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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 5 — Feb. 10, 2012
  • pp: 644–650

Ray matrix analysis of the fast Fresnel transform with applications towards liquid crystal displays

Jeffrey A. Davis and Don M. Cottrell  »View Author Affiliations


Applied Optics, Vol. 51, Issue 5, pp. 644-650 (2012)
http://dx.doi.org/10.1364/AO.51.000644


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Abstract

We reexamine a previously published algorithm for performing a fast Fresnel diffraction calculation that uses two Fourier transform operations and is computationally much faster than the conventional approach. We analyze this technique using a ray matrix analysis and find explicit expressions for the maximum and minimum distances over which this algorithm is accurate. These distances coincide with the experimental distances that are appropriate when patterns are encoded onto liquid crystal displays. We show two examples that confirm our ideas. We expect that these results will be very useful for computational comparison with experimental studies of a variety of diffraction phenomena.

© 2012 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(080.2730) Geometric optics : Matrix methods in paraxial optics
(070.2025) Fourier optics and signal processing : Discrete optical signal processing

ToC Category:
Fourier Optics and Signal Processing

History
Original Manuscript: November 11, 2011
Revised Manuscript: November 18, 2011
Manuscript Accepted: November 21, 2011
Published: February 9, 2012

Citation
Jeffrey A. Davis and Don M. Cottrell, "Ray matrix analysis of the fast Fresnel transform with applications towards liquid crystal displays," Appl. Opt. 51, 644-650 (2012)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-51-5-644

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