[fitswcs] Long-slit spectroscopy WCS

[Frank Valdes]

Hi Malcolm,

The responses have shown that the position angle of a slit or aperture
in a dispersed spectrograph can appear either in the pixel to intermediate
coordinate transformation (the CD step) or in the celestial projection.
Note that it could also occur in the DCF distortion transformation but
that would definitely be inobvious and not desirable in my opinion.

I think the celestial projection is a very interesting approach that
had not occured to me.  This could address various situations that
occur with cameras and spectrographs that can be rotated on the
telescope.  In cases where all the distortions occur between the
detector and the instrument rotator one could have a standard WCS and
then apply the final rotation to the sky with a single position angle
keyword.  Note that this would place a requirement on the tangent point
to correspond to the rotation axis.  I would be happier if there was
another celestial projection parameter that maps more directly to the
user's or instrument system's knowledge of position angle than LONGPOL
which I think is inobvious.

I'm a little concerned that the examples are again misleading because
of the assumption that there is no tilt in the path of the spectrum
through the image.  For a coarse WCS provided at the telescope where
the setup gets as close as possible this may be true but at higher
accuracy it will not be.  Of course there will be a curvature also which
will require use of the DCF transformation.  But if we just consider
a tilt of the spectrum then the simplest examples using just two
CD terms is not quite so simple.  In this case there is a rotation
between the spatial and spectral axes.

So maybe the proper conceptual model for long slit spectra is to start
by thinking of the coordinates as one spectral and one spatial.  This
is really what is taking place in a dispersed spectrum.  The spatial
axis is then degrees from the tangent point.

w = CD1_1 (x - CRPIX1) + CD1_2 (y - CRPIX2)
s1 = CD2_1 (x - CRPIX1) + CD2_2 (y - CRPIX2)
s2 = 0

The WCS is still 3D but in effect we set CRPIX3=1, CDj_3=0 and CD3_i=0.

Then the remaining submatrix is clearly a rotation to bring the w
axis to the best intermediate coordinates in angstroms or other units
and the s axis to degrees.  One then applies any DCF to eliminate
curvature, etc.

For the final projection of (s1,s2) to (RA,DEC) one uses whatever
keyword defines a rotation from the instrument system to the celestial
system.

The advantage of this approach is that one can setup the instrument
WCS, including tilts and distortions, and then, if the observations are
done by rotating the spectrograph for each object to align the slit as
needed, either for the source or for the paralactic angle, one would
just adjust one parameter in the celestial projection function.  I had
not had this in mind before but it makes good sense to me.  What do
people think?  The only change I might advocate is some keyword like
CPA that would work in addition to LONGPOL to define the mapping from
some arbitrary instrument/detector orientation to a standard celestial
system.

Frank