The controller only projects the wavefront onto the modes that are controlled, but since the modes aren't totally uncoupled irl, looking at these sequences don't tell the whole story. Instead, I projected the wavefront sequence onto ALL the modes and only looked at the the ones that are controlled. The difference is that there is some cross talk from the higher order modes that you don't see if you neglect them from the projection. For the plots here, the experiment used 25 control modes. The LTI predictor was estimated using 10000 frames with a prediction error around 0.38.
Anyway, one of the more useful plots is obviously the PSD's for each modal sequence. Clearly the classical controller is killing the low frequency/static disturbances but does shit for anything else as expected. The LTI controller does a decent job flattening the spectrum, with surprisingly little high frequency amplification like I was seeing before. My experience has been that this amplification shows up when the predictor model is crap, so I guess it was good enough this time. Plant modeling error should also contribute to that, so if the AO loop does even better I'll have an idea that the closed-loop plant isn't matching the theoretical version in the controller.
Next up is the modal sequence itself for a few of the modes. You can clearly see how the completely open-loop disturbances have zero mean (i.e. in Mode 1), a static error that's knocked out by the integrator. The LTI controller makes quick work of the remaining high-amplitude spikes. One thing I really have to do is estimate a noise floor that shows in the stead-state (with no disturbances) due to the WFS.
The temporal RMS for each mode is also instructive. This is key since sometimes the RMS improvement may not be so impressive even if the PSD's are white. Luckily the LTI improves the RMS for every mode, so I guess they're all fairly well formed on the DM. Note the the integrator sometimes does worse in certain modes, I guess those are being sacrificed for the sake of modes that contribute more to the noise power. i.e., modes with the largest RMS improvement should be the ones that have the highest open-loop value (ex. 6 and 9 compared to 8). Notice that after mode 25 there's almost no improvement as expected. But, there is some difference, indicating the influence of the controlled modes creeping in.
Finally, the time series of the spatial RMS. The top plot shows the spatial RMS from the modal sequence, i.e. the part of the wavefront in the range space of the DM. This is fine, but ultimately the Strehl ratio of the beam depends on the entire wavefront RMS, shown in the bottom plot. This was generated by reconstructing the phase directly from the slope vector instead of just projecting it onto the range of the poke matrix. Before, when few modes were used, I think there wasn't much improvement between the controllers in this plot, and subsequently that's why there was little improvement in the Strehl as measured by the target. Based on this guy, if the Marechall approximation is true I should see some significant improvement in the measured Strehl when I finally get the target camera set up again (hopefully tomorrow.
That's all for now. gjdm.
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