Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks
Considered in this work are the possibilities to use the method of FourierStokes polarimetry for diagnostics of optical anisotropy inherent to polycrystalline networks of biological layers. The authors have offered a generalized model for optical anisotropy of histological sections taken from bio...
Gespeichert in:
| Datum: | 2012 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2012
|
| Schriftenreihe: | Semiconductor Physics Quantum Electronics & Optoelectronics |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/118321 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks / A.O. Karachevtsev // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 3. — С. 252-260. — Бібліогр.: 10 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
nasplib_isofts_kiev_ua-123456789-118321 |
|---|---|
| record_format |
dspace |
| spelling |
nasplib_isofts_kiev_ua-123456789-1183212025-06-03T16:28:46Z Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks Karachevtsev, A.O. Considered in this work are the possibilities to use the method of FourierStokes polarimetry for diagnostics of optical anisotropy inherent to polycrystalline networks of biological layers. The authors have offered a generalized model for optical anisotropy of histological sections taken from biological tissues and films of biological liquids. Polarization maps for Fourier spectra of laser images describing the phaseinhomogeneous objects have been investigated. Grounded was application of the method for consistent spatial-frequency filtration of polarization maps formed by linear and circular birefringent of biological crystals. 2012 Article Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks / A.O. Karachevtsev // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 3. — С. 252-260. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS 33.50.-j, 34.35.+a, 73.20.Mf, 78.30.-j https://nasplib.isofts.kiev.ua/handle/123456789/118321 en Semiconductor Physics Quantum Electronics & Optoelectronics application/pdf 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 |
Considered in this work are the possibilities to use the method of FourierStokes
polarimetry for diagnostics of optical anisotropy inherent to polycrystalline
networks of biological layers. The authors have offered a generalized model for optical
anisotropy of histological sections taken from biological tissues and films of biological
liquids. Polarization maps for Fourier spectra of laser images describing the phaseinhomogeneous
objects have been investigated. Grounded was application of the method
for consistent spatial-frequency filtration of polarization maps formed by linear and
circular birefringent of biological crystals. |
| format |
Article |
| author |
Karachevtsev, A.O. |
| spellingShingle |
Karachevtsev, A.O. Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Karachevtsev, A.O. |
| author_sort |
Karachevtsev, A.O. |
| title |
Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks |
| title_short |
Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks |
| title_full |
Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks |
| title_fullStr |
Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks |
| title_full_unstemmed |
Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks |
| title_sort |
fourier-stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2012 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/118321 |
| citation_txt |
Fourier-Stokes polarimetry of fields corresponding to linearly and circularly polarized birefringent protein networks / A.O. Karachevtsev // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2012. — Т. 15, № 3. — С. 252-260. — Бібліогр.: 10 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
| work_keys_str_mv |
AT karachevtsevao fourierstokespolarimetryoffieldscorrespondingtolinearlyandcircularlypolarizedbirefringentproteinnetworks |
| first_indexed |
2025-11-24T18:38:45Z |
| last_indexed |
2025-11-24T18:38:45Z |
| _version_ |
1849698052654235648 |
| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 252-260.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
252
PACS 33.50.-j, 34.35.+a, 73.20.Mf, 78.30.-j
Fourier-Stokes polarimetry of fields corresponding to linearly
and circularly polarized birefringent protein networks
A.O. Karachevtsev
Chernivtsi National University named after Yuri Fed’kovych,
Department for Optics and Spectroscopy,
2 Kotsyubyns’kogo str., 58001 Chernivtsi, Ukraine.
Phone: +38067 783 0572
Abstract. Considered in this work are the possibilities to use the method of Fourier-
Stokes polarimetry for diagnostics of optical anisotropy inherent to polycrystalline
networks of biological layers. The authors have offered a generalized model for optical
anisotropy of histological sections taken from biological tissues and films of biological
liquids. Polarization maps for Fourier spectra of laser images describing the phase-
inhomogeneous objects have been investigated. Grounded was application of the method
for consistent spatial-frequency filtration of polarization maps formed by linear and
circular birefringent of biological crystals.
Keywords: polarization, Jones matrix, optical anisotropy, biological layer, polarization
map, Fourier spectrum, spatial-frequency filtration.
Manuscript received 08.02.12; revised version received 07.06.12; accepted for
publication 14.06.12; published online 25.09.12.
1. Introduction
Among the variety of systems for diagnostics of optical
anisotropy of biological objects [1-3], a new direction –
laser polarimetry of biological tissue images has been
separated [4, 5]. In this approach, the analysis of the
obtained data is based on approximation of linear
birefringence observed in polycrystalline protein
networks. Using the above model approach, the authors
found interrelation between the set of statistical
moments of the first to fourth orders that characterize
distributions of azimuths and ellipticity of polarizations
in laser images as well as parameters of anisotropy
inherent to the layers of biological tissues [6-7]. As a
result, developed was the method for polarization
mapping and successfully realized was the diagnostics of
oncological (malignant) changes in human biological
tissue [8, 9]. To further develop the methods of laser
polarimetric diagnostics, it seems topical to differentiate
various mechanisms of optical anisotropy. Up to date,
the above method of polarization mapping is not able to
solve this problem. One of the possible solutions lies in
using the consistent spatial-frequency filtration of laser
images [10]. The idea of this approach, which is novelty
in biomedical applications, is based on filtration of
spatial-frequency spectra for polarization images of
networks including biological crystals with different
mechanisms of anisotropy. Optical realization of this
method consists of the following stages: direct Fourier
transform, spatial-frequency and polarization-phase
filtration, inverse Fourier transform of biological layer
laser images.
This work is aimed at development of a generalized
model of phase anisotropy to describe formation of
fields inherent to scattered laser radiation and, with
account of this model, substantiation of new methods for
Fourier-Stokes polarimetry as well as consistent
polarization-phase filtration of manifestations inherent to
linear and circular birefringence for diagnostics of the
structure of polycrystalline networks observed in
biological tissues and liquids.
2. Model conceptions and computer modeling the
processes of formation of polarization-
inhomogeneous images and their Fourier spectra
As a basis for our investigations, we took the following
model conceptions:
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 252-260.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
253
1. Substance of optically anisotropic component of
biological tissue possesses some generalized
anisotropy that is a superposition of linear and
circular birefringence.
2. From the analytical viewpoint, processes of
interaction of laser radiation with this substance are
described using the Jones-matrix operators that are
the most adequate and adapted to the processes of
amplitude-phase modulation of coherent radiation.
3. Polarization-inhomogeneous distributions of laser
radiation fields in the far Fourier diffraction zone
can be determined using the Kirhhoff integrals.
The process of transformation of laser radiation
parameters by an optically anisotropic layer is described
with the following matrix equation
CDJ . (1)
Here, D is the Jones matrix for linear
birefringence, C - Jones matrix for optical activity
2221
1211
dd
dd
D , (2)
where
.exp1cossin
;expsincos
;expcossin
2112
22
22
22
11
idd
id
id
(3)
2221
1211
cc
cc
C , (4)
with
.sin
;cos
;cos
2112
22
11
cc
c
c
(5)
Fig. 1. On analysis of model conceptions. E0, α0 are the
amplitude and azimuth of probing beam polarization; Ex, Ey, α,
β, φ - orthogonal components, azimuth, ellipticity and phase of
the object beam E; {A}, {D}, {C} - Jones matrixes for
isotropic, linear and circular birefringent components of a
biological layer.
In a detailed look, the equation (1) can be re-
written as
.
coscossin
cossinsin
cossin)1(sincos
)1(sincossincos
0
0
0
0
2
2
22
22
y
x
y
x
i
x
i
x
ii
ii
i
y
i
x
eE
eE
ee
ee
eE
eE
(6)
From (6), one can obtain expressions for
orthogonal complex components of the laser wave
amplitude in an arbitrary point belonging to the studied
crystalline network:
;cos1sincos
sinsincos
sin1sincos
cossincos
22
0
22
0
0
i
i
y
i
i
i
xx
e
eEe
e
eEE
y
(7)
.cossincos
sin1sincos
cos1sincos
sin1sincos
22
0
22
0
0
i
i
y
i
ii
i
xy
e
eEe
ee
eEE
y
(8)
In the case of placing the biological tissue layer
into the objective focal plane, one can obtain the
following distribution of complex amplitudes in the
Fourier plane:
;
2
exp,,
dmdnnnmn
f
inmE
fi
A
nmU
(9)
Here, f is the objective focal distance; –
wavelength of laser radiation; nm, and nm , are
coordinates of points in the image and Fourier planes,
respectively.
3. Computer modeling the processes of polarization
map formation
To determine the main interrelations between optical-
and-geometrical characteristics of birefringent networks
inherent to biological crystals and coordinate
distributions for azimuths and ellipticities of polarization
in the Fourier plane, we performed computer modeling.
As virtual birefringent networks, we used two types
of objects, namely: i) a network of birefringent cylinders
ordered in the direction of optical axes and placed in the
same plane; ii) an ensemble of birefringent globes,
centers of which are located in the same plane.
The results of computer modeling for distributions
of polarization azimuths inherent to laser images of
cylindrical and spherical birefringent networks in the
Fourier plane are shown in Fig. 2.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 252-260.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
254
Fig. 2. Polarization maps for Fourier spectra and their statistical parameters.
Fig. 3. Optical scheme of the polarization Fourier spectrometer where: 1 – He-Ne laser; 2 – collimator; 3 – stationary quarter-
wave plate; 4, 10 – polarizer and analyzer, respectively; 5, 9 – mechanically movable quarter-wave plates; 6 – object under study;
7, 8 – micro-objectives; 11 – CCD camera; 12 – personal computer.
Performed by us complex statistical, correlation
and fractal analyses for coordinate distributions of
polarization states for scattered laser radiation in the
Fourier plane revealed:
1. Polarization-inhomogeneous structure in Fourier
patterns of laser images for ensembles of optically
anisotropic birefringent crystals.
2. Coordinate inhomogeneity of Fourier patterns for
laser images, which is caused by superposition of
differently polarized partial laser waves.
3. Scale-self-similar multifractal structure for azimuth
distributions and polarization ellipticities in the
Fourier plane for the field of scattered laser
radiation.
4. Dependence of the set for statistical, correlation
and fractal parameters on optical-and-geometrical
parameters of virtual ordered cylinders and spheres.
4. Experimental application of the Fourier method of
polarization mapping
Represented in Fig. 3 is the optical scheme of
experimental setup for Fourier spectrometry of laser
images inherent to biological tissues.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 252-260.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
255
Fig. 4. Polarization filtered out Fourier spectra of laser images corresponding to histological sections of biological tissues.
Illumination was performed using a parallel ( =
104 μm) He-Ne laser beam ( = 0.6328 μm, W =
5.0 mW). The polarization illuminator consists of the
quarter-wave plates 3 and 5 as well as polarizer 4, which
provides formation of the laser beam with an arbitrary
azimuth 1800 0 or ellipticity of polarization
900 0 .
Histological sections of biological tissue samples
were placed in the focal plane of the micro-objective 7
(focal distance f = 450 μm, magnification 4Х), their
images were projected into the plane of the light-
sensitive area (800x600 pixels) of CCD-camera 10
( pixpixnmP 800600 ) that was also placed at
the focal distance and provided the range of
measurements for structural elements in the Fourier
spectrum of biological tissue images for the following
geometric sizes: between 2 to 2000 μm.
Our experimental conditions were chosen in such a
manner that enabled us to practically eliminate spatial-
angular filtration when forming the Fourier spectra of
biological tissue laser images. It was reached by
matching the angular characteristics for indicatrixes of
light scattering in biological tissue samples ( 016БТ )
with the angular aperture of the micro-objective
( 020 ). Here, БТ is the angular cone of
indicatrixes, where 98% of the total energy belonging to
scattered radiation is concentrated.
The analysis of polarization structure in the Fourier
spectra corresponding to images of histological sections
of biological tissues was performed using the polarizer
10 and the quarter-wave 9.
We investigated the samples of histological
sections taken from biological tissues of two types:
- muscular tissue – as a system of ordered along
definite direction birefringent myosin fibrils;
- skin derma – as a system of disordered
birefringent collagen fibrils.
It has been ascertained that spatially-ordered
fibrilar network is characterized by asymmetric shape of
Fourier images (Figs 4a and 4c) in polarization filtered
out images. In the case of disordered birefringent
network (Figs 4b and 4d), the Fourier patterns are
azimuth-symmetrical.
From the quantitative viewpoint, this polarization-
inhomogeneous structure in Fourier patterns of laser
images obtained for histological sections is illustrated
with histograms for distributions of polarization
azimuths in Fig. 5.
The ordered network is characterized by
availability of several extremes related with predominant
directions of folding of myosin fibrils. The disordering
process observed for collagen fibrils network in healthy
skin derma is manifested as re-distribution of extremes
in the respective histogram to the side of more
equiprobable structure. The obtained data correlate well
with those of computer modeling. Quantitatively, the
differences between coordinate distributions for
polarization azimuths are illustrated with values of
statistical moments of the first to fourth orders that are
adduced in Table 1.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 252-260.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
256
Fig. 5. Polarization maps (a, b) and histograms of distributions
(c, d) of polarization azimuths in Fourier spectra corresponding
to images of muscular tissue (a, c) and skin derma (b, d).
Table 1. Statistical moments of the first to fourth orders for
polarization azimuth distributions.
Mi
Muscular tissue
(q=19)
Skin derma
(q=18)
M1 0.14±0.01 0.17±0.01
M2 0.11±0.02 0.24±0.01
M3 0.21±0.04 0.46±0.01
M4 0.43±0.05 1.28±0.01
It has been ascertained that statistical moments of
the third and fourth orders are the most sensitive to
orientation changes in optical axes distributions inherent
to biological crystals. The differences between them
reach 2 and 3 times, respectively.
The next step was studying the possibility to detect
changes in birefringence by using experimental
investigation of the correlation structure inherent to
Fourier patterns of maps for azimuths and ellipticities in
laser images. As objects for experimental investigations,
we chose two groups of experimental samples prepared
in the form of optically thin histological sections by
using a freezing microtome in accord with the standard
technique. The first group of the samples ( 17N ) was
histological sections of biopsy taken from benign tumor
of rectum. The second group of the samples ( 16N )
was histological sections of biopsy taken from malignant
tumor of rectum. The topicality of development of the
methods in Fourier-Stokes polarimetry for
differentiation of these states is related both with
physical and applied reasons. As to physical reasons,
interest stems from the possibility to ascertain
mechanisms of transformation of the optical-and-
geometrical structure observed in polycrystalline
network inherent to epithelial and connective tissues of
rectum wall. Benign changes are accompanied by
formation of definite spatially oriented directions for
protein fibrils. In other words, there formed are definite
statistically probable parts in distributions describing
orientations of optical axes observed in biological
crystals. In the case of malignant changes, the above
asymmetry in orientation structure is increased with
simultaneous enhancement in optical anisotropy due to
the increased concentration of proteins in newly formed
fibrilar structures-processes of a tumor.
Fig. 6 illustrates capabilities of the cross-
correlation analysis aimed at distributions of polarization
azimuths in the field of laser radiation transformed by
histological sections of tissue biopsy, when
differentiating benign and malignant changes.
In the case of malignant tumor processes, there
formed is a sub-ensemble of birefringent fibrils with
spatially determinate directions of optical axes. As a
consequence, coordinate-homogeneous distributions of
the polarization azimuth are formed. In the case of
malignant tumor, coordinate homogeneity of
polarization azimuth values is lower. Respectively,
autocorrelation dependences obtained for the direction
close to the growth one possess higher velocity of decay
and lower halfwidth.
Quantitatively, the above differences are
characterized by average values and standard deviations
in the set of cross-correlation moments of the second and
fourth orders, which is summarized in Table 2.
Table 2. Cross-correlation moments for distributions of
polarization azimuths
dKi Benign tumor Malignant tumor
dK2 0.83±0.08 1.79±0.13
dK4 0.91±0.07 2.84±0.18
It has been ascertained that the cross-correlation
moment of the fourth order is the most sensitive in
differentiation of Fourier spectra corresponding to laser
images of histological sections taken from benign and
malignant changed tissue of rectum. The differences of
these values reach three times.
5. The method of consistent spatial-frequency
filtration of polarization-inhomogeneous images of
biological layers
To determine the capabilities of the method for Fourier
polarimetry with spatial-frequency filtration applied to
optical separation of linear and circular birefringence
manifestations, we performed computer modeling by
using the network of birefringent polycrystalline
cylinders with ordered directions of optical axes.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 252-260.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
257
Fig. 6. Orthogonal autocorrelation functions of Fourier spectra corresponding to the field of laser radiation scattered by rectum
tissue with benign (a) and malignant (b) changes.
Fig. 7. Spatial-frequency filtration of the polarization map corresponding to the network of birefringent cylinders.
Using computer modeling, we studied the
efficiency of consistent spatial-frequency filtration when
obtaining polarization maps of polycrystalline networks
with linear (network of cylinders) and circular (network
of globes) birefringence. In this case, we used a special
vignetting diaphragm placed in the Fourier plane. Fig. 7
shows a series of respective coordinate (a, b, c) and
probabilistic (d, e) distributions nm .
The obtained data illustrate the possibility to
efficiently differentiate the low-frequency (a, c) and
high-frequency (b, d) components of distributions for
polarization azimuths formed in accord with different
birefringence mechanisms.
Depicted in Figs 8 and 9 is the series of
probabilistic (b, f), correlation (c, g) and spectral (d, h)
dependences that characterize the coordinate
distributions for polarization azimuths (a, e) of large-
scale (Fig. 8) as well as small-scale (Fig. 9) networks of
proteins in the films of blood plasma taken from a
healthy man (a – d) and that sick (e – h) with prostate
cancer.
It has been ascertained that histograms for the
distribution of polarization azimuths in blood plasma
film images for the healthy man possess more
asymmetric structure (Fig. 8b) as compared to the same
distribution for the patient sick with stomach cancer
(Fig. 9f). The revealed feature is related with a higher
order among directions of optical axes in the structure of
networks of needle-like albumin crystals in the blood
plasma taken from the group 1 than that from the group
2. This geometric structure is inherent to formation of
priority, the most probable among all the possible values
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 252-260.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
258
Fig. 8. Large-scale polarization maps of the linearly birefringent component of proteins in blood plasma films and their
statistical, correlation and fractal parameters. See explanations in the text.
Fig. 9. Small-scale polarization maps for the circular birefringent component of proteins in blood plasma films and their
statistical, correlation and fractal parameters. See explanations in the text.
of polarization azimuths, the set of which forms the main
extreme.
Dependences of autocorrelation functions for
polarization azimuth distributions of both samples of
blood plasma films decay smoothly and monotonically
(Figs 8c and 8g). This regularity is indicative of the
coordinate homogeneous structure for albumin crystal
polarization maps. Besides, we revealed a scale-self-
similar structure of these maps – logarithmic
dependences of the power spectra for polarization
azimuth distributions are characterized by the same
slope angle practically within the whole range from 2 up
to 1000 μm (Figs 8d and 8h).
It has been ascertained that the main feature of
oncological changes is formation of definite spatially
determinate directions of orientation of albumin needle-
like crystals and, related with it, transformation of the
histogram for the distribution of polarization azimuth
values.
Another picture takes place when using the
complex statistical, correlation and fractal analysis of
coordinate distributions for polarization azimuths
corresponding to optically active small-scale spherolytic
albumin networks.
We revealed the following signs of optical activity
transformations related with presence of oncological
state. Essential extending the range of changes in
random values α** of the histogram corresponding to
the spherolytic polycrystalline network owing to growth
of the globulin concentration (Figs 9b and 9f).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 252-260.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
259
Table 3. Statistical, correlation and fractal parameters for different scale components of polarization maps
corresponding to blood plasma films
Albumins α*(m×n) Globulins α**(m×n)Parametr
Norma Cancer Norma Cancer
M1 1.07 0.17 1.12 0.19 0.27 0.037 0.35 0.046
M2 0.14 0.021 0.19 0.025 0.082 0.012 0.19 0.031
M3 1.73 0.24 0.16 0.027 0.11 0.017 1.03 0.15
M4 0.89 0.011 0.12 0.017 1.54 0.22 0.63 0.077
Q2 0.28 0.045 0.29 0.047 0.015 0.0028 0.088 0.011
Q4 0.045 0.0077 0.05 0.009 4.38 0.74 1.82 0.31
V(η) Fractal Fractal Fractal Multifractal
D 0.31 0.055 0.29 0.051 0.095 0.013 0.17 0.028
“Pathological” growth of the amount of optically
active crystals results in formation of a more coordinate
homogeneous distribution for values. In the
correlation analysis, this regularity is pronounced as a
slow drop and wider halfwidths of autocorrelation
functions (Figs 9c and 9g). Reconstruction of the
globulin polycrystalline network is accompanied by
transformation of the practically fractal distribution
into the multifractal one – the logarithmic dependence of
the power spectrum is characterized by several different
slopes of the approximating curve (Fig. 9h).
Quantitatively, these differences between
polarization maps are illustrated with the data
summarized in Table 3.
Our comparative analysis enabled us to reveal the
following parameters diagnostically sensitive to the
oncological state of a man’s prostate:
– statistical moments of the third and fourth
orders for nm̂ distributions, differences between
values of which reach 7 ( 3Z ) up to 10 ( 4Z ) times;
– statistical moments of the second to fourth
orders for nm distributions, differences between
values of which reach 2 ( 2Z , 3Z ) up to 10 ( 4Z ) times;
– statistical moments of the second to fourth
orders for autocorrelation functions corresponding to
nm distributions, differences between values of
which reach 2.2 ( 2Q ) up to 4 ( 4Q ) times;
– dispersion D of logarithmic dependences for the
power spectra of nm distributions, differences
between values of which reach 2 times;
– transformation of fractal nm distributions
into the multifractal ones.
6. Conclusions
1. Offered in this work is the model of generalized
anisotropy inherent to protein networks of
biological tissues with different scales (polypeptide
chains, fibrils, fibers, bunches) and using the
computer modeling analyzed have been the main
scenarios providing formation and transformation
of polarization maps for azimuths and ellipticities
of laser images and their Fourier spectra. Also
ascertained is their dependence on optical-and-
geometrical structure observed in linearly and
circularly partial birefringent networks.
2. Developed is the method of Fourier-Stokes
polarinetry for spatial-frequency spectra of laser
images, which is based on cross-correlation
analysis of polarization maps. Using this method,
for the first time, we realized differentiation of
pathological states observed in biological tissues –
histological sections prepared from biopsy of
benign and malignant tumors of rectum.
3. We have investigated the efficiency of spatial-
frequency filtration applied to polarization-
inhomogeneous laser images of blood plasma
films. For the first time, we realized experimentally
the system of consistent Fourier-Stokes
polarimetric separation of mechanisms inherent to
linear and circular birefringence in polycrystalline
albumin and globulin networks of different scales.
4. In approximation of single-step scattering, we
found the interrelation between changes of
parameters describing anisotropy of linearly
(direction of the optical axes and phase shift
between orthogonal linearly polarized unit vectors)
and circularly (phase shift between circularly
polarized unit vectors) polarized amino acid
crystals in blood plasma as well as variations of
values characteristic for statistical, correlation and
spectral moments of the first to fourth orders that
characterize coordinate distributions for
polarization azimuths and ellipticities, which are
formed by partial networks of albumins and
globulins in human blood plasma.
References
1. Tuchin V. V. Handbook of coherent-domain optical
methods. Biomedical diagnostics, environmental
and material science / edited by Tuchin V. V. –
Boston. : Kluwer Academic Publishers, 2004. – P.
868.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 252-260.
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
260
2. Handbook of Optical Coherence Tomography /
edited by B. E. Bouma and G. J. Tearn //
Polarization-sensitive optical coherence
tomography / J. F. de Boer, T. E. Milner, M. G.
Ducros, S. M. Srinivas and J. S. Nelson. – New
York : Marcel Dekker Inc., 2002. – P. 237-274.
3. Sankaran. V. Comparison of polarized-light
propagation in biological tissue and phantoms / V.
Sankaran, M. J. Everett, D. J. Maitland, J. T. Walsh
// Opt. Lett. – 1999. – Vol. 24. – P. 1044-1046.
4. Pierce M.C. Birefringence measurements in human
skin using polarization-sensitive optical coherence
tomography / M.C. Pierce, J. Strasswimmer, B.
Hyle Park, B. Cense, J. F. de Boer // J. Biomed.
Opt. – 2004. – Vol. 9. – P. 287-291.
5. Angelsky O. V. Investigation of 2D Mueller matrix
structure of biological tissues for preclinical
diagnostics of their pathological states / O. V.
Angelsky, Yu. Ya. Tomka, A. G. Ushenko, Ye. G.
Ushenko, Yu. A. Ushenko // J. Phys. D: Appl.
Phys. – 2005. – Vol. 38. – P. 4227-4235.
6. Ushenko A. G. Evolution of statistic moments of
2D- distributions o f biological liquid crystal
netmueller matrix elements in the process of their
birefringent structure changes. / A. G. Ushenko, I.
Z. Misevich, V. Istratiy, I. Bachyns'ka, A. P.
Peresunko, O. K. Numan, T. G. Moiysuk //
Advances in Optical Technologies. – 2010. – ID
423145.
7. O.V. Angelsky. Polarization singularities of the
object field of skin surface / O.V. Angelsky, A. G.
Ushenko, Yu. A. Ushenko, Ye. G. Ushenko // J.
Phys. D: Appl. Phys. – 2006. – Vol. 39. – P. 3547 -
3558.
8. Yermolenko S. Spectropolarimetry of cancer
change of biotissues / Yermolenko S., Ushenko A.,
Ivashko P., Goudail F., Gruia I., Gavrilǎ C.,
Zimnyakov D., Mikhailova A. // Proceedings of
SPIE. – 2009. .– Vol. 7388. – P 73881D.
9. Ushenko A. Statistical and fractal approaches in
laser polarimetry diagnostics of the cancer prostate
tissues / Ushenko A., Yermolenko S., Prydij A.,
Guminetsky S., Gruia I., Toma O., Vladychenko K
// Proceedings of SPIE. – 2008. .– Vol. 7008. – P
70082C.
10. Laser Speckle and Related Phenomena / edited by
J. C. Dainty // Statistical properties of laser speckle
patterns / J.W. Goodman. – Berlin : Springer-
Verlag, 1975. – P. 9-75.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2012. V. 15, N 3. P. 252-260.
PACS 33.50.-j, 34.35.+a, 73.20.Mf, 78.30.-j
Fourier-Stokes polarimetry of fields corresponding to linearly
and circularly polarized birefringent protein networks
A.O. Karachevtsev
Chernivtsi National University named after Yuri Fed’kovych,
Department for Optics and Spectroscopy,
2 Kotsyubyns’kogo str., 58001 Chernivtsi, Ukraine.
Phone: +38067 783 0572
Abstract. Considered in this work are the possibilities to use the method of Fourier-Stokes polarimetry for diagnostics of optical anisotropy inherent to polycrystalline networks of biological layers. The authors have offered a generalized model for optical anisotropy of histological sections taken from biological tissues and films of biological liquids. Polarization maps for Fourier spectra of laser images describing the phase-inhomogeneous objects have been investigated. Grounded was application of the method for consistent spatial-frequency filtration of polarization maps formed by linear and circular birefringent of biological crystals.
Keywords: polarization, Jones matrix, optical anisotropy, biological layer, polarization map, Fourier spectrum, spatial-frequency filtration.
Manuscript received 08.02.12; revised version received 07.06.12; accepted for publication 14.06.12; published online 25.09.12.
1. Introduction
Among the variety of systems for diagnostics of optical anisotropy of biological objects [1-3], a new direction – laser polarimetry of biological tissue images has been separated [4, 5]. In this approach, the analysis of the obtained data is based on approximation of linear birefringence observed in polycrystalline protein networks. Using the above model approach, the authors found interrelation between the set of statistical moments of the first to fourth orders that characterize distributions of azimuths and ellipticity of polarizations in laser images as well as parameters of anisotropy inherent to the layers of biological tissues [6-7]. As a result, developed was the method for polarization mapping and successfully realized was the diagnostics of oncological (malignant) changes in human biological tissue [8, 9]. To further develop the methods of laser polarimetric diagnostics, it seems topical to differentiate various mechanisms of optical anisotropy. Up to date, the above method of polarization mapping is not able to solve this problem. One of the possible solutions lies in using the consistent spatial-frequency filtration of laser images [10]. The idea of this approach, which is novelty in biomedical applications, is based on filtration of spatial-frequency spectra for polarization images of networks including biological crystals with different mechanisms of anisotropy. Optical realization of this method consists of the following stages: direct Fourier transform, spatial-frequency and polarization-phase filtration, inverse Fourier transform of biological layer laser images.
This work is aimed at development of a generalized model of phase anisotropy to describe formation of fields inherent to scattered laser radiation and, with account of this model, substantiation of new methods for Fourier-Stokes polarimetry as well as consistent polarization-phase filtration of manifestations inherent to linear and circular birefringence for diagnostics of the structure of polycrystalline networks observed in biological tissues and liquids.
2. Model conceptions and computer modeling the processes of formation of polarization-inhomogeneous images and their Fourier spectra
As a basis for our investigations, we took the following model conceptions:
1. Substance of optically anisotropic component of biological tissue possesses some generalized anisotropy that is a superposition of linear and circular birefringence.
2. From the analytical viewpoint, processes of interaction of laser radiation with this substance are described using the Jones-matrix operators that are the most adequate and adapted to the processes of amplitude-phase modulation of coherent radiation.
3. Polarization-inhomogeneous distributions of laser radiation fields in the far Fourier diffraction zone can be determined using the Kirhhoff integrals.
The process of transformation of laser radiation parameters by an optically anisotropic layer is described with the following matrix equation
{
}
{
}
{
}
C
D
J
=
.
(1)
Here,
{
}
D
is the Jones matrix for linear birefringence,
{
}
C
- Jones matrix for optical activity
{
}
ú
û
ù
ê
ë
é
=
22
21
12
11
d
d
d
d
D
,
(2)
where
(
)
(
)
(
)
(
)
ï
î
ï
í
ì
-
-
=
=
-
+
=
-
+
=
.
exp
1
cos
sin
;
exp
sin
cos
;
exp
cos
sin
21
12
2
2
22
2
2
11
j
k
k
j
k
k
j
k
k
i
d
d
i
d
i
d
(3)
{
}
ú
û
ù
ê
ë
é
=
22
21
12
11
c
c
c
c
C
,
(4)
with
ï
î
ï
í
ì
=
-
=
=
=
.
sin
;
cos
;
cos
21
12
22
11
y
y
y
c
c
c
c
(5)
Fig. 1. On analysis of model conceptions. E0, α0 are the amplitude and azimuth of probing beam polarization; Ex, Ey, α, β, φ - orthogonal components, azimuth, ellipticity and phase of the object beam E; {A}, {D}, {C} - Jones matrixes for isotropic, linear and circular birefringent components of a biological layer.
In a detailed look, the equation (1) can be re-written as
.
cos
cos
sin
cos
sin
sin
cos
sin
)
1
(
sin
cos
)
1
(
sin
cos
sin
cos
0
0
0
0
2
2
2
2
2
2
÷
÷
ø
ö
ç
ç
è
æ
ú
ú
û
ù
ê
ê
ë
é
´
´
ú
ú
û
ù
ê
ê
ë
é
+
-
-
+
=
÷
÷
÷
ø
ö
ç
ç
ç
è
æ
-
-
-
-
y
x
y
x
i
x
i
x
i
i
i
i
i
y
i
x
e
E
e
E
e
e
e
e
e
E
e
E
j
j
j
j
j
j
j
j
y
y
y
y
y
y
k
k
k
k
k
k
k
k
(6)
From (6), one can obtain expressions for orthogonal complex components of the laser wave amplitude in an arbitrary point belonging to the studied crystalline network:
(
)
[
(
)
]
(
)
[
(
)
]
;
cos
1
sin
cos
sin
sin
cos
sin
1
sin
cos
cos
sin
cos
2
2
0
2
2
0
0
y
k
k
y
k
k
y
k
k
y
k
k
g
g
j
g
g
i
i
y
i
i
i
x
x
e
e
E
e
e
e
E
E
y
-
-
-
-
-
+
+
+
+
-
+
+
+
=
(7)
(
)
[
(
)
(
)
]
(
)
[
(
)
]
.
cos
sin
cos
sin
1
sin
cos
cos
1
sin
cos
sin
1
sin
cos
2
2
0
2
2
0
0
y
k
k
y
k
k
y
k
k
y
k
k
g
g
j
g
g
g
i
i
y
i
i
i
i
x
y
e
e
E
e
e
e
e
E
E
y
-
-
-
-
-
+
+
+
-
+
+
-
+
+
+
-
=
(8)
In the case of placing the biological tissue layer into the objective focal plane, one can obtain the following distribution of complex amplitudes in the Fourier plane:
(
)
(
)
(
)
;
2
exp
,
,
ò
+¥
¥
-
*
*
*
*
ú
û
ù
ê
ë
é
+
-
=
dmdn
nn
mn
f
i
n
m
E
f
i
A
n
m
U
l
p
l
(9)
Here,
f
is the objective focal distance;
l
– wavelength of laser radiation;
n
m
,
and
*
*
n
m
,
are coordinates of points in the image and Fourier planes, respectively.
3. Computer modeling the processes of polarization map formation
To determine the main interrelations between optical-and-geometrical characteristics of birefringent networks inherent to biological crystals and coordinate distributions for azimuths and ellipticities of polarization in the Fourier plane, we performed computer modeling.
As virtual birefringent networks, we used two types of objects, namely: i) a network of birefringent cylinders ordered in the direction of optical axes and placed in the same plane; ii) an ensemble of birefringent globes, centers of which are located in the same plane.
The results of computer modeling for distributions of polarization azimuths inherent to laser images of cylindrical and spherical birefringent networks in the Fourier plane are shown in Fig. 2.
Performed by us complex statistical, correlation and fractal analyses for coordinate distributions of polarization states for scattered laser radiation in the Fourier plane revealed:
1. Polarization-inhomogeneous structure in Fourier patterns of laser images for ensembles of optically anisotropic birefringent crystals.
2. Coordinate inhomogeneity of Fourier patterns for laser images, which is caused by superposition of differently polarized partial laser waves.
3. Scale-self-similar multifractal structure for azimuth distributions and polarization ellipticities in the Fourier plane for the field of scattered laser radiation.
4. Dependence of the set for statistical, correlation and fractal parameters on optical-and-geometrical parameters of virtual ordered cylinders and spheres.
4. Experimental application of the Fourier method of polarization mapping
Represented in Fig. 3 is the optical scheme of experimental setup for Fourier spectrometry of laser images inherent to biological tissues.
Illumination was performed using a parallel (( = 104 μm) He-Ne laser beam (( = 0.6328 μm, W = 5.0 mW). The polarization illuminator consists of the quarter-wave plates 3 and 5 as well as polarizer 4, which provides formation of the laser beam with an arbitrary azimuth
°
£
£
°
180
0
0
a
or ellipticity of polarization
°
£
£
°
90
0
0
b
.
Histological sections of biological tissue samples were placed in the focal plane of the micro-objective 7 (focal distance f = 450 μm, magnification 4Х), their images were projected into the plane of the light-sensitive area (800x600 pixels) of CCD-camera 10 (
pix
pix
n
m
P
800
600
´
=
´
=
) that was also placed at the focal distance and provided the range of measurements for structural elements in the Fourier spectrum of biological tissue images for the following geometric sizes: between 2 to 2000 μm.
Our experimental conditions were chosen in such a manner that enabled us to practically eliminate spatial-angular filtration when forming the Fourier spectra of biological tissue laser images. It was reached by matching the angular characteristics for indicatrixes of light scattering in biological tissue samples (
0
16
»
W
ÁÒ
) with the angular aperture of the micro-objective (
0
20
=
D
w
). Here,
ÁÒ
W
is the angular cone of indicatrixes, where 98% of the total energy belonging to scattered radiation is concentrated.
The analysis of polarization structure in the Fourier spectra corresponding to images of histological sections of biological tissues was performed using the polarizer 10 and the quarter-wave 9.
We investigated the samples of histological sections taken from biological tissues of two types:
- muscular tissue – as a system of ordered along definite direction birefringent myosin fibrils;
- skin derma – as a system of disordered birefringent collagen fibrils.
It has been ascertained that spatially-ordered fibrilar network is characterized by asymmetric shape of Fourier images (Figs 4a and 4c) in polarization filtered out images. In the case of disordered birefringent network (Figs 4b and 4d), the Fourier patterns are azimuth-symmetrical.
From the quantitative viewpoint, this polarization-inhomogeneous structure in Fourier patterns of laser images obtained for histological sections is illustrated with histograms for distributions of polarization azimuths in Fig. 5.
The ordered network is characterized by availability of several extremes related with predominant directions of folding of myosin fibrils. The disordering process observed for collagen fibrils network in healthy skin derma is manifested as re-distribution of extremes in the respective histogram to the side of more equiprobable structure. The obtained data correlate well with those of computer modeling. Quantitatively, the differences between coordinate distributions for polarization azimuths are illustrated with values of statistical moments of the first to fourth orders that are adduced in Table 1.
Fig. 5. Polarization maps (a, b) and histograms of distributions (c, d) of polarization azimuths in Fourier spectra corresponding to images of muscular tissue (a, c) and skin derma (b, d).
Table 1. Statistical moments of the first to fourth orders for polarization azimuth distributions.
Mi
Muscular tissue
(q=19)
Skin derma
(q=18)
M1
0.14±0.01
0.17±0.01
M2
0.11±0.02
0.24±0.01
M3
0.21±0.04
0.46±0.01
M4
0.43±0.05
1.28±0.01
It has been ascertained that statistical moments of the third and fourth orders are the most sensitive to orientation changes in optical axes distributions inherent to biological crystals. The differences between them reach 2 and 3 times, respectively.
The next step was studying the possibility to detect changes in birefringence by using experimental investigation of the correlation structure inherent to Fourier patterns of maps for azimuths and ellipticities in laser images. As objects for experimental investigations, we chose two groups of experimental samples prepared in the form of optically thin histological sections by using a freezing microtome in accord with the standard technique. The first group of the samples (
17
=
N
) was histological sections of biopsy taken from benign tumor of rectum. The second group of the samples (
16
=
N
) was histological sections of biopsy taken from malignant tumor of rectum. The topicality of development of the methods in Fourier-Stokes polarimetry for differentiation of these states is related both with physical and applied reasons. As to physical reasons, interest stems from the possibility to ascertain mechanisms of transformation of the optical-and-geometrical structure observed in polycrystalline network inherent to epithelial and connective tissues of rectum wall. Benign changes are accompanied by formation of definite spatially oriented directions for protein fibrils. In other words, there formed are definite statistically probable parts in distributions describing orientations of optical axes observed in biological crystals. In the case of malignant changes, the above asymmetry in orientation structure is increased with simultaneous enhancement in optical anisotropy due to the increased concentration of proteins in newly formed fibrilar structures-processes of a tumor.
Fig. 6 illustrates capabilities of the cross-correlation analysis aimed at distributions of polarization azimuths in the field of laser radiation transformed by histological sections of tissue biopsy, when differentiating benign and malignant changes.
In the case of malignant tumor processes, there formed is a sub-ensemble of birefringent fibrils with spatially determinate directions of optical axes. As a consequence, coordinate-homogeneous distributions of the polarization azimuth are formed. In the case of malignant tumor, coordinate homogeneity of polarization azimuth values is lower. Respectively, autocorrelation dependences obtained for the direction close to the growth one possess higher velocity of decay and lower halfwidth.
Quantitatively, the above differences are characterized by average values and standard deviations in the set of cross-correlation moments of the second and fourth orders, which is summarized in Table 2.
Table 2. Cross-correlation moments for distributions of polarization azimuths
dKi
Benign tumor
Malignant tumor
dK2
0.83±0.08
1.79±0.13
dK4
0.91±0.07
2.84±0.18
It has been ascertained that the cross-correlation moment of the fourth order is the most sensitive in differentiation of Fourier spectra corresponding to laser images of histological sections taken from benign and malignant changed tissue of rectum. The differences of these values reach three times.
5. The method of consistent spatial-frequency filtration of polarization-inhomogeneous images of biological layers
To determine the capabilities of the method for Fourier polarimetry with spatial-frequency filtration applied to optical separation of linear and circular birefringence manifestations, we performed computer modeling by using the network of birefringent polycrystalline cylinders with ordered directions of optical axes.
Using computer modeling, we studied the efficiency of consistent spatial-frequency filtration when obtaining polarization maps of polycrystalline networks with linear (network of cylinders) and circular (network of globes) birefringence. In this case, we used a special vignetting diaphragm placed in the Fourier plane. Fig. 7 shows a series of respective coordinate (a, b, c) and probabilistic (d, e) distributions
(
)
n
m
´
a
.
The obtained data illustrate the possibility to efficiently differentiate the low-frequency (a, c) and high-frequency (b, d) components of distributions for polarization azimuths formed in accord with different birefringence mechanisms.
Depicted in Figs 8 and 9 is the series of probabilistic (b, f), correlation (c, g) and spectral (d, h) dependences that characterize the coordinate distributions for polarization azimuths (a, e) of large-scale (Fig. 8) as well as small-scale (Fig. 9) networks of proteins in the films of blood plasma taken from a healthy man (a – d) and that sick (e – h) with prostate cancer.
It has been ascertained that histograms for the distribution of polarization azimuths in blood plasma film images for the healthy man possess more asymmetric structure (Fig. 8b) as compared to the same distribution for the patient sick with stomach cancer (Fig. 9f). The revealed feature is related with a higher order among directions of optical axes in the structure of networks of needle-like albumin crystals in the blood plasma taken from the group 1 than that from the group 2. This geometric structure is inherent to formation of priority, the most probable among all the possible values of polarization azimuths, the set of which forms the main extreme.
Dependences of autocorrelation functions for polarization azimuth distributions of both samples of blood plasma films decay smoothly and monotonically (Figs 8c and 8g). This regularity is indicative of the coordinate homogeneous structure for albumin crystal polarization maps. Besides, we revealed a scale-self-similar structure of these maps – logarithmic dependences of the power spectra for polarization azimuth distributions are characterized by the same slope angle practically within the whole range from 2 up to 1000 μm (Figs 8d and 8h).
It has been ascertained that the main feature of oncological changes is formation of definite spatially determinate directions of orientation of albumin needle-like crystals and, related with it, transformation of the histogram for the distribution of polarization azimuth values.
Another picture takes place when using the complex statistical, correlation and fractal analysis of coordinate distributions for polarization azimuths corresponding to optically active small-scale spherolytic albumin networks.
We revealed the following signs of optical activity transformations related with presence of oncological state. Essential extending the range of changes in random values α** of the histogram corresponding to the spherolytic polycrystalline network owing to growth of the globulin concentration (Figs 9b and 9f).
“Pathological” growth of the amount of optically active crystals results in formation of a more coordinate homogeneous distribution for
*
*
a
values. In the correlation analysis, this regularity is pronounced as a slow drop and wider halfwidths of autocorrelation functions (Figs 9c and 9g). Reconstruction of the globulin polycrystalline network is accompanied by transformation of the practically fractal distribution
*
*
a
into the multifractal one – the logarithmic dependence of the power spectrum is characterized by several different slopes of the approximating curve (Fig. 9h).
Quantitatively, these differences between polarization maps are illustrated with the data summarized in Table 3.
Our comparative analysis enabled us to reveal the following parameters diagnostically sensitive to the oncological state of a man’s prostate:
· statistical moments of the third and fourth orders for
(
)
n
m
´
a
ˆ
distributions, differences between values of which reach 7 (
3
Z
) up to 10 (
4
Z
) times;
· statistical moments of the second to fourth orders for
(
)
n
m
´
a
&
distributions, differences between values of which reach 2 (
2
Z
,
3
Z
) up to 10 (
4
Z
) times;
· statistical moments of the second to fourth orders for autocorrelation functions corresponding to
(
)
n
m
´
a
&
distributions, differences between values of which reach 2.2 (
2
Q
) up to 4 (
4
Q
) times;
· dispersion D of logarithmic dependences for the power spectra of
(
)
n
m
´
a
&
distributions, differences between values of which reach 2 times;
· transformation of fractal
(
)
n
m
´
a
&
distributions into the multifractal ones.
6. Conclusions
1.
Offered in this work is the model of generalized anisotropy inherent to protein networks of biological tissues with different scales (polypeptide chains, fibrils, fibers, bunches) and using the computer modeling analyzed have been the main scenarios providing formation and transformation of polarization maps for azimuths and ellipticities of laser images and their Fourier spectra. Also ascertained is their dependence on optical-and-geometrical structure observed in linearly and circularly partial birefringent networks.
2.
Developed is the method of Fourier-Stokes polarinetry for spatial-frequency spectra of laser images, which is based on cross-correlation analysis of polarization maps. Using this method, for the first time, we realized differentiation of pathological states observed in biological tissues – histological sections prepared from biopsy of benign and malignant tumors of rectum.
3.
We have investigated the efficiency of spatial-frequency filtration applied to polarization-inhomogeneous laser images of blood plasma films. For the first time, we realized experimentally the system of consistent Fourier-Stokes polarimetric separation of mechanisms inherent to linear and circular birefringence in polycrystalline albumin and globulin networks of different scales.
4.
In approximation of single-step scattering, we found the interrelation between changes of parameters describing anisotropy of linearly (direction of the optical axes and phase shift between orthogonal linearly polarized unit vectors) and circularly (phase shift between circularly polarized unit vectors) polarized amino acid crystals in blood plasma as well as variations of values characteristic for statistical, correlation and spectral moments of the first to fourth orders that characterize coordinate distributions for polarization azimuths and ellipticities, which are formed by partial networks of albumins and globulins in human blood plasma.
References
1. Tuchin V. V. Handbook of coherent-domain optical methods. Biomedical diagnostics, environmental and material science / edited by Tuchin V. V. – Boston. : Kluwer Academic Publishers, 2004. – P. 868.
2. Handbook of Optical Coherence Tomography / edited by B. E. Bouma and G. J. Tearn // Polarization-sensitive optical coherence tomography / J. F. de Boer, T. E. Milner, M. G. Ducros, S. M. Srinivas and J. S. Nelson. – New York : Marcel Dekker Inc., 2002. – P. 237-274.
3. Sankaran. V. Comparison of polarized-light propagation in biological tissue and phantoms / V. Sankaran, M. J. Everett, D. J. Maitland, J. T. Walsh // Opt. Lett. – 1999. – Vol. 24. – P. 1044-1046.
4. Pierce M.C. Birefringence measurements in human skin using polarization-sensitive optical coherence tomography / M.C. Pierce, J. Strasswimmer, B. Hyle Park, B. Cense, J. F. de Boer // J. Biomed. Opt. – 2004. – Vol. 9. – P. 287-291.
5. Angelsky O. V. Investigation of 2D Mueller matrix structure of biological tissues for preclinical diagnostics of their pathological states / O. V. Angelsky, Yu. Ya. Tomka, A. G. Ushenko, Ye. G. Ushenko, Yu. A. Ushenko // J. Phys. D: Appl. Phys. – 2005. – Vol. 38. – P. 4227-4235.
6. Ushenko A. G. Evolution of statistic moments of 2D- distributions o f biological liquid crystal netmueller matrix elements in the process of their
birefringent structure changes. / A. G. Ushenko, I. Z. Misevich, V. Istratiy, I. Bachyns'ka, A. P. Peresunko, O. K. Numan, T. G. Moiysuk // Advances in Optical Technologies. – 2010. – ID 423145.
7. O.V. Angelsky. Polarization singularities of the object field of skin surface / O.V. Angelsky, A. G. Ushenko, Yu. A. Ushenko, Ye. G. Ushenko // J. Phys. D: Appl. Phys. – 2006. – Vol. 39. – P. 3547 -3558.
8. Yermolenko S. Spectropolarimetry of cancer change of biotissues / Yermolenko S., Ushenko A., Ivashko P., Goudail F., Gruia I., Gavrilǎ C., Zimnyakov D., Mikhailova A. // Proceedings of SPIE. – 2009. .– Vol. 7388. – P 73881D.
9. Ushenko A. Statistical and fractal approaches in laser polarimetry diagnostics of the cancer prostate tissues / Ushenko A., Yermolenko S., Prydij A., Guminetsky S., Gruia I., Toma O., Vladychenko K // Proceedings of SPIE. – 2008. .– Vol. 7008. – P 70082C.
10. Laser Speckle and Related Phenomena / edited by J. C. Dainty // Statistical properties of laser speckle patterns / J.W. Goodman. – Berlin : Springer-Verlag, 1975. – P. 9-75.
�
Fig. 2. Polarization maps for Fourier spectra and their statistical parameters.
�
Fig. 3. Optical scheme of the polarization Fourier spectrometer where: 1 – He-Ne laser; 2 – collimator; 3 – stationary quarter-wave plate; 4, 10 – polarizer and analyzer, respectively; 5, 9 – mechanically movable quarter-wave plates; 6 – object under study; 7, 8 – micro-objectives; 11 – CCD camera; 12 – personal computer.
�
Fig. 4. Polarization filtered out Fourier spectra of laser images corresponding to histological sections of biological tissues.
�
Fig. 6. Orthogonal autocorrelation functions of Fourier spectra corresponding to the field of laser radiation scattered by rectum tissue with benign (a) and malignant (b) changes.
�
Fig. 7. Spatial-frequency filtration of the polarization map corresponding to the network of birefringent cylinders.
�
Fig. 8. Large-scale polarization maps of the linearly birefringent component of proteins in blood plasma films and their statistical, correlation and fractal parameters. See explanations in the text.
�
Fig. 9. Small-scale polarization maps for the circular birefringent component of proteins in blood plasma films and their statistical, correlation and fractal parameters. See explanations in the text.
Table 3. Statistical, correlation and fractal parameters for different scale components of polarization maps corresponding to blood plasma films
Parametr
�
Albumins α*(m×n)�
Globulins α**(m×n)�
�
�
Norma�
Cancer�
Norma�
Cancer�
�
M1�
1.07� EMBED Equation.3 ���0.17�
1.12� EMBED Equation.3 ���0.19�
0.27� EMBED Equation.3 ���0.037�
0.35� EMBED Equation.3 ���0.046�
�
M2�
0.14� EMBED Equation.3 ���0.021�
0.19� EMBED Equation.3 ���0.025�
0.082� EMBED Equation.3 ���0.012�
0.19� EMBED Equation.3 ���0.031�
�
M3�
1.73� EMBED Equation.3 ���0.24�
0.16� EMBED Equation.3 ���0.027�
0.11� EMBED Equation.3 ���0.017�
1.03� EMBED Equation.3 ���0.15�
�
M4�
0.89� EMBED Equation.3 ���0.011�
0.12� EMBED Equation.3 ���0.017�
1.54� EMBED Equation.3 ���0.22�
0.63� EMBED Equation.3 ���0.077�
�
Q2�
0.28� EMBED Equation.3 ���0.045�
0.29� EMBED Equation.3 ���0.047�
0.015� EMBED Equation.3 ���0.0028�
0.088� EMBED Equation.3 ���0.011�
�
Q4�
0.045� EMBED Equation.3 ���0.0077�
0.05� EMBED Equation.3 ���0.009�
4.38� EMBED Equation.3 ���0.74�
1.82� EMBED Equation.3 ���0.31�
�
V(η)�
Fractal�
Fractal�
Fractal�
Multifractal�
�
D�
0.31� EMBED Equation.3 ���0.055�
0.29� EMBED Equation.3 ���0.051�
0.095� EMBED Equation.3 ���0.013�
0.17� EMBED Equation.3 ���0.028�
�
© 2012, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
252
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
±
_1413265307.unknown
_1413265644.unknown
_1413266156.unknown
_1413266179.unknown
_1413267059.unknown
_1413268734.unknown
_1416061569.unknown
_1413267056.unknown
_1413266172.unknown
_1413266175.unknown
_1413266162.unknown
_1413265803.unknown
_1413266135.unknown
_1413265710.unknown
_1413265345.unknown
_1413265532.unknown
_1413265553.unknown
_1413265351.unknown
_1413265339.unknown
_1413265342.unknown
_1413265337.unknown
_1403152491.unknown
_1403152548.unknown
_1403152560.unknown
_1403152566.unknown
_1403152552.unknown
_1403152544.unknown
_1403096800.unknown
_1403152488.unknown
_1403152480.unknown
_1403152485.unknown
_1403152290.unknown
_1403096794.unknown
_1403096797.unknown
_1375159022.unknown
_1403096790.unknown
_1375159004.unknown
|