The majority of the past week has been dedicated to debugging; it looks
like cross-scanned simulations finally work.
The plot below is a derivation of the spatial transfer function for a
number of different intrinsic sky power-law power spectra.
Justifying the above plot is essential.
First, the very steep power-laws [-3 in the example below] show a
recovery fraction >1. This is simply because their S/N was inadequate -
the output power spectrum is nearly flat, but at a level higher than the
sky.
Second, the most plausible power-laws [-1.5 in the example below] show
pretty good recovery (90-95% over the relevant range):
There are some "white" power losses, particularly in the flatter
power-spectra. My best guess is that this has something to do with the
relative scales being offset from a mean of 1, but so far all tests to
show that that is the cause have in fact shown no problems at all. What
else could cause a scale-independent power loss?
Also, the flat power spectrum (and inverted) aren't quite flat because I
impose a "galactic scale height" on them. Should I stop doing that?