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

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.

[1]  Wei Wang,et al.  Correlation properties of the vector signal representation for speckle pattern. , 2014, Applied optics.

[2]  A. Bekshaev,et al.  Mechanical Action of Inhomogeneously Polarized Optical Fields and Detection of the Internal Energy Flows , 2011, 1102.3514.

[3]  Zhaoyang Wang,et al.  Equivalence of digital image correlation criteria for pattern matching. , 2010, Applied optics.

[4]  Wei Wang,et al.  Pseudo‐Stokes Vector Correlation From Complex Signal Representation of a Speckle Pattern and Its Applications to Micro‐Displacement Measurement , 2010 .

[5]  Wei Wang,et al.  Optical vortex metrology for nanometric speckle displacement measurement. , 2006, Optics express.

[6]  Alexander V. Volyar,et al.  The fine structure of singular beams in crystals: colours and polarization , 2004 .

[7]  Mark R. Dennis,et al.  Local phase structure of wave dislocation lines: twist and twirl , 2003, physics/0309069.

[8]  M. A. Oldfield,et al.  Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[9]  Mikael Sjödahl,et al.  Electronic speckle photography: increased accuracy by nonintegral pixel shifting. , 1994, Applied optics.

[10]  M Sjödahl,et al.  Electronic speckle photography: analysis of an algorithm giving the displacement with subpixel accuracy. , 1993, Applied optics.

[11]  D J Chen,et al.  Digital speckle-displacement measurement using a complex spectrum method. , 1993, Applied optics.

[12]  W. F. Ranson,et al.  Applications of digital-image-correlation techniques to experimental mechanics , 1985 .

[13]  Marcel Riesz,et al.  Sur les fonctions conjuguées , 1928 .