Mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility
A new azimuthally stable polarimetric method for processing microscopic images of optically anisotropic structures for different biological layers of histological sections has been proposed. A new model that enables to determine phase anisotropy of biological tissues by using superposition of Muelle...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2015
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| Цитувати: | Mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility / A.G. Ushenko, M.M. Dominikov, I.I. Lakusta, G.D. Koval // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 2. — С. 164-169. — Бібліогр.: 22 назв. — англ. |
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irk-123456789-1218172017-06-19T03:03:07Z Mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility Ushenko, A.G. Dominikov, M.M. Lakusta, I.I. Koval, G.D. A new azimuthally stable polarimetric method for processing microscopic images of optically anisotropic structures for different biological layers of histological sections has been proposed. A new model that enables to determine phase anisotropy of biological tissues by using superposition of Mueller matrices of linear birefringence and optical activity has been proposed. The matrix element М₄₄ has been chosen as the main information parameter, which value is independent of rotation angle of both sample and probing beam polarization plane. 2015 Article Mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility / A.G. Ushenko, M.M. Dominikov, I.I. Lakusta, G.D. Koval // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 2. — С. 164-169. — Бібліогр.: 22 назв. — англ. 1560-8034 DOI: 10.15407/spqeo18.02.164 PACS 87.50.wp, 87.57.-s, 87.64.-t, 87.85.Pq http://dspace.nbuv.gov.ua/handle/123456789/121817 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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A new azimuthally stable polarimetric method for processing microscopic images of optically anisotropic structures for different biological layers of histological sections has been proposed. A new model that enables to determine phase anisotropy of biological tissues by using superposition of Mueller matrices of linear birefringence and optical activity has been proposed. The matrix element М₄₄ has been chosen as the main information parameter, which value is independent of rotation angle of both sample and probing beam polarization plane. |
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Article |
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Ushenko, A.G. Dominikov, M.M. Lakusta, I.I. Koval, G.D. |
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Ushenko, A.G. Dominikov, M.M. Lakusta, I.I. Koval, G.D. Mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Ushenko, A.G. Dominikov, M.M. Lakusta, I.I. Koval, G.D. |
| author_sort |
Ushenko, A.G. |
| title |
Mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility |
| title_short |
Mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility |
| title_full |
Mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility |
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Mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility |
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Mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility |
| title_sort |
mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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2015 |
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http://dspace.nbuv.gov.ua/handle/123456789/121817 |
| citation_txt |
Mueller-matrix reconstruction of parameters of phase and amplitude anisotropy in diagnostics of endometriosis and infertility / A.G. Ushenko, M.M. Dominikov, I.I. Lakusta, G.D. Koval // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 2. — С. 164-169. — Бібліогр.: 22 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-07-08T20:34:21Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 164-169.
doi: 10.15407/spqeo18.02.164
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
164
PACS 87.50.wp, 87.57.-s, 87.64.-t, 87.85.Pq
Mueller-matrix reconstruction of parameters of phase and amplitude
anisotropy in diagnostics of endometriosis and infertility
A.G. Ushenko
1
, M.M. Dominikov
1
, I.I. Lakusta
1
, G.D. Koval
2
1
Chernivtsi National University, Optics and Publishing Department
2, Kotsyubinsky str., 58012 Chernivtsi, Ukraine
2
Bukovinian State Medical University, 58000 Chernivtsi, Ukraine
E-mail: a.dubolazov@chnu.edu.ua
Abstract. A new azimuthally stable polarimetric method for processing microscopic
images of optically anisotropic structures for different biological layers of histological
sections has been proposed. A new model that enables to determine phase anisotropy of
biological tissues by using superposition of Mueller matrices of linear birefringence and
optical activity has been proposed. The matrix element M44 has been chosen as the main
information parameter, which value is independent of rotation angle of both sample and
probing beam polarization plane.
Keywords: polarimetry, endometrium, laser image, filtering.
Manuscript received 05.11.14; revised version received 24.02.15; accepted for
publication 27.05.15; published online 08.06.15.
1. Introduction
Development of computational methodologies for
processing microscopic images is a new health-physical
method. It is laser polarimetry of histological sections
taken from biological tissues [1-3]. This method based
on measurements of the coordinate distributions
(polarization maps) in the plane of polarization states of
histological sections microscopic images of biological
tissues. This method provides a new, inaccessible to the
histological and mathematical methods of analysis,
information on the optical anisotropy (linear and circular
birefringence) of multiscale structural elements of
different biological objects.
At the same time, a complex analysis of the
polarization maps of a tissue specimen is azimuthally
dependent on the probing beam polarization plane and
sample rotation angle. It makes it difficult to use this
method in comparative research groups of histological
sections with different pathologies. Thus, further
progress of laser polarimetry may be related with the
development of azimuthally stable methods of direct
measuring the parameters of linear and circular
birefringence.
Solution of this task lies in using Mueller-matrix
mapping with the so-called rotational invariants. It has
been shown in the works [4-6] that the matrix elements
M44(Θ) = const are azimuthally stable and independent
of the sample rotation angle (Θ).
It has been determined that in the case of optically
thin (extinction coefficient τ ≤ 0.1) layers, the M44(Θ)
value is preferably defined by phase anisotropy
mechanisms – linear and circular birefringences [7-18].
Separation of these mechanisms
circular
linear
44
44
44
M
M
M is possible by using spatial-
frequency Fourier selection [12, 13].
Our research is aimed at designing the
experimental method of azimuthally stable Fourier
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 164-169.
doi: 10.15407/spqeo18.02.164
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
165
Fig. 1. Optical scheme of Fourier polarimeter, where 1 – He-Ne laser; 2 – collimator; 3 – stationary quarter-wave plate; 5, 9 –
mechanically movable quarter-wave plates; 4, 10 – polarizer and analyzer, respectively; 6 – object of study; 7, 8 – polarization
microobjectives; 11 – CCD camera; 12 – personal computer. F (x1,y1) – object plane, F (x2,y2) – image plane, F (u,v) – Fourier
plane with the diaphragms.
polarimetry and spatial-frequency selection of parameter
distributions for linear and circular birefringence in the
healthy donor films and samples taken from the patients
with endometriosis.
2. Theory of the method
The following model concepts have been assumed [1-3]
by us as the basis for analyzing the processes of
modulation of laser radiation by the network of
biological layers with linear and circular birefringence:
optical anisotropy of these structures is characterized
by the distribution of the coordinate matrix element,
where the direction of the optical axis is the phase
shift between linearly polarized orthogonal
components of the light beam amplitude;
the optical anisotropic component is formed by
spherolitic crystals (l ~ 5…10μm; L ≈ l) with
predominantly circular birefringence M44(θ), where
θ is the polarization plane rotation angle.
3. Optical realization of spatial-frequency of Fourier
selection of endometrium
Fig. 1 presents a diagram of laser Fourier polarimeter
with spatial-frequency filtration [9]. Illumination of the
sample under study was performed by the parallel ( =
10
4
μm) laser beam of He-Ne ( = 0.6328 μm, W =
5.0 mW). The polarization light source consisted of
quarter-wave plates 3, 5 and polarizer 4, it formed a right
circularly polarized beam. Section of endometrium was
placed in the focal plane of polarization microobjective 7
(focal distance 30 mm, aperture 0.1, magnification 4×).
Behind the Fourier focal plane the vignetting diaphragm
was located, its size changed within the range of 2 to
300 pix. Polarization microobjective 8 (focal distance
30 mm, aperture 0.1, magnification 4×) was located at
the focal length from the frequency plane of lens 7 and,
thus, performed inverse Fourier transform of the filtered
out polarization field of laser radiation. The coordinate
distribution of the intensity of these fields,
polarizationally filtered by the quarter-wave plate 9 and
polarizer 10, was registered in the plane of CCD-camera
11 (The Imaging Source DMK 41AU02.AS,
monochrome 1/2" CCD, Sony ICX205AL (progressive
scan); resolution 1280×960; light sensitive area size
7600×6200 μm; sensitivity 0.05 lx; dynamic range 8 bit;
SNR 9 bit; deviation of photosensitive characteristics
from linear is no more than 15%). It provided the range
of measuring the structural elements of the
polycrystalline network with the resolution of 2–
2000 μm [18-22].
The matrix element M44 was calculated for each
probing beam within every pixel (m×n)
9090
9090
00
00
44 5.0
II
II
II
II
II
II
M . (1)
Here 90;0;
I and 90;0;
I are the intensities of
spatial-frequency filtered images ( ; ) for each
polarization states of the probing beam ( 90;0; ).
To quantify the coordinate distributions, we used
statistical analysis [7-10]. We calculated a set of
statistical moments of the 1
st
to 4
th
orders Zj =1;2;3;4 by
using the following algorithms:
N
i
iq
N
Z
1
1
1 ,
N
i
iq
N
Z
1
2
2
1
,
N
i
iq
NZ
Z
1
3
3
2
3
11
,
N
i
iq
NZ
Z
1
4
4
2
4
11
. (2)
The obtained data indicate the distribution
histogram of random values of optically anisotropic
structures in the plane of the histological section.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 164-169.
doi: 10.15407/spqeo18.02.164
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
166
Fig. 3. “Low-frequency” coordinate maps M44(δ) (1),(3), histograms (2),(4) of linear birefringence distribution in the
endometrium of the group 1 (1), (2) and group 2 (3),(4).
4. Experimental results and discussion
As objects of investigation, we chose two groups of
optically-thin (extinction coefficient τ ≈ 0.087…0.098)
films with single scattering endometrium of donors (36
samples – group 1) and patients with pathology (36
samples – group 2).
The samples were prepared on a freezing
microtome, using a standard technique. From the optical
point of view, these samples are characterized by
transformation of polarization without depolarization.
Fig. 2 shows the classic microscopic images of
samples of both groups.
As can be seen, the coordinate large-scale structure
of these classic microscopic images is similar to each
other. This fact makes it difficult for histological
differentiation of endometrium.
5. Spatial-frequency Fourier polarimetry of linear
birefringence in endometrium
For the purpose of choosing optimal conditions of
spatial-frequency filtration, the following range Δr =
2…50 pix of possible sizes of the vignetting diaphragm.
The criterion for choosing the diaphragm size is the
simultaneous change of the set of statistic moments
Zj =1;2;3;4 of M44. In our case the optimal size was Δr =
30 pix.
Fig. 2. Microscopic images of the endometrium: group 1 (a) and
group 2 (b).
This geometric size was chosen for comparative
investigations of optical anisotropy of the fibrilar
networks of the endometrium tissue that is characterized
by coordinate distributions of rotational invariant M44(δ)
(Fig. 3).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 164-169.
doi: 10.15407/spqeo18.02.164
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
167
Fig. 4. “High-frequency” coordinate maps M44(θ) (1),(3), histograms (2),(4) of the linear birefringence distribution of the
endometrium samples in the group 1 (1),(2) and group 2 (3),(4).
A comparative analysis of aggregate parameters
that characterize matrix maps M44(δ) of linear
birefringence of large-scale optically anisotropic
networks of the endometrium samples revealed some
discrepancies between them. Namely, the main extrema
of histograms in the distributions of random matrix maps
M44(δ) values for histological sections of both types are
localized in different areas. Thus, the most probable
M44(δ) ~ 0.3 value is for the group 1 (Fig. 3(2)); for the
sample 2 M44(δ) ~ 0.6 (Fig. 3(4)). The revealed
peculiarity, in our opinion, is related with a more
developed structure of the endometrium of patient with
pathology. The quantitative differences between matrix
maps M44(δ) of the protein matrices of the endometrium
of both types illustrate average values and standard
deviations of the set of statistic Zi =1;2;3;4 parameters
summarized in Table 1. Also, let us introduce the
specificity parameter Sp =a (a + b) –1
(a, b are the
numbers of the correct and incorrect diagnoses within
each group) in differentiation of normal endometriosis.
A comparative analysis of the data of laser-
frequency Fourier polarimetry for linear birefringence of
the endometrium in both groups of patients revealed
sensitivity to differentiation of these states of all the
statistic moments of the 1
st
to the 4
th
orders with the
specificity level Sp ~ 78…83% (printed in grey color in
Table 1).
Table 1. Parameters of the statistic structure of matrix
maps M44(δ) for linear birefringence of endometrium.
Parameters
M44(δ)
Sp
normal pathology
Z1 0.23±0.059 0.52±0.11 78%
Z2 0.12±0.022 0.15±0.031 63%
Z3 1.26±0.37 0.78±0.14 83%
Z4 1.59±0.28 1.13±0.19 79%
6. Spatial-frequency Fourier polarimetry of circular
birefringence in endometrium
Diagnostic possibilities for differentiation of pathologically
changed samples of endometrium tissue, using the method
of high frequency spatial-frequency Fourier-domain
polarimetry of circular birefringence employing opaque
filter, illustrate probable dependences of matrix maps
M44(θ) and are adduced in the series in Fig. 4.
Comparing the findings about the structure of the
distributions of circular birefringence index under the
conditions of high frequency filtration of laser field
radiation, it is the range of expansion of the random
values that changes M44(θ) for a histogram of the matrix
map at the expense of a “pathologic” increase of the
endometrium tissue.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 164-169.
doi: 10.15407/spqeo18.02.164
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
168
Table 2. Parameters of the statistic structure of matrix
maps M44(θ) for circular birefringence of endometrium.
Parameters
M44(θ)
Sp
normal pathology
Z1 0.09 0.011 0.11 0.017 55%
Z2 0.15 0.018 0.18 0.031 61%
Z3 0.17 0.021 0.48 0.39 89%
Z4 0.38 0.043 0.58 0.071 78%
Quantitative differences between matrix maps
M44(θ) of circular birefringence of collagenous networks
of both types illustrate average values and standard
deviations of statistic set Zi =1;2;3;4 parameters adduced in
Table 2.
A comparative analysis revealed the following
condition with a high level of specificity (78% ≤
Sp ≤ 83%) of uterus tissue parameters (depicted in grey
color in Table 2):
statistic moments of the 1
st
and 2
nd
of orders
θ(m×n),
the differences between the values are within the
range from 2 to 3.5 times.
7. Conclusions
A set of criteria for polarization-phase differentiation of
endometrium (normal and endometriosis) has been
revealed and substantiated:
statistical moments of the 1
st
– 4
th
orders that
characterize distribution of azimuthally stable
matrix element M44(δ) are defined by linear
birefringence of the endometrium;
statistical moments of the 1
st
– 4
th
orders that
characterize distribution of azimuthally stable
matrix element M44(θ) are defined by circular
birefringence of the endometrium.
Acknowledgement
This work was supported by the grants № 0113U003239
and № 0112U002336 from the Ukrainian Foundation for
Basic Researches.
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