General formalism for Fourier based Wave Front Sensing: application to the Pyramid wave front sensors

TL;DR

This paper presents a unified formalism for Fourier-based Wave Front Sensors, analyzing how optical and modulation parameters influence performance, and providing guidelines for optimizing sensor design for various specifications.

Contribution

It introduces a comprehensive formalism for analyzing pyramidal wave front sensors and explores how different parameters affect their performance, aiding in sensor optimization.

Findings

Number of faces affects pixel requirements but not sensitivity or linearity.

Modulation radius and apex angle significantly influence performance criteria.

Adjusting modulation cycle time balances sensitivity and linearity.

Abstract

In this article, we compare a set of Wave Front Sensors (WFS) based on Fourier filtering technique. In particular, this study explores the "class of pyramidal WFS" defined as the 4 faces pyramid WFS, all its recent variations (6, 8 faces, the flattened PWFS, etc.) and also some new WFSs as the flattened cone WFS or the 3 faces pyramid WFS. In the first part, we describe such a sensors class thanks to the optical parameters of the Fourier filtering mask and the modulation parameters. In the second part, we use the unified formalism to create a set of performance criteria: size of the signal on the detector, efficiency of incoming flux, sensitivity, linear range and chromaticity. In the third part, we show the influence of the previous optical and modulation parameters on these performance criteria. This exhaustive study allows to know how to optimize the sensor regarding to performance specifications. We show in particular that the number of faces has influence on the number of pixels required to do the wave front sensing but no influence on the sensitivity and linearity range. To modify these criteria, we show that the modulation radius and the apex angle are much more relevant. Moreover we observe that the time spent on edges or faces during a modulation cycle allows to adjust the trade-off between sensitivity and linearity range.