Abstract

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.

© 2005 Optical Society of America

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