Diffraction Effects in the Ultrasonic Field of a Piston Source and Their Importance in the Accurate Measurement of Attenuation

TLDR

The ultrasonic field of a circular quartz crystal transducer and the integrated response of a similarly sized receiver are examined. The authors aim to derive correction formulas for diffraction effects to improve the accuracy of attenuation measurements. They model the coaxial transducer and receiver as a piston source, compute the average pressure over the receiver area, and perform numerical analyses over a megacycle frequency range (ka = 50–1000). The results reveal diffraction‑related features useful for correcting attenuation, compare favorably with experimental data, and indicate that diffraction attenuation is approximately one decibel per a²/λ.

Abstract

A study is made of the ultrasonic field produced by a circular quartz crystal transducer and the integrated response of a quartz crystal receiver with the same dimensions as the transducer. The transducer and receiver are taken to be coaxial, and it is assumed that the transducer behaves as a piston source while the integrated response is proportional to the average pressure over the receiver area. Computations are made for cases of interest in the megacycle frequency range (ka=50 to 1000; a=piston radius; λ=wavelength; k=2π/λ). The results contain features of use in identifying and correcting for diffraction errors. These features which apparently have been missed in previous investigations are compared with available experimental data. Finally correction formulas to account for diffraction effects in the accurate measurement of attenuation are discussed. It is shown that the order of magnitude of the diffraction attenuation is given by one decibel per a2/λ.