We compare two analytical methods for designing stigmatic lenses that are based on very different paradigms published recently [Appl. Opt. 57, 9341 (2018) [CrossRef] ; J. Opt. Soc. Am. A 37, 1155 (2020) [CrossRef] ]. 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.

中文翻译：

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独特的解决方案

我们比较了两种基于最近发布的范例而设计的散光镜片的分析方法[Appl。选择。57，9341（2018）[交叉引用] ; J.Opt。Soc。上午。甲37，1155（2020）[交叉引用] ]。在此过程中，我们得出了第三种混合方法，这是将两种原始方法结合在一起的结果。在相同的初始条件下，精确的数值分析表明这三种方法得出的结果相同。这清楚地证明，针对已知边界条件设计凸透镜的问题具有与所使用形式主义无关的独特解决方案。