Ultrasound field estimation method using a secondary source-array numerically constructed from a limited number of pressure measurements

A new and faster method for the accurate estimation of acoustic fields of u nderwater 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 constr ucts a virtual secondary source-array whose acoustic field is similar to th e field generated by the actual transducer (primary source). The measured d ata are used to obtain the normal particle velocity on the surface of the V irtual secondary source-array, which in turn permits the calculation of the forward propagating field using the Rayleigh-Sommerfeld diffraction integr al. The method is novel in that it constructs a virtual secondary source-ar ray, thus eliminating the problems associated with obtaining the excitation source of a real transducer; and it is faster because it uses finite diffe rences instead of a matrix inversion to obtain the excitation source. Resul ts showed that predicted ultrasound fields agreed quantitatively and qualit atively 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 MH z, 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 sour ce-array method (SSAM) is applicable to a wide range of radiator sizes, sha pes, 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 (CREP AM), UFFC 46, 830-841 (1999)] which require matrix inversions. The SSAM pro ved to be much faster and equally or more nearly accurate than the previous methods. (C) 2000 Acoustical Society of America. [S0001-4966(00)03006-X].