OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • 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)
http://dx.doi.org/10.1364/JOSAA.18.001862


View Full Text Article

Enhanced HTML    Acrobat PDF (1172 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

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

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

Citation
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)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-8-1862

You do not have subscription access to this journal. Citation lists with outbound citation links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

You do not have subscription access to this journal. Article level metrics are available to subscribers only. You may subscribe either as an OSA member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Log in to access OSA Member Subscription

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited