Modeling noise propagation in Fourier-filtering wavefront sensing, fundamental limits, and quantitative comparison

Abstract

Context. Adaptive optics (AO) is a technique allowing for ground-based telescopes’ angular resolution to be improved drastically. The wavefront sensor (WFS) is one of the key components of such systems, driving the fundamental performance limitations. Aims. In this paper, we focus on a specific class of WFS: the Fourier-filtering wavefront sensors (FFWFSs). This class is known for its extremely high sensitivity. However, a clear and comprehensive noise propagation model for any kind of FFWFS is lacking. Methods. Considering read-out noise and photon noise, we derived a simple and comprehensive model allowing us to understand how these noises propagate in the phase reconstruction in the linear framework. Results. This new noise propagation model works for any kind of FFWFS, and it allows one to revisit the fundamental sensitivity limit of these sensors. Furthermore, a new comparison between widely used FFWFSs is held. We focus on the two main FFWFS classes used: the Zernike WFS (ZWFS) and the pyramid WFS (PWFS), bringing new understanding of their behavior.