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
(030.6600) Coherence and statistical optics : Statistical optics
(100.4550) Image processing : Correlators
(100.5070) Image processing : Phase retrieval
(120.6150) Instrumentation, measurement, and metrology : Speckle imaging
Wei Wang, Nobuo Ishii, Steen G. Hanson, Yoko Miyamoto, and Mitsuo 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 measurement," Appl. Opt. 44, 4916-4921 (2005)