The Algorithm for Recognizing Superposition of Wave Aberrations from Focal Pattern Based on Partial Sums

In this paper, we investigate the possibility of recognizing a superposition of wave aberrations from a focal pattern based on a matrix of partial sums. Due to the peculiarities of the focal pattern, some types of the considered superpositions are recognized ambiguously from the intensity pattern in the focal plane by standard error-reduction algorithms. It is numerically shown that when recognizing superpositions of Zernike functions from the intensity pattern in the focal plane, the use of step-by-step optimization in combination with the Levenberg–Marquardt algorithm yields good results only with an initial approximation close to the solution. In some cases, the root mean square reaches 0.3, which is unacceptable for precise detection in optical systems that require prompt correction of aberrations in real time. Therefore, to overcome this drawback, an algorithm was developed that considers partial sums, which made it possible to increase the convergence range and achieve unambiguous recognition results for aberrations (root mean square does not exceed 10⁻⁸) described by superpositions of Zernike functions up to <i>n</i> = 5.

Abstract licence: CC BY

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.