Integral evaluation of the modal phase coefficients in curvature sensing: Albrecht’s cubatures

Abstract

The modal coefficients describing a given wave front as a linear combination of a set of orthogonal functions can be determined independently of each other by a suitable integration of the signal provided by a curvature sensor. This fact allows us to avoid the use of matrix inversion routines and overcomes some problems related to the modeling error arising in conventional modal fits. Several procedures for evaluating these integrals from a discrete set of intensity measurements are compared. The results show that, for a given number of sampling points, the combination of an Albrecht’s cubature in the inner pupil region with a composite trapezoidal integration of the edge signal can give more accurate results with smaller noise propagators than other methods also analyzed.