A diffraction corrected ray theory for the acoustic microscope

The ray-optical theory of V(z) for the acoustic microscope assumes the acoustic field incident on the lens aperture is uniform, which ignores diffraction in the lens rod. The acoustic field at the back plane of the lens is calculated as an expansion of Bessel functions assuming the transducer to be a piston source. For a typical lens geometry, the results show a significant amplitude variation that can be approximated as a sum of Gaussians. The phase variation is found to be small, which permits an analytic solution for the geometric component V_G(z) by direct integration in the back plane of a lens. To include diffraction effects in the calculation of the leaky wave contribution V_L(z ), it is merely necessary to scale the amplitude of the Rayleigh ray. Predictions of V(z) show significantly improved agreement with measurements made on Teflon, which gives only the geometric contribution, as well as glass, which also supports the leaky wave