[fitswcs] Polynomial Correction Function & Alternative-WCS

[Don Wells]

Dear Doug etal,

Yesterday I posted my draft memo to <fitswcs> for your comments.  It
appears to me that the polynomial functional form and keyword
conventions which I proposed are sufficient to replace the old idea of
an IMAGE extension containing a numerical map of the correction
function. My proposed polynomial notation is an improvement over prior
ideas of this type in several areas: (1) the ordering of the
coefficients removes any need for expressing order limits, (2) it is
an N-dimensional solution and (3) it is capable of completely
replacing the CRVALi and CDi_j keywords with polynomial coefficients
which have nearly mnemnonic forms. I expect that this polynomial form
will be sufficient for all optical problems. I hope that you will
agree with my expectation. 

I favor the addition of radial polynomial terms to the TAN
projection. It is true that the ARC-plus-polynomial projection which
is included in G&C/wcslib is mathematically equivalent to TAN+poly,
but the TAN+poly case is so common that we really should support it
explicitly. I expect that Greisen and Calabretta will have no trouble
implementing this.

My suggestion of a suffix and WCSNAME for alternate-WCS is a response
to the requirement of alternate-WCS capability which has been
expressed by many people. Please consider whether there will be any
problem with this idea.

I want you optical folks to consider the polynomial concept. If it is
sufficient for you, and you (collectively) are happy with it, then it
will be appropriate for Eric Greisen to review it to see if he
agrees. If he agrees, I expect that he will then incorporate some
version of this proposal in the first WCS paper (the meta rules) of
the proposed split of the G&C paper into two papers. I.e., the _same_
N-dimensional polynomial notation is going to apply to 1-D
spectroscopy, 2-D imaging and 3-D spectral-line cubes, and so the
rules for the polynomial must appear in the first paper. The second
paper will deal with the particular case of celestial
coordinates. Eric is reluctant to do the work of splitting the paper
and revising its content until he is assured that a sufficient
consensus exists.

Regards,
Don
-- 
  Donald C. Wells         Associate Scientist         dwells at nrao.edu
		    http://www.cv.nrao.edu/~dwells
  National Radio Astronomy Observatory                +1-804-296-0277
  520 Edgemont Road,   Charlottesville, Virginia       22903-2475 USA