Expected gain in the pyramid wavefront sensor with limited Strehl ratio

Abstract

Context. One of the main properties of the pyramid wavefront sensor is that, once the loop is closed, and as the reference star image shrinks on the pyramid pin, the wavefront estimation signal-to-noise ratio can considerably improve. This has been shown to translate into a gain in limiting magnitude when compared with the Shack-Hartmann wavefront sensor, in which the sampling on the wavefront is performed before the light is split into four quadrants, which does not allow the quality of the focused spot to increase. Since this property is strictly related to the size of the re-imaged spot on the pyramid pin, the better the wavefront correction, the higher the gain.Aims. The goal of this paper is to extend the descriptive and analytical computation of this gain that was given in a previous paper, to partial wavefront correction conditions, which are representative for most of the wide field correction adaptive optics systems.Methods. After focusing on the low Strehl ratio regime, we analyze the minimum spatial sampling required for the wavefront sensor correction to still experience a considerable gain in sensitivity between the pyramid and the Shack-Hartmann wavefront sensors.Results. We find that the gain can be described as a function of the sampling in terms of the Fried parameter.