## Design of diffractive optical elements for the fractional Fourier transform domain: phase-space approach

Applied Optics, Vol. 45, Issue 1, pp. 76-82 (2006)

http://dx.doi.org/10.1364/AO.45.000076

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### Abstract

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

**OCIS Codes**

(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

**Citation**

Markus Testorf, "Design of diffractive optical elements for the fractional Fourier transform domain: phase-space approach," Appl. Opt. **45**, 76-82 (2006)

http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-45-1-76

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