Idea: Stack all of the finders from spectroscopic observations. Finder images tend to be on lower-quality CCDs with no filter, but they frequently produce very deep observations. For example, the open K-band finder on TripleSpec (though it's technically not a CCD).
In order to stack them, you would need to mask out the bad pixels (already done) and compute astrometic solutions for the CCD. Un-warping the images will take some work, but there should be plenty of information available from thousands of observations of different fields to make this computation nearly ideal. Similarly, it should be possible to calibrate different pixels on the imager based on response to 2MASS standards.
Applications? Very deep imaging of spectroscopic targets. Short- and long-term variability (typical finder cadence is ~a few seconds). Deep imaging around stars and galaxies of interest - probably far deeper than you could get with classical observing requests.
This project should be achievable by a motivated undergraduate, but I think the tools for astrometric solutions need to be in place first. Astrometry.net is a great tool for this, but I think operates on spatial scales that are too large. Once basic astrometric solutions are available (e.g., pointing center for the image), I think IRAF tools could be automated to compute the complete solution, which would then be applied to all images.
Calibration might end up being the most challenging component, since there is variable atmospheric emission (absorption) that is not filtered by the finder. Depending on the application, though, large calibration errors may be acceptable. i.e., for deep nebular observations, morphology will be more important than absolute brightness, since the line responsible for the brightness cannot be directly determined. Whereas, for variability, calibration is important, but it can be computed directly from other stars in the field.
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