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## FITS World Coordinate System (WCS)

## Primary WCS Documents

An elaborate set of FITS conventions has been defined to specify the physical, or world, coordinates to be attached to each pixel of an N-dimensional image. By world coordinates, one means coordinates that serve to locate a measurement in some multi-dimensional parameter space. A common example is to specify the Right Ascension and Declination on the sky associated with a given the pixel location in a celestial image. An archive of discussions about WCS issues that have taken place on the fitswcs@nrao.edu email exploder is available on the NRAO web site.

The WCS conventions are defined in a set of formal papers, 4 of which have been officially approved as part of the FITS standard by the IAU-FWG. Much of the content of the first 3 papers has been directly incorporated into Version 3 of the FITS Standard document and the 4th paper on Time coordinates has been incorporated into Version 4.

- Representations of World Coordinates in FITS (Paper I), Greisen, E. W., and Calabretta, M. R., Astronomy & Astrophysics,
395, 1061-1075, 2002. (PDF, HTML).- Representations of celestial coordinates in FITS (Paper II), Calabretta, M. R., and Greisen, E. W., Astronomy & Astrophysics,
395, 1077-1122, 2002. (PDF, HTML).- Representations of spectral coordinates in FITS (Paper III), Greisen, E. W., Calabretta, M. R., Valdes, F. G., and Allen, S. L., Astronomy & Astrophysics,
446, 747-771, 2006. (PDF, HTML).

- The authors' Web sites, with supplemental background WCS information: Eric Greisen, Mark Calabretta
- An unofficial errata for Papers I, II, and II: Postscript or PDF format.
- "Representations of Time Coordinates in FITS", Rots, A., Bunclark, P., Calabretta, M., Allen, S., Manchester, R., Thompson, W. Astronomy & Astrophysics,
574, A36 (2015). (PDF, (HTML).

- Approved by the IAUFWG in June 2014
- The author's Web site, contains supplemental background information.
"Representations of distortions in FITS world coordinate systems",Calabretta, et al., latest draft (22 April 2004): Postscript, PDF. This paper proposes a set of conventions for describing the distortions inherent in the coordinate systems of real astronomical data. These proposed conventions have not yet been reviewed or endorsed by the IAU FITS Working Group.## World Coordinate Systems Conventions (non-standard)

The following registered local FITS conventions have been adopted by some segments of the FITS user community. These conventions are not necessarily recommended by the IAU FITS Working Group for reuse in new applications.

- Spatial Region File convention defines a spatial region within a 2-dimensional image.. The region is specified as the union or intersection of geometric shapes, such as 'circle' or 'rectangle'. The region file is often used to define an area that is to be included or excluded from certain data processing operations on the image
- Simple Imaging Polynomial convention provides a convenient means of representing non-linear geometric distortion of the coordinate system as polynomials in FITS header keywords.
- TNX World Coordinate System is a non-standard coordinate system for evaluating celestial coordinates from the image pixel coordinates. It follows the FITS conventions for undistorted tangent plane projections but adds a non-linear distortion term to the evaluation.
- TPV World Coordinate System is a non-standard convention that builds on the standard TAN projection by adding a general polynomial distortion correction.
- ZPX World Coordinate System is a non-standard convention that builds on the standard ZPN projection by adding a general polynomial distortion correction.
## Other WCS papers

- Mapping on the HEALPix grid, Calabretta, M. R. & Roukema, B. F. MNRAS,
381, 865, 2007 introduces the HPX spherical projection type as an addendem to the 2nd WCS paper listed above. The HEALPix projection, as defined in section 6 of this paper, was approved as part of the official FITS WCS standard by the IAU-FWG on 26 April 2006.- Coordinate Systems for Solar Image Data, Thompson, W., Astronomy & Astrophysics,
449, 791, 2006 - a proposed set of formal systems for describing the coordinates of solar image data, including heliographic and heliocentric coordinates.- A proposal by Steve Allen and Doug Mink for concatenating WCS keywords.
- Conventions for Mosaic Images - a draft document by Steve Allen.that discusses the need for standardized FITS keywords for reporting of world coordinates in mosaic images.
## WCS Software

The following software libraries are available to help simplify the implementation of the projections and coordinate transformations defined in the World Coordinate System conventions.

- WCSLIB - Mark Calabretta's subroutines for spherical projections and coordinate transformations.
- WCSTools - Doug Mink's subroutines and utilities to convert between sky and image coordinates.
- AST library - Astrometry and World Coordinate System handling routines from the U.K. Starlink Project. Includes graphical display routines for plotting axes and labeled coordinate grids.

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