Page "Distortion (optics)" Paragraph 13

In order to understand these distortions, it should be remembered that these are radial defects ; the optical systems in question have rotational symmetry ( omitting non-radial defects ), so the didactically correct test image would be a set of concentric circles having even separation — like a shooter's target.

It will then be observed that these common distortions actually imply a nonlinear radius mapping from the object to the image: What is seemingly pincushion distortion, is actually simply an exaggerated radius mapping for large radii in comparison with small radii.

A graph showing radius transformations ( from object to image ) will be steeper in the upper ( rightmost ) end.

Conversely, barrel distortion is actually a diminished radius mapping for large radii in comparison with small radii.

A graph showing radius transformations ( from object to image ) will be less steep in the upper ( rightmost ) end.