I spent most of today talking with my advisor about the ability of the DM to reproduce the actuator modes. He seems suddenly interested in this even though identifying a modal poke matrix is something I've been doing for months. At least he admits his obsession with modes is "a sickness."
Yesterday there was some concern that, even though there are only 31 actuators and hence 31 degrees of freedom, somehow more than 31 modes were being produced through some nonlinearity. We looked at this problem by applying a few hundred random commands and computing Karhunen-Loeve modes for the resulting phases and/or slope data. It was hard to tell from the eigenvalues of those modes what exactly was going on, but it looked like there were far fewer than 31 principle components that had a significant contribution to the phases. Even though there were nonzero values past the 31st largest eigenvalue, there is definitely some funny business going on with the rounding, pixel error, and other nonlinear noise affects that could be contributing.
On the control front I'm trying to learn as much as I can about Youla parameterization. Of course, my idea of combining this with adaptive filtering algorithms is about 10 years too late. Still, its a relatively unused technique and there's still some potential for exploration there. Even if I don't end up rewriting the adaptive controller code our lab is currently using, I think its important to know what's going on under the hood.
We've been experiencing all four season in one week here. I need cold weather.