Azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids
The model based on Mueller-matrix description of mechanisms providing optical anisotropy typical for polycrystalline smears of liquor (including optical activity, birefringence as well as linear and circular dichroism) has been suggested. Within the statistical analysis of such distributions, the ob...
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| Zitieren: | Azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids / Yu.O. Ushenko, O.V. Dubolazov, A.V. Motrich, G.B. Bodnar // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 2. — С. 158-163. — Бібліогр.: 27 назв. — англ. |
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irk-123456789-1218092017-06-19T03:02:44Z Azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids Ushenko, Yu.O. Dubolazov, O.V. Motrich, A.V. Bodnar, G.B. The model based on Mueller-matrix description of mechanisms providing optical anisotropy typical for polycrystalline smears of liquor (including optical activity, birefringence as well as linear and circular dichroism) has been suggested. Within the statistical analysis of such distributions, the objective criteria of differentiation of smears of liquor taken from dead patient at different moments after his death have been determined. From the viewpoint of probative medicine, the operational characteristics (sensitivity, specificity and accuracy) of the method of Mueller-matrix reconstruction of optical anisotropy parameters have been found and the efficiency of this method in another task – diagnostics of diseases of internal organs of rats – has been demonstrated. 2015 Article Azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids / Yu.O. Ushenko, O.V. Dubolazov, A.V. Motrich, G.B. Bodnar // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 2. — С. 158-163. — Бібліогр.: 27 назв. — англ. 1560-8034 DOI: 10.15407/spqeo18.02.158 PACS 87.50.wp, 87.57.-s, 87.64.-t, 87.85.Pq http://dspace.nbuv.gov.ua/handle/123456789/121809 en Semiconductor Physics Quantum Electronics & Optoelectronics Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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The model based on Mueller-matrix description of mechanisms providing optical anisotropy typical for polycrystalline smears of liquor (including optical activity, birefringence as well as linear and circular dichroism) has been suggested. Within the statistical analysis of such distributions, the objective criteria of differentiation of smears of liquor taken from dead patient at different moments after his death have been determined. From the viewpoint of probative medicine, the operational characteristics (sensitivity, specificity and accuracy) of the method of Mueller-matrix reconstruction of optical anisotropy parameters have been found and the efficiency of this method in another task – diagnostics of diseases of internal organs of rats – has been demonstrated. |
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Ushenko, Yu.O. Dubolazov, O.V. Motrich, A.V. Bodnar, G.B. |
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Ushenko, Yu.O. Dubolazov, O.V. Motrich, A.V. Bodnar, G.B. Azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Ushenko, Yu.O. Dubolazov, O.V. Motrich, A.V. Bodnar, G.B. |
| author_sort |
Ushenko, Yu.O. |
| title |
Azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids |
| title_short |
Azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids |
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Azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids |
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Azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids |
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Azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids |
| title_sort |
azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids |
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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/123456789/121809 |
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Azimuthally invariant laser polarimetry of polycrystalline smears of biological liquids / Yu.O. Ushenko, O.V. Dubolazov, A.V. Motrich, G.B. Bodnar // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 2. — С. 158-163. — Бібліогр.: 27 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-07-08T20:33:28Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 158-163.
doi: 10.15407/spqeo18.02.158
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
158
PACS 87.50.wp, 87.57.-s, 87.64.-t, 87.85.Pq
Azimuthally invariant laser polarimetry of polycrystalline smears
of biological liquids
Yu.O. Ushenko
1
, O.V. Dubolazov
1
, A.V. Motrich
1
, G.B. Bodnar
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. The model based on Mueller-matrix description of mechanisms providing
optical anisotropy typical for polycrystalline smears of liquor (including optical activity,
birefringence as well as linear and circular dichroism) has been suggested. Within the
statistical analysis of such distributions, the objective criteria of differentiation of smears
of liquor taken from dead patient at different moments after his death have been
determined. From the viewpoint of probative medicine, the operational characteristics
(sensitivity, specificity and accuracy) of the method of Mueller-matrix reconstruction of
optical anisotropy parameters have been found and the efficiency of this method in
another task – diagnostics of diseases of internal organs of rats – has been demonstrated.
Keywords: polarimetry, liquor, laser image, biological fluids.
Manuscript received 12.11.14; revised version received 27.02.15; accepted for
publication 27.05.15; published online 08.06.15.
1. Introduction
Biological tissues and fluids represent structurally
inhomogeneous media with absorption. To describe
interactions of polarized light with these complex
systems, the most general approaches based on Mueller-
matrix formalism are required. Nowadays in biological
and medical investigations, many practical techniques
based on measurement and analysis of Mueller matrices
of investigated samples are used [1-12]. In recent 10-15
years, a separate approach – laser polarimetry [13] – was
formed in matrix optics. On its basis, the interactions
between the set of statistical moments of the 1
st
-4
th
orders characterizing the Mueller-matrix elements
distribution and parameters of linear birefringence of
fibrillar protein networks of human biological tissues
have been determined. It enabled to diagnose
oncological changes of skin derma, epithelial and
connective tissue of women’s reproductive sphere
organs etc. [18-21]. In addition, laser polarimetry
techniques require further development and genera-
lization.
Firstly, not all elements of Mueller matrix prove to
be convenient for characterizing biological samples. The
reason of this is the azimuthal dependence of the
majority of matrix elements – generally 12 of 16
elements change at rotation of the sample around the
probing axis.
Secondly, the spectrum of mechanisms of optical
anisotropy of biological layers is not confined to linear
birefringence only. Taking into consideration the impact
of other mechanisms, circular birefringence as well as
linear and circular dichroism are topical in the aspect of
enlarging the range of diagnostic techniques.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 158-163.
doi: 10.15407/spqeo18.02.158
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
159
Thirdly, there is a wide range of optically
anisotropic biological objects, for which laser
polarimetry techniques did not spread widely. Biological
fluids – blood and its plasma, urine, bile, saliva and
others – belong to them. The objects of this class are
easily accessible and do not require the traumatic
surgery of biopsy.
This research is focused on generalization of
optical anisotropy of optically thin layers of liquor films
and histological sections of the internal organs of healthy
and diabetic rats and the development of the method of
“azimuthally stable” Mueller-matrix reconstruction of
anisotropy parameters of polycrystalline networks.
2. Brief theoretical background
Our work is based on modeling representations of phase
anisotropy (optical activity and linear birefringence) of the
polycrystalline structure of the films of blood plasma. In
this approximation, the experimentally measured matrices
have the following symmetry [22-27]:
444342
343332
2423221
11
0
0
0
0001
fff
fff
fff
fDF . (1)
Here, is the Mueller matrix circular
birefringence or optical activity of amino acid molecules
1000
00
00
0001
3332
2322
,
.2sin
;2cos
3223
3322
ik (2)
where θ is the rotation angle of polarization plane of the
light beam transformed by amino acids.
Linear birefringence of amino acids polypeptide
chains characterized by Mueller matrix D is of the
following form:
444342
343332
242322
0
0
0
0001
ddd
ddd
ddd
D ,
.cos
,sin2cos
,sin2sin
,cos2cos2sin
,cos12sin2cos
,cos2sin2cos
44
4334
2442
22
33
3223
22
22
d
dd
dd
d
dd
d
dik (3)
Here, ρ is the direction of optical axes; nl
2 –
phase shift between linearly polarized orthogonal
components of light beam amplitude; λ – wavelength;
Δn – birefringence; l – geometrical thickness.
44434241
34333231
24232221
141312
1
11
4
1
1
MMMM
MMMM
MMMM
MMM
MMM i
i
. (4)
Here, iM is the Mueller matrix that characterizes
the phase anisotropy ( , D ) and also amplitude
anisotropy ( , ) of amino acid molecules and their
aggregates.
Circular dichroism
100
000
000
001
41
33
22
14
,
.
1
2
;
1
1
24114
2
2
3322
C
C
C
C
ik (5)
Here,
gg
gg
C , gg , are the absorption
indices of left- ( ) and right-hand ( ) circularly
polarized components of light beam amplitude.
Linear dichroism
44
333231
232221
1312
000
0
0
01
,
.2
,2cos22sin1
,2sin1
,2sin22cos1
,2sin1
,2cos1
44
22
33
3223
22
22
3113
2112
ik (6)
Here,
y
x
,
sin
cos
y
x
, yx , are the
absorption coefficients of linearly polarized orthogonal
components of light beam amplitude.
DM . (7)
For analytical and practical application (7), we used
the data of investigations [1, 2, 4]. Here, it is shown that
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 158-163.
doi: 10.15407/spqeo18.02.158
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
160
Fig. 1. Optical scheme of polarimeter, where 1 – He-Ne(Cd) laser; 2 – collimator; 3 – stationary quarter-wave plate; 5, 8 –
mechanically movable quarter-wave plates; 4, 9 – polarizer and analyzer, respectively; 6 – object of investigation; 7 –
polarization.
the following elements of matrix M as well as their
combinations are azimuthally stable, independent of the
sample rotation angle Θ
,const;const
,const;const
4441
1411
MM
MM
.const
,const
32;233223
33;223322
MMM
MMM
(8)
3. Analysis and discussion of experimental data
The measurements of coordinate distributions of
Mueller-matrix elements (distribution of values in the
film plane of blood plasma) were performed in the setup
(Fig. 1) of the standard Stokes-polarimeter [13].
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.
Blood plasma films were 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 from 2 up 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.
For the series of linearly (0°; 45°; 90°) and right-
hand ( ) circularly polarized probing laser beams (λ1
and λ2), the Stokes-vector parameters
;90;45;0
4;3;2iS were
measured in the points of the digital image
.,
;,
;,
;,
;90;45;0;90;45;0
21
;90;45;0
4
;90;45;0
135
;90;45;0
4521
;90;45;0
3
;90;45;0
90
;90;45;0
021
;90;45;0
2
;90;45;0
90
;90;45;0
021
;90;45;0
2
IIS
IIS
IIS
IIS
i
i
i
i
(9)
Here,
;90;45;0
;;135;45;90;0I are the intensities of linearly
(0°, 45°, 90°, 135°), right- ( ) and left-hand ( )
circularly polarized components of the filtered (by
means of polarizer 10 and quarter-wave plate 9) laser
radiation.
Further, the Mueller-matrix invariants were
calculated (PC 10)
.5.05.0
,5.05.0
,5.0,
,5.0
,5.0
90
3
0
3
90
2
0
2
45
2
3223132;23
90
3
0
3
45
3
90
2
0
2
3322133;22
90
4
0
442144
90
4
0
4241
90
1
0
11214
SSSSS
MMM
SSSSS
MMM
SSSM
SSM
SSSM
(10)
The series of Figs. 2 to 5 present the results of the
technique of Mueller-matrix mapping of polycrystalline
liquor films, taken over 1 hour and 3 hours after death.
With a view to a possible use of the Mueller-matrix
method in determining the time of death for each group
of samples, the magnitude of the statistical moments
qZi 4;3;2;1 and standard deviations were
determined by the average (within group 1 and group 2).
The following settings determine the accuracy of
the time of death (ATD), the interval determines the
accuracy of the method ( ) and ATD (ΔT) (Table 1).
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 158-163.
doi: 10.15407/spqeo18.02.158
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
161
Table 1. Timeframe and accuracy of the time of death.
ATD, hours T Ω
3 24 ±0.1
6 32 ±0.15
12 48 ±0.2
Table 2. Operational characteristics of the method of
Mueller-matrix reconstruction.
Parameters Zi Kidney Liver Pancreas Spleen
Se(Zi),%
Z1 66.6% 71.9% 77.2% 77.2%
Z2 70.2% 70.2% 78.9% 82.4%
Z3 82.4% 85.9% 91.2% 92.9%
Z4 80.7% 89.4% 94.7% 94.7%
Sp(Zi),%
Z1 63.1% 66.6% 73.6% 73.6%
Z2 66.6% 66.6% 75.4% 78.9%
Z3 80.7% 82.4% 87.8% 89.4%
Z4 77.2% 85.9% 91.2% 92.9%
Ac(Zi),%
Z1 64.85% 69.25% 75.4% 75.4%
Z2 68.4% 68.4% 77.15% 80.65%
Z3 81.55% 84.15% 89.5% 91.15%
Z4 78.95% 87.65% 92.95% 93.8%
Note. Se(Zi) – sensitivity, Sp(Zi) – specificity, Ac(Zi) –
diagnostic test accuracy, Zi – the statistical moments of the 1st–
4th orders that characterize the distribution of Mueller-matrix
elements.
Table 2 illustrates the potential of this method
when dealing with another problem of Experimental
Medicine – differentiation of histological sections of the
internal organs of healthy and diabetic rats.
Fig. 2. Mueller-matrix image f44 taken by the film of liquor
1 hour (1, 2) and 3 hours (3 and 4) after death.
Fig. 3. Mueller-matrix image Δf taken by the film of liquor
1 hour (1, 2) and 3 hours (3, 4) after death.
Fig. 4. Mueller-matrix image f14 taken by the film of liquor
1 hour (1, 2) and 3 hours (3, 4) after death.
Fig. 5. Mueller-matrix image f41 taken by the film of liquor in
1 hour (1, 2) and 3 hours (3, 4) after death.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 2. P. 158-163.
doi: 10.15407/spqeo18.02.158
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
162
4. Conclusions
1. On the basis of the model of generalized optical
anisotropy, the two-wave technique of azimuthally
invariant Mueller-matrix reconstruction of optical
anisotropy parameters that are characteristic of
polycrystalline liquor smears has been developed.
2. The Mueller-matrix invariants characterizing
polarization manifestations of different (partial)
mechanisms of optical anisotropy of liquids smear
have been determined.
3. The method for determining the time of death
based on the time of monitoring changes in the
optical anisotropy of the polycrystalline films of
liquor has been proposed.
4. The interrelations between the set of statistical
moments of the 1
st
–4
th
orders characterizing the
distributions of optical anisotropy parameters and
the difference in the structure of histological tissue
sections of internal organs of rats have been
determined.
Acknowledgement
This work was supported by the grants № 0113U003239
and № 0112U002336 from the Ukrainian Foundation for
Basic Researches.
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