[fitsbits] Comments on image distortion conventions

[Doug Mink]

Dick Shaw wrote:
> Regarding the proposed Simple Imaging Polynomial (SIP) convention for 
> representing non-linear image distortions:
> 
> 1. The document should specify default values for any coefficients that are 
> absent from the header, but might be expected based upon the value of A_ORDER 
> or B_ORDER. Presumably either the values would be taken to be zero or the 
> convention should require that all keywords be present. Similarly, are A_ORDER 
> and B_ORDER restricted to be non-negative?

This should all be included in the document.

> 2. It is unfortunate that the transformation goes directly from raw array 
> pixels to world coordinates, without defining an intermediate pixel coordinate 
> system. This approach carries some liabilities, one of which follows:
> 
> 3. The convention would appear to mis-use the CTYPEi reserved keyword in a way 
> that at least technically violates the FITS standard. Quoting from the 
> definition of this term in Sect. 8.2 of the FITS V3.0 Standard: "All 
> non-linear coordinate system names _must_ be expressed in "4-3" form: the 
> first four characters specify the coordinate type, the fifth character is a 
> hyphen, and the remaining three characters specify an algorithm code for 
> computing the world coordinate value...."

First I should say that my WCSTools package can read both SIP and TNX distortion
parameters.  The SIP implementation is based on code from IPAC and the TNX
implementation is based on my translation of IRAF SPP code into C.  The Harvard
DASCH plate digitization project is using TNX with great success for very wide
field plates taken with small telescopes (though they have found a few bugs in
my subroutines).

SIP's 4-3-3 usage is an artifact of a time in the development of the FITS WCS
distortion standard when the 3-character suffix was proposed as a standard.
I think that there is an advantage in following the plate solution tradition
of including distortion in the pixel <-> world coordinate transformation directly.
If the appropriate keywords are provided so that a reasonable WCS is obtained
using the standard keywords and the first 8 characters of the CTYPEi, there
shouldn't be too much of a problem.

TNX adds a melange of nested multi-line/multi-value keywords to FITS, but it works
and has been used for lots of images.  There is also a ZPX variation on ZPN, but
that seems not to have been used as often.

-Doug Mink