Here we present a method for the coupled design of four freeform reflective surfaces that will control a bundle of rays. By this, we mean that given an input bundle of rays, we can construct an optical system that will map it to a given output bundle, where a ray-to-ray correspondence is realized as per the prescribed data. The method makes use of the Cartan–Kähler theorem of exterior differential systems. Sample imaging applications are given.
© 2014 Optical Society of America
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