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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 17, Iss. 24 — Nov. 23, 2009
  • pp: 22163–22170

Design of zero reference codes using cross-entropy method

Jung-Chieh Chen  »View Author Affiliations

Optics Express, Vol. 17, Issue 24, pp. 22163-22170 (2009)

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This paper considers the use of autocorrelation properties to design zero reference codes (ZRCs) for optical applications. Based on the properties of the autocorrelation function, the design of an optimum ZRC problem is transformed into a minimization problem with binary variables, and the objective is to minimize the second maximum of the autocorrelation signal σ. However, the considerable computational complexity for an exhaustive search through all combinations of ( n n 1 ) different code patterns is a potential problem especially for large codes, where n and n1 are the length of the ZRC and the number of transparent slits, respectively. To minimize σ while reducing the computational complexity at the same time, we introduce the Cross-Entropy (CE) method, an effective algorithm that solves various combinatorial optimization problems to obtain a good code. The computer simulation results show that compared with the conventional genetic algorithm (GA), the proposed CE obtains the better σ with low computational complexity.

© 2009 Optical Society of America

OCIS Codes
(050.2770) Diffraction and gratings : Gratings
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3940) Instrumentation, measurement, and metrology : Metrology
(220.0220) Optical design and fabrication : Optical design and fabrication
(230.0230) Optical devices : Optical devices

ToC Category:
Diffraction and Gratings

Original Manuscript: August 18, 2009
Revised Manuscript: November 14, 2009
Manuscript Accepted: November 15, 2009
Published: November 19, 2009

Jung-Chieh Chen, "Design of zero reference codes using cross-entropy method," Opt. Express 17, 22163-22170 (2009)

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