Point spread function for an adaptive telescope with a Hartmann-Shack wave front sensor

Abstract

In this paper we calculate numerically PSF of adaptive telescope implementing the program which simulates its basic components such as the wave front sensor (of the type of Hartmann sensor) and segmented corrector representing the matrix of the square shaped elements. Distribution of the intensity over the focal plane of each subaperture was calculated in the par-axial vproximation and thus the diffraction and aberration of wave front were allowed for. The photon noise was simulated with the help of procedure generating the sequence of random numbers distributed according to the Poisson law. Then the program calculated the displacements of the center of gravity of the intensity distribution over the focus of each subaperture relative to the diffraction position and determined the tilts and pistons for each corrector's element. The reconstruction algorithm is based on a modal representation of the wave front distortions and uses the least squares method1-2 for estimating for coefficients at the aberration polynomials. For each element of corrector the tilts and piston were determined from the condition of minimizing the residual distortions of wave front by the least-squares method.