WCS questions

[William Thompson]

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


>On Thu 1996/12/12 00:15:16 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.

>We appear to going around in circles here.  We have a 2-D spherical surface 
>embedded in a 3-D space seen in projection on the celestial sphere.  We want
>to coordinatise points on the surface in one way and points in the surrounding
>space in another way.  

As a solar astronomer, I disagree with this.  First of all, I don't believe
that the characterization of the Sun as a 2-D spherical surface is entirely
accurate.  Nor do I think that it's the most important way to characterize
solar data.  There are two reasons for this:

1.  As I have pointed out before, the Sun is a three dimensional object, with
    an atmosphere extending well beyond the solar photospheric "surface".  You
    suggest referencing pixels on the disk in one way, and pixels off the disk
    in another way.  However, these are not really separate and distinct data
    sets--solar features blend smoothly from one regime to the other.  Often
    one wants to compare data which is on the disk to data which is off the
    disk.

    Also, the concept of a solar surface is a somewhat fuzzy concept.  The
    apparent size of the Sun is different depending on what wavelengths one is
    looking at.  If one is looking in visible light, then one is looking at the
    photosphere, which is what most people think of as the solar surface.
    However, at certain wavelengths such as hydrogen H-alpha line, one is
    looking at the chromosphere, which is above the photosphere.  Even when
    discounting obviously elevated features such as prominences, the apparent
    size of the Sun is different.  This is especially true in other wavelengths
    in the UV and EUV where one the solar radius is driven by the transition
    region and lower corona.

2.  Although it is useful to convert pixels in image space to solar latitude
    and longitude, this is not the most accurate way to express the pointing of
    the data.  In order to make the conversion, one must know exactly where the
    center of the Sun is in your field of view.  This is not always a trivial
    task--many data come with only a rough determination of where disk center
    is.  Inaccuracies in the absolute pointing will lead to ever increasing
    errors in the latitude/longitude calculation as one approaches the limb.

    Data given in a projected coordinate system as an X,Y pair of distances
    from disk center, either angular or kilometers, also have a built-in
    uncertainty.  However, this uncertainty is easy to characterize, and is
    constant for all pixels.

At this point, one might ask what reasons one might have for converting from
projected coordinates to spherical coordinates.  The following come to mind:

a.  To generate synoptic maps of an entire solar rotation.

b.  To produce "butterfly" maps showing the evolution of the distribution of
    features such as sunspots over the 22 year solar cycle.

c.  To correct for solar differential rotation when comparing two images taken
    at different times, or to project where a given feature will appear at the
    time an observation will be made.  In the case of comparing two images, a
    conversion will be made from projected to 

d.  To explore center-to-limb variations, such as limb darkening.

Note that there are at least three different coordinate systems being discussed
here.  Items a, b, and c above all agree on the definition of latitude, while
items a and c use different definitions of longitude.  In fact, the latitude
and longitude used in synoptic maps isn't really a spherical coordinate system,
because the differential rotation of the sun has to be taken into account.
Item d essentially uses a completely different coordinate system with the
"pole" pointing straight at the observer.

(Note by the way that Steven Walton's original query was primarily addressing
item d.  To that end, he suggested a projected coordinate system similar to the
one I described in an earlier message.  The only difference was the
normalization to the solar (presumably photospheric) radius.)

>All I am saying is that, contrary to your original
>statement, and I believe answering Steven Walton's original query, WCS
>provides the tools to do this.  If you have to have Cartesian coordinates
>with units of metres rather than solar radii, then use secondary axis
>descriptors.

>I'm not saying that you won't need to define a simple convention tied to the
>CTYPEn (e.g. PLON/PLAT) which describes this system to the extent that points
>outside the limb are valid and what their interpretation is to be.

My understanding of the purpose of the World Coordinate System is to assist in
the comparison of data taken at different sites and with different instruments.
>From the standpoint of solar physics, we must ask ourselves what is the best
way to characterize our data to assist in this goal.

I agree with your earlier statement that the Sun is a three dimensional object
seen projected onto the celestial sphere.  To my mind, this is the most
important starting point.  Also, I think we can all agree that the ability to
convert image pixel data to traditional celestial coordinates such as RA and
DEC is rarely of any importance.  To my mind, unless the data has already been
projected into spherical coordinates, solar latitude and longitude has to be
considered a secondary

To a large respect, this is how most solar data is expressed, except that data
tends to be expressed in arcseconds or arcminutes rather than degress.  Also,
generally speaking, the exact type of projection (e.g. TAN or ARC) has not
always necessarily been made clear, because one is generally operating at small
angles.

Thus, the coordinate system that I argue makes the most sense for solar
observations has the following properties:

1.  The Sun would be at the equivalent of "RA" and "DEC" both being zero.

2.  The Sun, the zenith, and the projection of the north solar rotational pole
    would all fall on the same great circle.

Observed locally, this would be equivalent to the coordinate system I described
before, with North being "up" and the west limb being to the "right".  The
contribution made by using the WCS formalism for this, besides standardization,
would be in regularizing the description of exactly what projection system is
used.  I can imagine, as resolutions improve, that this could be a benefit in
future solar data.  Of course, the four letter designation that would appear in
the CTYPE keyword needs to be established.

Besides the above positions, the following information is also necessary when
analyzing solar data.

* The distance from the observer to the Sun.  (If the data were expressed in
  kilometers, or in units relative to the solar photospheric radius, then there
  would be no need for this parameter.  For groundbased and low-Earth-orbit
  satellites, the distance from the Earth to the Sun would suffice.
  Conversely, this could be expressed as the apparent size of the solar
  photospheric disk.

* The tilt of the solar north axis towards or away from the observer, known as
  the B angle.

* For observations made from vantage points other than the Earth's environs,
  one needs to know the latitude and longitude of the observers subsolar point,
  where the subsolar point of the Earth is at longitude zero.

We need to standardize on what keywords will be used for these parameters.

William Thompson


P.S.  I've looked at the most recent version of the WCS paper, and don't see
the terms PLAT/PLON described anywhere.  I can only imagine that they describe
the normal kind of latitude and longitude when applied to the Earth.  Where are
these described and reserved?  What about SLAT and SLON which was also
described as being reserved in a previous message?