Error analysis of moment-based modal wavefront sensing

TL;DR

This paper analytically models the errors in moment-based wavefront sensing caused by pixelation and noise, demonstrating that accurate error prediction is possible from measured PSF data, validated through simulations.

Contribution

It provides an analytical description of wavefront sensing errors due to pixelation and noise, enabling better error estimation from measured PSFs.

Findings

Models accurately predict modal estimation errors.

Error components depend on PSF shape but can be estimated.

Numerical simulations confirm the model's validity.

Abstract

The shape of a focus-modulated point spread function (PSF) is used as a quick visual assessment tool of aberration modes in the PSF. Further analysis in terms of shape moments can permit quantifying the modal coefficients with an accuracy comparable to that of typical wavefront sensors. In this letter, the error of the moment-based wavefront sensing is analytically described in terms of the pixelation and photon/readout noise. All components highly depend on the (unknown) PSF shape, but can be estimated from the measured PSF sampled at a reasonable spatial resolution and photon count. Numerical simulations verified that the models consistently predicted the behavior of the modal estimation error of the moment-based wavefront sensing.