Numerical solution for an inverse scattering problem of non-periodic rough surfaces

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].…”

“…This method was efficiently implemented in inverse scattering schemes for two-dimensional [6,16,17] and three-dimensional [18] scattering. However, one requisite of the method is that the incident field is a tapered wave, usually a gaussian beam.…”

Nanometric Resolution with Far-Field Optical Profilometry

“…When multiple scattering is predominant, the inverse scattering problem is traditionally expressed as an optimization problem solved iteratively. The Newton-Kantorovitch (NK) iterative procedure is one of the techniques that solve the inverse scattering problem [16][17][18]. The basic idea underlying the NK method is to retrieve gradually the surface profile by minimizing a cost functional describing the discrepancy between the measurement and the field that would be obtained via the scattering forward rigorous model [16].…”