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The Flexible Image Transport System, or FITS format, was first described by Wells et al. ([1981]). This format is characterized by a fixed logical record length of 2880 bytes, and the use of an unlimited number of character-format "header" records with an 80-byte, keyword-equals-value substructure. The header is followed by the header-specified number of binary data records, which are optionally followed by extension records of the specified length, but, at that time, of unspecified format. Since then, a number of authors have suggested various types of extensions (e.g. Greisen & Harten [1981]; Grosbøl et al. [1988]; Harten et al. [1988]; Cotton et al. [1995]). Because of its great flexibility, the FITS format has been, and continues to be, very widely used in astronomy. In fact, the FITS tape format was recommended (resolution C1) for use by all observatories by Commission 5 at the 1982 meeting of the IAU at Patras ([1983]) and the General Assembly of the IAU adopted (resolution R11) the recommendations of its commissions, including the FITS resolution. A committee of the NASA/Science Office of Standards and Technology has codified the current state of FITS into a document which has been accepted as the official definition of the standard (Hanisch et al. [2001]).

Wells et al. ([1981]) anticipated the need to specify the physical, or world, coordinates to be attached to each pixel of an N-dimensional image. By world coordinates, we mean coordinates that serve to locate a measurement in some multi-dimensional parameter space. They include, for example, a measurable quantity such as the frequency or wavelength associated with each point in a spectrum or, more abstractly, the longitude and latitude in a conventional spherical coordinate system which define a direction in space. World coordinates may also include enumerations such as "Stokes parameters", which do not form an image axis in the normal sense since interpolation along such axes is not meaningful.

Wells et al. ([1981]) viewed each axis of the image as having a coordinate type and a reference point for which the pixel coordinate, a coordinate value, and an increment were given. Note that this reference point was not required to occur at integer pixel locations nor even to occur within the image. An undefined "rotation" parameter was also provided for each axis. Since there are, in general, more coordinates to be attached to a pixel than there are "real" axes in the N-dimensional image, the convention of declaring axes with a single pixel was also established in both examples given by Wells et al. The keywords defined were

CRVAL n coordinate value at reference point
CRPIX n array location of the reference point in pixels
CDELT n coordinate increment at reference point
CTYPE n axis type (8 characters)
CROTA n rotation from stated coordinate type

A list of suggested values for CTYPE n was provided with few of the details actually required to specify coordinates. The units were specified to be The International System of Units "SI" (meters, kilograms, seconds) with the addition of degrees for angles.

The simplicity of this initial description was deliberate. It was felt that a detailed specification of coordinate types was a lengthy and complicated business, well beyond the scope intended for the initial paper. In addition, the authors felt that a detailed specification would probably be somewhat controversial and thus likely to compromise the possibility of wide-spread agreement on, and use of, the basic structures of the format. Hindsight also suggests that we were rather naive at the time concerning coordinates and it is fortunate that the detailed specification was postponed until greater experience could be obtained.

The descriptions of coordinates in the initial FITS paper are simply inadequate. They provide no description of the meaning of the world coordinates and suggest a rather incomplete list of coordinate types. The use of a single rotation per axis cannot describe any general rotation of more than two axes.

While participating in the development of the AIPS software package of the National Radio Astronomy Observatory, Greisen ([1983], [1986]) found it necessary to supply additional details to the coordinate definitions for both spectral and celestial coordinates. Since the latter have been widely used, a NASA-sponsored conference held in January 1988 recommended that they form the basis for a more general coordinate standard (Hanisch & Wells [1988]); such a standard is described below.

The present work generalizes the set of world coordinate system (WCS) FITS keywords with a view to describing non-linear coordinate systems and any parameters that they may require. Alternate keywords which should be supported are described. It also addresses the questions of units, multiple coordinate descriptions, uncertainties in the coordinate values, and various other coordinate related matters. Conventions for attaching coordinate information to tabular data are also described. Paper II (Calabretta & Greisen [2002]) and Paper III (Greisen et al. [2003]) extend these concepts to the ideal, but non-linear angular and spectral coordinates used in astronomy. Paper IV (Calabretta et al. [2003]) then provides methods to describe the distortions inherent in the image coordinate systems of real astronomical data. The complex questions related to time systems and to other kinds of coordinates will be deferred.

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