I was thinking a little more about the way we are training the network for the current topology - because the network has no recurrent layers, I guess it has no memory of past samples, and so it doesn't have any sense of the temporal axis. In fact, Keras by default shuffles the training data you give it randomly so the time ordering is lost. So the training amounts to requiring the network to identify the center of the Gaussian beam and output that. So in the training dataset, all we need is good (spatial) coverage of the area in which the spot is most likely to move? Or is the idea to develop some tools to generate video with spot motion close to that on the ETM in lock, so that we can use it with a network topology that has memory?
This looks like good progress. Instead of fixed sines or random noise, you should generate now a time series for the motion which is random noise but with a power spectrum similar to what we see for the ETM pitch motion in lock. You can use inverse FFT to get the time series from the open loop OL spectra (being careful about edge effects)