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8 June 2005 Wigner optics
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There seems to be no single simple representation or set of concepts available to provide an 'intuitive umbrella' under which, for example, classical speckles based metrology, quantum optics, and optical signal processing can be simultaneously seen by the student as part of the pleasing whole that is modern optics. In this paper we propose to show how the early introduction of the concepts of the Wigner (Ville) Distribution Function, can be achieved, without the early recourse to large amounts of mathematics. We show how a whole series of extremely high-level concepts and ideas then become accessible to the student. As examples of such ideas I mention the Linear Canonical Transformations, the Space Bandwidth Product and sampling issues in the numerical simulation of optical systems. We believe that the result, which we refer to as Wigner Optics, provides a consistent and intuitively pleasing structure, which not only unambiguously relates geometric and ray optics with Fourier and wave optics but also encourages the student to place these models in the context of signal processing. Familiarity and early exposure to the WDF has the further advantage that it prepares the student for material on more advanced concepts, i.e. partially coherent and quantum optics.
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John T. Sheridan, William T. Rhodes, and B. M. Hennelly "Wigner optics", Proc. SPIE 5827, Opto-Ireland 2005: Photonic Engineering, (8 June 2005);

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