180 IEEE GEOSCIENCE AND REMOTE SENSING LETTERS, VOL. 5, NO. 2, APRIL 2008 A Microwave Tomographic Approach for Nondestructive Testing of Dielectric Coated Metallic Surfaces Onur Mudanyalı, Selda Yıldız, O˘ guz Semerci, Ali Yapar, and Ibrahim Akduman, Member, IEEE Abstract—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 recon- struction 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 λ/500 can be recovered through the presented algorithm. Index Terms—Coated surfaces, inverse scattering, nondestruc- tive testing (NDT) and evaluation. I. I NTRODUCTION N ONDESTRUCTIVE testing (NDT) is a very important tool in a wide range of applications such as, but not limited to, the automotive industry, aerospace engineering, construction, manufacturing, medicine, etc. The main aim in an NDT problem is qualitative and quantitative detection of the possible defects on a given structure. During the last three decades, several methodologies have been developed for the NDT of different structures in the areas of electromagnetics, acoustics, optics, etc. The most common ones are the magnetic particle method, eddy current method, ultrasonic, visual-optical methods, infrared thermography, and radiography [1]. It should also be noted that according to the geometrical and material properties of the structure under test, special approaches may be needed. Besides the common methodologies, there is an increasing trend in the use of the microwave imaging techniques in the NDT applications [2]–[8]. “Microwave NDT and evaluation is the process of testing materials and evaluating their properties by studying the transmission and/or reflection properties of the high frequency electromagnetic signals interacting with them. Among the many advantages offered by microwave NDT techniques, nonconducting, one-sided inspection capabilities and ability of the signals to penetrate inside dielectric media and interact with their inner structures are the most significant ones. These techniques employ relatively simple measurement Manuscript received August 8, 2007. This work was supported by the TUBITAK, Turkish Scientific and Technological Research Council under the Grant 105E029. The authors are with the Electrical and Electronics Engineering Faculty, Istanbul Technical University, Istanbul 34469, Turkey. Digital Object Identifier 10.1109/LGRS.2008.915602 setups. The ability of microwave signals to penetrate inside di- electric media makes them suitable for inspecting a wide range of composite structures including cement-based materials such as concrete. Inspection of layered composites using microwave NDT techniques for thickness measurement, delamination de- tection, impact damage evaluation, etc., have been successfully performed in the past. The limited penetration of microwave signals in metals makes them suitable for examination of sur- face anomalies such as stress induced fatigue cracks” [2], [9]. One of the main applications of such methods is to inspect the mechanical damages such as cracks or irregularities on coated surfaces of aircrafts, automobiles or on perfectly conducting surfaces beyond a layered media. The main aim of this letter is to develop a new, fast, and simple method for the NDT of metallic surfaces beyond a lay- ered media such as lossy coatings. The method is an extension of the rough surface reconstruction technique in [14] to the present problem. The surface under test may be a flat or rough one. In case of rough surfaces, for the sake of simplicity, we consider surfaces having a variation in one direction. The NDT is achieved by a single illumination of a plane wave at a fixed frequency and the near-field measurements of the scattered field are performed on a planar surface in the accessible region. The data can also be collected on the surface of the coating. The method given here is based on the analytical continuation of the measured data to the perfectly conducting surface under test through a special representation of the scattered field in terms of Fourier transform and Taylor series expansion. Then the NDT problem is reduced to the solution of a nonlinear equation for the surface variation which is solved here iteratively by an application of the Newton method. A regularization scheme in the least squares sense is also applied. The method allows one to reconstruct the whole surface and to achieve the determination of possible defects by comparing it with the original one. It gives quite good reconstructions of the defects as small as λ/500. A time factor exp(−iωt) is assumed and omitted. II. NDT PROBLEM AND I TS ELECTROMAGNETIC MODEL The physical model of the NDT problem is illustrated in Fig. 1. In this model, a perfectly conducting surface Γ 0 is located beyond a layer composed of a nonmagnetic mater- ial having dielectric permittivity ε b and conductivity σ b . In real applications, the layer represents a coating located on a perfectly conducting surface. The surface can be a flat or a rough one which can be represented by the surface function 1545-598X/$25.00 © 2008 IEEE