[fitsbits] Question about CROTA

[Mark Calabretta]

On Wed 2005/10/26 18:47:17 -0400, William Thompson wrote
in a message to: FITSBITS <fitsbits at donar.cv.nrao.edu>

>We've always been in the habit of putting CROTAi keywords in for both spatial 
>coordinate axes, with exactly the same value for each.  That seems the most 
>reasonable interpretation of the original FITS documentation.

The original FITS paper simply says "The rotation parameters CROTAn
describe a coordinate system which is rotated with respect to the normal
(specified) coordinate system.  Users of this option should provide
extensive explanatory comments".

AIPS wrote FITS files with CROTAn attached to the latitude axis and
documented this usage in its memos and programming manuals.  It was an
informal usage, but the only one we know of and widely used in other
astronomical software packages (if you know of any other usage then
we would be extreeeemly interested to know).  This is fortunate because
if there had been two or more conflicting usages then interpretative
software would have been confronted with the problem of disambiguation.

Not withstanding that, if you want to write CROTAn with the old WCS
keywords, then according to the original spec you can do whatever you
like except that you "should provide extensive explanatory comments".
Realistically though, we believe that all software will interpret any
CROTAn according to the AIPS convention since that's the only one they
are likely to have been programmed for.

In fact, two CDELTn and two CROTAn, one on each axis, would have been
enough to construct a completely general 2 x 2 linear transformation
matrix; the CROTAn could even have been given a sensible geometric
interpretation.  However, that only works for 2-D images and was never
done, at least as far as we know.  But you never know, and how would
you know?

Thus the new WCS standard deprecates CROTAn because it has no formally
defined interpretation.  Writing it with the new WCS keywords/values,
whether on one axis or two, violates the spirit, if not always the
letter, of the standard.

Mark Calabretta
ATNF