Statistics of the derivatives of complex signal derived from Riesz transform and its application to pseudo-Stokes vector correlation for speckle displacement measurement

Shun Zhang, Yi Yang, Steen G Hanson, Mitsuo Takeda, Wei Wang

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1 Citation (Scopus)


As an improvement of the well-known intensity correlation used in conventional electronic speckle photography, we have proposed a new technique, to the best of our knowledge, for displacement measurement referred to as pseudo-Stokes vector correlation (PSVC). To provide a theoretical background for the superiority of the proposed PSVC technique, we study the statistical properties of the spatial derivatives of the complex signal representation generated from the Riesz transform. Under the assumption of a Gaussian random process, a theoretical analysis for the pseudo Stokes vector correlation has been provided. Based on these results, we show mathematically that PSVC has a performance advantage over conventional intensity-based correlation technique.

Original languageEnglish
Pages (from-to)8561-8565
Number of pages5
JournalApplied Optics
Issue number28
Publication statusPublished - 1 Oct 2015



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