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 $\ast$ ( 1 $+$ C $\ast$ R $\ast$ 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.

astPcdMap

The PcdMap class inherits from the Mapping class.

In addition to those attributes common to all Mappings, every PcdMap also has the following attributes:

• Disco: PcdMap pincushion/barrel distortion coefficient

• PcdCen(axis): Centre coordinates of pincushion/barrel distortion

The PcdMap class does not define any new functions beyond those which are applicable to all Mappings.