WCS questions

[Stephen Walton]

It is time for me to chime in again, now that finals are over.  Thanks to
William Thompson and Mark Calabretta for discussions that clarified many
of the issues in my absence.  I've trimmed the quotes quite a bit, I hope
enough to provide context without misquoting anyone.

In article <58niqk$2uh at post.gsfc.nasa.gov>,
William Thompson <thompson at orpheus.nascom.nasa.gov> wrote:
>Mark Calabretta <mcalabre at atnf.csiro.au> writes:
>
>>On Tue 1996/12/10 22:45:08 GMT, William Thompson wrote
>>in a message to: fitsbits at fits.cv.nrao.edu
>
>Right, which is why it is incorrect to force solar data to be expressed in a
>spherical coordinate system.

My original goal was to explore a format for the header in which the
linear part would translate to normalized distance from solar disk center
along the north and west axes, and the non-linear part would allow one to
take the additional step to solar longitude and latitude for features on
the disk. In one of Mark's earlier posts, he pointed out that the PC
matrix could define the former and the CDELT, CRVAL, and CTYPE values the
latter.  This sounds good to me.  Mark also points out that the AZP
projection is the appropriate one to describe the sun, though the negative
value for "mu" (defined as the number of radii from the surface of the
sphere to the viewer) for a sphere seen from the outside is an important
clarification which is not at all obvious from the WCS draft, at least not
to me.

>>>Another way to express the data would be in units of physical distance, rather
>>>than in arcseconds.
>
>>How do you interpret this "distance" if you don't know the angle between the
>>corresponding position vector and the plane of projection?
>
>Obviously, it is a projected distance rather than a true distance from the
>center of the sun.  That's immaterial.

I think distances in kilometers is an interesting alternative.  It gets
around the fact that the size of the solar limb depends on the wavelength
of observation, and would only depend on the observer's distance to the
Sun, which is known very accurately.  The CDELT values would then be equal
to (x degrees/solar radius), where x is the angle between the observer's
tangent to the solar limb and the line from the solar disk center to the
same point.  

>You are absolutely correct that additional information is needed.
>Specifically, one needs the solar B angle, which is the tilt of the solar
>rotational axis out of the projected plane.

But if I read the WCS spec correctly, the values of CRVAL1 and CRVAL2
would simply be the values of latitude and longitude at the pixels given
by CRPIX1 and CRPIX2.  However, this raises another problem:  for the
linear WCS I propose, CRVAL1 and CRVAL2 would both be zero.  It may still
be that two WCS's in the same header would be needed.

I'd like to address a couple of more points, more or less from memory,
rasised in earlier posts.  In a full-disk solar image, the position of the
limb can be determined very accurately.  An initial guess accurate to a
fraction of a pixel can be found by fitting an ellipse to limb points
found by looking for zero crossings of the Laplacian of the image, and can
then be refined by the technique in Toner and Jefferies 1993, Ap.J. 415,
852.  This measurement is at least as accurate as assumed sizes of the
solar disk in kilometers or arc seconds from ephemerides.  For data taken
of a small portion of the disk, or of sky points only, the WCS would
depend on the accuracy of one's offset pointing, but this is already the
case.

Mark made the point that the original goal of my proposal was not clear. 
It is to make easy intercomparisons between data from different sources. 
In particular, Lindsey Davis of the IRAF group has worked hard on an image
matching package which, among many other things, will do the geometric
rectifications required so that two images have matched WCS's.  This is
something I would find extremely useful, and I assume others would as
well.  To use this would, though, require coding in the CD matrix
formalism, which I'd assume would be back-supported by any software
developed once the present WCS draft is made final.

Steve Walton
------------
Stephen Walton, California State University, Northridge
"Be careful what you wish for;  you might get it."	swalton at csun.edu