WCS questions

[William Thompson]

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

>>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.

>Such a mapping from 2-D pixel coordinates (i,j) to 3-D spherical coordinates
>(r,phi,theta) is under-determined for a single image, ...

Right, which is why it is incorrect to force solar data to be expressed in a
spherical coordinate system.

>In any case, there's still nothing to prevent using WCS for heliographic
>coordinates of the solar surface in a 2-D map even if it extends past the
>solar limb.  The heliographic lng/lat of a feature beyond the limb would be
>undefined, which I believe makes sense.  ...

Unless of course that's the data you're interested in.

>... However, such features would still
>have meaningful (x',y') coordinates.

What if all the pixels in the image were off the limb?  If I'm understanding
things correctly, there would be no way to express the physical coordinates of
that data in the WCS system.

What we need to be able to do in solar physics is to express the data in a
standardized way.  Because the data can be both on and off the limb, this
standardized coordinate system cannot be based on solar latitude and longitude.
Of course, a parallel coordinate system for data such as synoptic maps which is
organized by latitude and longitude makes sense, but I believe that's already
accommodated within the WCS system.

It's common in solar physics to refer to coordinates as a pair of distances
from solar disk center, with one axis aligned with solar north, and the other
perpendicular to that.  If we can agree on a meaningful way to embed those kind
of data into the WCS system, then we have something.

>>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.

>How do you interpret this "distance" if you don't know the angle between the
>corresponding position vector and the plane of projection?  The best you can
>say about the projected distance is that it is less than the true distance
>from the solar centre so I think it could be misleading to assign it units of
>metres.

Obviously, it is a projected distance rather than a true distance from the
center of the sun.  That's immaterial.  It still gives the correct X,Y
positions in an X,Y,Z coordinate system.  From a scientific viewpoint, the
physical size in kilometers is the most relevant way to express the data.  One
wants to measure the height of a spicule, or the dimensions of a coronal loop.

>Also, since the sun's rotational axis is not perpendicular to the ecliptic the
>solar poles do not usually lie on the solar limb which means that not even
>they will have fixed coordinates in this Cartesian system. 

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.  For spacecraft such as SOHO which
are not in low earth orbit this can be different from the same value as
observed from earth.

It's possible that we're talking at cross purposes.  What I'm saying is that
the most natural coordinate system for solar images is a projected one.  It
should be straightforward to determine the spherical coordinates of a pixel
which is on the disk, but the coordinate system itself cannot be directly tied
to those spherical coordinates because of the need to also meaningfully
describe off-limb data.

I don't see any reason why we couldn't adopt a convention where solar data were
described in a coordinate system normalized to the solar photospheric radius,
or one using kilometers.

William Thompson