An Analytical Approximation for a Common Ultrasonic Grain Noise Diffraction Integral

The scattering of sound from small inhomogeneities in a medium often plays an important role in ultrasonic inspection. For example, backscattered grain noise in metals can be a useful tool for characterizing the metal microstructure: the noise can be analyzed to deduce a backscatter coefficient, η, which carries information about the distribution of grain sizes and orientations [1]. On the other hand, backscattered grain noise can limit the detect- ability of small or subtle defects in metals. However, if η is known, one can estimate the level of noise likely to be present in a given inspection, and subsequently estimate the probability of detecting a given defect in the presence of noise [2]