WCS problems on Optical Telescopes.

[Peter Bunclark]

WCS on Optical Telescopes.

WCS failed to mature into a standard at ADASS'97, and it seemed to me
that despite optimism over the progress made, the consensus churned rather
than converged.

Since we're obviously not going to reach even a sub-optimal consensus in
the short term, I feel we should discuss some of the issues that came out
of discussion at ADASS.

1. the WCS draft proposal seems to consider all wavelengths except optical,
   or at least it is causing considerable difficulties applying it to optical
   imagery.

2. I was a little surprised to realize that at least a few people are expecting
   WCS to support high-accuracy astrometry, as opposed to arcsecond-type
   stuff for object id and map-presentation.  There isn't enough power
   in the suggested transformations to do that.

3. Probably the worst case of everything is the Schmidt plate.  To do
   `real' astrometry, for example to configure a fibre spectrograph, you
   must fit the distortions with a `rubber-mat' for example, which APM software
   does.  Polynomials won't do because there are bends and wobbles on one
   side of the plate that are often uncorrelated with those on the other side;
   you need an unacceptably high-order polynomial to follow that kind of stuff;
   splines would be better.
   Much Schmidt-telescope imagery is now taken on film.  You can get nearly
   as good results as glass, but your mapping function has to hack it.
   Our friends at ST tell us they have to use the correction matrix under
   the WCS proposal to do this kind of stuff;  but it is clearly quite
   inelegant to use a transformation which was designed to regularize the image
   at the 0.1 pixel level to adjust it by 1-2 arcsec (15mu sampling is
   approx 1 pix per arcsec) which should be done in the projection stage.

4. The PC matrix wants you to put 1's on the diagonal and zeros elsewhere.
   This is hard to arrange for a ccd, and furthermore most optical 
   instruments are mounted on rotators, and so can move to arbitrary angles
   from exposure to exposure;  hence the PC matrix will have to have
   arbitrary values in the real world.  Also, with long-slit spectroscopy
   one will want the spatial axis to be at an arbitrary PA.

5. There is an engineering issue with optical telescopes.  The geometry
   of the detectors can change on shortish timescales, eg when you
   incorporate bigger and better chips; however, the geometry of the
   detector can be measured, and hence represented parametrically, to
   extremely high accuracy.  On the other hand, the mapping of the focal 
   plane to celestial coordinates will stay fixed for the lifetime of
   the telescope which is usually many decades, but can be somewhat
   imprecise;  even worse is the zero-point if that is determined at the
   time of observation from the telescope encoders (of course it can
   be tweaked to higher accuracy offline).
	It would be illuminating to include a discussion of errors in the
   WCS document; ideally a solution could be found which separates out
   high-precision factors from those with observational error.
	The point of this is that I would like to separate the complete
   transformation of pixels to celestial coordinates into two stages:
   (1) transform pixels on the chip/plate to `engineering units', ie 
   Cartesian meters at the focal-plane.  You can imagine inscribing a
   pair of axes on the instrument mounting-plate to which these coordinates
   correspond.  For a synthesis map this step could have unit scaling. Then
   step (2) is to transform linear measure in the focal plane to celestial
   coordinates.
	I believe a side-effect is to satisfy many people's requirements 
   for multiple-WCS's in headers; for example, this would give the physical
   relationship between the members of a CCD mosaic to high accuracy, and
   would help greatly in stitching together mosaic images;  whereas the
   transformation to celestial coordinates, which contains higher-order
   errors, is common to all the chips in the mosaic.  When you do an
   instrument change, half the transformation remains valid, and the other
   well-defined section is specific to the alternate instrument.

6. I feel it would be more elegant to include a mapping which adds radial-
   distortion onto a classical tangent plane, even though arc+radial
   probably gives about the same result.

7. Can you imagine a WCS that describes the coordinates on an objective-
   prism plate?

Peter.