# Optoelectronics, Instrumentation and Data Processing (v.48, #2)

Selection of basic parameters of adaptive optical systems by V. P. Lukin

*(111-118)*. One possible approach to determining the minimum set of parameters of an adaptive system whose operation is aimed at minimizing distortions arising in modern optoelectronic systems is considered. The basic source of distortions is assumed to be atmospheric turbulence, which imposes the most severe constraints on optical radiation in the atmosphere. The following basic parameters of the system are proposed: number of degrees of freedom, required frequency band (dynamic characteristic, and constraint on the spectral characteristics). Some parameters of the reference source (its size, position, and properties) are determined. The results are obtained in the form of analytical functions, which allows calculating the parameters of the adaptive system that can be used in numerous scenarios in the atmosphere.

**Keywords:**adaptive optics; atmospheric turbulence; laser system; telescope; coherence

Computer simulation of adaptive optics for laser systems in atmospheric applications by P. A. Konyaev

*(119-125)*. Software for computer simulations of adaptive optics systems for atmospheric laser applications designed on the basis of advanced parallel programming techniques is developed. The adaptive optics system model includes the emitting aperture geometry and beam propagation path scenario, vertical profiles of atmospheric parameters, fast parallel split-step Fourier algorithm for solving wave diffraction and propagation equations, time-dependent models of “frozen” atmospheric turbulence with a wide range of scales, and models of the wavefront sensor and controlled deformable mirror. The hardware system for computer simulations is an off-the-shelf desktop with a 6-core 12-thread Intel® Core™ i7-970 CPU at the maximum frequency of 3.5 GHz and an NVIDIA® GeForce GTX 580 graphic accelerator with 512 universal processors operating at 1.5 GHz. Results of simulations of adaptive imaging and laser beam shaping, aimed at estimating the efficiency of adaptive optics systems on atmospheric paths are presented.

**Keywords:**adaptive optics; laser systems; turbulent atmosphere; computer simulations; parallel algorithms

Thin dynamic holograms with an asymmetric fringe profile by V. Yu. Venediktov

*(126-133)*. Results of an investigation and a comparison of schemes used for recording dynamic holographic gratings in a liquid-crystal spatial light modulator, which ensure grating profile asymmetrization and, thus, a significant increase in its diffraction efficiency, are presented. Three approaches are considered: digital, analog, and self-asymmetrization of the profile due to the effect of a secondary field induced in the nematic volume. It is demonstrated that the first two approaches provide recording of gratings with low spatial frequencies (several mm

^{−}1) and with an approximately equal rate of asymmetry (the potential efficiency of diffraction to the first order is 70–75%), while the third approach provides recording of gratings with a much higher spatial frequency (hundreds of mm^{−}1), but with a lower efficiency (about 50%).**Keywords:**liquid crystal; spatial light modulator; dynamic holography

Phase correction of laser radiation with the use of adaptive optical systems at the Russian Federal Nuclear Center—Institute of Experimental Physics by S. G. Garanin; A. N. Manachinsky; F. A. Starikov; S. V. Khokhlov

*(134-140)*. Results obtained at the Institute of Laser Physics Research (which is part of the Russian Federal Nuclear Center — Institute of Experimental Physics) on phase correction of pulsed and continuous wave laser radiation by closed-loop adaptive optical systems (AOS) with flexible deformable mirrors are described. With the help of a conventional AOS including a Hartmann-Shack wavefront sensor and an adaptive mirror having a 220 × 220 mm aperture, aberrations of the beam of a powerful pulsed laser facility called Luch have been reduced by an order of magnitude. The development of special software for reconstruction of singular wavefronts by the Hartmann-Shack sensor has allowed us to perform the correction of a doughnut-shaped Laguerre-Gaussian vortex laser beam in an AOS with a bimorph mirror and to focus it into a bright axial spot that drastically increases the Strehl ratio. Adaptive optical systems have been developed where the adaptive mirror control is ensured by searching for an extremum of a chosen criterion functional with the help of a stochastic parallel gradient algorithm rather than by means of wavefront measurements. Embedding of microcontrollers into the control unit has allowed us to reach an AOS bandwidth of 5 kHz and to demonstrate the dynamic phase correction of tip-tilts and higher aberrations of the wavefront caused by turbulence induced by heating of the beam propagation path under laboratory conditions.

**Keywords:**adaptive optical system; wavefront sensor; wavefront aberrations; phase correction

Analysis of static errors of adaptive mirrors by A. V. Chernykh; O. I. Shanin; V. I. Shchipalkin

*(141-145)*. A technique for experimental studies of the compensatory abilities of adaptive mirrors (AM) is developed and substantiated. The structure of the static residual error of correction is analyzed on the basis of experimental data for a particular AM. The theory of optimal placement of drives on the AM aperture is confirmed by experimental results.

**Keywords:**adaptive optical system; wavefront sensor; adaptive mirror

Using photodetectors in Shack-Hartmann wavefront sensors by L. V. Antoshkin; V. V. Lavrinov; L. N. Lavrinova; V. P. Lukin

*(146-152)*. High-resolution cameras are used as photodetectors in the image recording plane of a Shack-Hartmann wavefront sensor to record centroid coordinates which provide basic information for wavefront reconstruction. A comparative analysis is made of the accuracy of determining the centroid coordinates for CCD and CMOS cameras. The modes of instantaneous sampling and frame-by-frame accumulation of information from the cameras are considered.

**Keywords:**centroid coordinates; photodetector; intensity distribution

Wavefront compensation method using a Shack-Hartmann sensor as an adaptive optical element system by A. V. Kudryashov; V. V. Samarkin; Yu. V. Sheldakova; A. G. Aleksandrov

*(153-158)*. This paper considers the use of an adaptive optical system for compensating aberrations of a laser radiation wavefront. Bimorph mirrors are used as correctors, and the wavefront is measured by a Shack-Hartmann sensor. Disadvantages of this adaptive system and ways to overcome them are discussed.

**Keywords:**adaptive optics; deformable mirror; correction of laser radiation; phase conjugation algorithm

Principles of designing adaptive relay systems for stratospheric power transmission by V. I. Kishko; V. F. Matyukhin

*(159-165)*. Problems of designing laser power transmission systems in a turbulent atmosphere using relay mirrors mounted on a stratospheric airship are analyzed. It is shown that such a system can be designed using a high-power ground-based ytterbium fiber laser, relay mirrors for transmitting highpower laser radiation, and an adaptive optical system for correcting the phase distortions of laser beams due to atmospheric turbulence. A model of a laser power transmission system was designed and tested under laboratory conditions; the tests confirmed the possibility of correcting atmospheric-turbulence distortions during guiding and high-accuracy stabilization of laser beams.

**Keywords:**laser power transmission systems; fiber lasers; adaptive optical system; stratospheric airships; laser relay mirror

Tests of an adaptive optical system on a model atmospheric turbulent path by S. V. Pikulev; V. V. Semenkov; A. V. Chernykh; O. I. Shanin; V. I. Shchipalkin

*(166-173)*. Physical modeling is a powerful tool for studying and testing various technical objects. In tests of an adaptive optical system (AOS), it is necessary to measure phase distortions of real objects (paths, devices, etc.) to identify real requirements and ranges of modeling. This paper presents estimates of modeling conditions and results of AOS tests under model conditions, namely, experimental results of adaptive correction of a laser radiation wavefront in a turbulent atmospheric path ∼100 m long. In the experiments, the standard deviation of the wavefront and the divergence of the radiation before and during the correction were recorded. In some cases, the correction efficiency in terms of standard deviation exceeded 10 times.

**Keywords:**modeling; turbulent atmospheric path; adaptive optics; wavefront sensor; adaptive mirror

Adaptive focusing of coherent radiation with the use of a fluctuating illuminating signal as a reference source by L. A. Bol’basova; V. P. Lukin

*(174-181)*. Adaptive focusing of a coherent beam in a turbulent atmosphere is considered. Distributions of the mean intensity of the field of a coherent laser beam focused in a turbulent medium by means of adaptive phase correction with the use of a point reference source are calculated. The source retains a random position on the object onto which laser radiation is focused. Results of adaptive focusing with moving and motionless reference sources are compared.

**Keywords:**correction; reference source; phase; coherence

Modified hartmann method for measuring wide-aperture adaptive mirrors by D. M. Lyakhov; O. I. Shanin; V. I. Shchipalkin

*(182-187)*. Various laser systems use wide-aperture adaptive mirrors containing dozens or hundreds of drives. Thousands of high-precision measurements are based on the use of such mirrors. A simple, cheap, high-precision, and rapid method specifically designed to study the characteristics of these mirrors with a large number of degrees of freedom is described.

**Keywords:**Hartmann method and diaphragm; mathematical model; wide-aperture adaptive mirror; control system

Advanced adaptive correction of turbulent distortions based on a Shack-Hartmann wavefront sensor measurements by L. B. Antoshkin; V. V. Lavrinov; L. N. Lavrinova

*(188-196)*. The propagation of laser radiation through the atmosphere is accompanied by a change in the light field under the influence of turbulence and is a random process. An adaptive system that includes a Shack-Hartmann wavefront sensor and a flexible mirror corrects distortions found at the previous time but changed before being corrected by the system. Analysis of turbulence within a given time period allows one to predict turbulent distortions at the subsequent time and use it to make a correction in the radiation phase distribution. The adaptive correction performance can also be improved by preparing the reflective surface of the adaptive mirror based on predictions of the state of the wavefront at the next time by the turbulence parameters and the transverse component of the wind speed found in previous Hartmann-Shack sensor measurements.

**Keywords:**prediction; centroid coordinates; frozen turbulence time; transverse wind speed; random phase screen; differential method; wavefront sensor

Usage of wavefront sensor for estimation of atmospheric turbulence parameters by M. S. Andreeva; N. G. Iroshnikov; A. B. Koryabin; A. V. Larichev; V. I. Shmalgauzen

*(197-204)*. A method is proposed to estimate the structure constant

*C**n*_{ }^{2}and the outer scale*L*_{0}of turbulent fluctuations in Hartmann sensor measurements of the wavefront parameters of a light beam transmitted through a turbulent path. The method is based on expansion of phase fluctuations within a given aperture into a series of Zernike polynomials and statistical analysis of the coefficients of this expansion. Application of the method to estimating the parameters of fluid cell turbulence yielded results which are in good agreement with estimates obtained by other methods. The paper also presents the results of modeling based on measurements of the transverse component of the wind velocity on the path determined by correlation of the local slopes at four virtual subapertures.**Keywords:**atmospheric turbulence; turbulence modeling; Zernike polynomials; radiation propagation; Shack-Hartmann sensor

Generation of control signals for adaptive systems using laser atmospheric backscatter by Ya. I. Malashko; V. M. Khabibulin

*(205-210)*. A method for controlling an adaptive optical system by using the intensity of laser atmospheric backscatter is studied. Mathematical modeling is used to study the generation of a control signal in a monostatic loop and, as a consequence, the range of beam focus with the closed loop. It is shown that this method of generation does not lead to beam collimation even for beams of diffraction quality.

**Keywords:**adaptive optics; laser radiation; atmospheric backscatter

Spectrophotometric method for measuring the groove depth of calibration reflection gratings by V. P. Korol’kov; S. A. Konchenko

*(211-217)*. A method for measuring the groove depth of calibration gratings is proposed which is based on measuring the spectral dependence of the the zero-order reflection diffraction efficiency. The errors of the method are determined by three main factors: the shift of the maxima of the spectrum due to the wall slope of the grating grooves, the error in setting the wavelength of the spectrophotometer, and the divergence of the light beam in the setup. It is shown theoretically that the measurement error is in the range of 0.25–1%, depending on the fabrication technology of the grating and measuring equipment. The method was tested experimentally using commercial calibration gratings. The range of applicability of the method is discussed in terms of the geometrical parameters of the microstructure of reflection gratings and the characteristics of the spectrophotometer used.

**Keywords:**measuring the depth of microrelief; calibration structures; spectrophototometric method; reflection measurements