A unified mathematical formulation for designing and analyzing even the most general optical processor is presented. It exploits the Wigner distribution function to characterize the illumination, the input, the inherent filter, and the output results. To characterize the propagation of the light through the optical processor setup, we exploit the Wigner matrix formalism, which is appealing because it allows simple geometric analysis. The Wigner distribution function was extended to include illumination of arbitrary coherence so that processors using either coherent light or partially coherent light can be designed and analyzed with the same Wigner formalism. The basic principles, design, and analysis of the imaging and Fourier-transform operations and use of the Wigner formalism to evaluate the performance and tolerances of optical processors are presented.
© 2001 Optical Society of America
(030.1640) Coherence and statistical optics : Coherence
(030.4280) Coherence and statistical optics : Noise in imaging systems
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(070.4550) Fourier optics and signal processing : Correlators
(080.2730) Geometric optics : Matrix methods in paraxial optics
Avi Pe’er, Dayong Wang, Adolf W. Lohmann, and Asher A. Friesem, "Wigner Formulation of Optical Processing with Light of Arbitrary Coherence," Appl. Opt. 40, 249-256 (2001)