On the nature of the measurements provided by a pyramid wave-front sensor

The Pyramid Wave-Front Sensor (PWS) [J. Mod. Opt., 43 (1996) 289] was first presented as a novel slope sensor which is similar to the well-known Shack-Hartmann Sensor (SHS), with the advantage of a better sensitivity in closed loop operation [Astron. Astrophys. 350 (1999) L23]. An ideal SHS measures the first derivative of an incident wavefront thus permitting the main properties of error propagation to be determined. In this paper, an easy-to-handle relationship between the PWS measurements and the wave-front phase is derived and the results are compared to an existing analytical model for the SHS [Proc. SPIE 3353 (1998) 1038]. This new model shows that the PWS inherits some properties of both slope and direct phase sensors. Comparison of results confirms the gain in limiting magnitude over the SHS and predicts a significantly lower sensitivity to aliasing and thus more contrast in corrected images. (C) 2004 Elsevier B.V. All right reserved.