Curvature sensing with a Shack-Hartmann sensor

Shack-Hartmann (SH) sensor, based on sampling of wavefront tilts in subapertures, is a simple, reliable, and widely used in adaptive optics wavefront sensor. A wavefront curvature sensor has the advantage of providing the results suitable for direct control of membrane and bimorph deformable mirrors [1], but requires linear registration of intensity in two planes. SH sensor modifications using astigmatic microlens array [2] and three SH sensors [3] provide measurement both in the form of wavefront gradients and Laplacian curvatures. In this work, we consider a simple arrangement that turns a standard SH sensor into a curvature sensor by moving the camera chip of the SH sensor into the optical plane conjugated to a deformable mirror. This establishes a direct geometric correspondence between the coordinates on the DM surface and the sensor chip. Then, change in the local centroid density corresponds to the Laplacian curvature of the mirror, and the phase at the boundary can be found from the centroid displacements along the edge of the pupil. We investigate the feasibility of this approach for direct control of membrane deformable mirror by measuring the dependence of the calculated centroid density on the control signal applied to the mirror actuators. The experimental results demonstrate a good linear dependence.