Design of zero reference codes using cross-entropy method

doi:10.1364/OE.17.022163

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)
http://dx.doi.org/10.1364/OE.17.022163

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Abstract

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 $({\overset{n}{n}}_{1})$ 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.

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

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

Citation
Jung-Chieh Chen, "Design of zero reference codes using cross-entropy method," Opt. Express 17, 22163-22170 (2009)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-24-22163

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References

J. Saez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Eusebio, and A. Bernabeu, "Optimal design of optical reference signals using a genetic algorithm," Opt. Lett. 30, 2734-2736 (2005). [CrossRef]
X. Yang and C. Yin, "A new method for the design of zero reference marks for grating measurement systems," J. Phys. E., Sci. Instrum. 19, 34-37 (1986). [CrossRef]
Y. Li, "Autocorrelation function of a bar code system," J. Mod. Opt. 34, 1571-1575 (1987). [CrossRef]
Y. Li, "Optical valve using bar codes," Optik 79, 67-74 (1988).
Y. Li, "Characterization and design of bar code systems for accurate alignment," Appl. Opt. 27, 2612-2620 (1988). [CrossRef] [PubMed]
Y. Li and F. T. S. Yu, "Design of bar code systems for accurate alignment: a new method," Appl. Opt. 29, 723-725 (1990). [CrossRef] [PubMed]
J. Saez-Landete, J. Alonso, and E. Bernabeu, "Design of zero reference codes by means of a global optimization method," Opt. Express 13, 195-201 (2005). [CrossRef] [PubMed]
R. Y. Rubinstein and D. P. Kroese, The Cross-Entropy Method. (Berlin, Germany, Springer, 2004).
S. Salcedo-Sanz, G. Camps-Valls, F. Perez-Cruz, J. Sepulveda-Sanchis, and C. Bousono-Calzon, "Enhancing genetic feature selection through restricted search and Walsh analysis," IEEE Trans. Syst., Man. Cybern. C, Appl. Rev. 34, 398-406 (2004). [CrossRef]

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[1] J. Saez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Eusebio, and A. Bernabeu, "Optimal design of optical reference signals using a genetic algorithm," Opt. Lett. 30, 2734-2736 (2005). [CrossRef]

[2] X. Yang and C. Yin, "A new method for the design of zero reference marks for grating measurement systems," J. Phys. E., Sci. Instrum. 19, 34-37 (1986). [CrossRef]

[3] Y. Li, "Autocorrelation function of a bar code system," J. Mod. Opt. 34, 1571-1575 (1987). [CrossRef]

[4] Y. Li, "Optical valve using bar codes," Optik 79, 67-74 (1988).

[5] Y. Li, "Characterization and design of bar code systems for accurate alignment," Appl. Opt. 27, 2612-2620 (1988). [CrossRef] [PubMed]

[6] Y. Li and F. T. S. Yu, "Design of bar code systems for accurate alignment: a new method," Appl. Opt. 29, 723-725 (1990). [CrossRef] [PubMed]

[7] J. Saez-Landete, J. Alonso, and E. Bernabeu, "Design of zero reference codes by means of a global optimization method," Opt. Express 13, 195-201 (2005). [CrossRef] [PubMed]

[8] R. Y. Rubinstein and D. P. Kroese, The Cross-Entropy Method. (Berlin, Germany, Springer, 2004).

[9] S. Salcedo-Sanz, G. Camps-Valls, F. Perez-Cruz, J. Sepulveda-Sanchis, and C. Bousono-Calzon, "Enhancing genetic feature selection through restricted search and Walsh analysis," IEEE Trans. Syst., Man. Cybern. C, Appl. Rev. 34, 398-406 (2004). [CrossRef]

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Design of zero reference codes using cross-entropy method