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Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy
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Windowed Fourier transform profilometry based on improved S-transform.

F Da1, F Dong

  • 1School of Automation, Southeast University, Nanjing 210096, China. dafp@seu.edu.cn

Optics Letters
|September 4, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces an improved S-transform for windowed Fourier transform (WFT) profilometry, enhancing phase map accuracy. By correcting deviations in instantaneous frequency, this novel method offers more precise fringe pattern analysis for practical applications.

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Area of Science:

  • Optics and Photonics
  • Signal Processing
  • Metrology

Background:

  • Windowed Fourier Transform (WFT) profilometry is a key technique for surface measurement.
  • Existing WFT methods can be limited by phase deviations affecting accuracy.
  • The S-transform offers time-frequency analysis but requires refinement for precise phase retrieval.

Purpose of the Study:

  • To develop a novel WFT profilometry method based on an improved S-transform.
  • To derive and address the impact of the second-order phase derivative on the S-transform ridge.
  • To achieve more accurate instantaneous frequency estimation and phase map generation.

Main Methods:

  • Development of an improved S-transform incorporating phase deviation analysis.
  • Derivation of the second-order phase derivative's impact (φ''(b)) on the S-transform.
  • Estimation and removal of phase deviation for accurate instantaneous frequency calculation.
  • Application of WFT using a window size map derived from instantaneous frequency.

Main Results:

  • The improved S-transform effectively estimates and corrects for phase deviations.
  • Accurate instantaneous frequency is obtained after deviation removal.
  • A precise phase map of fringe patterns is generated using the WFT with the derived window size map.
  • The novel method demonstrates superior performance compared to WFT based on wavelet transform.

Conclusions:

  • The proposed WFT profilometry method based on improved S-transform provides highly accurate phase maps.
  • The technique effectively addresses limitations of previous WFT approaches.
  • Numerical simulations and experimental results validate the method's practical applicability in metrology and surface analysis.