An inverse method for the design of freeform double-reflector imaging systems

This paper proposes an inverse method to design two-dimensional freeform imaging systems. The mathematical model to design a parallel-to-point double-reflector imaging system using inverse methods from nonimaging optics is presented. An imaging condition is imposed on the energy distributions at the source and target of the optical system. The inverse freeform design is compared to the classical Schwarzschild telescope, which is well-known for minimizing third-order aberrations. A raytracer using quasi-interpolation is employed to test the performance of both designs by comparing the spot sizes corresponding to on-axis and off-axis light rays. A numerical example demonstrates that the inverse freeform design outperforms the classical design.