Power series evaluation of Zernike covariances for turbulence-induced phase distortions including outer scale and servo lag effects

摘要

Abstract: Mellin transform techniques are applied to develop power series formulas to efficiently evaluate covariances for zernike representations of turbulence-induced phase distortions along a pair of ray paths through the atmosphere from one or several sources at finite or infinite range. The formulas also apply when the phase distortions are temporally filtered by a closed loop adaptive optics system. The power series formulas are developed using an automated computer logic algorithm designed to solve multiple contour integrals in multiple complex planes resulting from the application of Mellin transform techniques. Results are presented for the von Karman turbulence spectrum with a finite outer scale. Amplitude scintillation effects are neglected. The Taylor hypothesis is assumed to model the temporal behavior of the turbulence using either a fixed or random wind profile. The resulting formulas are weighted integrals of the refractive index structure constant C$- n$/$+2$/(z), where the weighting functions are power series in from one to six indices depending on the beacons used and the choices made regarding the atmospheric turbulence spectrum and the direction of the wind. !21