At group meeting, Dun Wang showed his first results from his work on the GALEX photons. He showed some example data from a scan across the Galactic plane and back, performed by Schiminovich in the spacecraft's last days. The naively built image has a double point-spread function, because the satellite attitude file is not quite right. Wang then showed that on second (or even half-second) time scales, he can infer the pointing, either by cross-correlating images, or else correlating with known stars. So the satellite pointing could be very well calibrated with a data-driven model. That's awesome!
Also at group meeting, Vakili discussed taking his model of the point-spread function up to super-resolution (that is, modeling the PSF at a resolution higher than the imaging data with which we constrain it). The model is super-degenerate, so we are in the process of adding (willy nilly) lots of different regularizations. My "big idea" at the meeting was to model the PSF using only smooth functions, because we know (for very deep physical reasons) that the PSF cannot have features or structure below some fundamental angular scale (set by the diameter of the telescope aperture!).
OK, I was thinking at first of diffraction spikes, but I see your point now: no power can exist at angles smaller than lambda/D. The pupil acts as an angular frequency filter, and where its reflectivity is zero at a corresponding angular frequency is zero. But is the power at higher angular frequencies really precisely zero in a real optical system?
ReplyDeleteWhat about the fact that the telescope is never perfectly in focus over the whole field? Can scattered light get vignetted or underfill downstream optics in ways that produce higher frequency power? (and that can still be mathematically described as part of an extended PSF?)
I ask because I'm wondering if we could use your insight to constrain the regularization of our spectrograph "PSF". The situation in spectroscopy is a bit different because we introduce high frequency power in the image plane (the slit!), or else we use fibers that generate speckles. But of course, our spectrograph optics themselves are the issue, not the slit/fiber. We should be calculating the angular resolution of the spectrograph looking at the slit/fiber, given by the limiting optic, likely the initial collimator that the light strikes before heading to the grating.
I'm still worried about downstream optics somehow introducing high frequency power.
This comment is very relevant. No, the aperture is not a strict frequency filter! So there can be some information at higher frequencies (you could in principle make an aperture that is a pure low-pass filter!). As for spectroscopy, I have always wanted to think about the equivalent limits. There are, of course! lambda / D applies to all coherent optical systems...
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