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

Jung-Chieh Chen1, Chao-Kai Wen

  • 1Department of Optoelectronics and Communication Engineering, National KaohsiungNormal University, Kaohsiung 802, Taiwan. jcchen@nknucc.nknu.edu.tw

Applied Optics
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Summary
This summary is machine-generated.

A new cross-entropy method optimizes 2D zero reference codes (ZRCs) for grating measurement systems. This approach improves absolute positioning accuracy by reducing signal noise compared to genetic algorithms.

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Area of Science:

  • Optics and Photonics
  • Metrology
  • Computational Science

Background:

  • Grating measurement systems require precise zero reference signals for absolute positioning.
  • Designing two-dimensional zero reference codes (2D ZRCs) is crucial for accuracy.
  • The autocorrelation approximation is a key challenge in 2D ZRC design.

Purpose of the Study:

  • To develop an optimal cross-entropy (CE)-based method for designing 2D ZRCs.
  • To generate a superior zero reference signal for grating measurement systems.
  • To enhance the accuracy of absolute position, coordinate origin, or machine home position detection.

Main Methods:

  • Formulating the 2D ZRC design as a combination optimization problem based on autocorrelation function properties.
  • Applying the cross-entropy (CE) method to search for optimal 2D ZRCs.
  • Utilizing computer simulations to evaluate the performance of the designed ZRCs.

Main Results:

  • The CE-based method achieved significant reductions in the second maxima value of the zero reference signal.
  • Demonstrated a 15.38% reduction for a 16x16 grating system (n(1)=64).
  • Showed a 14.29% reduction for a 100x100 grating system (n(1)=300) compared to genetic algorithms.

Conclusions:

  • The cross-entropy method provides an effective approach for designing optimal 2D ZRCs.
  • This method enhances the quality of the zero reference signal, leading to improved positioning accuracy.
  • The CE-based ZRC design offers a notable improvement over conventional genetic algorithms in grating measurement systems.