[fitswcs] Status of WCS negotiations

[Don Wells]

Mark Calabretta writes:
 > G&C does not support multiple linear transformation matrices, mainly on the
 > grounds of parsimony.  We took the view that the PC matrix would be used for a
 > one-time correction for instrumental setup, i.e. a simple rotation or affine
 > transformation introduced, say, by misorienting a photographic plate or CCD
 > array, or reorienting a long-slit spectrogram.  The only arguments I have
 > heard for multiple linear transformations have been related to storing
 > multiple plate solutions..

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.

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.

-Don