A simplified calibration for receiver transfer function and effects of its diffraction correction on the nonlinearity parameter of solids

Abstract

The determination of the acoustic nonlinearity parameter (β) for fluids or solids is composed of two-step measurements: receiver calibration and harmonic generation. The purpose of calibration is to find the receiver transfer function and convert the electrical output of the measured harmonic generation into physical displacements, from which the absolute β value is determined. Therefore, accurate measurement of the receiver transfer function is required for the accurate determination of β This paper presents an accurate and simplified calibration technique for receiving transducers that can eliminate the effects of impedance mismatch and minimize internal reflections from cabling/probe connections. The formula for the receiver transfer function is explicitly derived with the inclusion of diffraction and attenuation effects. After the transfer function is measured with minimal reflections from the cabling/probe connections, its effects on the β determination can be evaluated. Specifically, beam diffraction and material attenuation effects during calibration and harmonic generation measurements are systematically investigated. Diffraction and attenuation corrections were found to have more dominant effects on calibration measurements than on harmonic generation measurements in calculating the β value. After all necessary corrections are made, the β value of 6.46 ± 0.13 is obtained for Al 7075-T6511 samples with five different thicknesses (4, 6, 8, 10, and 12 cm), validating the proposed calibration and β measurement techniques.