OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.53.00B147


View Full Text Article

Enhanced HTML    Acrobat PDF (483 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

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

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

Citation
Wei Wang, Shun Zhang, and Ning Ma, "Correlation properties of the vector signal representation for speckle pattern," Appl. Opt. 53, B147-B152 (2014)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-53-10-B147


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. D. Gabor, “Theory of communication,” J. Inst. Elect. Eng. 93, 429–457 (1946).
  2. S. L. Hahn, Hilbert Transforms in Signal Processing (Arteche, 1996).
  3. J. W. Goodman, Statisitcal Optics (Wiley, 2000).
  4. L. Mandel and E. Wolf, Optical Coherence and Quantum Optics (Cambridge, 1995).
  5. M. Felsberg and G. Sommer, “The monogenic signal,” IEEE Trans. Signal Process. 49, 3136–3144 (2001). [CrossRef]
  6. S. L. Hahn, “Multidimensional complex signals with single-orthant spectra,” Proc. IEEE 80, 1287–1300 (1992). [CrossRef]
  7. M. Felsberg and G. Sommer, “A new extension of linear signal processing for estimating local properties and detecting features,” in Proc. 22nd DAGM Symp. Mustererkennung (Heidelberg, Germany, 2000).
  8. K. G. Larkin, J. D. Bone, and A. M. 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). [CrossRef]
  9. M. N. Nabighian, “Toward a three‐dimensional automatic interpretation of potential field data via generalized Hilbert transforms: fundamental relations,” Geophysics 49, 780–786 (1984). [CrossRef]
  10. M. Riesz, “Sur les fonctions conjuguées,” Mathematische Zeitschrift 27, 218–244 (1928). [CrossRef]
  11. W. Wang, T. Yomiaki, R. Ishijima, A. Wada, Y. Miyamoto, and T. Mitruo, “Optical vortex metrology for nanometric speckle displacement measurement,” Opt. Express 14, 120–127 (2006). [CrossRef]
  12. I. Yamaguchi, “Speckle displacement and decorrelation in the diffraction and image fields for small object deformation,” J. Mod. Opt. 28, 1359–1376 (1981).
  13. M. Sjödahl, “Calculation of speckle displacement, decorrelation, and object-point location in imaging systems,” Appl. Opt. 34, 7998–8010 (1995). [CrossRef]
  14. P. Šmíd, P. Horváth, and M. Hrabovský, “Speckle correlation method used to measure object’s in-plane velocity,” Appl. Opt 46, 3709–3715 (2007). [CrossRef]
  15. W. Wang, R. Ishijima, A. Matsuda, S. G. Hanson, and M. Takeda, “Pseudo-Stokes vector correlation from complex signal representation of a speckle pattern and its applications to micro‐displacement measurement,” Strain 46, 12–18 (2010).
  16. R. N. Bracewell, The Fourier Transform and its Applications, 3rd ed. (McGraw, 1999).
  17. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables (Dover, 1974).
  18. W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda, “Pseudophase information from the complex analytic signal of speckle fields and its applications. Part I: microdisplacement observation based on phase-only correlation in the signal domain,” Appl. Opt. 44, 4909–4915 (2005). [CrossRef]
  19. W. Wang, N. Ishii, S. G. Hanson, Y. Miyamoto, and M. Takeda,. “Pseudophase information from the complex analytic signal of speckle fields and its applications. Part II: statistical properties of the analytic signal of a white-light speckle pattern applied to the microdisplacement measurment,” Appl. Opt. 44, 4916–4921 (2005). [CrossRef]
  20. E. M. Stein, Singular Integrals and Differentiability Properties of Functions (Princeton, 1970).
  21. E. M. Stein and L. G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces (Princeton, 1971).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited