Phase-space optics is used to relate the problem of designing diffractive optical elements for any first-order optical system to the corresponding design problem in the Fraunhofer diffraction regime. This, in particular, provides a novel approach for the fractional Fourier transform domain. For fractional Fourier transforms of arbitrary order, the diffractive element is determined as the optimum design computed for a generic Fourier transform system, scaled and modulated with a parabolic lens function. The phase-space description also identifies critical system parameters that limit the performance and applicability of this method. Numerical simulations of paraxial wave propagation are used to validate the method.
© 2006 Optical Society of America
(050.1970) Diffraction and gratings : Diffractive optics
(080.2730) Geometric optics : Matrix methods in paraxial optics
(100.5070) Image processing : Phase retrieval
(350.6980) Other areas of optics : Transforms
Markus Testorf, "Design of diffractive optical elements for the fractional Fourier transform domain: phase-space approach," Appl. Opt. 45, 76-82 (2006)