Vectorial aberrations of biconic surfaces

For non-rotationally symmetric systems, spherical surfaces provide a non-sufficient effect in correcting aberrations. In anamorphic systems, biconic surfaces are used to provide different focal power in tangential and sagittal directions. The biconic surface shape is also used as the basic shape of the freeform surface representation. The different focal power in tangential and sagittal planes generates large field-constant astigmatism, which is decoupled from a coma generated by the biconic surface. In this paper, the biconic surface sag is expanded up to the fourth order and decomposed into the spherical part, the aspherical part, and the freeform part. The vectorial aberrations of the biconic surface are derived based on the extended nodal aberration theory. When biconic surfaces are used to obtain the initial setup of off-axis systems, it is beneficial due to the decoupling of astigmatism and coma. For instance, in the initial system design of reflective camera systems, biconic surfaces provide the possibility to obtain the nodal point in the center of the field of view, which is beneficial for systems with large field of view. This paper provides the insight of aberration analysis of biconic surfaces and the conversion of biconic surfaces into Zernike fringe freeform surfaces.