The spatial correlation of backscattered ultrasonic grain noise: theory and experimental validation

In ultrasonic pulse/echo inspections of metals, backscattered grain noise signals observed at different nearby transducer positions will be correlated. Such correlations have important practical implications. For example, the spatial correlation length (SCL) of the backscattered noise is a crucial quantity in designing denoising algorithms for image processing, and in inspection simulations of the probability of detection (POD) of a defect. In this paper an existing theory for the average backscattered grain noise level, based on the single scattering assumption and the Born approximation, is extended to obtain a formal theory for the spatial correlation of the backscattered grain noise. A special form of the theory for an incident Gaussian sound beam is also presented to demonstrate that the specimen microstructure and an overlap integral for the incident sound field are the important physical parameters controlling the grain noise level and spatial correlation, respectively. To validate the theory, a series of experiments are performed to collect backscattered grain noise signals from nickel alloy specimens having equiaxed microstructures. Good agreement between measured and predicted correlations is generally found. Further model computations are performed to better illustrate how amplitude and phase variations within the incident sound field control the dependence of the grain noise spatial correlation upon transducer separation.