[fitswcs] Status of WCS negotiations

[Don Wells]

Mark Calabretta writes:
 > On Mon 1998/07/20 11:21:15 -0400, Don Wells wrote
 > >I recommend that the TAN projection be augmented with radial terms
 > 
 > Sure, but won't you also need a plate solution projection which allows for
 > non-radial terms (such as DSS which includes pincushion and barrel
 > distortion). ..

Yes, in general, optical imaging systems with wide field do need some
x/y polynomial terms of second order (maybe third order sometimes) to
represent things like differential refraction and optical
misalignment.  However, the purely radial terms are the major
distortions of many such systems. It is true that x/y terms equivalent
to the radial terms exist in the polynomial expansions.  If only the
x/y polynomial expansion is supported for interchange, I think that
implementors should do their LS fits with radial terms and then
transform the coefficients to x/y polynomial form analytically for
export. My reasoning is that the LS solutions will be more stable if
the distortions are expressed in one or two radial coefficients than
if they are expressed in a much larger number of x/y polynomial
coefficients.

NOTE#1: in principle, the radial distortion coefficients of optical
systems can be calculated by their optical designers and can then be
inserted into astrometry calculations as givens. Has this been done
anywhere?

NOTE#2: my opinions regarding radial terms are based on my experiences
with a triplet prime-focus corrector in the 70s; newer corrector
lenses used with CCD mosaics today may have smaller radial distortion,
so maybe I am overemphasizing the importance of radial distortions.
Comments?

 > .. extra complexity.. should be quarantined as far as possible from
 > those who don't need it..

I want to agree with you on this philosophical point, Mark, but I
can't.  The problem is that radio and X-ray users now need fully
functional optical astrometry technology to support their
research. This was the conclusion of my initial posting on the
scientific requirements for WCS agreement.  Our whole community
(optical, radio, X-ray, infrared, ground-based and space-based) must
now implement WCS functionality for the worst cases. As a practical
matter, this means that we need at least one software package which
implements the functionality and which can be imported and used by
astronomy datasystems everywhere.  Your wcslib package fills this
need. If you program the extra complexity into wcslib and describe it
in the published paper so that others can produce equivalent
implementations now or in the future as needed, the science
requirement will be satisfied.

 > .. extending the CDij in this way [is]
 > .. virtually ruled out on practical grounds by the
 > requirement for inverse coordinate transformations.

Higher-ordered distortion terms are invertible by iteration.

 > ..we should have one pixel correction table, one linear transformation and
 > multiple projections on the grounds of parsimony since it is enough to do the
 > job..

The coefficients of the three steps of the mapping as listed above are
generally determined from observations of calibrator sources. The
number of calibrators is always limited, the distribution of the
calibrators is always suboptimal and the functions in the three steps
are not orthogonal, and so the solutions for the coefficients are
always correlated. Often the correlation coefficients are large. If
you leave out the pixel distortion correction, the linear transform
will change. If you are trying to determine both the projection and
pixel correction from the same dataset, the pixel correction will
change if you change the projection, and the linear transform will
change for each such solution you obtain. If you do the fit for a
subimage, rather than transforming the WCS for the full image, you
will get a different solution for pixel corrections and linear
transform, even for the same projection.

Furthermore, if we wish to attach two vastly different WCS
descriptions to a piece of data, for example celestial coordinates and
instrumental coordinates, all three steps of the mapping functions
will be different. The instrumental coordinates will have a different
pixel distortion correction, and even in PC notation the instrumental
system will have a different PC matrix because skew due to atmospheric
refraction is included in the celestial coordinate PC matrix.

In summary, the pixel distortion correction, the linear transformation
and the projection must be regarded as a unit, and we should support
multiple versions of the unit.

 > >.. a functional form which perturbs the pixel coordinates [is]
 > >mathematically equivalent to.. plate constant solutions..
 > 
 > Certainly, for plate solutions.  ..it shouldn't be used for this.
 > Use a plate solution projection instead..

If a solid majority of the optical community wants to define a TAN
projection function with enough PROJPk keywords instead of defining a
general pixel correction, I will cheerfully accept the decision.  I
expect that something like a TAN+three_term_radial+cubic_in_x/y would
be sufficient for worst cases.  The DSS projection (or equivalent)
will handle the Schmidt (ARC) case.  Such a decision would eliminate
the requirement for a general-purpose perturbation function. It would
also set a precedent. For example, the 'projection' functions for
optical and AOS spectroscopy would need to include analogous
perturbation terms. I hope that the long-slit case would be supported
satisfactorily (this should be checked).

-Don
-- 
  Donald C. Wells         Associate Scientist         dwells at nrao.edu
		    http://www.cv.nrao.edu/~dwells
  National Radio Astronomy Observatory                +1-804-296-0277
  520 Edgemont Road,   Charlottesville, Virginia       22903-2475 USA