title: Ultrasound field estimation method using a secondary source-array numerically constructed from a limited number of pressure measurements
abstract: A new and faster method for the accurate estimation of acoustic fields of underwater ultrasonic transducers was developed, tested experimentally, and compared to previously reported methods. Using a limited number of pressure measurements close to the transducer's face, the method numerically constructs a virtual secondary source-array whose acoustic field is similar to the field generated by the actual transducer (primary source). The measured data are used to obtain the normal particle velocity on the surface of the virtual secondary source-array, which in turn permits the calculation of the forward propagating field using the Rayleigh-Sommerfeld diffraction integral. The method is novel in that it constructs a virtual secondary source-array, thus eliminating the problems associated with obtaining the excitation source of a real transducer; and it is faster because it uses finite differences instead of a matrix inversion to obtain the excitation source. Results showed that predicted ultrasound fields agreed quantitatively and qualitatively with measured fields for three commonly used transducer types: two planar radiators (one circular, 0.5 MHz, 1.9-cm diam.; and one square, 1 MHz, 1.2 cm on a side), and a sharply focused radiator (1.5 MHz, 10-cm diam., 10-cm radius of curvature). The agreements suggest that the secondary source-array method (SSAM) is applicable to a wide range of radiator sizes, shapes, and operating frequencies. The SSAM was also compared to these authors' previous equivalent phased array methods (EPAM) [J. Acoust. Soc. Am. 102, 2734-2741 (1997); and Concentric ring equivalent phased array method (CREPAM), UFFC 46, 830-841 (1999)] which require matrix inversions. The SSAM proved to be much faster and equally or more nearly accurate than the previous methods.
authors.affiliation: Department of Radiology, University of Chicago, Illinois 60637, USA.
authors.initials: X
authors.lastname: Fan
authors.initials: EG
authors.lastname: Moros
authors.initials: WL
authors.lastname: Straube