In interferometry for example uncorrected radial distortion results in an SA component that depends on defocus.
Sources of distortion are the camera lens and the geometry of the test surface. When corrected for distortion (either optically or in software) the displacement of a point in the image from the centre is proportional to the tangent of the field angle.
This works well when mapping a flat surface to a flat image surface. Unfortunately most test surfaces of interest aren't flat.
For a spherical test surface a radial displacement of a point proportional to the sine of the field angle is better. Zygo define distortion as departure from such a mapping in their spherical wave Fizeau interferometers.
If a distortion corrected camera lens is used to image an aspheric surface then the variation of the tangent of field angle due to the finite length of the caustic and the sagitta of the test surface.
For a paraboloid measured with a distortion (rectilinear) free lens the fractional distortion is
(3/8)*(D/R)^2*(rho)^2 + (9/64)*(D/R)^4*(rho)^4 + .
1/3 of this is due to the finite sagitta 2/3 due to the finite length of the caustic (in effect SA of the entrance pupil of the camera lens).
Edited by BGRE, 13 October 2019 - 04:57 PM.