An electromagnetic imaging framework is implemented utilizing a single frequency reverse time migration (RTM) technique to accurately reconstruct inaccessible two-dimensional (2D) rough surface profiles from the knowledge of scattered field data. The unknown surface profile, which is expressed as a 1D height function, is either perfectly electric conducting (PEC) or an interface between two penetrable media. For both cases, it is assumed that the surface is illuminated by a number of line sources located in the upper medium. The scattered fields, which should be collected by real measurements in practical applications, are obtained synthetically by solving the associated direct scattering problem through the surface integral equations. RTM is subsequently applied to generate a cross-correlation imaging functional which is evaluated numerically and provides a 2D image of the region of interest. A high correlation is observed by the functional in the regions where the transitions between two media occur. Hence, it results in the acquisition of the unknown surface profile at the sites where the functional attains its highest values. The efficiency of the proposed method is comprehensively tested by numerical examples covering various types of scattering scenarios.

This letter addresses a reconstruction algorithm of locally rough inaccessible surface profiles via the knowledge of the scattered field data under the consideration of the impedance boundary condition (IBC). To this aim, first, the synthetic scattered field data are obtained through the solution of the conventional surface integral equation (SIE) written on the rough surface. Then, the same SIE together with the data equation is solved iteratively via Newton’s method to obtain the image of the rough surface profile. In the numerical implementation, the nonlinear ill-posed inverse problem is linearized in an iterative fashion via the Newton method and regularized by Tikhonov in the least-squares sense. The feasibility of the algorithm is provided via numerical examples, which shows that the method is effective and promising.

This paper presents a new method for the reconstruction of the perfectly electric conducting (PEC) rough surface profiles by utilizing electromagnetic waves. The inaccessible rough surface is illuminated by a tapered plane electromagnetic wave and the scattered field data are measured on a certain number of points above the surface under test. The method for the inverse electromagnetic imaging problem is based on a special representation of the scattered field in terms of a finite number of fictitious discrete line sources located along a plane below the rough surface. The current densities of these fictitious sources are obtained through the regularized solution of an ill-posed problem. Then, it is shown that the image of the rough surface can be directly retrieved by seeking the points in the space where the tangential component of the total electric field vanishes. Alternatively, a much more rigorous iterative method based on a regularized Newton algorithm is also presented. A comprehensive numerical analysis is provided to demonstrate the feasibility of the presented approach. In this context, the quantitative successes of both approaches are interpreted by considering a very sensitive ℓ2-norm based error function between the actual and the reconstructed surface profiles. Regarding different scattering scenarios taken into account, the error values obtained for satisfactory reconstructions are generally in the range of 10% - 30% for both methods. It is also shown that the presented algorithms are capable of reconstructing the rough surfaces which oscillate for every λ horizontally and have a peak to peak variation 0.5λ at most.

In this article, an efficient algorithm for the reconstruction of a 1-D random rough surface profile separating two lossy dielectric half-spaces is presented. First, the general scattering problem is formulated by the use of surface integral equations (SIEs). Then, the synthetic scattering field data are obtained through the use of these conventional SIEs. In the inverse problem, the same SIEs together with the data equation are solved in an iterative fashion to reconstruct the surface variation. In the numerical implementation, the so-called ill-posed inverse problem is regularized in the sense of Tikhonov, and a least squares solution is obtained by the use of appropriate basis functions. A very detailed numerical assessment of the presented approach is provided which shows that the method is very effective and promising.

In this letter, we address the problem of reconstructing the shape of a perfectly conducting object illuminated by a set of plane waves at a fixed frequency. The proposed method is made up of two parts. In the first one, for each incident wave, the field in the vicinity of a scatterer is reconstructed by means of a regularized single-layer potential approach. In the second part, the reconstructed fields are simultaneously exploited to build a system of polynomial equations whose solution yields to the unknown contour. As shown by numerical examples, the method is effective, robust against noise on data, and provides satisfactory reconstructions for star-shaped scatterers.

A microwave imaging method for nondestructive testing of perfectly conducting surfaces beyond a layered media is presented. The method is an adaptation of the surface reconstruction approach by Yapar et al. to the present problem. It is based on the analytical continuation of the measured data to the surface under test through a special representation of the scattered field in terms of Fourier transform and Taylor expansion. Then the problem is reduced to the solution of a nonlinear equation which is solved iteratively via the Newton method and regularization in the least squares sense. Numerical simulations show that defects as small as lambda/500 can be recovered through the presented algorithm.

A new approach for the scattering of electromagnetic (EM) waves from periodic dielectric rough surfaces is addressed. The method is an extension of the buried object approach (BOA), which is developed for rough surfaces of infinite extend, to the present problem. The BOA allows to model the original problem as the scattering of EM waves from cylindrical objects located in a two-half-space medium with planar interface. Then, the problem is reduced to the solution of a Fredholm integral equation of second kind through the periodic Green's function of two-half-space medium. The periodic Green's function of two-half-space medium is calculated via the Floquet mode expansion, whose numerical evaluation can be accelerated by using effective methods. The method can also be used to solve the scattering problems of rough surfaces of infinite extend and having a localized roughness. Numerical simulations show that the method yields effective and accurate results for surfaces of arbitrary variation.

We present a method to detect and locate dielectric objects buried under a rough surface. The method is based on the determination of appearing surface impedance of the half-space, where the dielectric objects are located. The equivalent surface impedance is obtained directly from the impedance boundary condition, which requires the knowledge of the electric field and its normal derivative on the surface. These field values are obtained by measuring the far-field data and using single-layer-potential representation of the scattered field. Using the equivalent surface impedance, one can detect and locate the buried objects. The efficiency and efficacy of the method are tested via numerical simulations

A new, simple, and fast method for the solution of electromagnetic scattering problems for perfectly conducting objects of arbitrary shape is presented. The method is based on an equivalent representation of the conducting object in terms of a circular one having a higher order impedance boundary condition on its surface. As a first result, a new universal relation between the higher order surface impedances and the shape of the object is obtained. Then, by taking advantage of this relationship, the scattering problem related to a conducting object is recast as the solution of a matrix equation whose coefficients are determined from the higher order impedances. Numerical simulations show that the method yields to accurate results, and that, it is computationally effective

A method for the scattering of electromagnetic waves from cylindrical bodies of arbitrary materials and cross sections buried beneath a rough interface is presented. The problem is first reduced to the solution of a Fredholm integral equation of the second kind through the Green's function of the background medium. The integral equation is treated here by an application of the method of moments (MoM). The Green's function of the two-part space with rough interface is obtained by a novel approach which is based on the assumption that the perturbations of the rough surface from a planar one are objects located at both sides of the planar boundary. Such an approach allows one to formulate the problem as a scattering of cylindrical waves from buried cylindrical bodies which is solved by means of MoM. The method is effective for surfaces having a localized and arbitrary roughness. Numerical simulations are carried out to validate the results and to show the effects of some parameters on the total field. The present formulation permits one to get the near and far field expression of the scattered wave.

A method to reconstruct the one-dimensional profile of a cylindrical layer with an inhomogeneous impedance boundary is proposed. Through the finite Fourier transformation of the field expressions the problem is first reduced to the solutions of a two-coupled system of operator equations which is solved iteratively starting from an initial estimate of the profile. The reconstruction of the profile is achieved by linearizing one of the equations in the Newton sense. The method is tested by considering several numerical examples and yields satisfactory reconstructions. As is typical for Newton-type methods, the convergence of the iteration depends on the initial guess.

A method to detect and locate the objects buried in a half-space is presented. The method is based on the reconstruction of the appearing surface impedance of the half-space through remote field measurements of scattered field for a single plane wave illumination. The existence of the objects causes surface impedance to be a function of location and by observing its variation along the surface one can achieve the detection. The method is applied to several examples to show its efficiency and accuracy. Effects of different parameters on the solution are also demonstrated.