Synthesis of Initial Plane-Symmetric Optical Systems using Parabasal Theory

Commonly in the early stage of an optical design procedure paraxial theory is used for the synthesis of an initial system design. However, this approach cannot be applied for generalized optical systems with arbitrarily tilted / decentered object, pupils, surfaces and images like EUV-objectives or integrated optical micro systems. To account for the occurring violation of rotational symmetry the base ray, defined by the object point and the center of the entrance pupil, is used as a reference instead of the classical optical axis. Evaluating only rays within a differential region around the base ray (parabasal rays) allows for analytical derivation of a full imaging framework for systems without symmetry named parabasal theory. In our contribution we present the determination of an initial plane-symmetric optical system satisfying optical specifications in a parabasal region (object and image plane orientation, magnification) as well as dimensional constraints. To this end an optimization is applied to the analytical system description. The system parameters are automatically transferred to commercial optical design software for final optimization steps based on real ray tracing.