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Applied Optics

Applied 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)

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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

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

Jung-Chieh Chen and Chao-Kai Wen, "Design of two-dimensional zero reference codes with cross-entropy method," Appl. Opt. 49, 3560-3565 (2010)

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  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.
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