Nearfield description of focused-unfocused transducers and transducer-lens systems

An algorithm is developed for calculating the field of focused ultrasonic transducers and transducer-lens systems in the Fresnel approximation. The approach is based on expanding the sound field in terms of Gaussian-Laguerre functions. The structure of the sound field depends largely on the ratio of the focal length to a squared/lambda, where a is the radius of a circular transducer and lambda is the ultrasound wavelength. By placing the transducer one focal distance from the lens, one finds the greatest uniformity in the field for a given focal length. The calculations are for a uniform velocity distribution on the transducer, but the algorithm can be modified to accept other distributions.