On an analogy between the Wiener–Hopf formulations of discrete and continuous diffraction problems

Abstract This article is dedicated to unifying the framework used to derive the Wiener–Hopf equations arising from some discrete and continuous wave diffraction problems. The main tools are the discrete Green’s identity and the appropriate notion of discrete normal derivative. The resulting formal analogy between the Wiener–Hopf equations allows one to effortlessly move between the discrete and continuous formulations. The validity is illustrated through several famous two-dimensional canonical diffraction problems and extended to three-dimensional problems. It is shown that the analogy preserves kernels of the Chebotarev–Daniele–Khrapkov class, which allows the solution of certain discrete problems.