Annular arrays for quantitative pulsed doppler ultrasonic flowmeters

A theory, based on the Fourier-Bessel series expansion, is developed to synthesize circularly symmetric field patterns by means of concentric annular arrays. The application of this theory to the formation of variable-width uniform sector beams is studied in detail and results in a canonical design procedure. Calculated beam patterns are compared to the actual measured patterns obtained from a prototype array suitable for transcutaneous investigation of the central blood-flow system and are observed to be in good agreement. The implementation of such arrays in the compensated-first-moment flowmeter is described. Methods of beam-pattern improvement are also discussed.