Abstract

A theoretical development is presented in this paper for describing and understanding the imaging and aberrations of a general form surface. The development is based on the Taylor expansion of an arbitrary ray trace from the object reference plane to the image reference plane, which is called the base mapping of the general form surface in this paper. The base mapping is expressed as two Taylor series of the object and pupil coordinates and the imaging and aberration coefficients in the third-order scope are derived and presented as analytical expressions relevant to the optic parameters, invoking no approximations. The situation with tilted object and observing plane is also considered, and the mapping from a tilted object to a tilted observing plane is derived via simple mathematical manipulations based on the base mapping.

© 2017 Optical Society of America

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