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
Original Manuscript: June 3, 2014
Revised Manuscript: August 8, 2014
Manuscript Accepted: August 13, 2014
Published: August 29, 2014
Christopher B. Croke and R. Andrew Hicks, "Solution to the bundle-to-bundle mapping problem of geometric optics using four freeform reflectors," J. Opt. Soc. Am. A 31, 2097-2104 (2014)