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Discrete Fourier Transform01:15

Discrete Fourier Transform

The Discrete Fourier Transform (DFT) is a fundamental tool in signal processing, extending the discrete-time Fourier transform by evaluating discrete signals at uniformly spaced frequency intervals. This transformation converts a finite sequence of time-domain samples into frequency components, each representing complex sinusoids ordered by frequency. The DFT translates these sequences into the frequency domain, effectively indicating the magnitude and phase of each frequency component present...

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Compact Lens-less Digital Holographic Microscope for MEMS Inspection and Characterization
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Highly contrasted Bessel fringe minima visualization for time-averaged vibration profilometry using Hilbert transform

Krzysztof Patorski1, Maciej Trusiak

  • 1Warsaw University of Technology, Institute of Micromechanics and Photonics, 8 Sw A. Boboli St., 02-525 Warsaw, Poland. k.patorski@mchtr.pw.edu.pl

Optics Express
|August 14, 2013
PubMed
Summary
This summary is machine-generated.

This study presents a robust method for visualizing dark Bessel fringes in microelectromechanical systems (MEMS) vibration testing. The technique corrects for noise and light variations without precise phase shifting, enhancing fringe pattern analysis.

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Area of Science:

  • Optical metrology
  • Microelectromechanical Systems (MEMS) analysis
  • Vibration testing

Background:

  • Time-averaged fringe patterns in MEMS vibration testing are additive moirés, insensitive to carrier displacements.
  • Existing methods may require precise phase shifting and specific recording conditions.

Purpose of the Study:

  • To develop a robust method for visualizing the centers of dark Bessel fringes in MEMS vibration testing.
  • To overcome limitations of traditional fringe analysis techniques.

Main Methods:

  • Utilizing Hilbert transform vulnerability to additive trends for fringe visualization.
  • Employing background and noise correction by subtracting frames with shifted carriers.
  • Subtracting normalized images with slightly different bias levels.

Main Results:

  • The proposed method effectively visualizes dark Bessel fringe centers.
  • It demonstrates robustness against light power variations and phase shifting nonuniformities.
  • No requirement for precise phase shifting, cosinusoidal carrier, or linear recording.

Conclusions:

  • The developed technique offers a reliable approach for analyzing MEMS vibration testing fringe patterns.
  • It enhances the accuracy and simplifies the process of fringe analysis.
  • The method's robustness is validated through synthetic and experimental results.