OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 18 — Jun. 20, 2010
  • pp: 3560–3565

Design of two-dimensional zero reference codes with cross-entropy method

Jung-Chieh Chen and Chao-Kai Wen  »View Author Affiliations


Applied Optics, Vol. 49, Issue 18, pp. 3560-3565 (2010)
http://dx.doi.org/10.1364/AO.49.003560


View Full Text Article

Enhanced HTML    Acrobat PDF (616 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

We present a cross-entropy (CE)-based method for the design of optimum two-dimensional (2D) zero reference codes (ZRCs) in order to generate a zero reference signal for a grating measurement system and achieve absolute position, a coordinate origin, or a machine home position. In the absence of diffraction effects, the 2D ZRC design problem is known as the autocorrelation approximation. Based on the properties of the autocorrelation function, the design of the 2D ZRC is first formulated as a particular combination optimization problem. The CE method is then applied to search for an optimal 2D ZRC and thus obtain the desirable zero reference signal. Computer simulation results indicate that there are 15.38% and 14.29% reductions in the second maxima value for the 16 × 16 grating system with n 1 = 64 and the 100 × 100 grating system with n 1 = 300 , respectively, where n 1 is the number of transparent pixels, compared with those of the conventional genetic algorithm.

© 2010 Optical Society of America

OCIS Codes
(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:
Instrumentation, Measurement, and Metrology

History
Original Manuscript: January 15, 2010
Revised Manuscript: May 21, 2010
Manuscript Accepted: May 21, 2010
Published: June 17, 2010

Citation
Jung-Chieh Chen and Chao-Kai Wen, "Design of two-dimensional zero reference codes with cross-entropy method," Appl. Opt. 49, 3560-3565 (2010)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-49-18-3560


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. J. Saez-Landete, S. Salcedo-Sanz, M. Rosa-Zurera, J. Eusebio, and A. Bernabeu, “Design of two-dimensional zero reference codes with a genetic algorithm,” Opt. Lett. 31, 1648–1650(2006). [CrossRef] [PubMed]
  2. Y. Chen, W. Huang, and X. Dang, “Design and analysis of two-dimensional zero-reference marks for alignment systems,” Rev. Sci. Instrum. 74, 3549–3553 (2003). [CrossRef]
  3. Y. Li, “Optical valve using bar codes,” Optik (Jena) 79, 67–74 (1988).
  4. X. Yang and C. Yin, “A new method for the design of zero reference marks for grating measurement systems,” J. Phys. E 19, 34–37 (1986). [CrossRef]
  5. J. Saez-Landete, J. Alonso, and E. Bernabeu, “Design of two-dimensional zero reference codes by means of a global optimization method,” Opt. Express 13, 4230–4236 (2005). [CrossRef] [PubMed]
  6. R. Y. Rubinstein and D. P. Kroese, The Cross-Entropy Method (Springer, 2004).
  7. J. Chen, “Design of zero reference codes using cross-entropy method,” Opt. Express 17, 22163–22170 (2009). [CrossRef] [PubMed]
  8. Y. Li, “Autocorrelation function of a bar code system,” J. Mod. Opt. 34, 1571–1575 (1987). [CrossRef]
  9. If no design was done, we may randomly generate a binary 2D ZRC c. In this case, however, we still need an extra operation to fix the number of 1s in the binary strings to n1. This can be carried out by the restricted search operator , which randomly adds or removes the necessary 1s to meet the number of the transparent pixels.
  10. 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 34, 398–406 (2004). [CrossRef]
  11. J. Saez-Landete, S. Salcedo-Sanz, F. Cruz-Roldan, P. Amo-Lopez, and M. Blanco-Velasco, “Design of two-dimensional optical alignment signals robust to diffractive effects,” J. Lightwave Technol. 26, 1702–1707 (2008). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited