Generation of two-dimensional optical reference signals based on parametric minimum cross entropy

Yi Sheng Su*, Tsung Cheng Wu, Chung-Hsuan Wang, Min Kuan Chang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


In this letter, a novel design of two-dimensional (2-D) zero reference codes (ZRCs) based on parametric minimum cross entropy (PMCE) is proposed to generate 2-D optical zero reference signals (ZRSs) with low second maximum for grating alignment systems. An optical ZRS is necessary to obtain an absolute measurement in grating alignment systems. A method to acquire an optical ZRS is by means of illuminating two identical superimposed ZRCs. Because the movement between the two ZRCs is in two-axis, 2-D ZRCs are required. However, they are hard to design due to the high computational complexity, especially for large codes. The proposed PMCE method not only reduces the second maximum of 2-D optical ZRSs, but also decreases the computational complexity. Simulation results indicate that there are 8.33%∼ 22.22% reductions in the second maximum of several 2-D optical ZRSs, as compared with those of the recently proposed cross-entropy (CE) method. The PMCE method proves to be a powerful tool for the design of 2-D ZRCs.

Original languageEnglish
Article number5744098
Pages (from-to)813-815
Number of pages3
JournalIEEE Photonics Technology Letters
Issue number12
StatePublished - 2011


  • Autocorrelation function
  • combinatorial optimization
  • optical position measurement
  • optimization method
  • parametric minimum cross entropy (PMCE)
  • two-dimensional (2-D) optical zero reference signal (ZRS)
  • two-dimensional (2-D) zero reference code (ZRC)


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