The calibration process for an adaptive optics system using modal control computes the reconstructor matrix in terms of a matrix whose columns are the measurements from a wavefront sensor. Each column of wavefront sensor measurements corresponds to a mode that is applied to the mirror. Since the measured gradients are corrupted by errors, the accuracy of the computed reconstructor is degraded by large condition numbers of the gradient matrix. A common method used to limit the condition number of this matrix is to reject all higher order modes when the condition number reaches the maximum desired value. However, it is possible (even likely) that one or a few modes are responsible for much of the increase in the condition number. By rejecting only those modes, an increased number of modes could be controlled. Unfortunately, computing the condition number of the gradient matrix for all possible combinations of modes is prohibitive.
This paper uses a genetic optimization algorithm to increase the number of modes that are retained for control. The genetic algorithm maximizes the number of modes retained. A bound on the condition number of the gradient matrix is imposed. The paper applies this method to both the ALFA adaptive optics system on Calar Alto (with 37 subapertures), and a proposed CHEOPS adaptive optics system with 1652 subapertures.