Wavefront reconstruction in adaptive optics systems using nonlinear multivariate splines

Abstract

This paper presents a new method for zonal wavefront reconstruction (WFR) with application to adaptive optics systems. This new method, indicated as Spline based ABerration REconstruction (SABRE), uses bivariate simplex B-spline basis functions to reconstruct the wavefront using local wavefront slope measurements. The SABRE enables WFR on nonrectangular and partly obscured sensor grids and is not subject to the waffle mode. The performance of SABRE is compared to that of the finite difference (FD) method in numerical experiments using data from a simulated Shack-Hartmann lenslet array. The results show that SABRE offers superior reconstruction accuracy and noise rejection capabilities compared to the FD method.

On distributed wavefront reconstruction for large-scale adaptive optics systems

“…In order to aid the reader in the understanding of the theory, preliminaries on the SABRE method will be provided in this section. The SABRE was first introduced in [5], to which we refer for a more in-depth coverage of the matter.…”

“…In [5] it is shown that on a single triangle, denoted t, the wavefront phase φ(x, y) is approximated with a SABRE model of degree d as follows:…”

“…Consequently, wavefront reconstruction with the SABRE essentially consists of estimating the values of the B-coefficients given a set of WFS measurements. It is shown in [5] that (2) leads to the following SABRE slope sensor model on a single triangle:…”

“…This new method is the Distributed Spline Based Aberration Reconstruction (D-SABRE ) method. The D-SABRE method is an extension of the recently introduced SABRE method which firstly used multivariate simplex B-splines to locally model wavefront aberrations on non-rectangular WFS arrays [5]. The D-SABRE is based on a decomposition of the global wavefront sensor domain into any number of triangular partitions, where each partition supports a local SABRE model which depends only on local WFS measurements.…”

Generalized orthogonal wavelet phase reconstruction

“…Rosensteiner has produced the cumulative reconstructor, which is a direct integration reconstructor [17]. More recently, de Visser has shown the SABRE algorithm using B-spline basis functions [18].…”