WCS questions

[William Thompson]

Mark Calabretta <mcalabre at atnf.csiro.au> writes:


>On Mon 1996/12/09 21:25:56 GMT, William Thompson wrote
>in a message to: fitsbits at fits.cv.nrao.edu

>>Good luck.  I'm personally not convinced that the WCS will ever be compatible
>>with datasets that are not in some way related to the celestial sphere.  It's
>>just a completely different mindset.  For example, the response from Mark
>>Calabretta

>If you're saying that WCS doesn't account for spherical deformations such as
>oblateness then I agree, it wasn't designed for that purpose (although you
>could apply a first-order approximation for oblateness through the PC matrix).

>Otherwise, the difference between mapping a sphere from the inside (i.e. the
>celestial sphere) and mapping it from the outside (e.g. planetary cartography)
>is essentially just that of changing the sign of the native longitude.

Now I understand what you're getting at.  You expect to be able to map data to
the solar surface.  Many solar features can be expressed as having a latitude
and longitude.  For example, an active region could be said to be at position
N30, W29 on a given date.  Of course, the longitude must be adjusted with time
to account for the (differential) solar rotation.

The trouble is that the sun is not a simple sphere like a planetary body.  It's
a three dimensional object.  Chromospheric structures such as prominences
extend several tens of thousands of kilometers above the surface, and
chromospheric loops extend well beyond that.  The corona can be observed out to
30 solar radii.  One has to be able to express data in a system which is valid
both for pixels which are on the disk and for pixels which are above the limb.
It's clear from Stephen Walton's original message that it's this kind of data
which he was considering.

When one is expressing data in solar latitude and longitude, such as a synoptic
map, it's clear that the data must be expressed in degrees.  The rationale for
using degrees for solar images, however, is not so well established.  In some
sense we do something similar in that many data are expressed in arcseconds
from disk center, with the "up" axis aligned with the solar northern rotational
axis.  That may not be an ideal solution, in that the apparent solar radius
changes with the seasons, and is different for some spacecraft, such as SOHO.
The scheme that Stephen Walton described, using coordinates normalized to the
solar radius, would remove this dependence from the data.

Another way to express the data would be in units of physical distance, rather
than in arcseconds.  The solar radius is 6.96x10^5 km, or 696 Mm.  Expressing
image pixels in units relative to the solar radius is really expressing it as a
distance.

Obviously, some other names need to be used for this Cartesian (X,Y) system
rather than PLAT and PLON.  It's evident that those names must be reserved for
data which are actually in latitude and longitude coordinates.  Let me throw
out a suggestion here for debate.  Suppose that we defined the following two
CTYPEs as

	CARN----	Cartesian north, measured from disk center towards the
			solar north rotational axis, and perpendicular to the
			line of sight to the observer, in units of the solar
			photospheric radius.

	CARW----	Cartesian west, measured from disk center towards the
			west limb, in units of the solar photospheric radius,
			and at right angles to CARN----, such that CARW----,
			CARN----, and the line of sight to the observer form a
			right-handed coordinate system.

William Thompson