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[TASS] how to deal with curvature in the focal plane of Mark IV
Tom and Ted have been discussing the distortion which occurs in
the Mark IV cameras -- or any wide angle camera -- as one attempts
to map a curved sky to a flat detector. As Tom guessed, this is
a "solved problem". One can go to any good book on spherical
trigonometry to find the solution (ugh), but let me suggest another
source of information. I found a nice paper in PASP by Olkin et al.,
(in the February 1996 issue), which discusses this very point.
You can find a copy of the paper at the ADS web site; go to
and search for author "Olkin", then scroll down until you see the
listing for 1996 PASP vol 108. On page 3 of that paper, there are
a set of equations which permit one to
1. pick a spot (point A) on the sky (some central RA and Dec)
2. for any other, nearby position in (RA, Dec) (point B),
calculate the distance from that central spot
in the focal plane at which point B will appear
And, in reverse,
3. given measured positions of objects on the flat focal plane,
4. and given some fiducial, central spot on the focal plane,
5. calculate the distance in (RA, Dec) between the objects and
the fiducial, central spot
In other words, the paper explains how to convert back and forth from
the curved sky to the flat focal plane.
One key point: the equations in this paper use "plate coordinates"
which have units of radians.