## Investigation of range profiles from buried 3-D object based on the EM simulation |

Optics Express, Vol. 19, Issue 13, pp. 12291-12304 (2011)

http://dx.doi.org/10.1364/OE.19.012291

Acrobat PDF (1402 KB)

### 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

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]

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]

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]

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]

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]

**4**(4), 611–615 (2007). [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]

## 2. Problem statement

*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

*H*above 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

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]

*O*, respectively. Then to calculate the path difference of path

*O*, the travel time that the wave needs to travel along

*O*in the upper region could be achieved as,

## 3. Numerical results

### 3.1 Far region range profiles under plane wave incidence

*x*coordinate ranges from

*x*axis is obtained, as shown in Fig. 2 . 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.

*1*to the reference point

*O*equals the buried depth

*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.

*1*,

*2*and

*4*.

*1*

*2*

*3*

*4*

*O*similar to formula (5): Where

*2*and path

*4*.

*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.

*1*and peak

*2*is accomplished in the following. As shown in Fig. 7 , the 1-D range profiles of the same dielectric object in the space

*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

*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

*1*calculated in Fig. 5 as 0.946.

*1*and peak

*3*) in Fig. 5 and the given geometrical relations in Fig. 6 with incident direction

*x*dimension could be reconstructed as

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

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]

*1*and

*3*in Fig. 8 correspond to these two paths respectively.

*1*

*2*

*3*

*4*

*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.

*1*,

*2*,

*3*and

*4*in Fig. 10.

*1*and path

*3*could be estimated according to the following explicit formulas,

*1*in Fig. 8, the buried depth is reconstructed as

*1*and peak 2) in Fig. 9 and the geometrical relations in Fig. 11 with given incident direction, it is deduced that

*x*dimension could be reconstructed as

*y*dimension could be reconstructed as

*x*axis and

*y*axis. And the observation range is from

*B*as an example, Fig. 14 shows the ray paths contributed by

*B*.

*u*is determined by the plane of incidence. The direct ray path is

*5*and peak

*7*contributed by the 1st order interaction of the diffraction corners

*5*is too close to peak

*3*to be distinguished.

*x*dimension could be reconstructed as

*y*dimension could be reconstructed successfully.

## 4. Conclusion

## Acknowledgments

## 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. |

2. | S. Vitebskiy, K. Sturgess, and L. Carin, “Short-pulse plane-wave scattering from buried perfectly conducting bodies of revolution,” IEEE Trans. Antenn. Propag. |

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. |

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. |

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. |

6. | F. Frezza, P. Martinelli, L. Pajewski, and G. Schettini, “Short-pulse electromagnetic scattering by buried perfectly conducting cylinders,” IEEE Geosci. Remote Sens. Lett. |

7. | K. T. Kim, D. K. Seo, and H. T. Kim, “Radar target identification using one-dimensional scattering cernters,” IEE Proc., Radar Sonar Navig. |

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. |

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. |

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. |

11. | W. C. Chew, |

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. |

**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

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