Diffraction correction in high-precision pulse-echo and multiple-reflection ultrasonic measurement systems for fluids

In high-precision ultrasonic measurement systems, diffraction correction models accounting for electrical and mechanical boundary conditions may be needed, as shown in prior work using a finite element diffraction correction (FEDC) model for one-way transmit-receive systems. Such descriptions may also be needed for pulse-echo and multiple-reflection ultrasonic measurement applications. The FEDC model is here generalized to n-way measurement systems (n = 1, 2, 3,…) using coaxially aligned piezoelectric transducers in a fluid medium. Comparisons are made with existing diffraction correction models, based on baffled-piston theory combined with (i) specular reflection or (ii) reflection modeled as radiation from a "new source." Numerical results are given for an example system with two identical cylindrical piezoelectric disks, operating in a fluid medium at ambient conditions. The piston-type diffraction correction models deviate notably from the FEDC model both in the near- and far-fields, and also from each other. The deviations are expected to be application-specific and depend, e.g., on the reflector-to-sound-beam diameter ratio, distance, frequency, and the transducers' vibration patterns. The results show that accurate description of the diffraction effects, such as the one provided by the FEDC model, may be needed in high-precision ultrasonic measurement systems.