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Fundamental limits on the digital phase measurement method based on cross-correlation analysis.

Yu-Rong Liang1, Hui-Zong Duan, Hsien-Chi Yeh

  • 1MOE Key Laboratory of Fundamental Physical Quantities Measurement, School of Physics, Huazhong University of Science and Technology, 1037 Luo Yu Road, Wuhan 430074, People's Republic of China.

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This study introduces a digital phase measurement method using cross-correlation analysis for laser interferometry. It achieves ultra-precision displacement measurement with a resolution of 63 pm, identifying a novel cyclic error source.

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Area of Science:

  • * Metrology and Optical Engineering
  • * Precision Measurement and Instrumentation

Background:

  • * Ultra-precision phase measurement is critical for advanced laser interferometry.
  • * Existing methods face challenges with noise and sampling inaccuracies.

Purpose of the Study:

  • * To develop and analyze a fully digital phase measurement method based on cross-correlation.
  • * To investigate measurement errors including quantization, white noise, and non-integral-cycle sampling.
  • * To demonstrate the application in an ultra-precision heterodyne laser interferometer for displacement measurement.

Main Methods:

  • * Implementation of a fully digital phase measurement technique utilizing cross-correlation analysis.
  • * Analysis of measurement errors stemming from sampling quantization, white noise, and non-integral-cycle sampling.
  • * Construction of an ultra-precision heterodyne laser interferometer with a digital phase measurement system and an ultra-stable optical bench.

Main Results:

  • * Achieved a noise level of 1.2 × 10⁻⁶ rad/√Hz at 1 Hz.
  • * Observed and characterized a novel cyclic phase error of approximately 10⁻² rad/√Hz due to non-integral-cycle sampling.
  • * Demonstrated a measurement resolution of 63 picometers (pm) for displacement measurement.

Conclusions:

  • * The developed digital cross-correlation method enables ultra-precision phase measurement.
  • * Non-integral-cycle sampling introduces a significant, previously unreported cyclic error.
  • * The heterodyne laser interferometer system achieves high-resolution displacement measurements, showcasing the method's practical utility.