Ray Mappings and the Weighted Least Action Principle
Two basic problems in optics are presented. The solutions to both problems are formulated in terms of the associated ray mappings. An alternative formulation based on a weighted sum of the actions along the rays is derived. Existence of solutions is established via the Weighted Least Action Principle. Numerical methods for computing the ray mappings are discussed. Finally, we demonstrate the theoretical considerations by presenting a complete solution to a specific beam shaping lens design.
This work is supported by grants from the Israel Science Foundation.
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