We propose a method to design freeform imaging systems using inverse methods from nonimaging optics. A linear optical map in phase space implies that the ratio of source and target energy distributions is a constant. The performance of the inverse freeform design is compared to a classical design by raytracing parallel beams of light and comparing the corresponding spot sizes. The inverse design significantly outperforms the classical design.
Verma et al. (2025) studied this question.