Representation of World Coordinate Systems in FITS

Current status of the negotiations

Eric Greisen (NRAO) and Mark Calabretta (ATNF) have been working on a proposed mechanism to transfer coordinate information in detail in FITS headers and tables. The work on the current papers was begun in 1992, following the ADASS meeting in Boston. It has a considerable history some of which is described in the following section. The state of these documents was discussed in the latest ADASS meeting, held in November 1998 at the University of Illinois and some tentative agreements were reached. As a result, Mark and I have reworked the documents, turning them into three separate papers. We have already received considerable feedback, particularly on the subject of units, which has led to significant improvements in the papers.

There will now be four papers: I on general matters, II on ideal celestial coordinates, III on ideal spectral coordinates, and IV on distortion corrections used to convert real instruments into these ideal coordinates. Draft documents for Papers I, II, and III are presently available. The 2001 ADASS directed us to make certain changes to the papers which we have done. These are color coded in green. The NOAO (IRAF) group reviewed those documents and further changes/corrections made (after 10/18) partly as a result of their comments are colored in blue. Recent changes are in red and those made after December 12, 2001 are in purple.. All changes since the last release of Paper II (11/2000) are in red. Note that the appendices have been moved into the main text. Frank Valdes has added a practical projection suited to optical instruments to Paper III. Please examine the following and, if you find any problems, please let us know as soon as possible:

  1. Representations of world coordinates in FITS by Greisen and Calabretta (gzipped 108 kbyte), or unzipped (283 kbyte) 1-March-2002.
  2. Representations of celestial coordinates in FITS by Calabretta and Greisen (gzipped 370 kbyte), or unzipped (1007 kbyte) 12-December-2001.
  3. Representations of spectral coordinates in FITS by Greisen and Valdes (gzipped 178 kbyte), or unzipped (464 kbyte) 06-February-2002.
The most current versions may not be referenced here due to caching by your browser. Refer to Eric Greisen for the latest versions. We believe that these are nearing readiness for submission to, consideration by, and (one hopes) prompt voting by the regional FITS committees. However, there are one or two serious matters still under advisement affecting all 3 papers before they can be submitted to these committees. Paper IV is being worked on as well, but it is complex and will take time.

Paper I describes a very general method for specifying coordinates. A pixel-to-coordinate matrix PCj_i will replace CROTAj, units will be described with a new keyword CUNITj, and secondary sets of coordinate descriptions may be specified. A complete system of unit specification is described and is expected to supplement the IAU standard system of units. Methods for describing the coordinates of matrices in binary tables are also described.

Paper II applies the general rules of Paper I to the specific problem of specifying celestial coordinates in a two-dimensional projection of the sky. The coordinate system is specified with the new keyword RADESYS and a large number of "projections" are defined. Oblique projections are described and illustrated. Several examples of header interpretation and construction are given including one that specifies coordinates on a planetary body rather than the celestial sphere. The application to binary tables is described.

Paper III applies the general rules and practices developed in the first two papers to spectral coordinates, namely frequency, wavelength, velocity, and the radio and optical conventional "velocities". These are defined and methods of computing one type of coordinate from a spectral axis gridded in another are given. A projection representative of optical spectrometers is also defined. Coordinate reference frames may be specified.

Paper IV is in preparation and is not yet ready for public comment. It will define Distortion Correction Functions (DCFs) which may be used to correct for instrumental "defects" including celestial coordinate warps ("plate defects"), variation of actual frequency with celestial coordinate, refaction, and the like.

These documents will change in response to feedback should we receive any - many thanks to Steve Allen for numerous helpful remarks. These papers were voted upon, at the ADASS meeting in Hawaii in October 1999. At that point they were - in principle - submitted to the United States, European, and Japanese FITS Committees to be voted upon. They were not voted upon and then Tody, Valdes, and Davis of NOAO made the suggestion to generalize and separate instrumental correction into a Paper IV. That has been done and the papers were voted upon at the ADASS in Victoria in 2001. We have now presented the results we were told to present and the papers should be ready fairly soon to go again to the committees for a vote. Should that ever happen, they will be submitted to Astronomy & Astrophysics (the Supplements have been subsumed) for publication and will go before the IAU FITS panel. Please read and consider these documents carefully and give us your considered comments. The FITS standard controls how we think about our data and you would not want to be stuck with a standard that you do not like.

Older papers giving the history of the negotiations

The following documents may be of interest in tracing the evolution of the current WCS proposals but do not form part of it.

The states of Papers I, II and III prior to the Victoria (2001) ADASS meeting are

  1. Representations of world coordinates in FITS by Greisen and Calabretta (100 kbyte, 4-July-2001)
  2. Representations of celestial coordinates in FITS, by Calabretta and Greisen (210 kbytes, 7-Nov-2000)
  3. Representations of spectral coordinates in FITS by Greisen (74 kbyte, 4-July-2001)

This anonymous ftp area ( has been set aside for the early documents concerning the representation of the coordinates of the pixels in FITS images. My two early AIPS Memos (27 and 46) have been recovered and recast into modern LaTeX (from TeX -1 or so). In so doing, I redrew the figures for both memos in PostScript, using AIPS to draw those for Memo 46 and "hand" drawing those for Memo 27. The files are called (of modest size) and (about 600 kbyte in uncompressed form). Therefore, it is stored only in the Unix compressed form Try "zcat | lpr -Pxxx" to avoid on-disk decompression; else "lpr -s -Pxxx " to avoid complaints about too-large files.

Another early document is found in the files wcs88.tex and This document is a draft by Hanisch and Wells concerning the meeting held in Charlottesville in 1988 on "world coordinates".

These earlier papers are intended to be superseded entirely by a new document found (partly) in a file called (the figures are separate files not included in wcs.tex). [This document in now superseded by the 3 documents described in the previous section.] The real working document for a FITS paper authored by myself and Mark Calabretta was called (no figures, prints quickly), and and (all figures). The figures are drawn with PostScript programs which have all been verified with our printers and ghostview. However, we have found several models of "postscript" printer which simply fail on the documents and others which work, but are exceedingly slow. Hence, the quicker-to-print version.

This was an evolving document, representing our opinion of the best ways to represent coordinates. To track earlier versions, I have left the .tex copies of versions from June 1993, August 1993, September 1994, November 1994 and October 1995. The June 1993 version was widely advertised and presented at the AAS meeting in Berkeley. The August version was advertised and contained the results of some discussions at Berkeley, primarily the reintroduction of the CDELTn keywords. The September 1994 version was discussed at the ADASS meeting in Baltimore. A document describing the changes from November 1994 to September 1996 is named wcs.9496.changes in the fits documents area.

Don Wells has asked me to include files representing my poster papers at the June 1993 AAS meeting and September 1994 ADASS meetings. I have added these as Talk93.tex.Z,, Talk94.tex.Z, Talk94.tex.Z,, and The 93 poster may have to be broken into separate pages for some printers. The page breaks are obvious (a full line of % signs).

Almost all of the files have been compressed using the standard Unix compress command to save space and to speed network transmission.

If you find that you cannot read the papers via ftp, or cannot get them to print, you may obtain paper copies of all 3 are by contacting

Ernest Allen, National Radio Astronomy Observatory

520 Edgemont Road, Charlottesville, VA 22903-2475


phone: 804-296-0209

fax: 804-296-0328

Please let us know your comments (well-considered and temperate only), so that we may develop a consensus which will allow the final to become a new FITS standard.


Eric W. Greisen, Scientist

National Radio Astronomy Observatory, 804-296-0348