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Related Experiment Videos

General n-dimensional quadrature transform and its application to interferogram demodulation.

Manuel Servin1, Juan Antonio Quiroga, Jose Luis Marroquin

  • 1Centro de Investigaciones en Optica A. C., Apartado Postal 1-948, 37150 Leon, Guanajuato, Mexico. mservin@cio.mx

Journal of the Optical Society of America. A, Optics, Image Science, and Vision
|May 16, 2003
PubMed
Summary

This study introduces a novel n-dimensional quadrature operator for accurately determining phase in signals, irrespective of their frequency spectrum. The operator enables precise phase calculation in applications like interferometry and electrical communications.

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Area of Science:

  • Signal Processing
  • Image Analysis
  • Optical Metrology

Background:

  • The Hilbert transform is conventionally used to obtain quadrature signals for phase retrieval in interferometry and electrical communications.
  • Existing methods using the Hilbert transform are limited to signals with monotonically increasing modulating phases.
  • Accurate phase determination is crucial for analyzing temporal signals and interferometric data.

Purpose of the Study:

  • To propose a generalized n-dimensional quadrature operator capable of retrieving phase information from signals with arbitrary frequency spectra.
  • To develop a method for calculating the modulating phase (phi) across the entire domain of interest.
  • To provide a robust numerical algorithm for phase retrieval in two-dimensional interferograms.

Main Methods:

Related Experiment Videos

  • Developed an n-dimensional quadrature operator based on two vector fields: local image gradient normalized by local frequency magnitude, and the sign of local frequency.
  • Derived the quadrature operator in image space using differential vector calculus.
  • Extended the derivation to the frequency domain using a generalized n-dimensional Hilbert transform.

Main Results:

  • The proposed operator successfully transforms cos(phi) into -sin(phi) for any signal, irrespective of its frequency spectrum.
  • The inner product of the defined vector fields yields the desired quadrature signal.
  • A robust numerical algorithm is presented for phase retrieval in two-dimensional single-image closed-fringe interferograms.

Conclusions:

  • The novel n-dimensional quadrature operator offers a significant advancement over the traditional Hilbert transform for phase retrieval.
  • This method allows for accurate phase calculation in a broader range of applications, including complex interferometric and communication signals.
  • The developed algorithm provides a practical tool for analyzing challenging two-dimensional interferometric data.