Wavefront sensing by optical differentiation

There are two main ways to address the wavefront sensing problem with modal wavefront sensors. First, the slope approximation that estimates a series of local first derivatives of the wavefront, as in the Hartmann-Shack sensor. Secondly, the curvature approximation, that estimates a series of second derivatives of the wavefront in different areas, as in the curvature sensor. It has been demonstrated that optical differentiation can be used as a useful first derivative wavefront sensor. Here we present a complete review of this new sensor along with a novel procedure to estimate the curvature of the wavefront phase using optical differentiation. This sensor consists of a telescopic system located in one of the arms of an interferometer and a phase step in the other arm. A variable amplitude transmission mask is placed at the focal plane of the telescopic system to perform the second derivative of the incoming field. A detailed description of the set-up and the mask is presented. The main advantages of this sensor are high resolution and easily adjusting of the sampling of the wavefront so allowing its use in high resolution wavefront sensing.