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Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

The Fourier series is instrumental in representing periodic functions, offering a powerful method to decompose such functions into a sum of sinusoids. This technique, however, necessitates modification when applied to nonperiodic functions. Consider a pulse-train waveform consisting of a series of rectangular pulses. When these pulses have a finite period, they can be accurately represented by a Fourier series. Yet, as the period approaches infinity, resulting in a single, isolated pulse, the...

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In Situ Time-dependent Dielectric Breakdown in the Transmission Electron Microscope: A Possibility to Understand the Failure Mechanism in Microelectronic Devices
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Non-destructive imaging using the time domain topological energy method.

N Dominguez1, V Gibiat

  • 1EADS (European Aeronautic Defence and Space Company), Innovation Works Department, 18 rue Marius Terce, 31025 Toulouse, France. nicolas.dominguez@eads.net

Ultrasonics
|September 25, 2009
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Summary

The time domain topological gradient method offers a low-cost, numerically implemented approach for imaging complex structures. This technique demonstrates effective defect detection in non-destructive testing, even with noisy experimental data.

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Area of Science:

  • Non-destructive testing
  • Ultrasonic imaging
  • Computational electromagnetics

Background:

  • The time domain topological gradient (TDTG) is a novel imaging technique.
  • Previous work demonstrated TDTG on simulated data for complex structures.
  • The method combines forward and adjoint ultrasonic fields.

Purpose of the Study:

  • To validate the TDTG method using experimental data.
  • To assess the TDTG method's performance in non-destructive testing (NDT) applications.
  • To evaluate the method's robustness in complex configurations, such as composite materials.

Main Methods:

  • Utilized a numerical time reversal operation for the adjoint field.
  • Employed a forward ultrasonic field analogous to a "photographic developer".
  • Combined computed forward and adjoint ultrasonic fields to generate images.

Main Results:

  • Successfully applied the TDTG method to experimental NDT data.
  • Demonstrated the method's efficiency in imaging defects within complex structures.
  • Confirmed the method's effectiveness even with noisy experimental data and in challenging composite material testing.

Conclusions:

  • The TDTG method is efficient for non-destructive testing of complex structures.
  • Numerical implementation of time reversal allows for low-cost systems.
  • The technique shows promise for real-world applications, including composite material inspection.