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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: 1871–1881

Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform

Kieran G. Larkin  »View Author Affiliations


JOSA A, Vol. 18, Issue 8, pp. 1871-1881 (2001)
http://dx.doi.org/10.1364/JOSAA.18.001871


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Abstract

Utilizing the asymptotic method of stationary phase, I derive expressions for the Fourier transform of a two-dimensional fringe pattern. The method assumes that both the amplitude and the phase of the fringe pattern are well-behaved differentiable functions. Applying the limits in two distinct ways, I show, first, that the spiral phase (or vortex) transform approaches the ideal quadrature transform asymptotically and, second, that the approximation errors increase with the relative curvature of the fringes. The results confirm the validity of the recently proposed spiral phase transform method for the direct demodulation of closed fringe patterns.

© 2001 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(100.2650) Image processing : Fringe analysis
(100.5090) Image processing : Phase-only filters
(110.6980) Imaging systems : Transforms
(120.2650) Instrumentation, measurement, and metrology : Fringe analysis

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

Citation
Kieran G. Larkin, "Natural demodulation of two-dimensional fringe patterns. II. Stationary phase analysis of the spiral phase quadrature transform," J. Opt. Soc. Am. A 18, 1871-1881 (2001)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-18-8-1871

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