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Differential Confocal Optical Probes with Optimized Detection Efficiency and Pearson Correlation Coefficient Strategy

Zhiyi Wang1,2,3, Tingyu Wang1,2,3, Yongqiang Yang1,2,3

  • 1Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun 130033, China.

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Summary

This study presents a new method using Pearson

Keywords:
Pearson correlation coefficientcompensation strategydifferential confocal microscopypeak clusteringstride length

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Area of Science:

  • Optical Metrology
  • Surface Characterization
  • Precision Engineering

Background:

  • Accurate quantification of free-form surfaces with differential confocal microscopy is hindered by axial scanning errors and surface slope.
  • Traditional linear fitting methods introduce significant measurement errors in the presence of sloshing and finite surface slopes.

Purpose of the Study:

  • To develop and validate a compensation strategy to reduce measurement errors in differential confocal microscopy.
  • To introduce a fast-matching algorithm for real-time, non-contact surface profiling.
  • To enhance the accuracy and efficiency of free-form surface measurements.

Main Methods:

  • Implementation of a compensation strategy utilizing Pearson's correlation coefficient.
  • Development of a peak clustering-based fast-matching algorithm for real-time processing.
  • Validation through detailed simulations and physical experiments.

Main Results:

  • Measurement errors were reduced to below 10 nm for slopes less than 12° (NA=0.4).
  • The proposed algorithm achieved an 83.37% speed improvement over traditional methods.
  • Repeatability and anti-disturbance tests confirmed the robustness and efficiency of the compensation strategy.

Conclusions:

  • The Pearson correlation coefficient-based compensation strategy effectively minimizes measurement errors in differential confocal microscopy.
  • The fast-matching algorithm enables high-speed, non-contact measurements of free-form surfaces.
  • The proposed method offers a simple, efficient, and robust solution with significant potential for industrial applications.