Hilbert's and Takeda's single-shot interferometry with a linear-carrier: a comparison

The purpose of the present work is to compare single-shot phase-retrieval methods based on Hilbert's transform with Takeda's spatial linear-carrier method. In addition, we briefly discuss the so-called slightly-off-axis method that involves two interferograms as an efficient way to remove background illumination bias. After carefully analyzing the assumptions implicit in both approaches, we demonstrate that the Hilbert transform based method is completely identical to the 30 years old Takeda's interferometry with a spatial linear-carrier. Validation experiments are presented.