A COMPLEX-TRANSDUCER-POINT MODEL FOR FINITE EMITTING AND RECEIVING ULTRASONIC TRANSDUCERS

The complex-source-point (CSP) technique, widely used to generate Gaus sian beams out of real point source fields by displacing the source lo cation into complex space, is here considered and extended to model fi nite flat and focused axisymmetric ultrasonic emitters and receivers w ith Gaussian profiles. The signal voltage generated by such transducer s upon reception of an acoustic pressure field p is shown to be propor tional to p sampled at a complex location. We arrive at this result by using a complex continuation of Helmholtz's theorem and the conventio nal surface integral for the voltage of a reciprocal electro-acoustic transducer. This extension to the CSP technique, called herein the com plex-transducer-point (CTP) technique, allows efficient modeling of fi nite emitting and receiving transducers in the presence of layered flu id-elastic configurations as well as in unbounded fluids. For a pair o f CTPs interacting in an unbounded fluid, we derive paraxial expressio ns and present numerical results for the voltage to help understand it s behavior with changing receiver parameters. We also show how transdu cers with arbitrary axisymmetric profiles can be expanded in terms of coaxial CTPs whose parameters are computed from a minimization scheme. We successfully demonstrate this approach by modeling the single-freq uency voltage generated in a pitch-catch experiment with a pair of pis ton transducers using a collection of three CTPs for each transducer, Furthermore, we extend this latter approach to model time-domain volta ges by deriving frequency-scaling rules for the CTP parameters for fla t and focused apertures. This is numerically implemented for piston tr ansducers and shown to agree well with experimental transient signals. The well-known singularities of the CSP field are also present for th e CTP field. Because of this, the range of transducer beam collimation is limited to cases for which the imaginary part of the complex displ acement (known as b) is larger than the operating wavelength hf. Howev er, this range remains usefully wide even when the CTP parameter b is varied with frequency to synthesize time-domain signals. Finally, we s how how to use the CTP technique for emitting and receiving CTPs inter acting with a plane layered fluid-elastic configuration.