[fitswcs] WCS documents

[Mark Calabretta]

On Tue 2001/09/25 10:18:41 MST, Doug Tody wrote
in a message to: FITSWCS <fitswcs at NRAO.EDU>

>o   It has been proposed that degenerate axes be used to carry WCS
>    information [...]
...
>    [...] The fundamental purpose of the NAXIS
>    keyword is to define the dimensionality of the image pixel matrix.
...
>o   NAXIS is one of the most fundamental keywords in all of FITS.  What
>    has been proposed would force a change in the usage of NAXIS, affecting
>    large segments of the FITS user community.  We feel this would be the
>    most fundamental, non-backwards compatible, change ever made in the
>    history of FITS.

Doug,

The above claims are readily refuted simply by reference to the example
headers given in Wells, Greisen & Harten (1981) which shows that NAXISi=1
was established ab initio.  The construct is not new - terabytes of radio
data have been written using it.  It is not a "radio convention" as you
later refer to it, it's a venerable FITS construct, as old as FITS itself.

As these points were made in my notes to your DCF proposal I can only
conclude that you have not read them.  I commend them to you, they address
much more substantial issues than this.

>I. WCS which are Independent of Images
>
>In some cases it might be desirable to store a WCS in a FITS header which
>has no associated pixel matrix, but which makes use of the FITS WCS
>formulation to store this information in a portable way.  The following
>simple examples illustrate some possibilities.

Setting NAXISi=0 seems plausible, at least superficially, but suffers from
the same drawback as NAXIS=0: non-zero NAXISi will be needed in defining the
extremal values of a distortion function within an image.  NAXISi=0 would
also preclude recording properties of the coordinate system integrated over
the extent of the image, such as area, volume, distortion measures, etc.

Given that BITPIX is the keyword which describes the data, Doug Mink's
BITPIX=0 proposal is the appropriate solution - zero BITs per PIXel says it
all.  This is data compression "in the limit": 64, 32, 16, 8, ...  (So why
not 4, 2, and 1 bit data as well, e.g. for 4-, 2-, and 1-bit sampled VLBI
data?)

>conventions for writing radio data.  Permitting the WCS to be decoupled
>from the image matrix avoids this problem.  This is illustrated in the
>following example, which is adapted from FITS paper II.

Header interpretation example 1 is not particularly interesting.  Header
construction example 3 is the one worth focussing on.  The radio community
has always used the method shown in this example - a creative combination
of the venerable NAXISi=1 construct with the well-established and only
slightly younger AIPS convention (originally using CROTAi).  I don't know
who thought of it but I certainly can't claim the credit.

Question: So how have you represented the WCS of a long-slit spectrum in
the past?  

>o Backwards compatibility problems
>
>    Many existing programs (at least within the optical community) are
>    written expressly for 1D or 2D images.  These programs may assume the
>    image is a certain dimension, or may abort if NAXIS does not correspond
>    to the dimensionality of image the program was written for.  Often

This seems to be the crux of your argument, helping software which can only
interpret a subset of the FITS standard, even as it stood in 1981.  Yet it
does not survive scrutiny.

As far as I am aware, all data reduction packages, being suites of separate
procedures, contain a FITS reader which translates FITS data into its own
internal format.  What you appear to be saying is that the optical community
has many programs which operate directly on FITS images.  Later you say that

  "Entire branches of astronomy and potentially thousands of programs are
   affected if we start routinely writing FITS images with degenerate axes
   throughout all of astronomy".

You will have to excuse me if I say that I don't believe you!  Can you name,
say, a dozen such programs?  And why would you persist in using them when
much better quality software is freely available?

"Once FITS always FITS" refers to the data, not the software!

Certainly there must be many specialized FITS readers (probably the
majority) which do only interpret that subset of the FITS standard required
for data from a particular source.  Thus, if (and only if) the source
generating this data is modified to add standardized WCS keywords then,
whatever standard is adopted, the FITS reader will have to be modified to
understand it.

The opportunity therefore presents itself for your overly-specialized FITS
readers to be modified to interpret the venerable NAXISi=1 construct as part
of a new WCS standard and, as a huge bonus, gain access to the terabytes of
radio and other data generated over the last two decades.  The changes
required are a mere bagatelle, not even slightly complicated; they are
SIMPLE = T.

Why not do astronomy a favour and grab this opportunity with both hands?

Mark Calabretta
ATNF