Finite element-based diffraction correction for piezoelectric transducers accounting for diffraction at transmission, propagation, and reception

Existing diffraction correction models for ultrasonic transmit-receive measurement systems rely on simplifying assumptions with respect to the boundary conditions at the transmitter or receiver. Common simplifications include approximating the sound field radiated by a piezoelectric transducer using a baffled piston model and assuming that the receiver's electrical response is proportional to the spatially averaged free-field pressure over its front surface. In many applications, such simplifications may be adequate, but their validity and accuracy need to be evaluated and quantified. Here, a diffraction correction model utilizing the full set of electrical and mechanical boundary conditions at the transmitter and receiver is presented, avoiding these simplifications. The model is based on finite element modeling of coaxially aligned piezoelectric transducers in a fluid medium. Comparison is made with existing models for an example case of cylindrical piezoelectric ceramic disk transducers operating in air at 50-300 kHz and 0.03-2 m apart, relevant for, e.g., sound velocity and absorption measurements in fluids and ultrasonic gas flow metering. In the near-field, errors introduced by the simplifications are up to 3 dB and 47(degrees) for the first radial resonance. Generally, such errors are application-specific and depend on distance, frequency, transducer construction, vibration pattern, and medium properties.