Eric W. Greisen

This page was last updated 15 August 2004.

I am a Scientist at the National Radio Astronomy Observatory, stationed at NRAO's Array Operations Center in Socorro, New Mexico. My main job at the present time is to develop and maintain the software package known as AIPS. I am also involved in FITS matters.

New stuff on this page includes updated WCS papers including a poster for ADASS IX (Oct 1999).

FITS Matters

I am a member of the NOST (NASA Office of Standard Technology) Committee on FITS which has prepared a document representing the FITS standard in a more correctly worded form. The committee also has a web site devoted to the subject. Although this document makes few changes from the standard as presented in the published papers, it has been reviewed and accepted by the various FITS committees and has become "the" FITS standard. It has now been accepted for publication in Astronomy and Astrophysics and have slightly outdated copies available in pdf format and in gzipped PostScript format. I am also a member of some of these FITS committees (AAS WGAS and IAU and ??), but I forget which since they aren't very active.

"World Coordinates" Proposal

I have worked with Mark Calabretta off and on for a number of years on a detailed proposal for representing world coordinates in FITS. The state of these documents was discussed in the 1998 ADASS meeting, held at the University of Illinois and some tentative agreements were reached. As a result, Mark and I have reworked the documents and are still revising them. Feedback on units and other matters have already improved the drafts. Further discussion at the 1999 ADASS in Hawaii led to a few more changes and then was supposed to lead to the submission of the papers for a vote by the regional FITS committees of North America, Europe, and Japan. The submission was made, but there was no discussion and no vote held.

Mark and I continued work and the states of Papers I, II, and III as of this summer --- but they are now obsolete --- was

  1. Representations of world coordinates in FITS by Greisen and Calabretta (gzipped 100 kbyte or unzipped 250 kbyte 4-July-2001 OBSOLETE)
  2. Representations of celestial coordinates in FITS, by Calabretta and Greisen (gzipped 211 kbytes or unzipped 652 kbyte, 7-November-2000 OBSOLETE)
  3. Representations of spectral coordinates in FITS by Greisen (gzipped 73 kbyte or unzipped 180 kbyte, 4-July-2001 OBSOLETE)
The above papers have been moved. They are obsolete and do not represent the state of the discussion. Nonetheless, they were being dowloaded almost as much as the current documents. I have moved them away to try to prevent this error. Paper I above contains a new provision to identify which pixel regularization matrix goes with which coordinate representation. It also contains a substantially expanded section on the structure of the CTYPE keyword for linear and non-linear axes. Paper II was updated with new examples. Paper III was updated to allow the Wells, Greisen, Harten CTYPEs when the axes are very simple.

On June 30, 2001, A significant proposed generalization of these papers was presented by Doug Tody, Francisco Valdes, and Lindsay Davis of NOAO. See Suggested Changes to FITS WCS Proposal and links therein for details. Mark Calabretta and (to a lesser extent) I have generated a mostly positive response to their proposal. That response generated little discussion since it was submitted to the fitswcs mail exploder, including at the FITS Birds of a Feather session at the Victoria, BC 2001 ADASS conference. On October 16, 2001, the NOAO people replied in detail with useful discussion of Mark's response. In the mean time, Mark and I have persevered. Mark is working on a Paper IV and is doing his usual marvelous job on it. However, it is not ready for public comment. I have modified Papers I and III and Mark has modified Paper II. The modifications include the new WCSAXES proposal as a solution to the "degenerate axes problem", corrections of a number of typos, elevation of the tables part to be a full part of the WCS proposal, moving both the tables and units appendices to full sections, and addition of a short paragraph on the [] comments convention for units. Paper III was revised prior to the ADASS to account for the existence of Paper IV and has been revised since to elevate the tables to full status rather than an appendix. The 2001 ADASS directed us to make certain changes to the papers which we have done along with subsequent suggestions from Bob Hanisch, Frank Valdes, and Steve Allen. In

Papers I, II, and III have been voted upon by the regional (North American, Japanese, European, and Australian) and IAU FITS Committees and passed by them. Paper III contains some material which perhaps should have been in Paper I except we chose not to delay publication of Paper I. The most important of these matters are a table lookup "projection" and a generalized discussion of the computation of coordinates. Papers I and II have been published and Paper III accepted for publication. It could still be fixed so please examine the following:

  1. Representations of spectral coordinates in FITS by Greisen, Calabretta, Valdes, and Allen (gzipped 206532 bytes) or unzipped (563395 bytes) or pdf (931812 bytes) 07-October-2005, red shows changes since submitted to A&A.
  2. Representations of spectral coordinates in FITS by Greisen, Calabretta, Valdes, and Allen (gzipped 203583 bytes) or unzipped (550094 bytes) or pdf (929866 bytes) 04-October-2005 astro-ph/0507293, accepted by A&A.

Paper III has been accepted for publication and endorsed by the regional and IAU FITS Committees. The already published papers are:

  1. Representations of world coordinates in FITS by Greisen and Calabretta (246829 bytes pdf file from A&A) Accepted: Volume 395, pages 1061-1075
  2. Representations of celestial coordinates in FITS by Calabretta and Greisen (1279957 bytes pdf file from A&A), Accepted: Volume 395, pages 1077-1122

Paper IV has been worked on, but has taken a back seat while we polish Papers I, II, and III.

The text of a proposal by Steve Allen and Doug Mink for "Concatenation of FITS World Coordinate Systems" is also now available for general review. This was raised on the fitswcs mailing list on 2002/01/01 and following and ideally would have been included in Paper I. However, we felt that the FITS community had not had adequate time to review it, yet we didn't want to delay Paper I further. Thus it is presented as a separate proposal.

General comments on these papers may be sent to which is a general mail exploder for discussion of such matters. Typographical corrections are best just sent to the authors.

Our April 2002 announcement of the documents included the following change information:

Overview of the main changes to Paper I & II:
   1) The formalism of the linear transformation has been recast to place
      equal emphasis on the use of the PC and CD matrices.  The use of
      mathematical matrix notation in Eq. (1) then led to interchanging
      the "i" and "j" indices on the keywords and changing the alternate
      axis descriptor suffix from "s" to "a".

   2) A header construction example has been added to Paper I.

   3) The tables summarizing new keywords have been revamped.

   4) Header construction example 3 of Paper II has been augmented with
      a detailed discussion of representations using the CD and PC

   5) The text has been carefully proofed by Bob Hanisch & Steve Allen.
Paper III was so heavily rewritten that it should be considered in its entirety.

Our December 2001 announcement of the documents included the following change information:

The most important changes stemmed from the decision to extract all material relating to "distortions" into a separate Paper IV provisionally titled "Representations of Distortions in FITS World Coordinate Systems" which is currently under development. The material removed includes the "pixel regularization correction" from Paper I, the polynomial distortion function attached to the TAN projection and the DSS header construction example from Paper II, and the polynomial spectral distortion correction from Paper III.

Work on Paper IV also convinced us to revert to the PCj_i + CDELTj construct. This was replaced by CDj_i late in 1998 to obtain quick agreement for the WCS proposal among various dissenting parties. That quick agreement did not eventuate. Therefore we have felt free to revert to what we believe is a much better formalism, as explained in Paper I. However, the current proposal requires that the CDj_i be fully supported in translation. Please read the discussion in Paper I before responding to this change.

A summary of the main changes are:

   Paper I:
	* CDj_i -> PCj_i + CDELTj.
        * Introduction of WCSAXES.
        * Specification of default values for CRPIXi, etc.
        * Formalization of BINTABLE and PIXLIST keywords.
        * Units in comment fields.
        * Removal of pixel regularization correction.
        * Specification of both PCj_i and CDj_i matrices.

   Paper II:
	* Detailed explanation and formal generalization of the meaning
	  of (phi_0,theta_0).
	* Introduction of user-specified (phi_0,theta_0).
	* Generalization of AZP to tilted planes of projection.
	* Introduction of SZP, slant zenithal projection.
        * Removal of polynomial distortion function from TAN.
	* Removal of the DSS header construction example.
	* Mathematical discussion of the matrix which results from
	  translating AIPS convention headers.
	* New header interpretation example 3.
	* New header construction example 1.
	* Derivation of the slant orthographic projection in aperture
	  synthesis radioastronomy.

   Paper III (now co-authored by Frank Valdes):
        * Removal of polynomial spectral distortion correction.
	* New section on gratings and prisms.
	* New header interpretation example.
	* Discussion of real-world complications arising from Doppler
	* Reversion to PC+CDELT.
A new version of WCSLIB which supports the generalized AZP and SZP projections is available from
This also contains an improved version of PGSBOX.

The above documents change, sometimes on a nearly daily basis. Do check occasionally to see if you have the latest drafts.

For the 1999 ADASS meeting we prepared a poster (gzipped 59 kbyte) poster and accompanying paper (gzipped 25 kbyte). These constitute an executive summary of the proposal, and Mark's art work in the poster is quite interesting. We are very interested in your comments. If you stay silent, you may find a FITS standard that you do not like.

An anonymous ftp area has been set up with a variety of older wcs documents available. Remember that these are of historical interest only. Chief among these are

Eric W. Greisen