Implementation and benchmarking of a crosstalk-free method for wavefront Zernike coefficients reconstruction using Shack-Hartmann sensor data

TL;DR

This paper implements and compares a crosstalk-free wavefront Zernike coefficients reconstruction method using Shack-Hartmann sensor data against the conventional least-squares approach, demonstrating improved accuracy in wavefront characterization.

Contribution

The paper provides an implementation of a crosstalk-free analytic estimator for Zernike coefficients and benchmarks it against traditional methods using Shack-Hartmann data.

Findings

Crosstalk-free method reduces reconstruction errors

Implementation shows improved accuracy over least-squares approach

Benchmarking validates the effectiveness of the analytic estimator

Abstract

In wavefront characterization, often the combination of a Shack-Hartmann sensor and a reconstruction method utilizing the Cartesian derivatives of Zernike circle polynomials (the least-squares method, to be called here Method A) is used, which is known to introduce crosstalk. In \citep{janssen2014zernike} a crosstalk-free analytic expression of the LMS estimator of the wavefront Zernike coefficients is given in terms of wavefront partial derivatives (leading to what we call Method B). Here, we show an implementation of this analytic result where the derivative data are obtained using the Shack-Hartmann sensor and compare it with the conventional least-squares method.