  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.
