Exact analytical calculation of the wavefront structure function for the case of Kolmogorov atmospheric turbulence
D.A. Yagnyatinskiy, V.N. Fedoseyev, A.V. Shepelev
Scientific Research Institute of Scientific and Production Association В«Luch», Podolsk, Russia
Keywords: adaptive optics, wavefront, structure function, Kolmogorov turbulence, analytical calculation, Zernike polynomials, Karhunen-LoСђve functions
Abstract
Due to the importance of using the structure function for problems of optical radiation propagation in a turbulent atmosphere, the task of determining this function from the known mode coefficients of wavefront expansion was set. New formulas have been derived for the exact analytical calculation of the wavefront phase structure function on a circular aperture. Unlike the previously published analytical method, the proposed approach correctly accounts the entire domain, including the area near the edge of the aperture. The new method is compared to the published one and a numerical calculation with the distretization chosen sufficiently fine. The test samples comprised Kolmogorov wavefronts and Zernike polynomials and Karhunen-Loѐve functions corresponding to the Kolmogorov turbulence model. The deviations of the results of the published before method from the new one and from the numerical calculation are provided. The advantages and generality of the new method are stated and explained. The result will make it possible to accurately determine the structure function of the wavefront by its mode coefficients in problems of optical radiation propagation in randomly inhomogeneous media.
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