Design of a three-dimensional parallel-to-point imaging system based on inverse methods

We present an inverse method for designing a three-dimensional imaging system comprising of freeform optical surfaces. We impose an imaging condition on the optical map and combine it with the law of conservation of energy to conclude that the ratio of energy distributions at the source and target of an imaging system must be constant. A mathematical model for the design of a parallel-to-point system consisting of two freeform reflectors is presented. A Schwarzschild telescope, a classical design known for maximum correction of third-order aberrations, is utilized to specify the design parameters in the mathematical model, enabling us to compute an inverse freeform imaging system. The performance of both designs is compared by ray tracing various parallel beams of light and determining the corresponding spot sizes of the image. We demonstrate that our inverse freeform design is superior to the classical design.