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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.

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.

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.

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.

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.

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.

A method is proposed to estimate the structure constant C_n² and the outer scale L₀ 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.

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.

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.

A new technology of visualization and diagnostics of transparent media with gradient inhomogeneities is described. This technology is called three-dimensional laser diffractometry; it is based on refraction of spatially structured laser radiation and digital recording and processing of twodimensional (in transmitted light) or three-dimensional (in scattered light) refractive patterns. Results of computer simulations of three-dimensional refractive patterns (3D refractograms) for spherically and plane layered media are presented. A setup for observation of 3D refractograms in scattered light is schematically described, the method of obtaining refractograms from experimental two-dimensional refractive patterns is presented, and examples of computer processing of experimental data are given.