The reconstruction of shallow rough-surface profiles from scattered field data

Abstract

A method for the reconstruction of a rough-surface profile s(x), from fixed frequency and fixed illumination angle data and assuming Dirichlet boundary conditions is described. The method is valid for surfaces of small roughness only. The resulting algorithm is FFT based and very simple. It is illustrated by numerical examples.

Acoustic imaging in application to reconstruction of rough rigid surface with airborne ultrasound waves

“…In case when wavelength λ is much bigger than the surface roughness height ζ (ζ/λ ≪ 1) small perturbation method and Fourier transform can be used to directly reconstruct the surface profiles 5 . For the surfaces satisfying Kirchhoff criteria 6 and for both source and receiver positioned in the Fraunhofer zone with respect to the illuminated surface, variety of optical techniques have been developed to reconstruct surface profiles 7 .…”

Inverse Wave Scattering of Rough Surfaces With Emitters and Receivers in the Transition Zone

“…Those single scattering approximations are of theoretical and practical importance, since they can often be inversed analytically. In the early nineties were published inversion schemes based on the small perturbation method [6][7][8], the Kirchhoff approximation [9,10] and the Rytov approximation [11]. More recently, a scattered field correlation procedure was developed in the framework of the small perturbation theory to characterize both the surface roughness and buried objects [12].…”

Compressive imaging of subwavelength structures: periodic rough surfaces

“…Rough surface scattering is of fundamental interest in optics, radiowave propagation, and acoustics [1][2][3][4][5][6][7][8] and forms the basis of near-field imaging, which is the operation principle behind such instruments as scanning near-field optical microscopy [9][10][11][12] and near-field acoustic microscopy [13]. Nearfield imaging is a microscopic technique that breaks the diffraction limit by exploiting the properties of evanescent waves.…”