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

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; >,=wavelength; k=2•r/>,). 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 a•/X.

Verification of crystal elastic anisotropy theory by ultrasonic diffraction experiments

“…(2) The last peak, peak 'A', in loss is at SA----1"6 for b=0 as found by Seki et al (1956). S is the Seki parameter, a normalized dimensionless distance parameter, S =z2/a 2.…”

“…The implications are that (1) the assumptions about the piston-source nature of the transducer as transmitter and the phase-and-amplitude sensitivity of the transducer as receiver are correct, (2) the theory of Lighthill (1960) concerning the transmission of energy from point to point by the Poynting vector as if a plane wave with a definite propagation vector were involved is correct, (3) the formulation of Waterman (1959)is correct for v and dp in terms of b and 0 for longitudinal elastic waves along the three, four, and sixfold axes of symmetry, (4) the use of Waterman's (1959) formulation for v and dp by the author (Papadakis, 1963(Papadakis, , 1964(Papadakis, , 1966 to derive an expression for Ii. r in the Rayleigh integral (Seki et al, 1956;Strutt, 1945) is correct and (5) the extension of the Rayleigh integral, first derived for fluids, to solids is correct.…”

“…The author utilized these theoretical concepts (Papadakis, 1963(Papadakis, , 1964(Papadakis, , 1966 to generalize the ultrasonic diffraction theory of Seki, Granato & Truell (1956) to include longitudinal waves along pure-mode axes of three, four, and sixfold symmetry. This theory is for circular piston sources of ultrasound and circular, coaxial, equal-sized receivers which are sensitive to both pressure and phase.…”

“…The amplitude (loss) and phase are calculated as functions of distance between the planes of the transmitter and receiver. The Rayleigh integral (Seki et al, 1956;Strutt, 1945) is used to express the radiation at a field point. In the generalization (Papadakis, 1963(Papadakis, , 1964(Papadakis, , 1966, the plane of the circular piston source is assumed exactly perpendicular to the pure-mode axis.…”

Numerical calculation of the frequency response of the radiation coupling in lossy medium.

“…The medium between the transmitter and receiver is isotropic and homogenous and supports only compressional waves. Rhyne used the Stepanishen potential impulse response solution9) to evaluate the surface integral of the velocity potential over the receiver face which is (1) is the wave propagation velocity, a is the transducer radius and z the distance between the transm tter and receiver. The force impulse response at the receiver due to a velocity impulse disturbance from the transmitter is given by differentiating Eq.…”