Reduction of speckle noise in laser energy distribution on the target by means of a modified Fourier hologram and incoherent averaging technique
Presented in this paper is the technique of formation of required laser intensity distribution on the target with reduced speckle noise. The method is based on the use of a modified Fourier hologram adapted to controlled phase modulators. Reduction of the speckle noise in the laser energy profile is...
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| Опубліковано в: : | Semiconductor Physics Quantum Electronics & Optoelectronics |
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| Дата: | 2018 |
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2018
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| Цитувати: | Reduction of speckle noise in laser energy distribution on the target by means of a modified Fourier hologram and incoherent averaging technique / A. Derzhypolskyi, O. Gnatovskyi, L. Derzhypolska // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2018. — Т. 21, № 4. — С. 429-433. — Бібліогр.: 10 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860479634139774976 |
|---|---|
| author | Derzhypolskyi, A. Gnatovskyi, O. Derzhypolska, L. |
| author_facet | Derzhypolskyi, A. Gnatovskyi, O. Derzhypolska, L. |
| citation_txt | Reduction of speckle noise in laser energy distribution on the target by means of a modified Fourier hologram and incoherent averaging technique / A. Derzhypolskyi, O. Gnatovskyi, L. Derzhypolska // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2018. — Т. 21, № 4. — С. 429-433. — Бібліогр.: 10 назв. — англ. |
| collection | DSpace DC |
| container_title | Semiconductor Physics Quantum Electronics & Optoelectronics |
| description | Presented in this paper is the technique of formation of required laser intensity distribution on the target with reduced speckle noise. The method is based on the use of a modified Fourier hologram adapted to controlled phase modulators. Reduction of the speckle noise in the laser energy profile is obtained using multiple incoherent superpositions of synthesized holographic images. Each hologram is synthesized with a different random diffuser. The advantages of this method: relative simplicity of hardware; robustness with regard to distortions of any kind in the input beam and/or optical path of the scheme; controlled reduction of the speckle noise in the final energy distribution.
|
| first_indexed | 2026-03-23T18:47:23Z |
| format | Article |
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ISSN 1560-8034, 1605-6582 (On-line), SPQEO, 2018. V. 21, N 4. P. 429-433.
© 2018, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
429
Linear and nonlinear solid-state optics
Reduction of speckle noise in laser energy distribution on the target by
means of modified Fourier hologram and incoherent averaging
technique
A.G. Derzhypolskyi, O.V. Gnatovskyi, L.A. Derzhypolska
Institute of Physics, NAS Ukraine, 46, prospect Nauky, 03680 Kyiv, Ukraine
Correspondence author: phone +38-(044)-525-99-68, e-mail: derzh.l@iop.kiev.ua
Abstract. Presented in this paper is the technique of formation of required laser intensity
distribution on the target with a reduced speckle noise. The method is based on the use of
modified Fourier hologram adapted to controlled phase modulators. Reduction of the
speckle noise in the laser energy profile is obtained using multiple incoherent superposition
of synthesized holographic images. Each hologram is synthesized with different random
diffuser. The advantages of this method: relative simplicity of hardware; robustness with
regard to distortions of any kind in input beam and/or optical path of the scheme; controlled
reduction of the speckle noise in the final energy distribution.
Keywords: Fourier holography, holographic image formation, speckle noise, spatial light
modulator.
doi: https://doi.org/10.15407/spqeo21.04.429
PACS 42.30.Ms, 42.40.-i
Manuscript received 02.11.18; revised version received 25.11.18; accepted for publication
29.11.18; published online 03.12.18.
1. Introduction
Development of methods enabling to form a given
amplitude-phase distribution of laser radiation on the
target is the actual problem of science and technology.
This is applicable in many areas including medicine,
biology, nanophysics, technology for manipulating
objects of different nature, size and shape [1], material
processing, photolithography [2, 3] and other tasks. Very
often, these problems are considered in context of
presence of some distortions or aberrations introduced
mostly, but not solely, by a transfer medium [4, 5]. An
efficient instrument used for these tasks is spatial light
modulator (SLM) device that is essentially the controlled
amplitude or phase transmitter based on liquid crystal or
micromechanical elements. The use of SLM allows
creating dynamically controlled holograms in real time
for shaping or modulating the light beams for the purpose
of the set task.
We consider here formation of the desired intensity
distribution on a target using SLM in the presence of
aberrations. If phase information is not important for
studies, and only intensity is of interest, then to create a
hologram it is possible to apply a random phase diffuser
(RPD). This allows the hologram to become less
susceptible to deformation (in particular, the loss of its
parts) when the image is restored. Restoration of a
hologram with an aberrated beam necessarily distorts the
restored image. But if the hologram is recorded or
synthesized using RPD, the restored image integrity
insignificantly improved against the aberrations in
restoring beam [6]. However, another problem arises
then – the speckle noise. The goal of this work is to
develop a method of eliminating or at least reducing the
speckle noise in the image stabilized by means of [6].
2. The problem
As demonstrated in [6], the use of RPD for producing
either real or synthesized Fourier-hologram makes a
significant stabilizing effect against aberrations in the
restoring beam. In a common case, the resultant intensity
distribution formed by Fourier-holography scheme is
described as:
2
haI c ∗= , (1)
where a is the amplitude of the original (required) image,
h – hardware function of the system and * – convolution
operator. In this case, the output intensity distribution is
particularly sensitive to any phase aberrations in the
system due to coherent (amplitude) type of convolution.
The hardware function h in case of phase distortions in
the system is complex and causes a significant skew in
the intensity distribution due to interference.
SPQEO, 2018. V. 21, N 4. P. 429-433.
Derzhypolskyi A.G., Gnatovskyi O.V., Derzhypolska L.A. Reduction of speckle noise in laser energy distribution on …
430
Fig. 1. Real image (a rectangular intensity step) formed by
transmitting SLM with binary Fourier hologram synthesized
with RPD (visual representation on the left and the plot of
intensity on the right).
But the use of good RPD with relatively small
radius of correlation converts the convolution type from
coherent (amplitude) to quasi-incoherent (intensity):
22
haI c ∗≅ . (2)
In this case, because of incoherent convolution, the
output image appears highly insensitive to phase
aberrations. The function |h|
2
is real and positive as well
as |a|
2
, so there are no significant changes in the intensity
distribution, even if severe phase distortions occur.
However, there is another problem with RPD.
Despite the output image is strongly stabilized, it is
covered with speckles, which may be undesirable. Fig. 1
shows a simple intensity distribution (a rectangular flat
intensity step) formed by spatial light modulator with
binary Fourier-hologram (0 and π phase values that
correspond to ±1 amplitude transmission values)
synthesizer with RPD. It is obvious that though the
envelope form of distribution is as the required one, but
the filling is messed up with speckle noise. Formation of
speckle pattern is inherent to RPD, as it always has a
finite radius of correlation. So, the coherence of the
waves forming the output image causes the residual
interference within the radius of correlation producing a
speckle pattern. This effect is especially notable in the
case of synthesized holograms as the radius of correlation
of digital RPD is limited by the pixel pitch.
From numerous experiments, we know that the
speckle pattern of each particular image is stable in time
and is defined by RPD used. This fact is used to build a
solution to the speckle problem.
3. The solution
The speckle pattern is the noise in output image (signal).
The basic and common solution to reduce the noise is to
average multiple samples of the signal. In the case of
independent and random noise in every sampled signal,
the expected reduction of noise level is proportional to
the square root of the number of samples. In this case, the
noise (speckle pattern) in the signal (image) is defined by
used RPD. So, to achieve noise reduction from
averaging, we should take every new image generated
with another independent RPD. Similar approach of the
use of RPD together with incoherent averaging is used
successfully in [7] for imaging through scattering
medium and also in [7-10] for improvement of image
quality from digitally reconstructed real holograms.
Fig 2. Speckle pattern reduction with the number of averaged
samples. The computational experiment (visual representation
above and intensity graphs below).
300 400 500 600 700 800
50
100
150
200
250
pixels
In
te
n
s
it
y
,
A
.U
.
n=1 n=10
n=100
n=50
SPQEO, 2018. V. 21, N 4. P. 429-433.
Derzhypolskyi A.G., Gnatovskyi O.V., Derzhypolska L.A. Reduction of speckle noise in laser energy distribution on …
431
Fig. 3. Experimental setup with SLM. L – solid state laser
(532 nm); T – telescope (beam expander); SLM – phase
transmittance spatial light modulator; O – Fourier-objective; C
– CCD-camera; PC – controlling PC.
Fig 4. Speckle pattern reduction with the number of averaged
samples. The real experiment with synthesized holograms and
SLM (visual representation above and intensity plots below).
3.1. The computational experiment
First, the computational experiment was made to check
the expectations. In MatLab environment, multiple
binary Fourier-holograms of square flat-top intensity step
with independent random RPDs were synthesized and
saved for further use by means of iterative algorithm.
Type of image was chosen for further clear calculation of
signal-to-noise ratio (SNR). The binary type of hologram
was chosen because of two reasons: 1) to test the method
on a simplest possible type of hologram, and 2) because
of limitation of displaying hardware available. All the
holograms were then digitally reconstructed in MatLab,
and output images were averaged. Fig. 2 represents the
results of computational experiment with 1, 10, 20, 50
and 100 samples averaged. A significant noise reduction
is visible both in the pictures and the intensity plots.
3.2. The real experiment
The second stage of the work was the real experiment
with synthesized holograms. To perform this used was
the setup shown in Fig. 3 (polarizer and analyzer required
for switching to the phase modulation mode, and neutral
density filters are omitted for visual simplification).
100 synthesized binary holograms with independent
RPDs were sequentially displayed using SLM (HoloEye
HEO-0017, 1024×768 pixels, transmittance mode) with
an average rate of 33 fps. The averaging factor was tuned
by means of exposure time of the camera. The calculated
averaging factor n = (Exposure × Frame rate).
Experiments were performed with a single picture
(averaging factor n = 1), and exposure times 200 ms
(n = 6), 500 ms (n = 17), 1 s (n = 33) and 3 s (n = 100).
Averaging factor estimation was not accurate, as the
frame rate was not controlled and thus might not be
strictly constant. The results together with the intensity
plots are shown in Fig. 4. The intensity plots were
produced from the side section (non-central) of
corresponding image to avoid the central intensity peak.
This peak is inherent to the use of SLM. It contains
non-diffracted light caused mostly by the fill factor of
SLM. The solution to this issue is the use of patterns
utilizing peripheral part of diffraction field and omitting
the center. Or, probably, SLM technology will be
enhanced to eliminate this fill factor problem. Apparent
curvature of the average intensity line reveals a slight
vignetting in the image caused by diffraction of light on
the aperture of single pixels of SLM. This was taken into
account when calculating the results. This effect also
could be reduced on the stage of generating the hologram
by means of incorporating an inverted single-pixel
diffraction function. Like to the computational
experiment, improvements in speckle noise are visible
both in the pictures and intensity plots.
3.3. Visual effect
To illustrate a visual effect of the method on the
generated images, a realistic gray-scale image was taken
and real experiment performed with the maximum
averaging factor of 100. Because of the fundamental
restrictions of binary hologram, one cannot use the whole
diffraction field for the generated image unless it is
center-symmetric. Thus, a full phase hologram was used
for generation. However, since the maximum available
phase modulation value at the hardware used is only 1.4π
and not 2π, the overall image quality is compromised.
The result is shown in Fig. 5. Enhancement of the details
is also shown in enlarged areas.
O
PC
L
T
SLM
C
f f0
100 200 300 400 500 600 700 800
0
20
40
60
80
100
120
pixels
In
te
n
s
it
y
, A
.U
.
n=6
(exp. 200ms)
100 200 300 400 500 600 700 800
0
50
100
150
200
pixels
In
te
n
s
it
y,
A
.U
.
n=1
100 200 300 400 500 600 700 800
0
20
40
60
80
100
120
140
160
180
pixels
In
te
n
s
it
y,
A
.U
.
n=100
(exp. 3 s)
100 200 300 400 500 600 700 800
0
20
40
60
80
100
120
pixels
In
te
n
s
it
y,
A
.U
.
n=33
(exp. 1 s)
SPQEO, 2018. V. 21, N 4. P. 429-433.
Derzhypolskyi A.G., Gnatovskyi O.V., Derzhypolska L.A. Reduction of speckle noise in laser energy distribution on …
432
Fig. 5. SNR improvement with the number of averaged
samples. SNRcomp and SNRreal are the calculated signal-noise
ratios from computational and real experiments, accordingly;
SQR – expected theoretical curve for SNR; Noise is the noise
calculated from the computational experiment.
3.4. Calculation and discussion of the results
For numerical characterization of the results, SNR has
been calculated in every case. The signal is defined as an
average on the top of the intensity step after subtraction
of the background value (downhill of the intensity step).
The noise is defined as a standard deviation of the signal
on the top of intensity step. In real experimental data, an
additional correction for the single-pixel diffraction
function is applied after subtraction of the background.
Displayed in Fig. 6 are the calculated results. Both
computational and real experiments are presented along
with the theoretical expectance curve. For the
computational results, it was possible to calculate SNR
after each new averaging iteration. So, the corresponding
curve is solid. While for the real experiment, only certain
points are available. Displayed also is the noise curve
from the computational experiment, for illustration
purposes only.
As seen from Fig. 6, both computational and real
data are quite close to the theoretical expectance curve.
Observed systematic deviation of SNRcomp curve from
the theoretical one could probably be caused by not
completely independent RPDs. As those have been
produced by pseudo-random number generator and could
have some residual correlation. Another reason may be is
not clearly established relation between the signal and
background. So, the signal level might be underesti-
mated.
For the SNRreal points, it should be noted that their
positioning on x-axis is not accurate. As the averaging
factor calculation is based on holograms displaying
frame rate, which is known only as average and could
deviate during the experiment. Nevertheless, the trend is
very close to theoretical expectance.
4. Conclusion
Formulated in the work is the problem of speckle noise in
intensity distributions formed by holograms created using
RPD. Offered here is the solution to this problem as
based on the well-known principle of averaging the
samples of the same signal with independent random
noise. Basic experimental implementation of the solution
Fig. 6. Visual enhancement of the image generated by pure digital hologram with RPD by incoherent averaging. The averaging
factor n = 1 (left) and n = 100 (right).
SPQEO, 2018. V. 21, N 4. P. 429-433.
Derzhypolskyi A.G., Gnatovskyi O.V., Derzhypolska L.A. Reduction of speckle noise in laser energy distribution on …
433
is provided with averaging factor of up to 100 showing
significant improvement of image quality. With more
fast-acting specialized equipment, an averaging factor of
1000 or even more is achievable. Taking into account
high robustness of image formation by holograms created
with RPDs, particularly against aberrations, the
combination of these two methods could be extremely
useful in a wide range of tasks to form the required
intensity distribution. The proposed method is virtually
unconstrained in terms of enhancement of final
image/intensity distribution, however for the cost of time.
So, for practical means, especially for dynamic
applications, further attention will have to be paid to the
time consumption issue. A maximum achievable
resolution will also have to be investigated.
References
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A.G., Medved N.V. The method of the stabilization
of the laser radiation on the technology target.
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2006. №6. P. 69–72 (in Ukrainian).
6. Derzhypolskyy A.G., Poperenko L.A. Random
phase modulator as the stabilizer of intensity
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Bulletin of Taras Shevchenko National Universiry
of Kyiv. Series: Physics & Mathematics. 2007. 4. P.
322–327.
7. Purcell M.J., Kumar M., Rand S.C., and
Lakshminarayanan V. Holographic imaging through
a scattering medium by diffuser-aided statistical
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1291–1297.
8. Yu. Wang, P. Meng, D. Wang, Lu Rong, S.
Panezai. Speckle noise suppression in digital
holography by angular diversity with phase-only
spatial light modula. Opt. Exp. 2013. 21, No. 17. P.
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9. Baumbach T., Kolenovic E., Kebbel V., and Jüptner
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Authors and CV
Andrii G. Derzhypolskyi. Currently,
Andrii is Researcher at the Institute of
Physics, NAS of Ukraine. Authored
of 22 scientific publications and 1
patent. The area of scientific interests
is correlation optics, laser technology,
optically inhomogeneous objects.
Olexandr V. Gnatovskyi. PhD and
Senior Researcher at the Institute of
Physics, NAS of Ukraine. Authored
over 200 articles, 33 patents. The area
of his scientific interests is
investigation of correlation methods
for formation and use of laser beams
with controlled spatial angular
characteristics.
Liudmyla A. Derzhypolska. She is
PhD and Senior Researcher at the
Institute of Physics, NAS of Ukraine.
Authored 15 scientific publications.
The area of scientific interests is
correlation optics, holographic
interferometry, speckle-interferometry
and optically inhomogeneous objects.
|
| id | nasplib_isofts_kiev_ua-123456789-215314 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-23T18:47:23Z |
| publishDate | 2018 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Derzhypolskyi, A. Gnatovskyi, O. Derzhypolska, L. 2026-03-12T08:53:03Z 2018 Reduction of speckle noise in laser energy distribution on the target by means of a modified Fourier hologram and incoherent averaging technique / A. Derzhypolskyi, O. Gnatovskyi, L. Derzhypolska // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2018. — Т. 21, № 4. — С. 429-433. — Бібліогр.: 10 назв. — англ. 1560-8034 PACS: 42.30.Ms, 42.40.-i https://nasplib.isofts.kiev.ua/handle/123456789/215314 https://doi.org/10.15407/spqeo21.04.429 Presented in this paper is the technique of formation of required laser intensity distribution on the target with reduced speckle noise. The method is based on the use of a modified Fourier hologram adapted to controlled phase modulators. Reduction of the speckle noise in the laser energy profile is obtained using multiple incoherent superpositions of synthesized holographic images. Each hologram is synthesized with a different random diffuser. The advantages of this method: relative simplicity of hardware; robustness with regard to distortions of any kind in the input beam and/or optical path of the scheme; controlled reduction of the speckle noise in the final energy distribution. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Linear and nonlinear solid-state optics Reduction of speckle noise in laser energy distribution on the target by means of a modified Fourier hologram and incoherent averaging technique Article published earlier |
| spellingShingle | Reduction of speckle noise in laser energy distribution on the target by means of a modified Fourier hologram and incoherent averaging technique Derzhypolskyi, A. Gnatovskyi, O. Derzhypolska, L. Linear and nonlinear solid-state optics |
| title | Reduction of speckle noise in laser energy distribution on the target by means of a modified Fourier hologram and incoherent averaging technique |
| title_full | Reduction of speckle noise in laser energy distribution on the target by means of a modified Fourier hologram and incoherent averaging technique |
| title_fullStr | Reduction of speckle noise in laser energy distribution on the target by means of a modified Fourier hologram and incoherent averaging technique |
| title_full_unstemmed | Reduction of speckle noise in laser energy distribution on the target by means of a modified Fourier hologram and incoherent averaging technique |
| title_short | Reduction of speckle noise in laser energy distribution on the target by means of a modified Fourier hologram and incoherent averaging technique |
| title_sort | reduction of speckle noise in laser energy distribution on the target by means of a modified fourier hologram and incoherent averaging technique |
| topic | Linear and nonlinear solid-state optics |
| topic_facet | Linear and nonlinear solid-state optics |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/215314 |
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