A PcdMap is a non-linear Mapping which transforms 2-dimensional positions to correct for the radial distortion introduced by some cameras and telescopes. This can take the form either of pincushion or barrel distortion, and is characterized by a single distortion coefficient.
A PcdMap is specified by giving this distortion coefficient and the coordinates of the centre of the radial distortion. The forward transformation of a PcdMap applies the distortion:
RD = R ( 1 C R R )
where R is the undistorted radial distance from the distortion centre (specified by attribute PcdCen), RD is the radial distance from the same centre in the presence of distortion, and C is the distortion coefficient (given by attribute Disco).
The inverse transformation of a PcdMap removes the distortion produced by the forward transformation. The expression used to derive R from RD is an approximate inverse of the expression above, obtained from two iterations of the Newton-Raphson method. The mismatch between the forward and inverse expressions is negligible for astrometric applications (to reach 1 milliarcsec at the edge of the Anglo-Australian Telescope triplet or a Schmidt field would require field diameters of 2.4 and 42 degrees respectively).
If a PcdMap is inverted (e.g. using astInvert) then the roles of the forward and inverse transformations are reversed; the forward transformation will remove the distortion, and the inverse transformation will apply it.
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