Abstract
An extension of paraxial theory to systems with a single plane of symmetry is provided. This parabasal model is based on the evaluation of a differential region around the reference ray that is defined by the center of the object and the center of the stop. To include freeform surfaces in this model, the local curvatures at the intersection point of the reference ray and the surface are evaluated. As an application, a generalized Scheimpflug principle is presented. The validity of the derived formulas is tested for highly tilted surfaces and is in good agreement with the exact ray tracing results. The analytical expressions are used to provide a first-order layout design of a planar imaging system. (C) 2014 Society of Photo-Optical Instrumentation Engineers (SPIE)