[fitswcs] Detector distortion correction representations in FITS

[Richard Hook]

Dear Mark,

Thanks for the detailed and clear reply to my question of representing
non-linear distortions modelled in pixel-space in the non-linear options
of the new FITS world coordinate systems. It is roughly what
I thought you would say! What you suggest is of course perfectly possible 
and very simple for the cases I was discussing (HST cameras).  Having 
said that it does have some obvious disadvantages: Firstly one loses the 
orientation and scale information in the CD matrix which becomes rather 
redundant. Having the first-order solution held in the CD+CRPIX+CRVAL set
of 8 numbers (for a 2d image) has its attractions particularly in a world
where software may well take some time to catch up with the new standards.
Secondly one loses the fact that the pixel distortion coefficients may be 
pretty
constant for a given camera independently of the telescope pointing - I feel
it would be nice for them to be constant in the header as well. Finally (and 
I think this has been discussed by other contributors to the mailing list) 
you are forced to go with TAN+poly whereas separating the detector related
"poly" bit from the sky projection would allow poly+SIN and other possibly
useful combinations (although this is not relevant for HST cameras).

Very early in the life of this mailing list, Doug Mink listed very clearly
several ways in which a non-linear component could be added to a WCS
description (5th May 1998). I think that the proposal adopted one of these 
and I am here pointing out the merits of another of them (type 1).
 
I certainly don't think any of my arguments are strong enough to justify
modifying your proposal which is very impressive and the result of a great 
deal of work. I am probably taking a rather narrow optical imaging 
perspective. But I do think they are worth pointing out. I am sure everyone 
feels that this
proposal is "nearly there" and it would be great for everyone when it is
finally formally accepted and can be widely adopted.

Your final question - whether there are enough terms in the polynomial - may
be particularly important for the HST Advanced Camera for Surveys (ACS) which 
has very large distortion. There is a current, preliminary model of this
use a cubic polynomial but it is quite likely that something considerably
more complex may be needed for an adequate representation for high-quality
geometric distortion correct once the instrument flies, probably early next
year. Several of the ACS group are copied on this message so they may
comment.

Thanks again for your help.

Richard