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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 18, Iss. 8 — Aug. 1, 2001
  • pp: 1862–1870

Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform

Kieran G. Larkin, Donald J. Bone, and Michael A. Oldfield  »View Author Affiliations

JOSA A, Vol. 18, Issue 8, pp. 1862-1870 (2001)

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It is widely believed, in the areas of optics, image analysis, and visual perception, that the Hilbert transform does not extend naturally and isotropically beyond one dimension. In some areas of image analysis, this belief has restricted the application of the analytic signal concept to multiple dimensions. We show that, contrary to this view, there is a natural, isotropic, and elegant extension. We develop a novel two-dimensional transform in terms of two multiplicative operators: a spiral phase spectral (Fourier) operator and an orientational phase spatial operator. Combining the two operators results in a meaningful two-dimensional quadrature (or Hilbert) transform. The new transform is applied to the problem of closed fringe pattern demodulation in two dimensions, resulting in a direct solution. The new transform has connections with the Riesz transform of classical harmonic analysis. We consider these connections, as well as others such as the propagation of optical phase singularities and the reconstruction of geomagnetic fields.

© 2001 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(100.2960) Image processing : Image analysis
(100.5070) Image processing : Phase retrieval
(100.5090) Image processing : Phase-only filters
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5050) Instrumentation, measurement, and metrology : Phase measurement

Original Manuscript: August 24, 2000
Revised Manuscript: January 16, 2001
Manuscript Accepted: January 16, 2001
Published: August 1, 2001

Kieran G. Larkin, Donald J. Bone, and Michael A. Oldfield, "Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform," J. Opt. Soc. Am. A 18, 1862-1870 (2001)

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