Analysis of the signal-to-noise ratio in the optical differentiation wavefront sensor

High resolution wavefront sensors are devices with a great practical interest since they are becoming a key part in an increasing number of applications like extreme Adaptive Optics. We describe the optical differentiation wavefront sensor, consisting of an amplitude mask placed at the intermediate focal plane of a 4-f setup. This sensor offers the advantages of high resolution and adjustable dynamic range. Furthermore, it can work with polychromatic light sources. In this paper we show that, even in adverse low-light-level conditions, its SNR compares quite well to that corresponding to the Hartmann-Shack sensor.