5.20.09

I gave up waiting for a reply about the SLM cables, so I went ahead and ordered what I think are the right ones. Hopefully they'll be here next week.

Until then I've gone back to testing out gradient descent methods on a more complicated model, and using the "Marishal approximation" of the strehl ratio. Because this equation is a log-concave function of the wavefront (spatial) variance, I should be able to apply any number of nonlinear, first-order optimization techniques as long as I can get an accurate estimate of the gradient. In contrast to my previous experiments with this, I've added a colored noise term that corrupts the wavefront with some bandwidth. The question is how can I obtain an accurate gradient estimate in the presence of such garbage? And how are those estimates corroded by increasing the bandwidth (and hence correlation) of the noisy input?

Another person in my lab is trying to work the same problem with an extended Kalman filter, which know nothing about. This perspective views the Strehl ratio approximation as a nonlinear observer of the system's state. There are some notes online from some Stanford course (EE236) that has a good explanation of the EKF, so I might have to read that over at some point.