Providing a Visual Understanding of Holography Through Phase Space Representations

Digital holograms are a prime example for signals, which are best understood in phase space—the joint space of spatial coordinates and spatial frequencies. Many characteristics, as well as optical operations can be visualized therein with so called phase space representations (PSRs). However, literature relies often only on symbolic PSRs or on, in practice, visually insufficient PSRs like the Wigner–Ville representation. In this tutorial-style paper, we will showcase the S-method, which is both a PSR that can be calculated directly from any given signal, and that allows for a clear visual interpretation. We will highlight the power of space-frequency analysis in digital holography, explain why this specific PSR is recommended, discuss a broad range of basic operations, and briefly overview several interesting practical questions in digital holography.