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Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 53, Iss. 10 — Apr. 1, 2014
  • pp: B147–B152

Correlation properties of the vector signal representation for speckle pattern

Wei Wang, Shun Zhang, and Ning Ma  »View Author Affiliations

Applied Optics, Vol. 53, Issue 10, pp. B147-B152 (2014)

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In one-dimensional (1D) signal analysis, the complex analytic signal built from a real-valued signal and its Hilbert transform is an important tool providing a mathematical foundation for 1D statistical analysis. For a natural extension beyond 1D signal, Riesz transform has been applied to high-dimensional signal processing as a generalized Hilbert transform to construct a vector signal representation and therefore, to enlarge the traditional analytic signal concept. In this paper, we introduce the vector correlations as new mathematical tools for vector calculus for statistical speckle analysis. Based on vector correlations of a real-valued speckle pattern, we present the associated correlation properties, which can be regarded as mathematical foundation for the vector analysis in speckle metrology.

© 2014 Optical Society of America

OCIS Codes
(030.6600) Coherence and statistical optics : Statistical optics
(100.2960) Image processing : Image analysis
(100.4550) Image processing : Correlators

Original Manuscript: November 1, 2013
Revised Manuscript: January 15, 2014
Manuscript Accepted: January 27, 2014
Published: March 3, 2014

Wei Wang, Shun Zhang, and Ning Ma, "Correlation properties of the vector signal representation for speckle pattern," Appl. Opt. 53, B147-B152 (2014)

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