits of various biological liquid groups possess a
high (up to 90%) level of superposition (Fig. 4,
fragments (a, b)). Considerably larger differences (Fig.
4, fragments (c, d)) are observed when comparatively
408
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2011. V. 14, N 4. P. 403-410.
analyzing the dependences ( )ZA Δ and ( )ZE Δ . The
superposition level in the case of circle diagrams for the
3-rd statistical moment is clos e 4-th
– 20 - 25%.
The respective diagrams ( )zK Δ2 ,
e
© 2011, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
to 25 - 35%, for th
( )zK Δ3 and
( )zK Δ4 for parameters of autoco nces
) corresponding to Jones-matrix images
)n are not practically overlapped (Fig. 4,
g, h)).
o the set of spectral statistical moments
3;2=iS , we have asc
rrelation
m×ℵ11
fragments (f,
As t
ertained the possibility to efficiently
spherol
depende
( xG Δ11
(
4;
entiate the polarization properties of dendrite,
ite and cluster optically anisotropic networks –
the diagrams ( )zS Δ2 ,
differ
( )zS Δ3 and ( )zS Δ4 are not
overlapped (Fig. 4, ents (k, l, m)).
7. Conclusions
fragm
this work is the method of superposition
of Jones matrixes to describe polarization
2.
line layers of
3.
ostics and classification of
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