[fitswcs] Detector distortion correction representations in FITS

[Mark Calabretta]

On Tue 2000/01/18 10:20:08 CDT, Richard Hook wrote
in a message to: fitswcs at NRAO.EDU
and copied to: hook at stsci.edu, sparks at stsci.edu, clampin at stsci.edu,
     koekemoer at stsci.edu, rfosbury at eso.org, apasqual at eso.org

>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?

Firstly, there have been some changes to the text of CCS Section 4.1.2
in a non-public version dated 2000/01/14 which you can obtain from the
following unpublished URL:

   http://www.atnf.csiro.au/~mcalabre/ccs_latest.ps

The changes are mainly to provide more explanatatory material but note
the second last paragraph; it effectively suggests that you invert the
order of the polynomial and matrix corrections - the six-constant plate
solution comes first with the residuals mopped up by the polynomial.

However, if you do have to do the fit in the reverse order, i.e.
polynomial followed by matrix, then given the caveats of Paper I, I would
advise against using the pixel regularization correction and instead
suggest that you use TAN+poly with the CD matrix set to unity and combine
your matrix and polynomial corrections.  Specifically, you have

   (i,j)    -> (I,J)           To corrected pixel position, poly correction
   (I,J)    -> (xi,eta)        To tangent plane, using the CD matrix
   (xi,eta) -> (alpha,dec)     To equatorial position on the sky

So you have some polynomial

   I = Sigma c_mn * i^m * j^n
   J = Sigma d_mn * i^m * j^n

and some matrix

   xi  = M11*I + M12*J
   eta = M21*I + M22*J

Thus the coefficients of TAN+poly (CCS Eqs. 25 & 26) are given by

   a_mn = M11*c_mn + M12*d_mn
   b_mn = M21*c_mn + M22*d_mn

So this is quite a straightforward translation.

The question which really interests me is whether we have allowed enough
terms in the polynomial itself for you to do this.


Regards,
Mark Calabretta