Riesz transform-based digital four-step phase-shifting interferometer

Yassine Tounsi, Manoj Kumar, Ahmed Siari, Fernando Mendoza Santoyo, Osamu Matoba, Abdelkrim Nassim

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations


Phase-shifting interferometry is a highly accurate technique for obtaining phase distribution from the recorded fringe patterns. Generally, phase-shifting interferometry requires recording several fringe patterns with varying phase shifts experimentally and during the acquisition, the object must be stable. Also, the atmospheric turbulence and mechanical conditions should also remain constant during this time. These requirements limit the use of these phase-shifting interferometric techniques in dynamic event studies. In the present work, we introduce Riesz transformed based digital four-step phase-shifting interferometer to obtain phase distribution from a single recorded fringe pattern. All the experimental phase-shifting setups necessary to realize the phase-shifting are removed. The idea is based on the recording of a single fringe pattern, and computes its Riesz transform at first, second and third-orders. The obtained Riesz transform components are combined to generate three p/2 phase-shifted fringe patterns, and then, the phase distribution is obtained from these phase-shifted fringe patterns. The performance of this method is demonstrated first by using numerical simulation and the quantitative appraisal is given by using image quality index. Further, we apply this technique on a real fringe pattern recorded in digital speckle pattern interferometry (DSPI). The obtained results reveal that our method provides a simple and accurate solution for phase evaluation, therefore, makes it suitable for real-time measurements.

Original languageEnglish
Title of host publicationOptics, Photonics and Digital Technologies for Imaging Applications VI
EditorsPeter Schelkens, Tomasz Kozacki
ISBN (Electronic)9781510634787
StatePublished - 1 Jan 2020
Externally publishedYes
EventOptics, Photonics and Digital Technologies for Imaging Applications VI 2020 - Virtual, Online, France
Duration: 6 Apr 202010 Apr 2020

Publication series

NameProceedings of SPIE - The International Society for Optical Engineering
ISSN (Print)0277-786X
ISSN (Electronic)1996-756X


ConferenceOptics, Photonics and Digital Technologies for Imaging Applications VI 2020
CityVirtual, Online


  • Digital speckle pattern interferometry
  • Phase evaluation
  • Phase-shifting interferometry
  • Riesz transform

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics
  • Computer Science Applications
  • Applied Mathematics
  • Electrical and Electronic Engineering


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