[fitswcs] Status of WCS negotiations

[Mark Calabretta]

On Mon 1998/07/20 11:41:18 -0400, Don Wells wrote
in a message to: fitswcs at fits.cv.nrao.edu

>Real instruments need multiple linear mappings, for several reasons. 
>
>First, it is generally true that a physical pixel in a camera
>represents both a point on the celestial sphere and a point in the
>focal plane of the camera. Many instrumental corrections are
>associated with the latter coordinate system, and so there will often
>be a good reason to carry two entirely different sets of linear
>mapping keywords. My memory is that this argument was first advanced
>by Doug Tody.

I probably don't understand your example, perhaps it would help if you
described some of these instrumental corrections.  As I see it you don't need
even one CD matrix in this case if you have a projection type similar to DSS
which includes it's own linear transformation - and you can have as many
secondary descriptions as you like.  It just requires G&C to generalize the
PROJPn to WCmiijjj and for the optical community to define or adopt a plate
solution projection.

>Second, multiple combinations of linear mappings and nonlinear
>projections can be used to represent a piece of data. It is true that
>there is generally one combination which represents the physical
>situation "best", but it is also true that alternative combinations
>may provide acceptable accuracy and may be preferred for various
>reasons. For example, the geometry of a 2000-square image might be
>represented well by a TAN projection with radial terms, but if a
>500-square subimage is extracted from it the same accuracy might be
>achieved without the radial terms. If the subimage is offaxis the
>missing radial terms would be compensated by changes in the CDij
>linear transformation. It would be nice if both combinations of
>linear+TAN could be carried in the header of the subimage.

Do I understand you correctly that the subimage is of reduced resolution and
that there are three descriptions?  Before:

   1) The 2000x2000 image with the CDij matrix and a TAN+ projection (this
      CDij matrix being inapplicable to the subimage).

After:

   2) The 500x500 offset subimage with the same CRVALn but with the CRPIXn and
      CDij reset so that the value of (x,y) in the plane of projection is
      maintained, plus the original TAN+ projection.  This describes exactly
      the same coordinate system as (1), or

   3) The 500x500 subimage with truncated TAN+ projection and with CRVALn,
      CRPIXn and CDij subtly modifed to account for the discarded radial
      terms - effectively a new plate solution.

The simple answer is not to throw away the radial terms - why would you?
An alternative answer is that if the optical community wants this sort of
functionality it can have it by incorporating the linear transformation
in the plate solution projection equations (such as in DSS).  You can have
multiple such descriptions without inflicting multiple CD matrices on people
who aren't interested in them.

The optical community just has to define or adopt a plate solution projection
(e.g. DSS).


Cheers, Mark