## Targets recognition using subnanosecond pulse laser range profiles |

Optics Express, Vol. 18, Issue 16, pp. 16788-16796 (2010)

http://dx.doi.org/10.1364/OE.18.016788

Acrobat PDF (1366 KB)

### Abstract

The 3-D target information can be obtained directly by the analysis of the 1-D data of the pulse laser range profile (LRP). In this paper, a new calculational method to generate and process the LRP which is based on the lidar equation is established. The LRPs of different targets are simulated by the new method, and the corresponding profile information is achieved. The effect of the some parameters including the target shape, surface material, incident pulsewidth and incident angle on the LRP is analyzed. In order to validate the theory, the relevant experiment is implemented, and the experimental data agrees well with the simulation result.

© 2010 OSA

## 1. Introduction

2. H. Li and S. Yang, “Using Range Profiles as Feature Vectors to Identify Aerospace Objects,” IEEE Trans. Antenn. Propag. **41**(3), 261–268 (1993). [CrossRef]

3. S. Adachi and T. Uno, “One-dimensional target profiling by electromagnetic backscattering,” J. Electromagn. Waves Appl. **7**(3), 403–421 (1993). [CrossRef]

6. V. Galdi, D. A. Castanon, and L. B. Felsen, “Multifrequency reconstruction of moderately rough interfaces via quasi-ray Gaussian beams,” IEEE Trans. Geosci. Rem. Sens. **40**(2), 453–460 (2002). [CrossRef]

## 2. Laser Range Profile Theory

*P*is received signal power,

_{s}*P*is transmitter power,

_{i}*σ*is effective target scattering cross-section,

*R*

_{0}is the distance between the target center and the transmit-receive system,

*D*is receiver aperture diameter,

*T*is attenuation factor, and

_{a}*η*is system efficiency.

_{syst}*w*

_{0}is waist radius,

*w*(

*z*) is beam radius,

*R*

_{0}between the target center and the transmit-receive system is very large compared to the radial length of the target,

*z*=

*R*

_{0}.

*σ*

^{0}is unit area laser scattering cross-section, and

*T*

_{0}is the full width

*T*at half maximum of the pulse, the laser range equation can be written as:

*R.*

*t*. Then, the backscattering signal contains the information of the girdle band in the target surface which radial width is

## 3. Laser Range Profile Simulation and Analysis

*z*-axis which is defined as the central axis of the target. The incident waveform is a Gaussian function,

*R*

_{0}is 50

*m*in the following cases.

### 3.1 Flat plane

*S*and the hemispherical reflectance of the Lambert flat plane is

*ρ*which depends on the character of the material in the target surface. The LRP equation of the flat plane can be written as:where,

_{r}*t*= 2

*z/c*.

*ρ*of the Lambert flat plane is 0.9, 0.6, and 0.3. Where, the value of the incident power is normalized to unity and the relative backscattering power is plotted along the vertical axis. It can be seen that the backscattering pulse is still a Gaussian-shaped pulse and its pulsewidth is the same as the incident pulse. In addition, the backscattering power is proportional to

_{r}*ρ*.

_{r}### 3.2 Sloped-plane

*l*and the incident angle (the angle between the incident direction and normal direction of the sloped-plane) is

*θ*. The LRP equation of the sloped plane can be written as:where,

*θ*= 60° and

*T*

_{0}= 300ps for

*l*= 0.03m, 0.1m, 0.2m and 0.3m. As it can be seen, when

*l*increases, the backscattering power increases and the top of the LRPs become flatter. This is because that the incident pulse intensity increases and the backscattering power increases with

*l*increasing when the beam can cover the targets. When

*T*

_{0}is fixed, Δ will keeps invariant, which means the ability of distinguishing the radial range is invariant. When the radial size of the target is much bigger than Δ, the pulse top is flat and it shows the scattering cross section of each part of the target is same. The peak length coincides with the radial size of the sloped-plane. Figure 3(b) shows the LRPs of the sloped-plane when

*θ*= 60° and

*l*= 30mm for

*T*

_{0}= 300ps, 100ps, 50ps and 30ps. As it can be seen, with the decreased pulsewidth, the backscattering power decreases and the backscattering pulse can reflect the target profile shape exactly. This is because the smaller the incident pulsewidth, the lower the pulse power at the given pulse peak power. With the

*T*

_{0}decreasing Δ decreases, the ability of distinguishing the radial range increases and the LRPs can reflect the target profile shape.

### 3.3 Circular cone

*a*,the half-cone angle

*α*and the height

*h*are studied. The laser is incidence from the central axis on the circular cone top. The LRP equation of the circular cone can be written as:

*α*= 11.3° and

*T*

_{0}= 300ps for

*h*= 0.1m, 0.2m and 0.3m. Figure 4(b) shows the LRPs of the circular cone when

*α*= 11.3° and

*h*= 0.1m for

*T*

_{0}= 300ps, 100ps and 50ps. It can be seen that the LRPs rise slowly but fall quickly, the peak position is near the bottom position of the circular cone and the LRP width is the height of the circular cone. In Fig. 4(a), when it keeps

*α*invariant, the enlarged

*h*increases the scattering cross section, which causes the backscattering power increase. In Fig. 4(b) it can be seen that the narrow incident pulsewidth causes the decrease of the peak power of the LRPs. It is because when the pulsewidth is narrow down, the backscattering power in one radar cross section, section, which causes the backscattering power increase. In Fig. 4(b) it can be seen that the narrow incident pulsewidth causes the decrease of the peak power of the LRPs. It is because when the pulsewidth is narrow down, the backscattering power in one radar distinguishing unit is weaken, so that the LRP intensity is decreased. While, the LRP shape is close to the exact circular cone profile and the imaging effect will be better.

*θ*

_{0}. It can be seen that the peak value and position are all different. When incident pulse wave is parallel to the axis of the circular cone (

## 4. Experiment setup

### 4.1 Flat plane

*ρ*of the Lambert flat plane is 0.9 and 0.6. Figure 7 shows that theoretical calculation and experimental data is complete match. Backscattering pulse is still a Gaussian-shaped pulse with the same pulsewidth, and the backscattering power is proportional to

_{r}*ρ*.

_{r}### 4.2 Sloped-plane

*l*of the sloped-plane is 30mm and the incident angle

*θ*is 30° and 60°. Figure 8 shows that theoretical calculation is consistent with the experimental results. The backscattering pulse is more width than the incident pulse, the broadening coincide with the radial range of the target. And the scattering power decrease with increasing incident angle. It is because the larger the incident angle is, the smaller the scattering cross section is.

### 4.3 Circular cone

*h*is 0.1m, bottom radius

*a*is 0.02m and the material is aluminium and teflon. The laser is incidence from the central axis on the circular cone top. Figure 9 shows that theoretical calculation is close approximately to the experimental data. The backscattering pulse is more width than the incident pulse and the broadening coincide with the radial range of the target. Meanwhile, the scattering power is different with the different material and increases with increasing target reflectance.

## 5. Conclusion

## Acknowledgments

## References and links

1. | D. Mensa, |

2. | H. Li and S. Yang, “Using Range Profiles as Feature Vectors to Identify Aerospace Objects,” IEEE Trans. Antenn. Propag. |

3. | S. Adachi and T. Uno, “One-dimensional target profiling by electromagnetic backscattering,” J. Electromagn. Waves Appl. |

4. | K. Umashankar, S. Chaudhuri, and A. Taflove, “Finite-difference time-domain formulation of an inverse scattering scheme for remote sensing of inhomogeneous lossy layered media: Part I-One dimensional case,” J. Electromagn. Waves Appl. |

5. | K. Harada and A. Noguchi, “Reconstruction of two dimensional rough surface with Gaussian beam illumination,” IEICE Trans. Electron. |

6. | V. Galdi, D. A. Castanon, and L. B. Felsen, “Multifrequency reconstruction of moderately rough interfaces via quasi-ray Gaussian beams,” IEEE Trans. Geosci. Rem. Sens. |

7. | L. G. Shirley, and G. R. Hallerman, |

8. | P. P. Johan, C. van den Heuvel, Herman H. P. Th. Bekman, Frank J. M. van Putten, and R. H. M. A. Schleijpen, “Experimental Validation of Ship Identification with a Laser Range Profiler,” Laser Radar Technology and Applications XIII, vol. Proc. SPIE |

9. | A. M. J. v. E. Johan, C. van den Heuvel, Herman H. P. Th. Bekman, L. H. C. Frank, J. M. van Putten, and P. W. Pace, “Laser applications in the littoral: search lidar and ship identification,” Atmospheric Optics: Models, Measurements, and Target-in-the-Loop Propagation II, vol. Proc. SPIE |

10. | R. M. S. Johan, C. van den Heuvel, and R. H. M. A. Schleijpen, “Identification of air and sea-surface targets with a laser range profiler,” Laser Radar Technology and Applications XIV, vol. Proceedings |

11. | Y. H. Li, Z. S. Wu, and Y. J. Gong, “Ultra-short pulse laser one-dimensional range profile of a cone,” Nucl. Instr. and Meth. A (2010), doi:. |

**OCIS Codes**

(100.2960) Image processing : Image analysis

(290.1350) Scattering : Backscattering

(140.3538) Lasers and laser optics : Lasers, pulsed

**ToC Category:**

Image Processing

**History**

Original Manuscript: June 14, 2010

Revised Manuscript: July 11, 2010

Manuscript Accepted: July 14, 2010

Published: July 23, 2010

**Citation**

Yanhui Li and Zhensen Wu, "Targets recognition using subnanosecond pulse laser range profiles," Opt. Express **18**, 16788-16796 (2010)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-16-16788

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### References

- D. Mensa, High resolution radar imaging, (Artech House Norwood, Mass, 1981).
- H. Li and S. Yang, “Using Range Profiles as Feature Vectors to Identify Aerospace Objects,” IEEE Trans. Antenn. Propag. 41(3), 261–268 (1993). [CrossRef]
- S. Adachi and T. Uno, “One-dimensional target profiling by electromagnetic backscattering,” J. Electromagn. Waves Appl. 7(3), 403–421 (1993). [CrossRef]
- K. Umashankar, S. Chaudhuri, and A. Taflove, “Finite-difference time-domain formulation of an inverse scattering scheme for remote sensing of inhomogeneous lossy layered media: Part I-One dimensional case,” J. Electromagn. Waves Appl. 8, 489–508 (1994).
- K. Harada and A. Noguchi, “Reconstruction of two dimensional rough surface with Gaussian beam illumination,” IEICE Trans. Electron. 79, 1345–1349 (1996).
- V. Galdi, D. A. Castanon, and L. B. Felsen, “Multifrequency reconstruction of moderately rough interfaces via quasi-ray Gaussian beams,” IEEE Trans. Geosci. Rem. Sens. 40(2), 453–460 (2002). [CrossRef]
- L. G. Shirley, and G. R. Hallerman, Appications of Tunable Lasers to Laser Radar and 3D Imaging, (Lincoln Laboratory, 1996).
- P. P. Johan, C. van den Heuvel, Herman H. P. Th. Bekman, Frank J. M. van Putten, and R. H. M. A. Schleijpen, “Experimental Validation of Ship Identification with a Laser Range Profiler,” Laser Radar Technology and Applications XIII, vol. Proc. SPIE 6950, 1–12 (2008).
- A. M. J. v. E. Johan, C. van den Heuvel, Herman H. P. Th. Bekman, L. H. C. Frank, J. M. van Putten, and P. W. Pace, “Laser applications in the littoral: search lidar and ship identification,” Atmospheric Optics: Models, Measurements, and Target-in-the-Loop Propagation II, vol. Proc. SPIE 7090, 1–9 (2008).
- R. M. S. Johan, C. van den Heuvel, and R. H. M. A. Schleijpen, “Identification of air and sea-surface targets with a laser range profiler,” Laser Radar Technology and Applications XIV, vol. Proceedings 7323, 1–9 (2009).
- Y. H. Li, Z. S. Wu, and Y. J. Gong, “Ultra-short pulse laser one-dimensional range profile of a cone,” Nucl. Instr. and Meth. A (2010), doi:.

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