Angular spectral approach to reflection of focused beams with oblique incidence in spherical-planar-pair lenses

The characteristics of the output signal from spherical-planar-pair (SPP) lenses in the ultrasonic microspectrometer (UMSM) are described. The angular spectral approach is used to obtain the mathematical formula of the output signal. Although isotropic specimens are assumed, anisotropic materials can be treated as well with a small modification. A 2-D approximation is introduced to analyze the specular reflection, the Rayleigh critical angular phenomenon, and V (z) of the specular reflection. Numerical calculations are also performed for specimens with copper substrate, steel substrate, and layered structures, by numerically integrating the 2-D formulas of the output signal. It is found that a ray optical treatment is a good approximation of the wave propagation in the SPP lenses. The incident angular dependence of a reflection coefficient can be estimated by tilting the sensor unit.