Second-order semi-aplanatic freeform optics as a limit case of the SMS 3D design method

Second-order semi-aplanatism provides better imaging quality along a line of the object plane close to a point than conventional aplanatic optics, which is of interest in applications with high aspect ratio sensors. Designing an optic with second-order semi-aplanatism requires the use of freeform surfaces, and can be done as a limit case of the SMS 3D design method applied to stigmatically image 3 collinear object points. The algorithm for this specific design problem is described and a lens example with 3 freeform surfaces is designed and analyzed.