[fitswcs] Long-slit spectroscopy WCS

[Frank Valdes]

Hi Malcolm,

The basic orientation of the slit is determined by the CD matrix.
Ignoring the CRVALi terms that set the actual pointing on the sky and
are added at the end of the calculation,  the intermediate
coordinates are given by

w = CD1_1 (x - CRPIX1) + CD1_2 (y - CRPIX2) + CD1_3 (z - CRPIX3)
r = CD2_1 (x - CRPIX1) + CD2_2 (y - CRPIX2) + CD2_3 (z - CRPIX3)
d = CD3_1 (x - CRPIX1) + CD3_2 (y - CRPIX2) + CD3_3 (z - CRPIX3)

where w=wavelength, r=RA, and d=DEC.  In these intermediate coordinates
r and d are degrees from the the tangent point.  This is a 3D WCS but
the image is 2D.  So WCSAXES is set to 3 though NAXIS is 2.  Since the
missing axes supply a pixel coordinate of 1 this means that z=1.
Generally this means that you would chose CRPIX3=1 and the last terms
drop out.  So for the RA and DEC axes you have

r = CD2_1 (x - CRPIX1) + CD2_2 (y - CRPIX2)
d = CD3_1 (x - CRPIX1) + CD3_2 (y - CRPIX2)

If there is no tilt in the spectrum on the image relative to one of
the image axes, for example let x be the wavelength axis which is
exactly aligned, then the CDj_1 terms are set to zero to get

r = CD2_2 (y - CRPIX2)
d = CD3_2 (y - CRPIX2)

So as you move in y (say along a night sky line) you get a variation in
both RA and DEC in the coordinates.  So you use something like

CD2_2 = scale * cos (PA)
CD3_2 = scale * sin (PA)

Whether the RA or the DEC term is the cosine depends on the definition of
the position angle.

Yours,
Frank


PS  I did get your earlier question about the spectral WCS conventions
but other things have come up.  Certainly it would be good to include
more examples in paper III but right now we still need to settle on
paper I.  If I have time I should put more examples in my web document
but that is unlikely until we get nearer finishing the spectral WCS
paper.