Representation of phase of distorted optical wave through the orthonormal bases including the outer scale of turbulence. Numerical experiment

It is usual in the problems of adaptive optics that the phase of optical wave is expanded into an orthogonal basis for a convenience of analysis. Zernike polynomials are popular for this expansion because they have simple analytical expression and their first modes coincide with the classical aberrations. However, if the power spectrum of distortions is known, its egienfunctions named Karhunen-Loeve-Obukhov (KLO) functions are a natural choice for such basis. Authors have derived the KLO functions represented through the Zernike polynomials and developed the effective method to expand distorted phase through the orthonormal bases. Usually, in investigations the Kolmogorov model of turbulence is used. However, the nature experimental data do not agree always with this model. But the range of validity for the Kolmogorov model can be extended introducing in it the outer scale of turbulence. Authors developed the algorithm to obtain analytically the KLO functions allowing for the outer scale of turbulence (von Karman model). The results of numerical experiment for representation of a random phase in different bases for various atmospheric conditions are presented.