Spatial approximation of leaky wave surface amplitudes for three-dimensional high-frequency scattering: Fresnel patches and application to edge-excited and regular helical waves on cylinders

Abstract

For sonar imaging systems and other situations where scattering amplitudes are resolved spatially (e.g., ultrasonic microscopy and nondestructive testing) approximations of outgoing leaky wave amplitudes are needed as a function of position on the imaged surface. The approach developed here approximates the amplitude of a leaky wave pole contribution to the total scattering as a spatial convolution of the local incident pressure with a spatial response function. Leaky rays to a surface point of interest follow a Fermat path having a stationary phase whereas the pole contribution becomes a surface integral that includes defective paths. Increased curvature of the surface or of the incident wavefront ordinarily cause more rapid dephasing along defective paths and a corresponding reduction in size of the Fresnel coupling patch. Examples given include leaky wave excitation on a partially coated cylinder at normal incidence and regular helical leaky wave excitation on tilted cylinders. A helical wave is found to be excited by diffraction at the edge of an idealized coating truncated along the cylinder’s axial direction. The leaky wave amplitude becomes proportional to a Fresnel integral of complex argument which accounts for the partial blockage of the Fresnel coupling patch.