Direct demodulation of Hartmann-Shack patterns

Hartmann-Shack wave-front sensors produce a distorted grid of spots whose deviation from perfection is linear with the wave-front gradient. Usually, the centroid of each spot is calculated to provide that deviation, but it is also possible to perform the calculation by Fourier demodulation of the spot pattern [Opt. Commun. 215, 285, 2003]. We show that this demodulation can be performed directly on the grid, without reverting to Fourier transforms. Tracking the motion of each centroid individually is limited to well-defined spots with motions smaller than their pitch. In contrast, our method treats the image as a whole, is not limited to non-overlapping or sharp spots, and allows large spot motions. By replicating the array of spots slightly beyond the edge of the aperture, we reduce the chance for boundary phase dislocations in the reconstruction of the wave front. The method is especially suited to very large arrays.