General formalism for Fourier based Wave Front Sensing

TL;DR

This paper presents a unified Fourier-based formalism for wave front sensors, generalizing existing sensors like PWFS and ZWFS by treating their parameters as free variables, and introduces new performance metrics.

Contribution

It introduces a general formalism that unifies and extends Fourier-based wave front sensors, allowing for flexible parameterization and analytical performance evaluation.

Findings

Unified formalism for Fourier-based wave front sensors.

Introduction of the meta-intensity for phase linearity analysis.

Definition of the SD factor for sensitivity and linearity trade-off.

Abstract

We introduce in this article a general formalism for Fourier based wave front sensing. To do so, we consider the filtering mask as a free parameter. Such an approach allows to unify sensors like the Pyramid Wave Front Sensor (PWFS) and the Zernike Wave Front Sensor (ZWFS). In particular, we take the opportunity to generalize this two sensors in terms of sensors' class where optical quantities as, for instance, the apex angle for the PWFS or the depth of the Zernike mask for the ZWFS become free parameters. In order to compare all the generated sensors of this two classes thanks to common performance criteria, we firstly define a general phase-linear quantity that we call meta-intensity. Analytical developments allow then to split the perfectly phase-linear behavior of a WFS from the non-linear contributions making robust and analytic definitions of the sensitivity and the linearity range possible. Moreover, we define a new quantity called the SD factor which characterizes the trade-off between these two antagonist quantities. These developments are generalized for modulation device and polychromatic light. A non-exhaustive study is finally led on the two classes allowing to retrieve the usual results and also make explicit the influence of the optical parameters introduced above.