Deriving, explicating, and extending interferometric methods using Green's theorem

Abstract

Interferometry has its foundation in Green's theorem. Dual measurements (pressure data and its normal derivative) are required to satisfy this theorem. Interferometry makes one approximation for each normal derivative in the theorem to avoid needing dual measurements, compromising the theory and giving rise to artifacts or spurious multiples. In this paper, an analytic example is provided to explicitly show the creation of spurious multiples. An analogous analytic example using Green's theorem will demonstrate its inner workings and the fact that the information in the normal derivative is necessary to avoid creating artifacts. A different form of Green's theorem, where the normal derivatives are not required, will also be provided.