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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 48, Iss. 32 — Nov. 10, 2009
  • pp: 6132–6142

Digital simulation of scalar optical diffraction: revisiting chirp function sampling criteria and consequences

David G. Voelz and Michael C. Roggemann  »View Author Affiliations


Applied Optics, Vol. 48, Issue 32, pp. 6132-6142 (2009)
http://dx.doi.org/10.1364/AO.48.006132


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Abstract

Accurate simulation of scalar optical diffraction requires consideration of the sampling requirement for the phase chirp function that appears in the Fresnel diffraction expression. We describe three sampling regimes for FFT-based propagation approaches: ideally sampled, oversampled, and undersampled. Ideal sampling, where the chirp and its FFT both have values that match analytic chirp expressions, usually provides the most accurate results but can be difficult to realize in practical simulations. Under- or oversampling leads to a reduction in the available source plane support size, the available source bandwidth, or the available observation support size, depending on the approach and simulation scenario. We discuss three Fresnel propagation approaches: the impulse response/transfer function (angular spectrum) method, the single FFT (direct) method, and the two-step method. With illustrations and simulation examples we show the form of the sampled chirp functions and their discrete transforms, common relationships between the three methods under ideal sampling conditions, and define conditions and consequences to be considered when using nonideal sampling. The analysis is extended to describe the sampling limitations for the more exact Rayleigh–Sommerfeld diffraction solution.

© 2009 Optical Society of America

OCIS Codes
(050.1940) Diffraction and gratings : Diffraction
(070.2580) Fourier optics and signal processing : Paraxial wave optics
(050.1755) Diffraction and gratings : Computational electromagnetic methods
(070.7345) Fourier optics and signal processing : Wave propagation

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: June 19, 2009
Manuscript Accepted: August 17, 2009
Published: November 2, 2009

Citation
David G. Voelz and Michael C. Roggemann, "Digital simulation of scalar optical diffraction: revisiting chirp function sampling criteria and consequences," Appl. Opt. 48, 6132-6142 (2009)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-48-32-6132

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