General formalism for Fourier-based wave front sensing: application to the pyramid wave front sensors

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, and also some WFSs as the 3-faces pyramid WFS. First, we describe such a sensors class due to the optical parameters of the Fourier filtering mask and the modulation parameters. Second, we use a 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. Finally, we show the influence of the previous optical and modulation parameters on these performance criteria. This exhaustive study allows one to know how to optimize the sensor regarding performance specifications. We show in particular that the number of faces has influence on the size of the signal 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. (C) 2017 Society of Photo-Optical Instrumentation Engineers (SPIE)