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SECTION 8. WORLD COORDINATE SYSTEMS

the image plane. Use of the CROTA2 keyword is now deprecated, and instead the newer

PCi_j or CDi_j keywords are recommended because they allow for skewed axes and fully

general rotation of multi-dimensional arrays. The CDELTi and CROTA2 keywords may co-

exist with the CDi_j keywords (but the CROTA2 must not occur with the PCi_j keywords)

as an aid to old FITS interpreters, but these keywords must be ignored by software

that supports the CDi_j keyword convention. In all these formalisms the reference pixel

coordinates rj are encoded in the CRPIXi keywords, and the world coordinates at the

reference point are encoded in the CRVALi keywords. For additional details, see [11].

The third step of the process, computing the final world coordinates, depends on

the type of coordinate system, which is indicated with the value of the CTYPEi key-

word. For some simple, linear cases an appropriate choice of normalization for the scale

factors allows the world coordinates to be taken directly (or by applying a constant

offset) from the xi (e.g., some spectra). In other cases it is more complicated, and may

require the application of some non-linear algorithm (e.g., a projection, as for celestial

coordinates), which may require the specification of additional parameters. Where nec-

essary, numeric parameter values for non-linear algorithms must be specified via PVi m

keywords and character-valued parameters will be specified via PSi m keywords, where

m is the parameter number.

The application of these formalisms to coordinate systems of interest is discussed in

the following sub-sections: §8.2 describes general WCS representations (see [11]), §8.3

describes celestial coordinate systems (see [12]), and §8.4 describes spectral coordinate

systems (see [14]).

8.2

World Coordinate System Representations

A variety of keywords have been reserved for computing the coordinate values that are to

be associated with any pixel location within an array. The full set is given in Table 8.2;

those in most common usage are defined in detail below for convenience. Coordinate

system specifications may appear in HDUs that contain simple images in the primary

array or in an image extension. Images may also be stored in a multi-dimensional vector

cell of a binary table, or as a tabulated list of pixel locations (and optionally, the pixel

value) in a table. In these latter 2 types of image representations, the WCS keywords

have a different naming convention which reflects the needs of the tabular data structure

and the 8-character limit for keyword lengths, but otherwise follow exactly the same

rules for type, usage, and default values. See reference [12] for example usage of these

keywords. All forms of these reserved keywords must be used only as specified in this

Standard.

The keywords given below constitute a complete set of fundamental attributes for a

WCS description. Although their inclusion in an HDU is optional, FITS writers should

include a complete set of keywords when describing a WCS. In the event that some

FITS Standard