Calibration of focused ultrasonic transducers and absolute measurements of fluid nonlinearity with diffraction and attenuation corrections

This paper presents analytical and experimental techniques for absolute determination of the acoustic nonlinearity parameter (β) in fluids using focused transducers. When focused transducers are used for β measurements, the geometrical and mechanical calibrations are generally required for accurate determination of the receiver transfer function from which the absolute pressure can be calculated. The fundamental and second harmonic wave amplitudes in harmonic generation measurements should be modified to account for beam diffraction and material absorption. All these issues are resolved in this study and the proposed technique is validated through the β measurement in water. An experimental method is developed to determine the effective radius and focal length of focused transducers. A simplified self-reciprocity calibration procedure for a broadband focused receiver is described. The diffraction and attenuation corrections for the fundamental and second harmonic waves are explicitly derived using the multi-Gaussian beam model, and the effects on the β determination are discussed. When the diffraction and attenuation corrections are all properly made, the measurement of β over a large range of propagation distances is possible with errors less than 8%.