31 December 2003 Wigner optics and wave optics: fundamentals and practical applications
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Proceedings Volume 5182, Wave-Optical Systems Engineering II; (2003); doi: 10.1117/12.509133
Event: Optical Science and Technology, SPIE's 48th Annual Meeting, 2003, San Diego, California, United States
Abstract
We discuss the significance of the Wigner Optics (WiO) and the Wigner Distribution Function (WDF), in understanding problems usually dealt with using Wave Optics (WaO). We first present a derivation of the WDF transport equation, equivalent to the Helmhotz equation. We then discuss the corresponding first order WDF differential equation and the 'paraxial’ equation. The Fresnel transform can be derived from the Paraxial Approximation (PA). However another integral transform is required to describe our first order equation. This equation is not a paraxial transform but does take account of the characteristics of the field. We clarify how these transforms are linked to electromagnetic theory. Finally we justify the practical significance we attach to WiO by describe how a new way of understanding motion measurement systems can be achieved using these ideas.
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John T. Sheridan, Bryan Hennelly, Damien Kelly, "Wigner optics and wave optics: fundamentals and practical applications", Proc. SPIE 5182, Wave-Optical Systems Engineering II, (31 December 2003); doi: 10.1117/12.509133; http://dx.doi.org/10.1117/12.509133
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KEYWORDS
Wigner distribution functions

Speckle

Differential equations

Paraxial approximations

Integral transforms

Photography

Fourier transforms

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