[fitswcs] WCS with NAXIS=0

[Eric Greisen]

Perry Greenfield writes:
 > > 
 > > William Pence writes:
 > >  > Is the use of WCS keywords (like CRPIX1 and CRVAL1) now 
 > > allowed in image
 > >  > HDUs which have NAXIS = 0?  This question has to do with 
 > > whether our FITS
 > >  > verification program (fverify) should issue any warning or 
 > > error message if
 > >  > this occurs.
 > >  > 
 > > 
 > > That is what WCSAXES is all about.  See
 > >       http://www.aoc.nrao.edu/~egreisen
 > > for links to versions of Paper I and info about its volume and page
 > > numbers.
 > > 
 > Since I think I may have indirectly been the originator of this
 > question, I'll note that I could not find any text in Paper I
 > that excluded use of WCS keywords when NAXIS = 0. I did note
 > WCSAXES, but the same section also says (page 6 section 2.2):
 > 
 >   To provide a solution for this world-coordinate dimensionality
 >   problme that does not require the use fo degenerate axes, we
 >   reserve the keyword
 >  
 >      WCSAXES (integer-valued)  
 > 
 >   to specify the highest value of the index of any WCS keyword in
 >   the header (i.e. CRPIXi, PCi_j or CDi_j, CDELTi, CTYPEi, CRVALi,
 >   or CUNITi). The default value is the larger of NAXIS and the
 >   largest index of these keywords found in the FITS header...

      I do not see how this is ambiguous.  No WCS keyword may have an
index in excess of WCSAXES and its default in this case is the highest
value in the header.  This allows anything - which is why neither Mark
nor I liked WCSAXES in the first place.

      And my reply to Bill just now is one of style not legality.  Any
use of WCS that purports to be "modern" in the sense of Papers I, II,
and III and depends on defaults and fails to provide WCSAXES while
using axes > NAXIS is extremely unprofessional.

Eric

 >   There is debate within the community as to whether the official
 >   definition of FITS (Hanisch et al. 2001) prohibits the occurence
 >   of WCS-related keywords with indices greater than the value of 
 >   NAXIS. We make no claims one way or the other, but rather assert
 >   that in order to accommodate WCS specifications whose dimensionality
 >   exceeds NAXIS without the use of degenerate coordinate axes, such 
 >   use must be allowed. Consistent with Hanisch et al. (2001), however
 >   no NAXISj keywords may exist for j>NAXIS. ...

This is one of those awkward things that I wish we were not forced to
accept, but...
 > 
 > That seems to suggest that not even WCSAXES is necessary to use
 > WCS keywords when NAXIS=0, but if that isn't so, please clarify.
 > This relates to some HST internal convention that uses null
 > data sets when all the values are constant (the header has a keyword
 > to indicate what the constant value is, as well as the dimensions
 > of the array. Naturally the question is whether it is legal to 
 > retain the WCS keywords in this case. It does appear that it is
 > as they exist now, and certainly so if WCSAXES is added.
 > 

Eric