Modeling the measurement of ultrasonic beams transmitted through a penetrable acoustic cone

The interaction of ultrasonic beams with conical scatterers is governed by a combination of diffraction effects occurring at the aperture of the acoustic source/receiver and refraction through the cone. Accordingly, the outcome of a transmission experiment is dependent upon the many physical parameters characterizing the transducers and the cone. We develop a simplified model which describes the deflection caused by refraction through the cone using ray theory, then uses Huygens' summation to calculate the transducer response from this deflection. The model's accuracy is verified by comparison to simulated data. The model shows that transmission occurs in two different regimes, depending on the parameters of the particular problem. In the first regime, the cone alters the spatial phase distribution of the incident field along the receiver's aperture, whereas its amplitude remains almost unchanged. Because the receiver integrates the field over the aperture, the phasing affects the measurements via constructive and destructive interference. In the second regime, the phase alteration is accompanied by large amplitude variations around an average value that is significantly smaller than the amplitude observed in the first regime. The approximation will aid the design of ultrasound tomography arrays, such as those being developed for breast cancer detection.