[fitswcs] Status of WCS negotiations

[Patrick Wallace]

Mark is going to be very surprised to read this, but the scales have
fallen from my eyes and I now agree with him.  I understand where the
confusion lies, and can see where in G+C some extra explanation is
needed in order to prevent others falling into the same trap I did.
In particular, Eq. 132 needs to be plucked from its present obscurity
and introduced much earlier in the paper;  it's not just about converting
old formats as its current location implies.

The seeds of the problem lie in the way CDELTn are defined in the
current NOST FITS definition, namely (i) in terms of a world coordinate
axis CTYPEn which is not necessarily aligned to the corresponding pixel
axis and (ii) without any separate information describing the geometry
of the "detector".  This is concise but (to me) hard to visualize.

In the case where the rotation angle CROTAn is non-zero and the pixel
axis is therefore not aligned with the specified world coordinate axis,
you nonetheless specify the scale as if the two axes *were* aligned.
Perhaps the FITS User's Guide could spell this out, as it can have
unexpected results.  For example, if you have a long-slit spectrum taken
with CROTA2=90 you end up specifying the spectral direction on the
detector in spatial units (mm of slit, say) per pixel, and the spatial
direction in spectral units (Angstroms, say) per pixel.

Combining the pixel aspect-ratio with the world-coordinate scaling makes
it harder to see what's going on, because the two are logically on opposite
sides of the rotation stage.  The first thing I feel I want to do to the
pixel coordinates is to scale them to make the pixel aspect ratio unity.
Then I want to rotate the grid through CROTA2, which leaves the pixels
square and lined up with the world coordinate axes.  Finally I want to
scale to physical units - mm along the slit and Angstroms for instance.
However, once you combine these two scaling step, you can no longer
employ a pure rotation...except in the special case where both world
coordinates are in the same units!

With sky coordinates, both axes are in degrees.  As a result, my final
mm-to-deg scaling step is equivalent to multiplication by a scalar, and
you can equally well do that first.  Thus Eq. 1 and 2 in G+C appear to
show unmistakeably that the order in pre-G+C days was (i) apply the
CDELTns, (ii) rotate.  This is the source of the confusion.  Only because
the physical units are the same for latitude and longitude is it possible
to carry out the transformation in this way.  If you tried to write the
mm/Angstrom example the same way, it wouldn't work.

A sentence or two of explanation at that point in the paper would help.
More importantly, after Eq. 3 it might be worth stressing that the writer
is *not* free to adopt any combination of CDELTn and PC matrix that happen
to deliver the correct result.  CDELTn *must* conform to the definition in
the FITS standard, and consequently *only one sort of PC matrix will do*.
In particular, if the transformation is expressible as a pure rotation
then the PC matrix *must* take on the form given in Eq. 132.

I would still, myself, prefer to separate the three steps:  pixels
to mm (say), rotate (and skew if required), mm to world units.  However,
I accept Mark's parsimony argument, except that I'd go all the way and
combine the CDELTn and PC into a CD matrix.  Multiple CD matrices would
accomplish a range of effects including different axis scalings and
different celestial frames, and at the same time sweep away all the
confusion.

Apologies for taking so long to grasp what was going on.


Patrick Wallace
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Starlink Project Manager                        Internet:  ptw at star.rl.ac.uk
Rutherford Appleton Laboratory                       Tel:    +44-1235-445372
Chilton, Didcot, Oxon OX11 0QX, UK                   Fax:    +44-1235-446667
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