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Section 8

World Coordinate Systems

Representations of the mapping between image coordinates and physical (i.e., world)

coordinate systems (WCSs) may be represented within FITS HDUs. The keywords that

are used to express these mappings are now rigorously defined in a series of papers on

world coordinate systems [11], celestial coordinate systems [12], and spectral coordinate

systems [14]. An additional spherical projection, called HEALPix, is defined in reference

[22]. These WCS papers have been formally approved by the IAUFWG and therefore

are incorporated by reference as an official part of this Standard. The reader should

refer to these papers for additional details and background information that cannot be

included here. Various updates and corrections to the primary WCS papers have been

compiled by the authors, and are reflected in this section. Therefore, where conflicts

exist, the description in this Standard will prevail.

8.1

Basic Concepts

Rather than store world coordinates separately for each datum, the regular lattice struc-

ture of a FITS image offers the possibility of defining rules for computing world coor-

dinates at each point. As stated in §3.3.2 and depicted in Figure 3.1, image array data

are addressed via integral array indices that range in value from 1 to NAXISj on axis

j. Recognizing that image data values may have an extent, for example an angular

separation, spectral channel width or time span, and thus that it may make sense to

interpolate between them, these integral array indices may be generalized to floating-

point pixel coordinates. Integral pixel coordinate values coincide with the corresponding

array indices, while fractional pixel coordinate values lie between array indices and thus

imply interpolation. Pixel coordinate values are defined at all points within the image

lattice and outside it (except along conventional axes, see §8.5). They form the basis of

the world coordinate formalism in FITS depicted schematically in Figure 8.1.

The essence of representing world coordinate systems in FITS is the association

FITS Standard