Fresnel approximations for acoustic fields of rectangularly symmetric sources

A general approach is presented for determining the acoustic fields of rectangularly symmetric, baffled, time-harmonic sources under the Fresnel approximation. This approach is applicable to a variety of separable source configurations, including uniform, exponential, Gaussian, sinusoidal, and error function surface velocity distributions, with and without focusing in either surface dimension. In each case, the radiated field is given by a formula similar to that for a uniform rectangular source, except for additional scaling of wave number and azimuthal distance parameters. The expressions presented are generalized to three different Fresnel approximations that correspond, respectively, to diffracted plane waves, diffracted spherical waves, or diffracted cylindrical waves. Numerical results, for several source geometries relevant to ultrasonic applications, show that these expressions accurately depict the radiated pressure fields, except for points very near the radiating aperture. Highest accuracy near the source is obtained by choice of the Fresnel approximation most suited to the source geometry, while the highest accuracy far from the source is obtained by the approximation corresponding to diffracted spherical waves. The methods are suitable for volumetric computations of acoustic fields including focusing, apodization, and attenuation effects.