Uniqueness of stigmatic solutions

We compare two analytical methods for designing stigmatic lenses that are based on very different paradigms published recently [Appl. Opt.57, 9341 (2018)APOPAI0003-693510.1364/AO.57.009341; J. Opt. Soc. Am. A37, 1155 (2020)JOAOD60740-323210.1364/JOSAA.392795]. In the process, we derive a third hybrid approach, which is the result of combining the two original methods. Given the same initial conditions, an accurate numerical analysis shows that the three methods yield the same results. This is clear evidence that the problem of designing a stigmatic lens for a known boundary condition has a unique solution independent of the formalism used.