4.1 Indexes and Physical Coordinates

  When the data matrix represents a digital image, transformation between the data matrix and the physical picture requires knowledge of where in the pixel -- center or corner -- the data point is. Historically, astronomers have generally assumed that the index point in a FITS file represents the center of a pixel. This interpretation is endorsed by GC. It differs from the common practice in computer graphics of treating the center of a pixel as a half-integral point. GC note that the pixel in a FITS file is commonly regarded as a volume element in physical space, which might be viewed from different perspectives via transposition and rotation. Under such operations, only the center of an element remains invariant. Pending adoption of a standard convention by the astronomical community, FITS writers should use appropriate comments in the comment field of the card image or the COMMENT keyword to inform readers of the file which convention is being used. Once the community has accepted a convention, a single comment noting that the convention is being used will be sufficient.

The relation between array order and position in the displayed image, for example whether the first pixel is at the top or bottom, is also a matter of convention. GC recommend that FITS writers order pixels starting in the lower left hand corner of the image, with the first axis increasing to the right, as in the rectangular coordinate x-axis, and the second increasing upward (the y-axis). Readers may choose to use a different display, as might be done when picturing how a field mapped visually would look through a telescope. Use of this convention does not replace the description of the coordinate axes using CRVALn and the other keywords.

Although the original description of the CRPIXn, CRVALn, and CDELTn keywords was in the context of linear transformations, these keywords can be used to define non-linear transformations. The key point is that in such a case CDELTn must represent the rate of change in the physical coordinate per unit change in counting index at the reference point given by CRPIXn. For a non-linear scale, the ratio between change in the physical coordinate and in the counting index could be different at other pixels. Conventions for such transformations have not been established. Development or use of any such convention, including the definition of any new keywords, should be in cooperation with the others in the FITS community who need such conventions.