An analytical description for the field of a focusing source is derived. It is valid for spherically concave sources with small aperture angle and large ka (radius a, wavenumber k.) The solution furnishes easy access to the sound distribution along the axis and in the focal plane, as well as to parameters such as focusing gain, width of the focal spot, and phase shifting in the focal region. Experiments conducted with an f/2 lens coupled to a planar array are discussed. The results support the utility of the analytical model for describing the distribution of sound along the acoustic axis and across the focal plane.
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Lucas et al. (1982) studied this question.