Comparison stars are used in differential photometry to correct the
target star for transparency variations - the brighter the comparison
star, the better the differential photometry. This form allows you to
calculate the probability of finding a comparison star of a given
R-band magnitude with ULTRACAM. The probability depends on the
galactic latitude of the star, with the all-sky average given by a
galactic latitude of approximately 30 degrees, and the search
radius. The latter depends on the size of the CCD chip or
window. ULTRACAM uses 1024x1024 E2V CCD47-20 detectors with a
platescale of 0.3 arcseconds/pixel on the WHT, 0.35 arcseconds/pixel
on the NTT and 0.15 arcseconds/pixel on the VLT, resulting in
maximum search radii of approximately 300, 360 and 150 arcseconds on
these three telescopes (as the target star can be put
at one end of the detector and the comparison star at the other).
The star counts used in this probability calculation have been taken from the Gemini techical note written by Doug Simons in August 1995: Longitudinally averaged R-band field star counts across the entire sky.