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Continuous -time Fourier Transform01:11

Continuous -time Fourier Transform

746
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...
746

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High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
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Improve Temporal Fourier Transform Profilometry for Complex Dynamic Three-Dimensional Shape Measurement.

Yihang Liu1, Qican Zhang1, Haihua Zhang1

  • 1College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China;.

Sensors (Basel, Switzerland)
|March 29, 2020
PubMed
Summary
This summary is machine-generated.

This study presents an improved Temporal Fourier Transform Profilometry (TFTP) algorithm for high-speed 3-D shape measurement. The new method accurately captures dynamic scenes with sharp edges and abrupt changes, overcoming limitations of traditional techniques.

Keywords:
Temporal Fourier Transform Profilometry (TFTP)dynamic scene measurementfringe projectionhigh-speed 3-D measurementmechanical projectorphase unwrapping

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Area of Science:

  • Optical Metrology
  • 3-D Shape Measurement
  • Dynamic Scene Analysis

Background:

  • High-speed 3-D shape measurement is crucial for dynamic scene analysis.
  • Fourier Transform Profilometry (FTP) is suitable for dynamic scenes but limited by band-pass filters for objects with sharp edges or abrupt changes.

Purpose of the Study:

  • To develop an improved Temporal Fourier Transform Profilometry (TFTP) algorithm for accurate dynamic 3-D shape measurement.
  • To overcome the limitations of traditional FTP methods in capturing objects with sharp edges and abrupt reflectivity changes.

Main Methods:

  • An improved TFTP algorithm combined with a reference plane-based 3-D phase unwrapping algorithm was developed.
  • The method avoids spatial domain band-pass filtering and unwraps 3-D phase distribution along the temporal axis.
  • A high-speed, low-cost structured light pattern sequence projector with kHz projection frequencies was designed.

Main Results:

  • The improved TFTP method successfully measured the 3-D shape of isolated objects with sharp edges and abrupt changes.
  • High-frequency information of the measured object was well preserved, with each pixel processed independently.
  • Dynamic 3-D reconstruction was demonstrated at a rate of 297 Hz, limited by camera speed.

Conclusions:

  • The proposed TFTP algorithm is effective for high-speed dynamic 3-D shape measurement, especially for challenging objects.
  • The combination of the improved algorithm and a high-speed projector enables kHz-level dynamic measurements.
  • This technique offers a robust solution for capturing complex dynamic 3-D shapes.