Aberrations and spherocylindrical powers within subapertures of freeform surfaces.

A method is described for the derivation of refractive properties and aberration structure of subapertures of freeform surfaces. Surface shapes are described in terms of Zernike polynomials. The method utilizes matrices to transform between Zernike and Taylor coefficients. Expression as a Taylor series facilitates the translation and size rescaling of subapertures of the surface. An example operation using a progressive addition lens surface illustrates the method.