Optimal arrangement of actuators for square mirrors with free edges

Abstract

It has been shown that the problem of optimal actuator placement for adaptive square mirrors can be reduced to the analytical solution using elements of the theory of unbiased designs for the natural vibrations of a square plate with free edges. A stochastic model for the wavefront has been developed using regression analysis. Formulas are given for calculating the bias in working-out the desired optical surface geometry of an adaptive mirror.