Analytical Expression For Power Spectrum Research Articles

The performance of digital image correlation is closely associated with the quality of speckle pattern. In this paper, the performance of digital speckle pattern is analyzed theoretically concerning four critical factors: uniqueness, accuracy, precision, and spatial resolution. Pattern uniqueness could be characterized by secondary autocorrelation peak height; based on a theoretical analysis on autocorrelation function of digital speckle pattern, analytical formulas are derived to estimate the secondary autocorrelation peak height. Measurement accuracy and precision are descriptions of systematic error and random error respectively; by deriving analytical expression for power spectrum of digital speckle pattern, theoretical models are built for analyzing both systematic errors and random errors. Spatial resolution characterizes the ability of a given technique to distinguish close features; empirical formulas are presented to describe the dependence of spatial resolution upon subset size and shape function order; besides, a rudimentary model is proposed, which provides conservative estimates for spatial resolution. Considering all these four factors, we make recommendations for selection of generation parameters of digital speckle pattern, which can eventually improve the measurement performance of digital image correlation technique.