The clear take away from this is that the 9x11 array is essentially crap, and doesn't really provide much performance enhancement over the 18x22 case at the current camera frame rates. Also, it'd be nice to get more of the beam measured since there's clearly some peripheral detail that's missing. I've ordered some new lenses that should help do that...which means more alignment.
In the mean time, I'm still trying to do some kind of system ID using the experiment as a channel, but I'm running into some mysterious Simulink problems that haven't been sorted out yet. I think the idea is solid though; the basic idea is to generate a random command sequence by passing white noise through an FIR filter. The game is to identify the filter coefficients using only the data from the WFS and the original white noise sequence. This is essentially just a basic channel identification process, except the experiment is shoe horned in between. In a perfect world the WFS would be able to perfectly reconstruct the modal commands exiting from the FIR filter, thus identifying the filter coefficients is just a least-squares problem. However in this case the original modal commands are estimated from the WFS data (the estimate is itself a least-squares approximation based on the identified poke matrix). The question is how close will the FIR estimate be given the finite resolution of the WFS? How would changing the WFS resolution affect convergence if a LMS or RLS algorithm is used instead of just a batch process? Does this even make sense?
I was attempting to explain this to my advisor this afternoon but he instead thought I was trying to identify a FIR model for the DM itself, since it looks like there are some dynamics to it after all. This actually might not be a bad experiment to try either. The simplest case would involve identifying a moving average model for the DM, i.e. the current wavefront sequence would be some linear combination of current and past inputs (with a poke matrix stuck in between). If its true that the DM dynamics are negligible, then the MA model should only have order 1. On the other hand it probably doesn't make sense to try to identify a full ARMA model.
Experimentally, the problem with this is the frame rate of the camera. In the past catching the mirror dynamics required frame rates higher than what I'm using right now to read from the WFS, so I might have to use a pretty reduced measurement area to see anything interesting. This might not be a problem though, if I'm apply random commands to the entire mirror surface. I wouldn't even have to use the modes necessarily since I could do a multichannel identification based just on the number of lenslets used.
Anyway, tomorrow I leave for Wyoming on a family vacay, so I'll have 32 hours of driving over the next week to iron these issues out en cerebrum before getting to work in front of the keyboard.
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