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.