International Symposium (NDT-CE 2003)Non-Destructive Testing in Civil Engineering 2003
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A COMPARATIVE STUDY OF DATA PROCESSING ALGORITHMS FOR RADAR IMAGING OF STRATIFIED BUILDING STRUCTURESValeri Mikhnev, Institute of Applied Physics, Minsk, Belarus/ Helsinki University of Technology, Radio Laboratory/SMARAD, Espoo, Finland
Pertti Vainikainen, Helsinki University of Technology, Radio Laboratory/SMARAD, Espoo, Finland
This work is devoted to the reconstruction of layered dielectric structures in civil engineering using solution of the inverse problem, when the measured reflection coefficient is given in the frequency domain. The two-stage iterative 1D inverse scattering technique has been applied to derive the permittivity profile. In the first stage, positions of the reflecting interfaces are obtained by the inverse Fourier transform of the reflection coefficient. Then, the unknown profile is represented in the form of steps built on the interfaces, with the step amplitudes being determined from a linear integral equation. The comparisons showed apparent advantage of the reconstructive approach over conventional digital signal processing techniques when dealing with layered structures in civil engineering. Besides, although 1D inverse scattering methods are generally valid only for stratified dielectric media, they can be nevertheless successfully utilized for the detection and discrimination of simple subsurface 2D objects. Corresponding results for the reconstructive imaging of metal rod and void buried in the moist sand are presented.
During the last decade, step-frequency radar has become a popular tool for subsurface imaging, in particular for the inspection of non-metallic building structures and bridge decks. This can be attributed to its better flexibility from a viewpoint of antenna design, applicability of calibration and better signal-to-noise ratio. The simplest data processing algorithm for step-frequency radar is merely the inverse Fourier transform that converts frequency domain data to the impulse characteristics. This method is fast but its range resolution is limited. Numerous available techniques of super-resolution and parametric estimation [1-2] provide better resolution at the expense of computation time and stability. Synthetic aperture focusing and migration methods widely used for the detection of small subsurface inclusions are not effective for stratified dielectric media that are often encountered in civil engineering.
In this work, recently modified 1D inverse scattering method  for the reconstruction of highly contrasted layered dielectric structures is presented. It is based on iterative inversion procedure of Newton type with the permittivity profile represented in the form of multiple dielectric interfaces. The method is fast and robust enough to deal with experimental data obtained for real dielectric structures such as concrete and brick walls.
The input data had been collected using vector network analyzer HP8753D and bistatic tapered-slot antenna systems operating in the frequency bands of 1 to 4 GHz and of 1.5 to 6 GHz. Experimental examples demonstrate advantage of the reconstruction method over algorithms of digital spectral analysis including super-resolution ones. Even when simple two- and three-layered building structures are inspected, techniques of spectral analysis suffer from artefacts, lack of resolution and possible obscuring really existing objects. It is shown that understanding building structure from the conventional radar range profile may be completely wrong. All these drawbacks have been successfully avoided using microwave reconstruction algorithm applied to the same input data. Finally, possibilities of detection and discrimination of buried metal rods and voids with the use of the 1D reconstructive algorithm applied to real experimental data are demonstrated.
The 1D inverse scattering method is based on the Newton-Kantorovich iterative scheme applied to the Riccati nonlinear differential equation. This method derives the permittivity of the stratified medium as a function of depth by successive solution of the forward problem and a local linear inverse problem. The inversion procedure described in  can be summarized as follows:
Details of formulation and solution of the inverse problem are given in . In this work, however, a set of step functions of finite width are used at the stage 3 instead of abrupt Heaviside steps. Step width in the expanding functions has been chosen to be a fraction of the radar range resolution. This modification removes from the reconstructed permittivity profile sharp narrow peaks arising sometimes due to the ill-posedness of the inverse problem.
For the research purposes, the step-frequency radar can be built of a wideband vector network analyzer equipped by transmitting and receiving antennas. The experimental setup used in this work includes the network analyzer HP8753D and bistatic antenna system consisting of a pair of tapered-slot Vivaldi antennas.
Wideband free space measurements of the reflection coefficient from building constructions suffer from near field effects and dispersion of the radar system, especially antenna dispersion. Thus, raw input data should be preprocessed to reduce measurement errors. This is especially important for the reconstruction algorithms that are very sensitive to the accuracy of the input information. Single-reference free-space calibration method  has been applied here to account for the antenna dispersion and multiple reflections between the antenna and the object under test. After the calibration, the 1D inverse scattering algorithm outlined above has been employed to reconstruct the dielectric permittivity profile.
Consider a layered dielectric structure consisting of two equal brick slabs with the thickness of 75 mm separated by an air gap of 60 mm (Fig. 1). The reflection coefficient measured over the frequency range of 1 to 4 GHz had been processed by the inverse Fourier transform (dotted line in Fig. 1) and the Burg's method (solid line). For the sake of comparison, processed data as well as the dielectric permittivity profile are plotted versus effective thickness, or optical path length. All the reflecting interfaces are clearly visible in the synthetic range profiles computed by the both techniques of digital spectral analysis. The super-resolution approach produces sharper peaks, but some of them do not correspond exactly to the interface position. Besides, understanding of such structure may be difficult.
The 1D inverse scattering method applied to the same input data yields the dielectric permittivity profile shown in Fig. 2. Although the second dielectric slab as seen in Fig. 2 is not reconstructed accurately, the internal structure of the wall is much more clear compared to the range profiling (Fig. 1).
The task becomes more difficult when the air gap between the brick layers decreases to 30 mm (Fig. 3).
From Fig. 3, disadvantages of spectral analysis are apparent. First, two dielectric interfaces adjacent to the air gap (near effective depth of 22 cm) are not resolved by the inverse Fourier transform (dotted line), because the range resolution for the given bandwidth is insufficient. The super-resolution algorithm (solid line) yet shows the air gap in the form of two peaks. However, there exists another, more important drawback. The peak corresponding to the last dielectric interface (at the effective distance near 40 cm) has very low amplitude, even lower than artefact at the effective distance of 56 cm. This can be explained by obscuring the reflection from the last interface by a signal corresponding to double reflection inside the first slab. As a result, it's impossible to understand satisfactorily structure of the layered medium in Fig. 1 using only range profile obtained by the spectral analysis.
Inverse scattering method applied to the same measured data reconstructs the permittivity profile successfully as shown in Fig. 4. The first slab is reconstructed almost perfectly, the second one can be also easily distinguished. The reconstruction of deeper interfaces in the building structure deteriorates here due to divergence of the wave beam in space and material losses that were accounted neither in calibration procedure nor in the inversion algorithm. Nevertheless, the disadvantages of the both methods of digital spectral analysis mentioned above have been successfully overcome by the reconstructive approach.
Consider now detection and discrimination of cylindrical objects inside the dielectric medium. Fig. 5 shows results of frequency domain signal processing for the case of reinforcing bar with a diameter of 3 cm buried in moist sand at a depth of 10 cm. The input data have been measured in the frequency range of 1.5 to 6 GHz. The Fourier range profiling (dashed line) is capable to detect both the back wall of the sand box and the bar inside. The response of the back wall is low because of losses in the moist medium. However, the one-dimensional range profiling cannot help in understanding nature of the buried object. Reconstruction of the permittivity distribution yields more information. So, the metal bar is seen as a positive step in the dielectric permittivity profile (solid line in Fig. 5).
Microwave imaging of the void with diameter of 4 cm formed in the sand box at about the same depth is demonstrated in Fig. 6. The synthetic range profile obtained by the Fourier transform is very similar to the previous case. Thus different objects can be hardly discriminated. In the permittivity distribution derived by the inversion technique (solid line in Fig. 6), the void is seen as an object of lower dielectric permittivity buried in the surrounding medium. Both front and back walls of the sand box are seen, too. It is worth noting that the geometrical distances are also reconstructed quite correctly in the both cases.
Therefore, 1D reconstructive algorithm applied to the step-frequency radar data provides important additional information as compared to conventional methods of digital spectral analysis and thus allows distinguishing simple buried objects.
A novel frequency-domain 1D inverse scattering method has been applied to the imaging of layered structures of civil engineering. The method demonstrates obvious advantage over range profiling of layered media using different techniques of digital spectral analysis. The quality of the permittivity profile reconstruction is good for interfaces both poorly resolved and obscured by multiple reflections. Despite of considerable discrepancy between the 1D theoretical model and most real objects under test, quality of reconstruction was found satisfactory enough to discriminate some underground targets in non-transparent media.