A fast and efficient microwave tomographic algorithm is proposed for 2-D and 3-D real-time intrawall imaging. The exploding reflection model is utilized to simplify the imaging formulation, and the half-space Green’s function is expanded in the spectral domain to facilitate the easy implementation of the imaging algorithm with the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT). The linearization of the inversion scheme and employment of FFT/IFFT in the imaging formula make the algorithm suitable for various applications pertaining to the inspection of a large probed region and allow real-time processing. Representative numerical and experimental results are presented to show the effectiveness and efficiency of the proposed algorithm for real-time intrawall characterization.
Ground penetrating radar (GPR) provides unique noninvasive means for retrieving information on the internal construction of the building walls. The ability to determine fidelity information of the wall, such as hidden wires and tubes, cracks, and voids, and/or the existence of reinforcements is beneficial for both military and civilian applications, that is, building safety and durability assessment, bridge/dam defect characterization, and through-the-wall radar imaging (TWRI) [
The detection and imaging of concealed targets inside a visually opaque building wall can be addressed by means of the inverse scattering technique. In the past decade, various linear and nonlinear inverse scattering algorithms have been developed for nondestructive testing of abnormalities in concrete structures. In [
Although successful imaging results can be achieved with the aforementioned algorithms, these algorithms mainly deal with 2-D intrawall imaging, which only reconstruct the cross sections of the concealed objects in the wall. In [
In this paper, a fast and efficient microwave tomographic algorithm is proposed for 2-D and 3-D real-time intrawall imaging. The imaging algorithm is based on the first-order Born approximation and exploits the half-space Green’s function. The exploding reflection model is employed, and then, the Green’s function is expanded in the spectrum domain to facilitate the implementation of the imaging algorithm with the fast Fourier transform (FFT) and inverse fast Fourier transform (IFFT). The linearization of the inversion scheme and employment of FFT/IFFT in the imaging formula make the imaging algorithm suitable for various applications pertaining to the inspection of large probed domain and allow near real-time processing.
Consider a typical scenario for 3-D intrawall inspection using monostatic synthetic aperture radar (SAR), as shown in Figure
Configuration of 3-D intra-wall imaging.
As shown in Figure
The scattered electric field observed at the receiver location can be expressed as
As the total electrical field inside the target is also a function of the contrast function, (
Substituting (
For simplicity, (
Then the image can be formulated as
It is found from (
It is noticed that the radar system both transmits and receives in the
The 3-D intrawall imaging formulation in (
The above derivation of a 3-D imaging algorithm can be simply reduced to 2-D intrawall imaging by replacing the half-space dyadic Green’s function with 2-D half-space Green’s function [
Substitute the 2-D half-space Green’s function into (
Representative numerical examples are presented in this section to verify and show the efficiency of the proposed algorithms for 2-D and 3-D intrawall imaging. In all the following examples, the imaging is performed on a four-core P4 2.66 GHz desktop computer with 16 GB of RAM.
In the first example, we present the 2-D imaging of a reinforced wall with a sinusoidal distribution of steel bars inside the wall as shown in Figure
Imaging of a reinforced wall. (a) Geometrical distribution of the steel bars inside the wall. (b) Time domain raw data. (c) Imaging result using the proposed algorithm, correct wall parameter,
In the following simulations, unless otherwise specified, we assume that the wall dielectric constant is known and is used in the imaging. The estimation of wall parameters associated with single or multilayered building walls has been extensively studied in the past decade within the framework of a one-dimensional inverse scattering problem [
Figure
Incorrect estimation of the wall parameters could result in the shift of target position and defocussing of the target image. Figures
In the above simulation, the radar scans the wall from −2 m to 2 m at a step size of 2.5 cm. To investigate the effect of step size on the imaging, we present imaging results with 2.5 cm, 5 cm, and 10 cm step sizes in Figures
Imaging results with different step sizes. (a) Step size = 2.5 cm. (b) Step size = 5 cm. (c) Step size = 10 cm.
The downrange resolution is primarily determined by the bandwidth of the transmitted signal. Figures
Imaging results with different signal bandwidths. (a) BW = 2.4 GHz (Freq = 0.8–3.2 GHz). (b) BW = 1.2 GHz (Freq = 1.4–2.6 GHz). (c) BW = 0.6 GHz (Freq = 1.7–2.3 GHz).
To quantitatively characterize the results, the signal fidelity factor in [
The signal fidelity factor (SFF) is then defined as the peak of the cross-correlation of the normalized transmitted and received signals and is given as [
We note that a 180-degree phase change occurs as the signal is reflected from the wall; thus, the minimum of the correlation is used and a minus sign is included in (
SFF of the reinforced wall versus antenna location.
In the second example, we present the 3-D imaging of a reinforcement grid inside the wall. Figure
Imaging of the grid reinforcement. (a) Geometrical layout of the reinforcement grid inside the wall. (b) 3-D imaging result.
In the last example, we present the 3-D imaging of two perpendicular tubes hidden inside the wall. The dimension and orientations of the tubes are shown in Figure
3-D imaging of the tubes hidden inside the wall. (a) Dimension of tubes and (b) 3-D imaging result.
Some experimental examples are presented in this section to verify the proposed algorithm for 2-D and 3-D intrawall imaging in a controlled lab environment. The 2-D imaging algorithm was applied to three experimental cases of a solid concrete wall with (1) embedded rebar, (2) the wall with no backing, and (3) a mirror placed on the back face of the wall. The last test of the mirror behind the concrete wall was also processed using the 3-D imaging algorithm.
The 2-D intrawall imaging algorithm was applied to the case of metallic rebar embedded within a solid concrete wall. Due to the limitations of fabricating this type of scenario in full scale, a 1/3 scale model was created which utilized multiple layers of a cement board readily available in home improvement stores. Multiple layers of the board were required as it was sourced at 1/4
1/3 scale cement board with metallic inclusions. (a) Measurement setup. (b) Layout of the wall interior. (c) Imaging result. The small circles indicate the true locations of the metallic bars.
In the next set of experiments, radar measurements were performed for a concrete wall, with and without backing. The wall under test was constructed using solid concrete bricks with a known dielectric constant of 7.66 and a loss tangent of 0.158 S/m and downrange thickness of 6 inches. The measurement array was fixed at 3 m standoff distance, measured from the front of the wall to the feed point on the antenna. The backing, which was a mirror, was placed at the rear surface of the wall in a configuration which allowed for the most direct contact between the backing and the rear surface of the wall. A frequency range of 0.7 GHz to 3.1 GHz was chosen for imaging using a step size of 3 MHz. An Agilent ENA 5071B was used for signal transmission and data collection. A dual-polarized horn antenna, with an operational bandwidth from 0.7 GHz to 6 GHz, was used as the transceiver. Figure
Solid concrete block wall with no backing. (a) Measurement setup. (b) Geometry. (c) Recorded reflection coefficient. (d) Imaging result.
(a) Photo from behind the solid concrete block wall with centered vertical mirror in direct wall contact. (b) Measurement setup and geometry. (c) Imaging result using the proposed 2-D microwave tomographic algorithm.
SFF of the received radar signals from the solid concrete wall.
The 3-D imaging algorithm, discussed above, was also applied to the measured scenario of a mirror on the rear surface of the wall in both vertical and horizontal configurations. Measured data was collected in a grid with 97 positions in the x-direction and 23 positions in the y-direction and at a 3 m standoff distance from the wall. At each location, step frequency data was collected from 1 GHz to 6 GHz with 1601 frequency steps. Both measured data sets were then processed using the 3-D microwave tomography algorithm given in (
Imaging results using the proposed 3-D microwave tomographic algorithm for (a) vertically and (b) horizontally oriented mirror behind a solid concrete wall.
The fast and nondestructive inspection of wall interior structures has promising applications in building safety and durability assessment as well as in various defense and law-enforcement scenarios. In this paper, a fast and efficient microwave tomographic algorithm is proposed for near real-time 2-D and 3-D intrawall imaging. The linearization of the inversion scheme and employment of the FFT/IFFT in the imaging formulation make the proposed imaging algorithm suitable for various applications pertaining to the inspection of a large probed region and allow real-time processing. Numerical and experimental 2-D and 3-D examples are presented with each showing the successful retrieval and localization of the wall interior or wall backing information using the proposed imaging algorithm. It takes less than one second/minute for 2-D/3-D imaging using the proposed algorithm, a feature that is very attractive for many applications which require on-site processing. Although this paper is concentrated on the intra-wall inspection, the presented algorithm is applicable to other concrete structure nondestructive testing, such as bridge/dam defect characterization, pavement inspection, and archeology. We note that the proposed radar imaging algorithm utilizes a linearization scheme to significantly speed up the imaging of intrawall objects and results in the object’s accurate geolocation and shape reconstruction but not its material composition, such as permittivity and loss tangent. The later requires nonlinear inverse-profiling schemes which usually necessitate a numerically computed forward model and a global optimization inversion scheme thus making the inversion very time-consuming and not suitable for on-site processing.
The authors declare that they have no conflicts of interest.