[fitswcs] Detector distortion correction representations in FITS

[Richard Hook]

Dear FITS WCS task force,

I am at present involved with discussions on future schemes for representing
the geometrical distortion of HST cameras and specifically the Advanced Camera
for Surveys (ACS) to be installed on HST during the next servicing mission.
ACS has very marked geometric distortion, much greater than than of WFPC2.

Up to now the HST community has handled geometric distortion using some form
of polynomial in two dimensions to correct the pixel positions onto a uniformly
spaced image - typically corresponding to a TAN projection of the sky. Such
polynomials normally are arranged so that the centre of the image retains
its scale and orientation. I think this is equivalent to a polynomial
representation of the "optional regularization" first stage in the diagram
on page 1 of Calabretta and Greisen's paper. To go from original
pixel position to sky coordinate one uses the following steps:

(x,y) -> (x-corr,y-corr)           To corrected pixel position, poly correction
(x-corr,y-corr) -> (xi,eta)        To tangent plane, using the CD matrix
(xi,eta) -> (alpha,dec)            To equatorial position on the sky

At present, for WFPC2, these polynomials are just stored either as an external
file or as hard-coded coefficients in some software or other. Neither is an
elegant solution but this approach does have its advantages - for example
one can treat the file as a "calibration reference file" and have different
ones for different times and circumstances. Such files can be maintained under
configuration control and are very suited to "on-the-fly" recalibration of
images at a later date when better information is available in a way not
easily possible if the information has to be immediately put into a header.

However, I feel that there are occasions when it will be desirable to put this
distortion correction polynomial coefficient set into the image header and
obviously one would want to do this in a manner compatible with FITS standards.
I expected that this would be easy but I see that there isn't an obvious way
of doing it except by transforming the polynomial (which is really a property
of the detector and is tied to the pixel grid and not to the sky, or at
least is typically handled that way at present) into part 
of a modified sky projection such as the TAN-poly one under discussion.

My question is - what do you think the best way to proceed is for this case?
To put the question in brief - how best should a polynomial form of the
pixel regularization image be represented in a FITS header?

I apologise if my question is naive or misguided.

Thanks for your time.
Richard Hook