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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 13 — Jun. 20, 2011
  • pp: 12291–12304
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Investigation of range profiles from buried 3-D object based on the EM simulation

Siyuan He, Lei Zhuang, Fan Zhang, Weidong Hu, and Guoqiang Zhu  »View Author Affiliations


Optics Express, Vol. 19, Issue 13, pp. 12291-12304 (2011)
http://dx.doi.org/10.1364/OE.19.012291


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Abstract

The 1-D range profiles are suitable features for target identification and target discrimination because they provide discriminative information on the geometry of the target. To resolve features of the buried target, the contribution from individual scattering centers of the buried target in the range profiles need to be identified. Thus, the study of complex scattering mechanisms from which the range profiles are produced is of great importance. In order to clearly establish the relationship between the range profile characteristics and the complicated electromagnetic (EM) scattering mechanisms, such as reflections and diffractions, a buried cuboid possessing straight edges is chosen as the buried target in this paper. By performing an inverse discrete Fourier transform (IDFT) on the wideband backscattered field data computed with an accurate and fast EM method, the 1-D range profiles of the buried cuboid is successfully simulated. The simulated range profiles provide information about the position and scattering strength of the cuboid’s scattering centers along the range direction. Meanwhile, a predicted distribution of the scattering centers is quantitatively calculated for the buried cuboid based on the ray path computation. Good agreement has been found between simulated and predicted locations of the range profiles. Validation for amplitudes of the range profiles is further provided in the research. Both the peak amplitudes and locations of the range profiles could be understood and analyzed based on the knowledge of the scattering mechanisms. The formation of the 1-D range profiles has been revealed clearly from the full analysis of the scattering mechanisms and contributions. The problem has been solved for both near and far field regions. Finally, the buried depth and the characteristic size of the object are reasonably deduced from the simulated range profiles.

© 2011 OSA

1. Introduction

A lot of studies have been done for scattering from target buried in a lossy half-space [1

1. S. Vitebskiy and L. Carin, “Moment-method modeling of short-pulse scattering from and the resonances of a wire buried inside a lossy, dispersive half-space,” IEEE Trans. Antennas Propag. 43(11), 1303–1312 (1995).

6

6. F. Frezza, P. Martinelli, L. Pajewski, and G. Schettini, “Short-pulse electromagnetic scattering by buried perfectly conducting cylinders,” IEEE Geosci. Remote Sens. Lett. 4(4), 611–615 (2007). [CrossRef]

]. The impact caused by the lossy media mainly reflected in the wave attenuation. In order to focus on the formation of the range profiles and the study of the high frequency scattering mechanisms, the ground is chosen as lossless dry sand ground in this research.

Since antennas for the buried target detection usually work in near earth condition, the EM wave is non-uniformly incident on the buried object in the near field condition, which makes the analysis of the EM scattering mechanisms more complicated than the case that the far field condition is satisfied. From the angle of simplicity, firstly the plane wave incidence is chosen and the far region range profiles (by Fourier transforming the wide band field data received in the far field) of the buried target are studied. Afterwards, the near region range profiles are investigated under the excitation of the dipole located in near field. To summarize, the investigation of the range profiles will be carried out according to the different location set of the transmitters and receivers.

The remainder of the paper is organized as follows. In Section 2 we briefly describe the numerical model of a buried 3-D dielectric object and the problem in this paper. In Section 3, the 1-D range profiles of a buried 3-D dielectric cuboid are presented and their relationship with complicated scattering mechanisms is fully analyzed. Finally, conclusions are addressed in Section 4.

2. Problem statement

Figure 1
Fig. 1 Coordinate system of a 3-D dielectric object buried in a half-space.
shows the geometry of our problem, a 3-D dielectric object is buried in the lower region of a half-space characterized by relative permittivities ε1 and ε2. Suppose the buried object is a dielectric cuboid with complex permittivity εr(r) and located parallel to the interface with the size of Lx×Ly×Lz. The cuboid top is separated from the interface by h. The transmitters are set on the survey line parallel to x axis. Then the wideband scattered response from the buried cuboid is collected by the receivers located on the survey line at a height of Habove the interface. The survey line of the transmitters or the receivers is set in the far or near field. The coordinate of the receiver could be described as (L,0,H).

During the following numerical simulations, the upper region is assumed to be free space ε2=1 and the lower region is assumed to be dry sand ε1=4. For analysis convenience, the first example is chosen as a dielectric cuboid with size of 3m×2m×0.05m. Then for further validation and real application, a cuboid of size 3m×0.5m×0.8mwith increased height is considered. The frequency response of the scattering system is simulated by stepped frequency waveform (SFW). The backscattered field is sampled from 100MHzto 600MHz. Thus, the bandwidth is B=500MHzand the high-resolution is ΔR=c1/2B=0.15m. A frequency step Δf=5MHz is considered to obtain the sufficient unambiguous range Ru=c1/2Δf=15m.

SupposeRT andRR is the distance between the transmitter/receiver and the reference point O, respectively. Then to calculate the path difference of path abcd to the reference pointO, the travel time that the wave needs to travel along RT and RR is calculated firstly,

τo=(RT+RR)/c2
(2)

The path difference to the reference point O in the upper region could be achieved as,

ΔR2=((ττo)c2)/2
(3)

ΔR1/ΔR2=c1/c2
(4)

So we get,

ΔR1=ΔR2/(ε1/ε2)=((ε1/ε2)(b+c)+a+dRTRR)/(2ε1/ε2)
(5)

Note that the contribution of the planar surface to the radar return only exists when the incident direction is normal to the air-ground interface. In order to focus on the independent scattering of the target, the direct scattering contribution from the ground surface is subtracted in the radar echoes. In Section 3.1 the transmitters and the receivers are set in the far field region while in Section 3.2 the near field condition is satisfied and considered.

3. Numerical results

3.1 Far region range profiles under plane wave incidence

In this case, both the transmitter and the receiver are set at the same location in the far field region for the monostatic case as shown in Fig. 1. A plane wave with parallel polarization and normalized electric field is incident from the upper space. As shown in Fig. 1, the backscattered fields are collected at N=99 receivers on the survey line at a height of H=200m, where thex coordinate ranges from 200m to 200m.

By performing an IDFT on the wideband backscattered field at multi receivers along the survey line, the lateral distribution of 1-D range profiles along xaxis is obtained, as shown in Fig. 2
Fig. 2 The lateral distribution of far region range profiles along x axis.
. The reference point O in Fig. 1 corresponds to a range location of zero in Fig. 2. The lateral distribution is symmetrical in the cross range along x axis due to the symmetry of the scattering model.

It is illustrated that when the incident direction is normal to the air-ground interface, the peak amplitude of the range profile is the largest. That’s because the strong specular scattering from the top surface of the cuboid AA'BB' leads to the strongest peak amplitude at the incident angleθ=ϕ=0. Specifically, the range profiles at θ=ϕ=0 are separated from the lateral distribution of 1-D range profile and the peaks are marked as 1 and 3 in Fig. 3
Fig. 3 Range profiles of the buried object along θ=ϕ=0.
. The simulated locations of the peaks in Fig. 3 are listed in Table 1

Table 1. Simulated and Expected Range Locations of a Buried Object (Unit: m)

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and will be validated by the predictions based on the ray path computation. According to the ray theory, peak 1 is caused by the echo reflected directly from the cuboid top surface and peak 3 is caused due to a reverberation (viz. the 1st-order interaction) between the cuboid top and the air-ground interface. The path difference of peak 1 to the reference point O equals the buried depth h=1.5m. And path difference of peak 3 to the reference point O is twice the depth. In Table 1, the simulated results and the predicted locations agree well with each other.

Furthermore, the peak amplitudes of the range profiles could be evaluated according to the Fresnel theory. Suppose that the buried object is one layer of the stratified structure, the simplified four planarly layers with relative permittivities ε1=4,ε2=8,ε3=4,ε4=1 are illustrated in Fig. 4
Fig. 4 The equivalent multilayered media.
.

In Fig. 5
Fig. 5 Range profiles of the buried object along θ=π/4,ϕ=0.
, the incident direction is set asθ=π/4,ϕ=0 and the range profiles along the direction obliquely to the air-ground are demonstrated and indicated by three peaks marked as 1, 2 and 4.

Figure 6
Fig. 6 Ray paths of the buried object.
shows the ray paths of the buried target when the oblique incident direction is considered. The scattering mechanisms of the range profiles strongly depend on the aspect angle between the radar and target. Instead of the specular reflections from the top surface in Fig. 3, the contribution to the range profiles in Fig. 5 corresponds to the diffractions of the two edges AA' and BB', which lead to path 1 abba and path 2 abbaas illustrated in Fig. 6. Due to the 1st-order interaction between the edges and the air-ground interface, the 1st-order ray paths are formulated, viz. path 3 abccba and path 4 abccba .

The range locations of the range profiles caused by path 1 and path 3 could be estimated by calculating the paths difference to the reference pointO similar to formula (5):
ΔR(path1)=(a+ε1bR)/ε1
(7a)
ΔR(path3)=(a+ε1(b+c)R)/ε1
(7b)
Where RT=RR=R. The path length of a,b,c could be calculated by the geometrical relations and Snell's law:

a=R+(Lx/2htanθ)sinθb=h/cosθ,c=h,sinθ=ε1sinθ
(8)

The same prediction could be done for path 2 and path 4.

It is found in Table 1 that the simulated locations of peak 1, 2, 4 in Fig. 5 match with the predicated range locations well. However the expected peak by path 3 at the position of 2.373m is hardly observed in the simulated results. This may be caused because the contribution to the anticipated peak by path 3 is too small to be reflected. Furthermore, a huge peak (peak 2 at the location of 1.933m) close to the location of the expected peak 3 makes it even difficult for the small peak to be distinguished.

To further validate the simulated results in Fig. 5, a detailed study of the range profile amplitudes for peak 1 and peak 2 is accomplished in the following. As shown in Fig. 7
Fig. 7 Range profiles of the same object in free space along θ=sin1(sin(π/4)/2),ϕ=0.
, the 1-D range profiles of the same dielectric object in the spaceε1=4 are simulated for comparison. The incident angle is chosen the same as the refraction angle in the half-space problem, viz, θ=sin1(sin(π/4)/2),ϕ=0 . Compared with marked peaks 1 and 2 in Fig. 5, the range profiles marked as 1 and 2 in Fig. 7 are also caused by the diffractions from the edges of AA' and BB'under the same incident angle and in the lower space. The amplitude ratios of peak 2 to peak 1 are supposed to be the same in the two cases. In fact, the amplitude ratio of peak 2 to peak 1 in Fig. 7 is calculated as 0.938, which provides a reference for the amplitude ratio of peak 2 to peak 1calculated in Fig. 5 as 0.946.

According to the distribution of the individual scattering centers (peak 1 and peak 3) in Fig. 5 and the given geometrical relations in Fig. 6 with incident direction θ=π/4, the length of the buried cuboid in xdimension could be reconstructed as L'x=2.9698m, which matches well with the real size Lx=3m.

3.2 Near region range profiles under the excitation of the dipole in near field

E1inc(r,r)=η2k2G¯ee12(r,r)e^x
(9)

Here, k2,η2are the wavenumber and wave impedance in the upper space; G¯ee12is the spatial-domain electric field dyadic Green’s function when the observation point in lower space and the source point is in upper space.

Figure 8
Fig. 8 Range profiles of the buried object when the dipole locates at (0m,0m,2m).
, Fig. 9
Fig. 9 Range profiles of the buried object when the dipole locates at (4m,0m,2m).
and Fig. 10
Fig. 10 Range profiles of the buried object when the dipole locates at (0m,4m,2m).
show the 1-D range profiles indicated by marked peaks when the dipole locates at (0m,0m,2m), (4m,0m,2m)and (0m,4m,2m)respectively.

Figure 11
Fig. 11 Ray paths of the buried object.
illustrates the ray paths of the buried target when the dipole is located at a certain point on the survey line in the near field.

When the condition thatLLx/2satisfies, the ray paths contributed by the direct reflection of the cuboid top surface exist, viz. path abba and path abbbba. The marked peaks 1 and 3 in Fig. 8 correspond to these two paths respectively.

For the simulated results in Fig. 9, the condition thatLLx/2doesn’t satisfy, so the range profiles are expected to correspond to the four paths contributed by the edge diffractions, viz. path 1 abba and path 2 abba, path 3 abccba and path 4 abccba . As shown in Table 2

Table 2. Simulated and Expected Range Locations of Fig. 8, Fig. 9 and Fig. 10 (Unit: m)

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, it is observed that the marked peaks 1, 2 and 3 in Fig. 9 match well with the predicted locations of the ray paths. However, the expected peak by path 4 is too small to be distinguished.

For the simulated results in Fig. 10, the condition thatLLy/2doesn’t satisfy either, so the four ray paths could be derived similarly. All the expected peaks are observed at the corresponding range locations marked as 1, 2, 3 and 4 in Fig. 10.

Specifically, the range locations of the range profiles in Fig. 9 and Fig. 10 caused by the path 1 and path 3 could be estimated according to the following explicit formulas,

ΔR(path1)=(a+ε1bR)/ε1
(10a)
ΔR(path3)=(a+ε1(b+c)R)/ε1
(10b)

And the path length of a,b,c is calculated based on the geometrical relations and Snell’s law, where θ1 is determined by a numerical root searching method such as Muller’s method,

asinθ1+bsinθ1=Lx/2+Lb=h/cosθ1,a=H/cosθ1,c=h,sinθ=ε1sinθ
(11)

According to the location of peak 1 in Fig. 8, the buried depth is reconstructed as h=1.575m. Based on the distribution of the individual scattering centers (peak 1 and peak 2) in Fig. 9 and the geometrical relations in Fig. 11 with given incident direction, it is deduced thatOA(A')=1 .631mand OB(B')=1 .491m. Then the length of the buried cuboid in x dimension could be reconstructed as L'x=OA+OB=3 .122m, which matches well with the real size Lx=3m. Similarly, the length of the buried cuboid in y dimension could be reconstructed as L'y=2 .134m, which matches well with the real size Ly=2m.

Suppose the survey line is parallel to xaxis which is the diagonal of xaxis and yaxis. And the observation range is from 6.4m to 6.4malong xaxis. Then the lateral distribution of 1-D range profiles along xaxis is demonstrated in Fig. 12
Fig. 12 The lateral distribution of near region range profiles along x'axis.
.

Figure 13
Fig. 13 Range profiles of the buried object when the dipole locates at (4.5255m,4.5255m,2m).
shows the 1-D range profiles when the dipole locates at (4.5255m,4.5255m,2m) on the diagonal survey line.

Instead of the edge diffractions in Fig. 9 and Fig. 10, the individual scattering centers of the buried object correspond to the diffractions of four cornersA,A',B,B'in Fig. 13. Take the diffraction point B as an example, Fig. 14
Fig. 14 Ray paths of the buried object.
shows the ray paths contributed by B. E' is the intersection point between the ray path and the air-ground interface. The angles satisfy the relationshipsinθ=ε1sinθ. Axis u is determined by the plane of incidence. The direct ray path is abba and the 1st order path is abccba. So in all, eight paths are contributed by diffractions of the four corners and the corresponding reverberations. The range locations caused by the paths could be estimated and illustrated in Table 3

Table 3. Simulated and Expected Range Locations of Fig. 13 (Unit: m)

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based on the ray path prediction. It is observed that the expected peak 5 and peak 7 contributed by the 1st order interaction of the diffraction corners B'andA'seem too small to be discovered in the simulated results. While the other simulated range profile locations match well with the expected results.

For real application, the height of the cubic is increased in the following case and a 3-D cuboid with size of 3m×0.5m×0.8mis considered. The other parameters are chosen the same as εr=8 and h=1.5m. Figure 15
Fig. 15 Range profiles of the buried object when the dipole locates at (4m,0m,2m).
shows the 1-D range profiles when the dipole locates at (4m,0m,2m).

The range locations caused by the scattering centers of the buried object could be estimated according to Fig. 11 based on the ray path prediction and the expected results match well with the simulated locations in Table 4

Table 4. Simulated and expected range locations of Fig. 15 (Unit: m)

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. Only the expected peak 5 is too close to peak 3 to be distinguished.

Based on the distribution of the individual scattering centers in Fig. 14 and the geometrical relations in Fig. 11 with given incident direction, it is deduced thatOA(A')=1 .418mand OB(B')=1 .418m. Then the length of the buried cuboid in x dimension could be reconstructed as L'x=OA+OB=2 .899m, which matches well with the real size Lx=3m. Similarly, the length of the buried cuboid in y dimension could be reconstructed successfully.

In all, the buried depth of the object can be estimated from the locations of the range profiles when the incident direction is normal to the air-ground interface. Then, given the oblique incident direction, the characteristic size of the buried object can be deduced from the simulated range profiles.

4. Conclusion

The detail contributions from individual scattering centers of the buried target in the range profiles have been studied and identified in this paper. The 1-D range profiles of the buried target are simulated based on the accurate and fast EM numerical method. A cuboid possessing straight edges is chosen as the buried target to focus on the important scattering mechanisms, such as reflections and diffractions. The ray path prediction is employed to analyze the scattering features of the buried target. Good agreement has been found between the simulated and the predicted locations of the range profiles. The relationship between the range profile characteristics and the complicated scattering mechanisms is clearly established. Finally, the buried depth and the characteristic size of the object are reconstructed from the simulated results, which is helpful for target identification and target discrimination.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 61001059), the China Postdoctoral Science Foundation, and the Fundamental Research Funds for the Central Universities. The authors would like to thank the reviewers for their helpful and constructive suggestions.

References and links

1.

S. Vitebskiy and L. Carin, “Moment-method modeling of short-pulse scattering from and the resonances of a wire buried inside a lossy, dispersive half-space,” IEEE Trans. Antennas Propag. 43(11), 1303–1312 (1995).

2.

S. Vitebskiy, K. Sturgess, and L. Carin, “Short-pulse plane-wave scattering from buried perfectly conducting bodies of revolution,” IEEE Trans. Antenn. Propag. 44(2), 143–151 (1996). [CrossRef]

3.

S. Vitebskiy, L. Carin, M. A. Ressler, and F. H. Le, “Ultra-wideband, short-pulse ground-penetrating radar: simulation and measurement,” IEEE Trans. Geosci. Rem. Sens. 35(3), 762–772 (1997). [CrossRef]

4.

N. Geng and L. Carin, “Wide-band electromagnetic scattering from a dielectric BOR buried in a layered lossy dispersive medium,” IEEE Trans. Antenn. Propag. 47(4), 610–619 (1999). [CrossRef]

5.

V. Losada, R. R. Boix, and F. Medina, “Fast and accurate algorithm for the short-pulse electromagnetic scattering from conducting circular plates buried inside a lossy dispersive half-space,” IEEE Trans. Geosci. Rem. Sens. 41(5), 988–997 (2003). [CrossRef]

6.

F. Frezza, P. Martinelli, L. Pajewski, and G. Schettini, “Short-pulse electromagnetic scattering by buried perfectly conducting cylinders,” IEEE Geosci. Remote Sens. Lett. 4(4), 611–615 (2007). [CrossRef]

7.

K. T. Kim, D. K. Seo, and H. T. Kim, “Radar target identification using one-dimensional scattering cernters,” IEE Proc., Radar Sonar Navig. 148(5), 285–296 (2001). [CrossRef]

8.

S. He, F. Deng, H. Chen, W. Yu, W. Hu, and G. Zhu, “Range profile analysis of the 2-D target above a rough surface based on the electromagnetic numerical simulation,” IEEE Trans. Antenn. Propag. 57(10), 3258–3263 (2009). [CrossRef]

9.

Y. H. Zhang, B. X. Xiao, and G. Q. Zhu, “An improved weak-form BCGS-FFT combined with DCIM for analyzing electromagnetic scattering by 3-D objects in planarly layered media,” IEEE Trans. Geosci. Rem. Sens. 44(12), 3540–3546 (2006). [CrossRef]

10.

L. Zhuang, S. Y. He, X. B. Ye, W. D. Hu, W. X. Yu, and G. Q. Zhu, “The BCGS-FFT method combined with an improved discrete complex image method for EM scattering from electrically large objects in multilayered media,” IEEE Trans. Geosci. Rem. Sens. 48(3), 1180–1185 (2010). [CrossRef]

11.

W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, 1990).

12.

T. J. Cui, W. C. Chew, A. A. Aydiner, and Y. H. Zhang, “Fast-forward solvers for the low-frequency detection of buried dielectric objects,” IEEE Trans. Geosci. Rem. Sens. 41(9), 2026–2036 (2003). [CrossRef]

OCIS Codes
(280.0280) Remote sensing and sensors : Remote sensing and sensors
(290.0290) Scattering : Scattering

ToC Category:
Remote Sensing and Sensors

History
Original Manuscript: May 2, 2011
Revised Manuscript: May 26, 2011
Manuscript Accepted: May 27, 2011
Published: June 9, 2011

Citation
Siyuan He, Lei Zhuang, Fan Zhang, Weidong Hu, and Guoqiang Zhu, "Investigation of range profiles from buried 3-D object based on the EM simulation," Opt. Express 19, 12291-12304 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-13-12291


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References

  1. S. Vitebskiy and L. Carin, “Moment-method modeling of short-pulse scattering from and the resonances of a wire buried inside a lossy, dispersive half-space,” IEEE Trans. Antennas Propag. 43(11), 1303–1312 (1995).
  2. S. Vitebskiy, K. Sturgess, and L. Carin, “Short-pulse plane-wave scattering from buried perfectly conducting bodies of revolution,” IEEE Trans. Antenn. Propag. 44(2), 143–151 (1996). [CrossRef]
  3. S. Vitebskiy, L. Carin, M. A. Ressler, and F. H. Le, “Ultra-wideband, short-pulse ground-penetrating radar: simulation and measurement,” IEEE Trans. Geosci. Rem. Sens. 35(3), 762–772 (1997). [CrossRef]
  4. N. Geng and L. Carin, “Wide-band electromagnetic scattering from a dielectric BOR buried in a layered lossy dispersive medium,” IEEE Trans. Antenn. Propag. 47(4), 610–619 (1999). [CrossRef]
  5. V. Losada, R. R. Boix, and F. Medina, “Fast and accurate algorithm for the short-pulse electromagnetic scattering from conducting circular plates buried inside a lossy dispersive half-space,” IEEE Trans. Geosci. Rem. Sens. 41(5), 988–997 (2003). [CrossRef]
  6. F. Frezza, P. Martinelli, L. Pajewski, and G. Schettini, “Short-pulse electromagnetic scattering by buried perfectly conducting cylinders,” IEEE Geosci. Remote Sens. Lett. 4(4), 611–615 (2007). [CrossRef]
  7. K. T. Kim, D. K. Seo, and H. T. Kim, “Radar target identification using one-dimensional scattering cernters,” IEE Proc., Radar Sonar Navig. 148(5), 285–296 (2001). [CrossRef]
  8. S. He, F. Deng, H. Chen, W. Yu, W. Hu, and G. Zhu, “Range profile analysis of the 2-D target above a rough surface based on the electromagnetic numerical simulation,” IEEE Trans. Antenn. Propag. 57(10), 3258–3263 (2009). [CrossRef]
  9. Y. H. Zhang, B. X. Xiao, and G. Q. Zhu, “An improved weak-form BCGS-FFT combined with DCIM for analyzing electromagnetic scattering by 3-D objects in planarly layered media,” IEEE Trans. Geosci. Rem. Sens. 44(12), 3540–3546 (2006). [CrossRef]
  10. L. Zhuang, S. Y. He, X. B. Ye, W. D. Hu, W. X. Yu, and G. Q. Zhu, “The BCGS-FFT method combined with an improved discrete complex image method for EM scattering from electrically large objects in multilayered media,” IEEE Trans. Geosci. Rem. Sens. 48(3), 1180–1185 (2010). [CrossRef]
  11. W. C. Chew, Waves and Fields in Inhomogeneous Media (Van Nostrand Reinhold, 1990).
  12. T. J. Cui, W. C. Chew, A. A. Aydiner, and Y. H. Zhang, “Fast-forward solvers for the low-frequency detection of buried dielectric objects,” IEEE Trans. Geosci. Rem. Sens. 41(9), 2026–2036 (2003). [CrossRef]

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