Steady state spherically focused, circular aperture beam patterns.

This review was written to aid ultrasonic investigators using spherically focused transducers. It introduces a new direct method for computing steady state focused beam patterns on personal computers in nonattenuating and attenuating fluids and tissues. The method results in single integral expressions for uniform transducer excitation that can easily be altered for nonuniform surface excitation (apodization) or focused ring transducers. Procedures for verifying the accuracy of the derived equations are demonstrated. It is shown that beam diffraction errors are larger the higher the fluid or tissue attenuation. An experimental procedure is presented for measuring the effective focal length and effective aperture size of a spherically focused transducer with a single experimental measurement in a fluid with known acoustic velocity. Procedures are suggested for reducing the errors caused by beam diffraction in fluid attenuation measurements, avoiding them entirely or estimating their magnitude when they cannot be avoided.