I am just a little confused about Tim's discussion of Andrew's thesis.
I don't understand how to do step (1) without knowing the colors for all
the stars and including a term in projected tan(ZD). We routinely
remove differential color refraction at the sub-milliarcsecond level
by the following brain dead prescription.
0) Since many of my colleagues never had Scopes-For-Dopes, I feel the
need to remind them of the historically accepted terminology. There
is something called the Astronomical Triangle, and it is defined
by the Pole, Zenith, and Star. The angles are Hour Angle, Azimuth,
and Parallactic Angle, and the sides are Zenith Distance,
90-Declination, and 90-Latitude. Note that the "Parallactic Angle"
is not the same as the stellar parallax, the parallax factor, etc.
1) What we really want is the differential displacement of images as
a function of the circumstances of the observation. In the bad old
days, we actually wasted a good night and took data on a few fields
as they rose and set. At our accuracy, this sets the proper motion
and parallax to zero, and lets us model the apparent motion as
the action of the atmosphere alone. On the basis of doing this
for many stars, we found that there is a pretty good relationship
between DCR and V-R color, and we now use this relationship.
2) To a decent accuracy, the refraction in a given band is some number
times tan(ZD). When you observe the star away from the meridian,
you get displacements like
delta_RA = Number*tan(ZD)*sin(PA)
delta_Dec = Number*tan(ZD)*cos(PA)
So in our least squares fit for the apparent place of a star based
on an ensemble observations, we include
ra_i = ra_0 + A*epoch + B*ra_parallax_factor + C*tan(ZD)*sin(PA)
dec_i = dec_0 + a*epoch + b*dec_parallax_factor + c*tan(ZD)*cos(PA)
True, b should equal B and c should equal C, and I have a long standing
argument with Lupton about the proper way to do this solution. At
least in my dumb view of doing separate solutions in (X,Y) which are
aligned with (RA,Dec), we can compare (B,b) and (C,c) as a sanity
check that both solutions are fitting the same signal. One loses this
test by doing a single solution for (RA,Dec).
Also note that in the differential case, one need not correct positions
to the zenith. It is sufficient to put them back on the meridian
(assuming that there is a single LSST), which effectively lets you
ignore Number*tan(ZD_0).
So going back to Andrew's algorithm, I don't see how you can align the
red and blue template images without doing some sort of color based
correction if the data were not taken exactly on the meridian. I suppose
that if one just ignores this effect that you get a mean mapping for stars
of mean color, and this may be good enough for frame subtraction wherein
the astrometric tolerance is something like 0.1 pixel (from what I can
understand of the various explanations I have been given).
Given the SDSS experience, one ought to be able to do a bit better than
assuming a black body given alphabet soup photometry. Sure, QSOs and
other curious spectra will never behave properly. In the fullness of
time, the revisits should give us enough samples to allow least squares
to separate parallax, proper motion, and refraction. All of this just
reinforces the epiphany I had in later life (several years ago) that
you can't do good astrometry without good photometry, and vice versa.
This also reinforces my jaundiced opinion that the image subtractors
can do whatever they want so long as the astrometrists can get their
fingers on the raw images. My brain shuts down during the discussions
of the precise image shapes in the added/subtracted images.
-Dave Monet is [EMAIL PROTECTED]
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