Our completeness works by adding stars, with the correct
into each CCD image.
This ensures overlap regions (where stars have twice the exposure time
or more) are correctly allowed for.
We also add the stars in with the correct luminosity function for the
PMS we're interested in.
This allows for magnitude creep (the way more faint stars creep up
your PMS than bright stars creep down, as the latter's errors are smaller).
These stars are scaled copies of nearby brighter stars, hence the
name of the technique, ghosting.
This ensures our test stars are independent of any assumptions we have
made about the PSF.
The resulting completeness functions (shown as circles joined by a
line in the left hand figure) have a vary sharp cutoff.
This allows us to draw conclusions which are independent of our
completeness correction, except for one bin which includes the last
We've tested the derived completeness function against deeper
exposures of the same field, and the two match. (The measured
completeness is shown as bars with stars.)