In a spectrograph, many of the the raw calibration images are taken with something like arcs or flat-field lamps illuminating the slits or fibers, so that the spectral traces are lit up with calibration light. If the spectrograph flexes or changes, these traces move in two dimensions on the spectrograph image plane, or relative to the detector pixels. I am looking at whether we could have a generative model for these calibration images, so I spent the weekend toying with ways to represent the relevant kinds of small distortions of images. If the distortions are extremely small (as they are, say, for EXPRES) they can be represented with just a compact linear basis. But if they are a few pixels (as they appear to be for BOSS), I need a better representation.
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