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

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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