Subject: Spherical coordinates in FITS

From: egreisen at primate.CV.NRAO.EDU (Eric Greisen)
Date: Tue, 26 Jan 93 10:49:30 EST

At the request of Don Wells and others, I have been working with
Mark Calabretta (Australia Telescope) on a relatively definitive
discussion of celestial coordinates in FITS.  I began by converting
my old AIPS Memos No. 27 and 46 into modern postscript files.  I
did not release these to the FITS community since I expected that
any new agreement might have some differences with them - and the
draft document does have some semi-serious differences as well as
a rather better understanding of the whole subject.  That draft
is nearly ready for comment and will be announced in this forum,
along with the old AIPS Memos dressed up in modern postscript.

During the course of this work I was also made aware of the text
in Chapter 4 of the NOST FITS Reference Guide which directly
reflects a draft of the Hanisch/Wells paper on "World Coordinate
Systems" of which I had not been aware.  That draft contains a
set of formulae for determining the new CDi_j matrix from the old
CDELTn and CROTAn.  Unfortunately, those formulae - specifically
the cross terms - are wrong.  The correct formulae are

  CDi_i = Di cos(rho)
  CDj_j = Dj cos(rho)
  CDi_j = -Dj sin(rho)
  CDj_i = Di sin(rho)

where i < j refers to the first of either longitude or latitude,
j refers to the other, Dn = CDELTn, and rho = CROTAm where m is
the latitude-like axis.

Eric W. Greisen, Scientist
National Radio Astronomy Observatory
Charlottesville, VA