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Transmission of Multiple Signals through an Optical Fiber Using Wavefront Shaping
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Published on: March 20, 2017

Wavelet ridge techniques in optical fringe pattern analysis.

Sikun Li1, Xianyu Su, Wenjing Chen

  • 1Department of Opto-Electronics, Sichuan University, Chengdu 610064, China.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|May 29, 2010
PubMed
Summary
This summary is machine-generated.

This study clarifies wavelet ridge techniques for optical fringe pattern analysis. It confirms phase accuracy and introduces a simple scale selection method, validated by simulations and experiments.

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Area of Science:

  • Optics and Photonics
  • Signal Processing
  • Applied Mathematics

Background:

  • Optical fringe patterns are crucial in metrology and imaging.
  • Wavelet transform methods offer powerful tools for analyzing such patterns.
  • Understanding wavelet behavior is key to accurate fringe analysis.

Purpose of the Study:

  • To theoretically clarify wavelet ridge techniques for optical fringe pattern analysis.
  • To investigate the impact of different daughter wavelet definitions.
  • To establish relations between fringe patterns and wavelet transform parameters.

Main Methods:

  • Theoretical analysis of wavelet ridge techniques with two daughter wavelet definitions.
  • Verification of phase equivalence between fringe patterns and wavelet coefficients on the ridge.
  • Theoretical clarification of instantaneous frequency and scale parameter relations for phase gradient method.
  • Introduction of a novel scale vector selection method.

Main Results:

  • Phase of optical fringe patterns equals wavelet transform coefficients' phase on the ridge for both definitions.
  • Theoretical differences in wavelet transform algorithm performance identified.
  • Strict relations between instantaneous frequency and scale parameter at the wavelet ridge clarified.
  • A simple scale vector selection method was proposed.

Conclusions:

  • The theoretical clarification validates wavelet ridge techniques in optical fringe pattern analysis.
  • The proposed scale selection method is effective and experimentally verified.
  • This work enhances the understanding and application of wavelet methods in optical metrology.