Phase-space optics was one of Adolf Lohmann’s favorite research topics and appears frequently in his work. With a unique style he applied the phase-space perspective to a variety of optical problems, with a focus on more comprehensible problem solutions and a particular interest to analyze optical signals and systems in terms of their space–bandwidth product requirements. In his work, optical phase space is promoted as a hybrid of paraxial wave optics and geometrical optics. In contrast to more rigorous notions of phase space, Lohmann preferred a heuristic approach that avoids almost entirely the mathematical formalism associated with the Wigner distribution function. This approach is introduced for the first time as a distinct way to apply phase-space optics. The application of Lohmann’s phase-space optics to paraxial optical cloaking, the Lohmann–Alvarez lens, and holography is not only used to exemplify this unique form of phase-space optics, but also to highlight Lohmann’s unique and creative way of problem solving.
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