4.13.10

On Friday I got back from my first academic "workshop" up in Monterey. To my surprise it was actually informative, both in terms of AO and in witnessing the unique social interactions that take place at these things. My advisor's assertion that some of the people there were "world class pricks" turned out to be a good assessment of character in some cases.

But that's for another day. For all the interesting stuff I heard there, there were only a few thoughts that materially affect my work at the moment. Even though its April, there's more snow in the forecast for the mountains, so this week is bound to be a short one. Here's what I've been focusing on:

Fourier transforms. One presenter at the workshop extolled the benefit of using Fourier modes to do predictive wavefront control. A common theme among the talks was this idea of frozen flow; basically modeling turbulence as a superposition of a finite number of static layers, each moving with an independent velocity. Under this model, decomposing the wavefront using the DFT is beneficial since shifting a Fourier mode with a certain velocity simply involves rotating the (complex valued) modal coefficient some number of degrees. For a given coefficient, each moving layer would impart a certain periodicity related to the layer's velocity. Thus one could identify the layers by looking at the PSD of each mode and looking for spikes corresponding to this periodic behavior....I think.

DM ARX model. I've been meaning to do this for a while, but its only now that I think I know how to compute MIMO ARX models using least-squares. Of course its close to the scalar version, but I wanted to work everything out to make sure. Because I'm anal about verifying every segment of code, its taken some time to get the actual m-file written up. I finished the MA part on Sunday, and just finished the full ARX code a few hours ago. I'll test it all tomorrow.

Return of the SLM. One of the other grad students at this workshop had a working experiment very similar to mine, but using SLM's as disturbance generators. My advisor was intrigued, especially since there seemed to be an easy way to use it in Matlab, and it now looks like we'll be ordering one of these puppies soon. What exactly I'll use it for I don't know, but maybe I can put it to work mitigating the static bias.