Spectral integral formulae for the response of acoustic transducers in cylindrically curved configurations

Abstract

High-frequency spectral integral formulae are derived for the frequency-domain voltage of reciprocal electro-acoustic ultrasonic transducers interacting with a fluid-immersed cylindrically-layered elastic configuration. The transducers may insonify the cylindrical configuration from either the interior or the exterior and may be operated in either pulse-echo or pitch-catch mode. The formulae are arrived at through the use of a traveling wave spectral representation of all pertinent wave fields along the azimuthal and axial directions and use of Plancherel's theorem to convert the conventional surface integral for the transducer voltage into a spectral one. Within this representation, the transducers are expressed in terms of their radiation and reception spectral amplitudes on a cylindrical surface and the interaction of their fields with the cylindrically layered environment is expressed in terms of a composite spectral reflection coefficient. The integral formulae allow for computation of the transducer voltage and transducer beam interaction with the cylindrical environment in one step. The derivation is carried out for three-dimensional beams and specialized to two-dimensional (sheet) beams that extend to infinity along the axial direction. Furthermore, the formulae are applied to the case where complex transducer points are used to simulate transducers with quasi-Gaussian distribution profiles.