Feodor Yu. Kanev

Detection of dislocations as branching points of interference pattern

In the present article the problem of Gaussian beam propagation in the turbulent atmosphere is considered on the base of numeric methods. Singular points (dislocations) development in the wavefront is analyzed. Two algorithms of dislocation detection were proposed. One of them based on the interferogram processing and can be realized in a laboratory experiment. In the second algorithm the whole wavefront is analyzed and dislocations are localized as points where cuts of the surface in 2(pi) begin. The precision of the algorithms is compared and statistics of dislocations on the path of propagation is represented.

Possibility of adaptive correction for atmospheric turbulent layer

With the use of the methods of numeric simulation the possibility is analyzed of adaptive correction for randomly inhomogeneous layer of a turbulent atmosphere on the base of phase conjugation. The atmosphere was simulated as a set of random screens. The influence of different parts of distributed lens on distortions of a laser beam is considered as well as efficiency of corrections for screens placed on various distances from the transmitting aperture. It was shown that the most severe distortions were induced by turbulent layers located on the maximum distance from the plane of observation. At the same time correction for these layers is the most efficient.

Adaptive forming beams and image simulation through the atmosphere

The problem of compensation for atmospheric distortions of a wavefront has been studied for a sufficiently long time. The first papers on this subject were published in the mid 1960s. At that time, however, the engineering base gave no way for designing the efficient devices for compensating for atmospheric distortions. In recent years much progress has been made in developing wavefront sensors and correctors and then fitting the optical facilities operating under atmospheric distortions with these devices. In this connection there has been an increased interest in theoretical works concerning the optical design and configuration of the wavefront corrections.

Four-dimensional computer dynamic model of an atmospheric optical system

A computer code for simulation of high-power beams thermal blooming in the turbulent atmosphere and imaging in a ground- based telescope is described. This code also allows one to simulate the components of adaptive systems, such as the Hartmann-Shack wavefront sensor and various flexible and segmented mirrors. Our software can be used for estimation of beams and images parameters in the atmosphere and for the investigations of adaptive optical system efficiency.

Numerical Simulation in Adaptive Optics

A numerical model of a typical adaptive optics system is described in the report. The developed computer application corresponding to the model includes all the main elements of a real system, namely, computer codes simulating radiation propagation in a turbulent atmosphere with thermal blooming and codes simulating the elements of adaptive optics system (a model of a Shack-Hartmann wavefront sensor, two algorithms of dislocation localization, and a model of adaptive mirror with continuous surface). In the report we include solutions to the some of adaptive optics problems obtained with the model: realization of amplitude-phase control in two-mirror adaptive system, the method to improve the stability of correction for thermal blooming, evaluation of a Shack-Hartmann sensor performance, and some others. These results demonstrate that the set of the developed models is a powerful tool for simulations in the field of adaptive optics.

Compensation of atmospheric turbulence with the use of a two-mirror adaptive system

It was shown that there exist two sources of errors in an adaptive optics system. The first source appears due to limitations induced by the elements of the system such as a Shack Hartmann sensor and deformable mirror. The second associated with the violation of the optical reciprocity principle in algorithm of phase conjugation, namely, with substitute of beacon amplitude distribution by distribution of a Gaussian beam generated by a laser. Absolute correction of turbulent aberration is possible only in case of strict maintenance of a principle, i.e. in case of phase reversal. In the paper the possibility is considered to realize phase reveresal in a linear system and only with the use of phase control of the beam. The system should include two mirrors separated by the vacuum gap of a finite size. Estimations were obtained by correction efficiency on the base of phase conjugation and with the use of two mirror adaptive system.

Algorithm for phasing a segmented mirror

This paper considers the problem of forming a preset surface of a segmented mirror of a telescope. An iteration algorithm based on analysis of the interference pattern of the radiation reflected from the mirror is used for phasing the mirror segments. At every iteration, the current interferogram is compared with the reference one obtained for the surface of a preset shape. The value of the control goal function, whose minimum is determined in the algorithm, decreases with the decreasing discrepancy between the interferograms. This technique provides for formationof a plane-reflecting surface of the mirror, if the relative displacement of segments does not exceed the half wavelength. It is shown that to extend the range of acceptable displacements, it is necessary to introduce additional sources of radiation of specially chosen wavelengths. In such a case, the dynamic range of the algorithm can be extended up to 30 μm.

Limitations of adaptive control efficiency due to singular points in the wavefront of a laser beam

Correction for turbulent distortions with an adaptive optics system including Shack-Hartmann sensor is considered in the paper. Efficiency of control was analyzed under conditions of singular points development in a wavefront of a laser beam. It was shown that the presence of dislocations causes the discrepancy of wavefront detection by the sensor and as a consequence leads to the control instabilities. It was also shown that dislocations appear mainly in the peripheral regions of the beam. Using this feature and optimizing the size of the sensor the stable adaptive control could be achieved in an adaptive optics system.

Principal limitations of phase conjugation algorithm and amplitude-phase control in two-mirror adaptive system

In the paper an analysis was performed on the base of numeric experiment methods of a laser beam propagation in a turbulent atmosphere. Comparison of efficiency was carried out of phase and amplitude-phase adaptive control algorithms. It was noted that only wavefront reversion insures the absolute compensation for turbulent distortions of laser beams. It is also shown that wavefront reversion is possible to realize in two-mirror adaptive optics system. The mirrors should be divided by a gap where a beam propagates under conditions of free diffraction.

Cophasing of a telescope segmented mirror

The algorithm of a segmented mirror co-phasing is described in the paper. The algorithm is based on the analysis of interference pattern, special criterion is introduced for this purpose. It is shown that initial shift of the segments must be less than half of the wavelength. To increase the dynamic range of the system the second (or even third) wavelength should be used in the algorithm. In this case the dynamic range can be increased up to 30 mkm.