We obtained images of the full moon from Sydney with the Canon
35 mm camera, reaching out to about 15 degrees from the moon
-- three times further out than the King profile reaches. We are
curious about how far out it goes as a power law.
The plot shows the profile done for a range of exposure
times, getting longer and longer, at the cost of overexposing the
moon and halo around it, but better sampling the faint halo
I have shown the raw data merging into the background sky in the
bottom panels. Subtracting this sky gives the halo only profile in
the middle panel for the range of exposures.
Top panel shows the overall profile by using only the valid (not
overexposed) parts of each curve -- by simply accounting for the
different exposure times -- nothing more has been done. They
sit on a pretty well defined locus all the way from the edge of the
moon out to the edge of the frame (~15 degrees out) and follow
roughly r^-1.8. It's probably flatter than this closer in. This is of
course the scattered light, not the PSF per se, but very far from the
moon -- like > a few degrees -- the moon is essentially a point source
anyway (it's only 30 pixels across on a chip 3900 pixels wide).
I learned something important! The profile is r^-1.8 when sky subtracted!
We can follow it well beyond the point that the halo is much fainter than
the sky. So King I think is talking about the sky subtracted profile as well.
I have been wondering when the King profile would actually join
the sky and become a DC component... of course it doesn't, that's
the point. The DC component, i.e. Rayleigh scattering (?) is caused
by the bright source as well, but is not considered part of the profile.
I guess. So if we were trying to model the scattering over very large angles
we'd have to consider both components. My guess is that for our
ES telescope the field of view is so small that the scattered light is
the halo only -- the Rayleigh component is negligible. One starts
to see it in the 35mm camera data at about 1000 pixels (1 pix
is approx 1 minute in these data) so about 10 degrees to 15
degrees from the moon (lower panel shows a blue curve which
essentially joins the bias level at large r, whereas the green and
black curves are flattening out to a level which is bias + a fair
bit of sky). In these data, the sky is about 5*2.5 = 7.5 magnitudes
below the full moon surface brightness (seen in upper panel, with
brightness of the moon at log(r)=0 and the (subtracted) sky having
similar brightness as the halo at about log(r)=3 -- beyond which one
traces the halo below the sky).