4.16.09

I finally got the wavefront reconstructor working by using a different geometry from the Southwell paper. This particular model averages the slope vector, rather than the phase, so there is only one zero singular value corresponding to a constant phase. Essentially, this method involves solving an equation Hp=Ds for the phase vector p. D is a matrix that averages the slopes in s, thus the least-norm solution in MATLAB is given by p = pinv(H)*D*s. However, calculating this pseudo inverse is still glacially slow, so we can make H full rank by requiring the phase to have zero mean, and then solve using QR factorization: p = H\(D*s). (Recall that if H is full rank there is a unique solution).

Because H and D can be constructed ahead of time, reconstruction is pretty quick: around 1 sec. for most slope vectors. Fast enough to be useful for visualization, but probably not for realistic control. There are a few test cases I came up with where solving the equations takes several minutes, but so far actual measurements seem to be ok.

Because everyone likes pretty pictures, here are the reconstructed residual phases (total minus the bias) when the first 15 DM modes are applied:


Pretty nice having a sensor with such high resolution. Remember that these are the actual measured phases, not merely the predicted DM shapes from the modal commands. These modes are actually the columns of the modal poke matrix, so its nice to know that the DM and sensor are actually capable of resolving such high frequency phase profiles.

Ahh what the hell here are the next 15 modes: