In recent work, we adapted the classic backscattering method for conventional transducers to utilize full matrix capture datasets from an ultrasonic array to measure material microstructure grain size, proposing an inverse process that incorporates three-dimensional ultrasonic models. In this paper, we further develop the inverse process to increase its efficiency by using two-dimensional ultrasonic models of the wave field generated by one-dimensional ultrasonic arrays. The computational cost is reduced by a factor of three thousand without compromising calculation accuracy. Experimental validations were performed on a metallic material, copper (EN1652), using ultrasonic arrays with various array element elevation lengths. The measurement uncertainty is also qualified through statistical model. This work will contribute to the eventual use of the developed inverse process for on-line grain size measurements.
Wang et al. (Sun,) studied this question.