[fitswcs] Status of WCS negotiations

[Don Wells]

Don Wells writes:
 > .. I
 > expect that something like a TAN+three_term_radial+cubic_in_x/y would
 > be sufficient for worst cases.  The DSS projection (or equivalent)
 > will handle the Schmidt (ARC) case.  Such a decision would eliminate
 > the requirement for a general-purpose perturbation function. ..

Doug Mink writes:
 > ..I think that the DSS projection, other than--perhaps--its choice of
 > keywords, is a fine representation of what optical astrometrists want
 > in a projection.  My plate projection is mostly a simplification of
 > the DSS projection, leaving out the image to plate terms..

Until I read Mark's fine description of his DSS projection
implementation, which he posted to 'fitswcs' on 07-17 as about 45_KB
of Postscript, I had not realized that the underlying projective
geometry of the DSS is what we call 'TAN' (gnomonic); I assumed it
must be what we call 'ARC', the natural geometry of cameras like the
Palomar Schmidt.  The DSS projection appears to me to be a
TAN+two_term_radial+cubic_in_x/y, almost identical to what I had
previously concluded (see above) would probably be sufficient for
everything.  I therefore find that I am now in agreement with Doug's
statement above---a DSS-like projection would be sufficient.

The terms like $a_{12}X(x^2+Y^2)$ and $b_{13}Y(X^2+Y^2)^2$ in
equations (3) and (4) of Mark's document appear to me to implement a
two-term radial correction function. In fact, this will probably be
sufficient---I specified 'three-term' above in order to add one more
term to the two-term radial solutions that I used in the 70s. DSS is
able to do the Schmidt case because the two radial terms are able to
express the difference between the ARC and TAN projections.  The set
of terms in DSS includes all of those in Eq.1a/b on p.174 of Holtzman
etal, PASP, 107, 156 (1995), so we know that the DSS functions would
also be sufficient for WFPC2, which is definitely one of the harder
cases.

I suggest that we consider modifying the TAN projection to include the
polynomial PROJPn terms as used in the DSS implementation in order to
obtain a universal WCS interchange notation for all of optical astronomy.

-Don
-- 
  Donald C. Wells         Associate Scientist         dwells at nrao.edu
		    http://www.cv.nrao.edu/~dwells
  National Radio Astronomy Observatory                +1-804-296-0277
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