Method for replacing objects in 4F correlator: testing
The method of pattern recognition based on replacement of object images incoming to the correlator by object-dependent synthesized phase objects calculated using the iterative Fourier-transform algorithm was developed by us earlier. In this work, we performed experimental testing the above method by...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2005
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| Cite this: | Method for replacing objects in 4F correlator: testing / P.V. Yezhov, A.V. Kuzmenko, Т.N. Smirnova, A. A. Ivanovskyy // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 2. — С. 75-80. — Бібліогр.: 13 назв. — англ. |
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| author | Yezhov, P.V. Kuzmenko, A.V. Smirnova, Т.N. Ivanovskyy, A. A. |
| author_facet | Yezhov, P.V. Kuzmenko, A.V. Smirnova, Т.N. Ivanovskyy, A. A. |
| citation_txt | Method for replacing objects in 4F correlator: testing / P.V. Yezhov, A.V. Kuzmenko, Т.N. Smirnova, A. A. Ivanovskyy // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 2. — С. 75-80. — Бібліогр.: 13 назв. — англ. |
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| description | The method of pattern recognition based on replacement of object images incoming to the correlator by object-dependent synthesized phase objects calculated using the iterative Fourier-transform algorithm was developed by us earlier. In this work, we performed experimental testing the above method by using an optical-digital 4F-correlator. Synthesized phase objects were inputed into the correlator through the spatial light modulator LC2002. Holographic matched filters were recorded using self-developing photopolymers PPC-488. For two test objects, we obtained unified (δ-like) correlation signals with the signal-to-noise ratio reaching 24 dB, while the diffraction efficiency of these filters was up to 30%.
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 2. P. 75-80.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
75
PACS: 05.50. +q, 61.50.Em, 82.20.Fd
Method for replacing objects in 4F-correlator: testing
P.V. Yezhova, A.V. Kuzmenkob, T.N. Smirnovaa, A.A. Ivanovskyyc
aInstitute of Physics, NAS of Ukraine, 46, prospect Nauky, 03028 Kyiv, Ukraine
Phone: (38 044) 525 5072, e-mail: yezhov@iop.kiev.ua
bInternational Center “Institute of Applied Optics”, NAS of Ukraine,
10G, Kudryavskaya str., 04053 Kyiv, Ukraine
c“Specialized Enterprize “Holography”, 34/1, Grushevskogo str., office 29, 01021 Kyiv, Ukraine
Abstract. The method of pattern recognition based on replacement of object images
incoming to the correlator by object-dependent synthesized phase objects calculated
using the iterative Fourier-transform algorithm was developed by us earlier. In this work,
we performed experimental testing the above method by using an optical-digital 4F-
correlator. Synthesized phase objects were inputed into the correlator through the spatial
light modulator LC2002. Holographic matched filters were recorded using self-
developing photopolymers PPC-488. For two test objects, we obtained unified (δ-like)
correlation signals with the signal-to-noise ratio reaching 24 dB, while the diffraction
efficiency of these filters was up to 30%.
Keywords: pattern recognition, hybrid optical-digital 4F-correlator, synthesized phase
object, iterative Fourier-transform algorithm.
Manuscript received 15.04.05; accepted for publication 18.05.05.
1. Introduction
As shown in [1], when solving the recognition problem
for binary or half-tone objects by using 4F-correlators,
the replacement of these objects with unambiguously
related to them synthesized-phase objects (SP-objects)
results in increasing values of signal-to-noise (SNR)
correlation signals as well as in unification of their form:
the signal possesses a δ-like shape independently of the
object type. The latter allows to formalize the pattern
recognition problem at the stage of choosing some
characteristic (distinctive) features of the object.
It is well known [2–5] that the procedure for
choosing the characteristic, often multiple signs of the
object in most of the cases takes a subjective (heuristic)
character and is rather laborious. In the offered method,
this procedure is excluded and changed by a single
mathematical criterion for all the recognized objects. It
is this criterion that is used in iteration calculations for
respective SP-objects. In the case, the recognized object
is considered as a whole – all its distinctive features are
reflected in the structure of respective SP-objects by
some integrated way.
In this work, we represent experimental results after
testing the offered method by using an optical-digital 4F-
correlator. As the test-objects, we chose a random
amplitude and a phase masks.
In the section 2, represented is the schematic view of a
hybrid optical-digital correlator using the spatial light mo-
dulator (SLM) LC2002 as a dynamic transparency. Also
considered are regimes of the correlator operation capable
to realize the recognition procedure with SP-objects.
In the section 3, we represent results of testing and
calibrating SLM at λ = 441.6 nm when operating in the
phase regime. Summarized there are calculation results
for SP-objects, recording the holographic filters and
matched filtering, as well as the analysis of results
obtained. In the section 4 we summarized our results.
2. Correlator layout
The principle scheme of the hybrid optical-digital
correlator is represented in Fig. 1. The correlator is
nominally divided by two parts: digital, Fig. 1(1), and
optical, Fig. 1(2), ones. The recognition procedure [1]
implies the following operations.
1) Record of the holographic matched filter for the
standard object:
i) input amplitude image of the standard object
ast(x, y) into the correlator digital module
(Fig. 1(1));
ii) obtain the SP-object φst(x,y) from ast(x,y) and
input it into the entrance plane P2 of the
correlator optical part by using SLM (Fig. 1(2));
iii) record the holographic matched filter of the
φst(x,y) using PPC-488 in the Fourier plane P3
of the correlator optical part (the reference
beam is not shown).
2) Matched filtering:
i) input the SP-object φin(x, y) obtained from
ain(x, y) into the entrance plane P2 of the cor-
relator optical part by using SLM;
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 2. P. 75-80.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
76
ii) realize the matched filtering procedure for the
φin; obtain of the correlation signal r(x,y) =
= ∫∫φin(x1,y1) φ*
st(x + x1,y + y1)dx1dy1 at the exit
plane P4 of the correlator optical part;
iii) record r(x, y) by using the CCD2 camera and
estimate the recognition result in according
with the threshold criterion.
Matched filter recording regime. Fig. 2 illustrates the
recording scheme suitable to obtain holographic filters
by using self-developing photopolymers. The He-Cd
laser beam passing through the attenuator Att and
dividing cube Bs is divided by the referent and object
beams. The half-wave plate λ/2 sets the necessary
polarization for the object beam, which provides the
mostly phase regime for SLM operation.
The analyzer А sets the vertical plane for the
polarization of the phase-modulated wavefront. Using
the controlling computer PC1, SLM is given with a
graphic file containing the necessary amplitude
distribution of gray halftones which is obtain by taking
the characteristic curve into account. The object beam
and the collimated referent beam created the holographic
matched filter on PPC-488 at the correlator Fourier plane
Pt. The He-Ne laser, photodiodes Ph1,2, analog-digital
converter unit and computer PC2 form the registration
system, which enabled us to control recording the
holographic filters on self-developing polymers in the
real time scale.
The use of photopolymer compositions developed in
the Institute of Physics, NAS of Ukraine [6-7] as
holographic registration media is caused by the fact that
matched filters recorded in these media are formed
during exposing them by an interferential field and do
not require any additional operations to develop and fix
the respective interferential structure. Diffraction
efficiency of the plane gratings reached to an 99.8 % and
matched filters about 70% [8].
Matched filtering regime. The scheme of the
correlator operating in the matched filtering regime is
depicted in Fig. 3. The collimated laser beam with the
necessary polarization direction passes SLM addressed
with the respective SP-object and the lens L1, falls onto
the plane Pt where the filter MF is located. Then, in the
correlation plane the CCD camera register the
correlation signal obtained as a result of the inverse
Fourier-transform performed by the lens L2 with the
product of the Fourier-images inherent to SP-objects of
the incoming and standard objects. To register the
correlation signal in the output correlator plane, we used
the special software and analog-digital converter made
by "Spiricon", camera Sony4800 with the pixel
dimensions 30x30 μm and the size 580×470 pixels.
3. Experiment
As recognized objects, we chose the following ones:
a) f1 – the binary amplitude mask (AM) with the optical
density [0,1] containing randomly distributed
elements, where the number of transparent elements
is equal to that of the opaque ones;
b) f2 – the binary phase mask (PM) with the random
distribution of the ±π pixel elements where the
number of +π-elements is equal to that of –π-ele-
ments.
The image size is equal to 600×800 pixels. The
recognition procedure for f1 object was defined as
follows:
a) calculation of the SP-objects φ1 for f1;
Fig. 1. Scheme of an optical-digital correlator.
a) 1, 2 – digital and optical parts of the correlator;
b) P1, P2, P3 and P4 – the input, object, Fourier, and
correlation planes of the correlator;
c) CCD1 and CCD2 – the input camera for images and the
registration camera for correlation signals;
d) К, L1 and L2 – collimator and Fourier-objectives;
e) PC, SLM and MF – computer, phase spatial light
modulator LC2002 and the matched filter.
Fig. 2. Scheme of a Vander Lugt optical-digital correlator in
the recording mode.
1) Mr1,2,3,4 and Bs – mirrors and a beamsplitter; 2) Att –
attenuator; 3) λ/2 – half-wave plate; 4) k – collimators;
5) SLM, A, PC1 – spatial light modulator, the analyzer and a
computer to control SLM; 6) L1 – Fourier-objective; 7) L2,
Ph12, PC2, He-Ne laser – lens, photodiodes, computer with an
analog-to-digital converter and a laser (λ = 633 nm) of the
registration system; 8) Pt – photopolymer; 9) He-Cd Laser –
a laser with λ = 441.6 nm.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 2. P. 75-80.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
77
b) inputing φ1 into correlator by using SLM and
recording the holographic MF-filters using the
scheme of Fig. 2;
c) obtaining the correlation signals for φ1 in accord with
the scheme in Fig. 3 in the course of matched
filtering.
The object f2 – PM with the random distribution of
elements – served as the test sample to check the
correlator operation by comparing results as to their
SNR and shape of correlation signals obtained for f2 with
the known results [9-10]. In this case, the recognition
procedure was performed using the usual recognition
scheme (without calculations of the respective SP-
object).
3.1. Obtaining the characteristic curve for an SLM
SLM of the transmission type LC2002 (“HoloEye”)
holds the SVGA standard 600×800 pixels with the
frequency 60 Hz, the rated value of power density for
incident radiation Pmax = 1 W/cm2, dimensions of the
elementary LC-cell is 32×32 μm, matrix dimensions
832×624 cells. We performed testing and choice of the
operation regime for this SLM at the wavelength
λ = 441.6 nm.
When SLM transfers the phase linearly, the phase of
the set distribution φ(x, y) should be re-calculated into
gray scale gradation N(x, y) = φ(x, y)(256/2π) and
introduced by controlling voltages into SLM as a
standard graphic file. The passing laser beam acquires
the phase shift corresponding to φ(x,y). But in practice,
SLM transfers the phase is non-linearly. Therefore,
when working with it, it is necessary to make an account
of the characteristic curve relating the phase shift with
the gray scale gradation. This curve was obtained by us
experimentally. Its shape depends on such parameters of
SLM as the brightness (N1), contrast (N2), horizontal
distortion (N3), vertical distortion (N4) – all of them are
available for tuning in the program controlling SLM.
To obtain the characteristic curve for LC2002 at
λ = 441.6 nm, was realized in the following way: in the
first diffraction order we compared the intensity of the
laser beam diffracted from the phase grating intputed
into SLM (Fig. 4) and the calculated intensity for this
grating under sequential increasing the grating effective
height measured fractions of π.
The grating effective height implies the relief height
(for calculations) or values of the LC-cell refraction
index (when realizing the diffraction grating in SLM)
corresponding to the definite phase shift measured
fractions of π. The characteristic curve shown in Fig. 5
(1) corresponds to the SLM tuning parameters Ni
summarized in Table 1. It is known that the error in
transferring the phase by using SLM consists of the
systematic (Fig. 5(2)) and random ones. The former
arises due to inaccuracy of the characteristics and
influences on the range width for transferred phases, and
the latter is mainly determined by inaccuracy in
rounding when quantizing the gray levels and can reach
π/128. The choice of optimal Ni-values provides phase
modulation in the range [0-2π] for the signal level in 256
gray gradations.
Depicted in Fig. 6 is the dependency of the
normalized intensity Po for the zeroth order of the
grating with the effective relief height π inputed into
SLM on the density of power incident Pin onto the
grating: 1 – experiment; 2 – the straight line corresponds
to the grating diffraction efficiency η2; 3 – the straight
line corresponds to the grating diffraction efficiency η3,
when η3 > η2. As seen from the figure, the power density
taken from the range from 1 to 17 mW/cm2 is suitable to
obtain the most efficient modulation of the phase of the
transmitting wavefront.
Fig. 4. Calibration scheme of SLM LC2002 in the phase
mode for λ = 441.6 nm.
1) k – collimator; 2) P, D, SLM, PC1 – polarizer, an aperture,
spatial light modulator, an analyzer and a computer to control
spatial light modulator; 3) L – Fourier-objective, 4) Ph, PC2 –
photodiode, a computer of the registration system.
Fig. 3. Scheme of a Vander Lugth optical-digital correlator
in the matched filtering mode.
1) Mr1,2 – mirrors; 2) Att – attenuator; 3) λ/2 – half-wave
plate; 4) k – collimator; 5) SLM, A, PC1 – spatial light
modulator, the analyzer, and a computer to control SLM;
6) L1,2 – Fourier-objectives; 7) CCD, PC2 – output camera,
and a computer of the registration system; 8) He-Cd Laser –
a laser with λ = 441.6 nm.
Table 1. Tuning parameters for a SLM.
Brightness,
N1
Contrast,
N2
Horizontal
distortion, N3
Vertical
distortion, N4
176 118 1054 200
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 2. P. 75-80.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
78
3.2. Calculation of SP-objects
In [1], SP-object is defined as an object-dependent
diffuser [11], the form of the function for which is
determined by the form of the object function f(x,y) and
calculated using the classical scheme of the iterative
Fourier-transform (IFT) algorithm [12].
SP-object φ1 for the objects f1 was calculated using
the starting phase distribution φo(x, y) ≡ const. Beginning
even from the first iterations, the structure of SP-object
is PM with a random distribution of the phase values
within the interval [0-2π]. While at first iterations φ1 is
binary, they become 256-level by their phase values with
increasing the iteration number. Its Fourier-spectrum
amplitude is homogeneous, the shape of the correlation
functions is δ-like, the autocorrelation function
φ1(n)⊗φ1(n) being maximal by its value and does not
depend on the iteration number n. This form of SP-
objects, their Fourier-spectra and correlation signals is
typical for recognized objects of any type.
As each recognized object fi is potentially
corresponded by a set of SP-objects {φi(n)} calculated
for various iteration numbers n, it is necessary to
introduce the criterion to choose the only one of them
the most suitable to replacement fi-object in the
correlator when recognizing the objects. By another
words, it is necessary to define the criterion for
determining the iteration number when calculating SP-
object by using the IFT-algorithm. In the experiments,
we used two criteria, namely: the calculation of SP-
objects is finished at the iteration step providing a
minimum to the parameter
А(n) = max⏐ℑ+1(φ(n))⏐ (1)
or to the dispersion
∑∑
∑∑ +ℑℑ−
=
x y
st
in
n
in
x y
st
yxf
yxfyxyxf
n 2
2)(11
|),(|
|)))),(),((arg(||),((|
)(
φ
σ
(2)
where ℑ±1 is the direct (inverse) Fourier transformations,
∑∑
x y
st yxf 2|),(| is the full energy of the standard
object, n is the iteration number.
As was established for n = 2, the spectrum is the
most homogeneous by its amplitude, which give the
optimal conditions to record holographic filters, SP-
object structure being binary. It provides the optimal
conditions to display them in SLM.
In the case of a weak dependency for the criterion
(1) on the iteration number, one can use the criterion
(2) that is identical to the criterion used in [11] for
choosing an optimal phase diffuser, which is imposed
on the object when calculating the kinoform. As it was
noted in Introduction, this formalized procedure to
choose the number of the optimal iteration in
calculations of SP-objects φi(n) substitutes a heuristic
procedure aimed at the choice of characteristic signs in
recognized objects fi.
1
2
Gray scale
Ph
as
e
sh
ift
Ph
as
e
er
ro
r
Fig. 5. Phase shift (1) and the phase error (2) in radians
relatively to the gray levels.
Fig. 6. Power of the zeroth order versus the power density
incident on to SLM.
Fig. 7. Fourier-spectrum for SP-object.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 2. P. 75-80.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
79
3.3. Recording the holographic filters
The standard holographic filters for φ1(2) and f2 were
recorded using PPC-488 and the scheme shown in
Fig. 2. The angle between beams provided the spatial
frequency 1000 mm–1, the ratio of intensities inherent to
the referent and object beams Iref /Iobj being 2:1. All the
filters are of the Bragg type. Therefore, when using the
scheme shown in Fig. 3 for matched filtering, one can
observe the only correlation signal from all the signal
components. As it was shown in [8], the diffraction
efficiency of holograms and matched filters for PM
recorded using PPC-488 lies within the range (15-70)%
under the condition that Iref /Iobj changes from 26:1 down
to 1:1. In our experiments, the diffraction efficiency was
25-30%, which can be explained by the fact that the
image inputed into SLM is quasi-stationary, as this SLM
operates at the frequency 60 Hz.
Shown in Figs 7 the Fourier-spectrum is registered
using the CCD camera in the plane of recording the
holographic filters for SP-objects – φ1(2). Since the SLM
cell is a square with the dimensions 32×32μm, the
spectrum structure for SP-objects is very similar
(identical) to that of the phase mask spectrum.
The spatial frequency spectrum in the main order is
limited with the maximal frequencies 32.3 mm–1 for SP-
object and phase mask. Both of the Fourier-spectra have
the zeroth order, which is indicative of the presence of
intrinsic noise in the optical-digital correlator itself
caused at least by the following reasons:
- quasi-stationary regime of SLM operation;
- errors when transferring the SLM phase;
- presence of the optical noise in the correlator.
3.4. Obtaining the correlation signals
Concerning the matched filtering, our experiments were
performed to estimate SNR for correlation signals when
realizing the recognition procedure with SP-objects and
comparison of the results obtained with those known for
phase masks.
Before carrying out the experiments with SP-objects,
the optical-digital correlator was tested using the
standard procedure of matched filtering for the usual
(non-synthesized) object f2. In doing so, we registered
the δ-like correlation signal with SNR reaching up to
43 dB.
The correlator intrinsic optical noise measured in the
absence of the object was no more than 19 dB. Taking
this fact into account, the correlation signal SNR was
determined as the ratio of the correlation signal peak
value to the correlator intrinsic noise one in all the
following measurements. For our object f2 and φ1(2),
SNR was equal to 24 dB.
Comparing the correlation signals obtained for PM
[10] with our, one can draw the conclusion that the
correlator noise was increased, but the signal peak
values can be icreased by optimisation by the correlator
operation. The growth of the correlator intrinsic noise is
the consequence of reasons listed in the paragraph 3.2 as
well as the development of the structure inherent to SLM
LC2002 providing the constant part into the correlation
signal.
Using the method offered in [1], we realized the
matched filtering procedure and obtained δ-like
recognition signals. Fig. 8 show the fragment of SP-
object φ1(2). Shown in Fig. 9 is the correlation peak
describing φ1(2).
Fig. 8. Phase distribution of the φ1 in the gray scale format
(a fragment).
Fig. 9. Correlation signal of an SP-object.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2005. V. 8, N 2. P. 75-80.
© 2005, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
80
Thus, our experiments show that application of SLM and
PPC-488 in the recognition procedure with the 4F-
correlator by using the method gives results comparable
with that known for random phase masks [10, 13] and
provides a high fidelity of recognition.
4. Conclusions
The results obtained allows to draw the following
conclusions:
• phase distributions of SP-objects have a random
character, in the first iteration steps the structure of
these distributions being close to the binary one [0, π],
with increasing the number of iterations the binary
structure is smoothed, and eventually the phases
almost homogeneously fill in the interval [0–2π];
• as a consequence of their random nature, SP-objects
and their Fourier-spectra are practically homoge-
neous by their amplitude;
• correlation functions of SP-objects have the δ-like
shape and provide the maximum possible signal-to-
noise ratio inherent to phase masks with a random
distribution. Obtained is the qualitative coincidence
between calculated and experimental correlation
dependencies;
• defined is the only criterion to choose SP-objects for
replacing the recognized real objects. Application of
it changes by itself the heuristic procedure of
choosing the characteristic signs of the object in the
common recognition method.
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| id | nasplib_isofts_kiev_ua-123456789-121649 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2025-11-28T03:35:39Z |
| publishDate | 2005 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Yezhov, P.V. Kuzmenko, A.V. Smirnova, Т.N. Ivanovskyy, A. A. 2017-06-15T03:54:37Z 2017-06-15T03:54:37Z 2005 Method for replacing objects in 4F correlator: testing / P.V. Yezhov, A.V. Kuzmenko, Т.N. Smirnova, A. A. Ivanovskyy // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2005. — Т. 8, № 2. — С. 75-80. — Бібліогр.: 13 назв. — англ. 1560-8034 PACS: 05.50. +q, 61.50.Em, 82.20.Fd https://nasplib.isofts.kiev.ua/handle/123456789/121649 The method of pattern recognition based on replacement of object images incoming to the correlator by object-dependent synthesized phase objects calculated using the iterative Fourier-transform algorithm was developed by us earlier. In this work, we performed experimental testing the above method by using an optical-digital 4F-correlator. Synthesized phase objects were inputed into the correlator through the spatial light modulator LC2002. Holographic matched filters were recorded using self-developing photopolymers PPC-488. For two test objects, we obtained unified (δ-like) correlation signals with the signal-to-noise ratio reaching 24 dB, while the diffraction efficiency of these filters was up to 30%. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Method for replacing objects in 4F correlator: testing Article published earlier |
| spellingShingle | Method for replacing objects in 4F correlator: testing Yezhov, P.V. Kuzmenko, A.V. Smirnova, Т.N. Ivanovskyy, A. A. |
| title | Method for replacing objects in 4F correlator: testing |
| title_full | Method for replacing objects in 4F correlator: testing |
| title_fullStr | Method for replacing objects in 4F correlator: testing |
| title_full_unstemmed | Method for replacing objects in 4F correlator: testing |
| title_short | Method for replacing objects in 4F correlator: testing |
| title_sort | method for replacing objects in 4f correlator: testing |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/121649 |
| work_keys_str_mv | AT yezhovpv methodforreplacingobjectsin4fcorrelatortesting AT kuzmenkoav methodforreplacingobjectsin4fcorrelatortesting AT smirnovatn methodforreplacingobjectsin4fcorrelatortesting AT ivanovskyyaa methodforreplacingobjectsin4fcorrelatortesting |