It turns out that using the full wavefront norm as the cost function works pretty well with a limited number of control modes. Previously, if only the first m modes were used, I was projecting the slope vector S onto the modes giving the cost function J=U(:,1:m)\S, where U is the modal poke matrix. Apparently this representation fails to capture enough detail in the cost function perturbations to really achieve good convergence.
As a result convergence is pretty good when using a limited number of modes for control, especially when enough perturbations are generated per iteration to allow a least-squares approximation of the gradient.
Once I get a faster WFS this algorithm should be golden. First though I have a host of tests to run to characterize the DM in more detail. Is the response really linear wrt the square of the voltage commands? Does superposition really hold? Should I use the given influence functions in estimating the poke matrix? We shall see.
Next I'm going to try constructing a cost function using image data instead. Again, this is something that's been done in papers so it should be possible here. The first step is to find a function (eg peak intensity, intensity variance, etc) that has a positive correlation with the WF norm that I'm using now.
Only one more 236 lecture left in the semester. How will I get by without my biweekly dose of olfactory stimulus? I might have to start huffing some mouldering cheese as a replacement.
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