A time-domain model and experimental validation of the acoustic field radiated by air-coupled transducers

This paper presents a time-domain model for the prediction of an acoustic field in an air-coupled, non-contact, ultrasonic setup, which includes an air-coupled Emitter, the Propagation space and an air-coupled Receiver (EPR). The model takes into account the finite size of the aperture receiver, attenuation in air, and the electric response of the emitter-receiver set h_e. The attenuation is characterized by a causal time-domain Green's function, allowing the wideband attenuation of a lossy medium obeying the power law α(ω)=α₀ω^η,1⩽η⩽2 to be included. The electrical response is recovered experimentally using a procedure which includes the deconvolution of air absorption effects. The model is implemented numerically using a discrete representation approach. In order to study the influence of receiver size and attenuation, five different computational approaches are proposed; each of these is evaluated quantitatively, by comparing the predicted acoustic field with the experimentally measured signal. The prediction error is studied in both the near and far fields, for three typical field features: the system's impulse response, the on-axis field distribution, and the directivity pattern, for the case of air-coupled transducers operating at two different central frequencies, namely 50kHz and 350kHz, with a 10mm diameter wideband receiver. It is shown that when the attenuation in air, the receiver size, and the accurately recovered electric response h_e, are correctly taken into account, the model allows the system's impulse response to be accurately predicted, with on-axis errors ranging between 0.2% in the far field and 1% in the near field. In the near-field area and within the far field -3dB beam spread width, the error is generally greater than on the axis, but globally remains smaller than 1%. Inclusion of the size of the receiver dimension in the model appears to be crucial to the accuracy of the near field predictions, and an approximate criterion is proposed for the evaluation of the influence of receiver. The procedure used to recover the electric response h_e is also presented in detail. The results obtained from this study are used to formulate various recommendations related to EPR modelling.