V. V. Voitsekhovich

Density of turbulence-induced phase dislocations

Under certain conditions, light-wave propagation through turbulent media causes a specific type of phase distortion: so-called phase dislocations. A salient feature of phase dislocations is an appearance of zones where the phase turns out to be a multivalued function of coordinates. The problem of turbulence-induced phase dislocations is considered. Both a theoretical treatment and simulations based on the numerical solution of a parabolic equation are used for estimation of the dislocation density. Various turbulence conditions, ranging from weak to very strong ones, are considered as well as the dependences on wavelength, and the inner scales of turbulence are presented. An empirical formula for the dislocation density suitable for a wide range of turbulent and propagation conditions is derived. The results obtained can be useful for both atmospheric and adaptive optics.

Simulations of turbulence-induced phase and log-amplitude distortions.

A new method, to our knowledge, allowing one to simulate correlated random processes is suggested. Structure (or correlation) functions of the processes under simulation are assumed to be given. The method is based on the generation of random wave vectors that allows one to simulate processes for a wide class of structure functions. The validity of the method proposed is illustrated by simulations of the turbulence-induced log-amplitude and phase distortions.

Minimum-variance phase reconstruction from Hartmann sensors with circular subpupils

Analytical expressions for the minimum-variance phase reconstructor for Hartmann sensors with circular subpupils are presented in this work. The approach assumes a wavefront expansion in terms of orthogonal Zernike polynomials, and takes advantage of the a priori knowlegde of the phase correlation function associated to phase distortions produced by atmospheric turbulence with Kolmogorov statistics.

Influence of scintillations on the performance of adaptive astronomical systems with Hartmann-like wavefront sensors

The influence of scintillations on image centroid measurements and on the phase reconstruction from Hartmann-like wavefront sensors is investigated quantitatively by means of computer simulations. It is shown that under the conditions of astronomical observations, the magnitude of the effect is between 10% (for excellent seeing) and 18% (for poor seeing). However, because the magnitude of the effect increases with the increasing of the turbulence strength, one can expect that under the strong-turbulence conditions the influence of scintillations on the image centroid can be quite strong. So, starting from agiven turbulence strength, it can be impossible to make a successful phase reconstruction from image centroid measurements. It is also shown that the scintillations affect in a different and complicated way the reconstruction quality of different aberrations. Nevertheless one can notice some general tendencies: The scintillations affect more strongly the reconstruction quality of the tip-tilt and high-order aberrations than the reconstruction quality of intermediate aberrations.

Efficiency of the Hartmann test with different subpupil forms for the measurement of turbulence-induced phase distortions.

The reconstruction quality of turbulence-induced phase distortions from Hartmann data is calculated for masks with different subpupil forms by means of computer simulations. Four subpupil forms are considered: the circle, the square, the hexagon, and the polar segment. We show that, for the case of a circular aperture, the mask with polar segment subpupils provides the best reconstruction quality.

Role of boundary measurements in curvature sensing

The role of boundary measurements in curvature sensing is analyzed in basis of the method of weighting functions. It is shown that depending on the orthogonal basis chosen to expand the wavefront some modes can be exactly restored from the curvature data only, without the boundary information. This fact implies that curvature sensing technique can be used without contour measurements to evaluate some given modes. Therefore, if the contribution to the total phase distortion of the non-estimated modes is relatively small compared to the estimated ones, the method can be successfully applied avoiding edge measurements.

Method of random wave vectors in simulation of anisoplanatic effects

A generalization of the method of random wave vectors [Appl. Opt. 36, 464 (1997)] that is suitable for a simulation of turbulence-induced anisoplanatic effects is proposed. A simulation of the cross-correlated phase fluctuations produced by two initially plane waves propagating through weak turbulence is considered. The variation of C(n)(2) along a propagation path and an effect of the finite outer scale of the turbulence are included in the simulation. The validity of the simulation method is verified by comparison of theoretical and simulated results. The simulation approach developed can be used in the problems related to adaptive optics, speckle inteferometry, guide stars, and imaging through turbulence.

Efficiency of optimum Kolmogorov estimators for different atmospheric statistics: Hartmann test

The performance of wavefront sensing with Hartmann sensors is generally suboptimal when the statistics associated to the random processes is not accurately known. Turbulence-induced atmospheric phase distortions are commonly described in terms of the Kolmogorov power spectral density or -11/3 power law, although different atmospheric behaviors have also been reported. In this work we investigated how the wavefront sensing accuracy is degraded when optimum estimators computed under the usual assumption of Kolmogorov turbulence are used to reconstruct sets of wavefronts whose statistics differs from the Kolmogorov one. The results assuming noiseless measurements show that optimum Kolmogorov estimators demonstrate a noticeable robustness, with a small loss of accuracy if the real turbulence statistics deviate from this model. The cases of the generalized power law spectrum and the outer-scale dependent exponential model are investigated. The influence of noise is briefly discussed.

Modal compensation and the atmospheric-turbulence outer scale: computer simulations.

The influence of the turbulence outer scale on the Strehl ratio obtained with low-order adaptive optics systems is examined by numerical simulation. The Karhunen-Loeve approach is used to generate wave-front samples. A method that allows construction of the outer-scale-dependent Karhunen-Loeve functions is described. It is shown that the Strehl ratio produced by a second-order adaptive optics correction (tip-tilt, defocus, and astigmatism) is affected quite strongly by the finite outer scale. For the higher-order correction, the effect under study is weak and appears only when the outer-scale magnitude becomes less than the aperture diameter. It is also shown that the finite outer scale has a positive effect on the Strehl ratio of the uncorrected long-exposure image.

Effect of scintillations in curvature sensing

The effect of scintillations on the curvature sensing which is used in astronomic adaptive systems is investigated. It is shown that the magnitude of the effect depends on two atmospheric turbulence parameters: on the Fried parameter which characterizes the seeing conditions, and on the turbulence inner scale which is responsible for small-sized turbulence inhomogeneities. Depending on the turbulence conditions, the magnitude of the effect ranges from 3% to 20%, while for the typical ones it is of the order of 10%-15%.