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Appl Opt. 2005 Aug 10;44(23):4916-21.

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 measurement.

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  • 1Department of Information and Communication Engineering, Laboratory for Information Photonics and Wave Signal Processing, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan.


To provide a theoretical background for the superiority of the signal-domain phase-only correlation (SDPOC) technique proposed here for microdisplacement measurement, we study the first- and the second-order statistical properties of the complex amplitude of an analytic signal of a white-light speckle pattern, under the assumption of a Gaussian random process, and give a formula for the autocorrelation function of the pseudophase associated with the complex analytic signal. Based on these results, we show mathematically that SDPOC has a performance advantage over conventional intensity-based correlation techniques.

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