Field characterization of steady state focused transducers using hydrophones based on Fresnel approximation

This paper is intended to estimate the spatial averaging effects of the hydrophone in field characterization of focused transducers. The analytical model derived was based on Fresnel approximation and enabled modifications of the results for both on-axis and off-axis measurement arrangements. The axial and lateral field distributions in the focal plane measured by the hydrophone were derived for both non-attenuating and attenuating fluids in the model. The spatial averaging effects result in underestimating the absolute acoustic pressure amplitudes, and overestimating the cross-sectional size of the beam directivity pattern in the focal plane. The validity of the Rayleigh integral and the Fresnel approximation for curved transducers were discussed. The results indicate that, for $\sqrt{k\frac{(a_{\text{h}}+b)}{2}}\gg \pi$ (where k is the circular wave number, a _h is the chord from the center of curved surface to the boundary and b is the effective radius of the hydrophone), the Fresnel approximation remains valid for all locations of the hydrophone in the focused field. Particularly, in the focal plane, the spatial averaging effects of the hydrophone on the directivity pattern of the acoustic beam can be neglected for $k\frac{b^2+4ab}{2l_{\text{f}}}\ll 1$ (where a and l _f are the effective radius and focal distance of the focused transducer). (paper)