Abstract

Profile information about a three-dimensional target can be obtained directly by analyzing two-dimensional data of the pulse laser range profile (LRP). The profile, shape, and posture of the target can be detected using LRPs. An analytical LRP model from rough convex quadric bodies of revolution is presented. This model can be used to analyze the effects of geometric parameters, surface material, and orientation on LRPs. The numerical results of the effects on LRPs of four typical targets are given. Based on the results of the simulated model and theoretical analysis, the rough convex quadric bodies of revolution can be identified. The analytical expressions of this model are significant in the application of LiDAR imaging.

© 2012 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Mensa, High Resolution Radar Imaging (Artech House, 1981).
  2. H. Li and S. Yang, “Using range profiles as feature vectors to identify aerospace objects,” IEEE Trans. Antennas Propag. 41, 261–268 (1993).
    [CrossRef]
  3. S. Adachi and T. Uno, “One-dimensional target profiling by electromagnetic backscattering,” J. Electromagn. Waves Appl. 7, 403–421 (1993).
    [CrossRef]
  4. R. Schoemaker and K. Benoist, “Characterisation of small targets in a maritime environment by means of laser range profiling,” Proc. SPIE 8037, 803705 (2011).
    [CrossRef]
  5. L. G. Shirley and G. R. Hallerman, Applications of Tunable Lasers to Laser Radar and 3D Imaging (Lincoln Laboratory, 1996).
  6. G. J. Kunz, H. H. P. T. Bekman, K. W. Benoist, L. H. Coen, J. C. van den Heuvel, and F. J. M. van Putten, “Detection of small targets in a marine environment using laser radar,” Proc. SPIE 5885, 128–139 (2005).
    [CrossRef]
  7. B. Jutzi and U. Stilla, “Precise range estimation on known surfaces by analysis of full-waveform laser,” in Proceedings of the Symposium of ISPRS Commission III: Photogrammetric Computer Vision (PCV06) (International Archives of Photogrammetry, Remote Sensing, and Spatial Information Sciences 36, Part 3, 2006), pp. 234–239.
  8. Y. Li and Z. Wu, “Targets recognition using subnanosecond pulse laser range profiles,” Opt. Express 18, 16788–16796 (2010).
    [CrossRef]
  9. Y. H. Li, Z. S. Wu, and Y. J. Gong, “Ultra-short pulse laser one-dimensional range profile of a cone,” Nucl. Instr. Meth. A 637 (Suppl.), S149–S152 (2011).
    [CrossRef]
  10. C. G. Bachman, Laser Radar Systems and Techniques (Artech House, 1979).
  11. A. V. Jelalian, Laser Radar Systems (Artech House, 1992).
  12. K. J. Voss, A. Chapin, M. Monti, and H. Zhang, “Instrument to measure the bidirectional reflectance distribution function of surfaces,” Appl. Opt. 39, 6197–6206 (2000).
    [CrossRef]
  13. R. Latifovic, J. Cihlar, and J. Chen, “A comparison of BRDF models for the normalization of satellite optical data to a standard sun-target-sensor geometry,” IEEE Trans. Geosci. Remote Sens. 41, 1889–1898 (2003).
    [CrossRef]
  14. T. J. Papetti, W. E. Walker, C. E. Keffer, and B. E. Johnson, “Coherent backscatter: measurement of the retroflective BRDF peak exhibited by several surfaces relevant to ladar applications,” Proc. SPIE 6682, 66820E (2007).
    [CrossRef]
  15. L. B. Wolff, “Diffuse-reflectance model for smooth dielectric surfaces,” J. Opt. Soc. Am. A 11, 2956–2968 (1994).
    [CrossRef]
  16. D. Barrick, “Rough surface scattering based on the specular point theory,” IEEE Trans. Antennas Propag. 16, 449–454 (1968).
    [CrossRef]
  17. Y. Q. Zhang and Z. S. Wu, “Character of light scattering of spatial dynamic objects at different stations and analysis of relativity,” J. Electromagn. Waves Appl. 22, 1071–1080 (2008).
    [CrossRef]
  18. R. M. J. Watson and P. N. Raven, “Comparison of measured BRDF data with parameterized reflectance models,” Proc. SPIE 4370, 159–168 (2001).
    [CrossRef]
  19. H. Zhang, Z. Wu, Y. Cao, and G. Zhang, “Measurement and statistical modeling of BRDF of various samples,” Opt. Appl. 40, 197–208 (2010).

2011 (2)

R. Schoemaker and K. Benoist, “Characterisation of small targets in a maritime environment by means of laser range profiling,” Proc. SPIE 8037, 803705 (2011).
[CrossRef]

Y. H. Li, Z. S. Wu, and Y. J. Gong, “Ultra-short pulse laser one-dimensional range profile of a cone,” Nucl. Instr. Meth. A 637 (Suppl.), S149–S152 (2011).
[CrossRef]

2010 (2)

H. Zhang, Z. Wu, Y. Cao, and G. Zhang, “Measurement and statistical modeling of BRDF of various samples,” Opt. Appl. 40, 197–208 (2010).

Y. Li and Z. Wu, “Targets recognition using subnanosecond pulse laser range profiles,” Opt. Express 18, 16788–16796 (2010).
[CrossRef]

2008 (1)

Y. Q. Zhang and Z. S. Wu, “Character of light scattering of spatial dynamic objects at different stations and analysis of relativity,” J. Electromagn. Waves Appl. 22, 1071–1080 (2008).
[CrossRef]

2007 (1)

T. J. Papetti, W. E. Walker, C. E. Keffer, and B. E. Johnson, “Coherent backscatter: measurement of the retroflective BRDF peak exhibited by several surfaces relevant to ladar applications,” Proc. SPIE 6682, 66820E (2007).
[CrossRef]

2005 (1)

G. J. Kunz, H. H. P. T. Bekman, K. W. Benoist, L. H. Coen, J. C. van den Heuvel, and F. J. M. van Putten, “Detection of small targets in a marine environment using laser radar,” Proc. SPIE 5885, 128–139 (2005).
[CrossRef]

2003 (1)

R. Latifovic, J. Cihlar, and J. Chen, “A comparison of BRDF models for the normalization of satellite optical data to a standard sun-target-sensor geometry,” IEEE Trans. Geosci. Remote Sens. 41, 1889–1898 (2003).
[CrossRef]

2001 (1)

R. M. J. Watson and P. N. Raven, “Comparison of measured BRDF data with parameterized reflectance models,” Proc. SPIE 4370, 159–168 (2001).
[CrossRef]

2000 (1)

1994 (1)

1993 (2)

H. Li and S. Yang, “Using range profiles as feature vectors to identify aerospace objects,” IEEE Trans. Antennas Propag. 41, 261–268 (1993).
[CrossRef]

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

1968 (1)

D. Barrick, “Rough surface scattering based on the specular point theory,” IEEE Trans. Antennas Propag. 16, 449–454 (1968).
[CrossRef]

Adachi, S.

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

Bachman, C. G.

C. G. Bachman, Laser Radar Systems and Techniques (Artech House, 1979).

Barrick, D.

D. Barrick, “Rough surface scattering based on the specular point theory,” IEEE Trans. Antennas Propag. 16, 449–454 (1968).
[CrossRef]

Bekman, H. H. P. T.

G. J. Kunz, H. H. P. T. Bekman, K. W. Benoist, L. H. Coen, J. C. van den Heuvel, and F. J. M. van Putten, “Detection of small targets in a marine environment using laser radar,” Proc. SPIE 5885, 128–139 (2005).
[CrossRef]

Benoist, K.

R. Schoemaker and K. Benoist, “Characterisation of small targets in a maritime environment by means of laser range profiling,” Proc. SPIE 8037, 803705 (2011).
[CrossRef]

Benoist, K. W.

G. J. Kunz, H. H. P. T. Bekman, K. W. Benoist, L. H. Coen, J. C. van den Heuvel, and F. J. M. van Putten, “Detection of small targets in a marine environment using laser radar,” Proc. SPIE 5885, 128–139 (2005).
[CrossRef]

Cao, Y.

H. Zhang, Z. Wu, Y. Cao, and G. Zhang, “Measurement and statistical modeling of BRDF of various samples,” Opt. Appl. 40, 197–208 (2010).

Chapin, A.

Chen, J.

R. Latifovic, J. Cihlar, and J. Chen, “A comparison of BRDF models for the normalization of satellite optical data to a standard sun-target-sensor geometry,” IEEE Trans. Geosci. Remote Sens. 41, 1889–1898 (2003).
[CrossRef]

Cihlar, J.

R. Latifovic, J. Cihlar, and J. Chen, “A comparison of BRDF models for the normalization of satellite optical data to a standard sun-target-sensor geometry,” IEEE Trans. Geosci. Remote Sens. 41, 1889–1898 (2003).
[CrossRef]

Coen, L. H.

G. J. Kunz, H. H. P. T. Bekman, K. W. Benoist, L. H. Coen, J. C. van den Heuvel, and F. J. M. van Putten, “Detection of small targets in a marine environment using laser radar,” Proc. SPIE 5885, 128–139 (2005).
[CrossRef]

Gong, Y. J.

Y. H. Li, Z. S. Wu, and Y. J. Gong, “Ultra-short pulse laser one-dimensional range profile of a cone,” Nucl. Instr. Meth. A 637 (Suppl.), S149–S152 (2011).
[CrossRef]

Hallerman, G. R.

L. G. Shirley and G. R. Hallerman, Applications of Tunable Lasers to Laser Radar and 3D Imaging (Lincoln Laboratory, 1996).

Jelalian, A. V.

A. V. Jelalian, Laser Radar Systems (Artech House, 1992).

Johnson, B. E.

T. J. Papetti, W. E. Walker, C. E. Keffer, and B. E. Johnson, “Coherent backscatter: measurement of the retroflective BRDF peak exhibited by several surfaces relevant to ladar applications,” Proc. SPIE 6682, 66820E (2007).
[CrossRef]

Jutzi, B.

B. Jutzi and U. Stilla, “Precise range estimation on known surfaces by analysis of full-waveform laser,” in Proceedings of the Symposium of ISPRS Commission III: Photogrammetric Computer Vision (PCV06) (International Archives of Photogrammetry, Remote Sensing, and Spatial Information Sciences 36, Part 3, 2006), pp. 234–239.

Keffer, C. E.

T. J. Papetti, W. E. Walker, C. E. Keffer, and B. E. Johnson, “Coherent backscatter: measurement of the retroflective BRDF peak exhibited by several surfaces relevant to ladar applications,” Proc. SPIE 6682, 66820E (2007).
[CrossRef]

Kunz, G. J.

G. J. Kunz, H. H. P. T. Bekman, K. W. Benoist, L. H. Coen, J. C. van den Heuvel, and F. J. M. van Putten, “Detection of small targets in a marine environment using laser radar,” Proc. SPIE 5885, 128–139 (2005).
[CrossRef]

Latifovic, R.

R. Latifovic, J. Cihlar, and J. Chen, “A comparison of BRDF models for the normalization of satellite optical data to a standard sun-target-sensor geometry,” IEEE Trans. Geosci. Remote Sens. 41, 1889–1898 (2003).
[CrossRef]

Li, H.

H. Li and S. Yang, “Using range profiles as feature vectors to identify aerospace objects,” IEEE Trans. Antennas Propag. 41, 261–268 (1993).
[CrossRef]

Li, Y.

Li, Y. H.

Y. H. Li, Z. S. Wu, and Y. J. Gong, “Ultra-short pulse laser one-dimensional range profile of a cone,” Nucl. Instr. Meth. A 637 (Suppl.), S149–S152 (2011).
[CrossRef]

Mensa, D.

D. Mensa, High Resolution Radar Imaging (Artech House, 1981).

Monti, M.

Papetti, T. J.

T. J. Papetti, W. E. Walker, C. E. Keffer, and B. E. Johnson, “Coherent backscatter: measurement of the retroflective BRDF peak exhibited by several surfaces relevant to ladar applications,” Proc. SPIE 6682, 66820E (2007).
[CrossRef]

Raven, P. N.

R. M. J. Watson and P. N. Raven, “Comparison of measured BRDF data with parameterized reflectance models,” Proc. SPIE 4370, 159–168 (2001).
[CrossRef]

Schoemaker, R.

R. Schoemaker and K. Benoist, “Characterisation of small targets in a maritime environment by means of laser range profiling,” Proc. SPIE 8037, 803705 (2011).
[CrossRef]

Shirley, L. G.

L. G. Shirley and G. R. Hallerman, Applications of Tunable Lasers to Laser Radar and 3D Imaging (Lincoln Laboratory, 1996).

Stilla, U.

B. Jutzi and U. Stilla, “Precise range estimation on known surfaces by analysis of full-waveform laser,” in Proceedings of the Symposium of ISPRS Commission III: Photogrammetric Computer Vision (PCV06) (International Archives of Photogrammetry, Remote Sensing, and Spatial Information Sciences 36, Part 3, 2006), pp. 234–239.

Uno, T.

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

van den Heuvel, J. C.

G. J. Kunz, H. H. P. T. Bekman, K. W. Benoist, L. H. Coen, J. C. van den Heuvel, and F. J. M. van Putten, “Detection of small targets in a marine environment using laser radar,” Proc. SPIE 5885, 128–139 (2005).
[CrossRef]

van Putten, F. J. M.

G. J. Kunz, H. H. P. T. Bekman, K. W. Benoist, L. H. Coen, J. C. van den Heuvel, and F. J. M. van Putten, “Detection of small targets in a marine environment using laser radar,” Proc. SPIE 5885, 128–139 (2005).
[CrossRef]

Voss, K. J.

Walker, W. E.

T. J. Papetti, W. E. Walker, C. E. Keffer, and B. E. Johnson, “Coherent backscatter: measurement of the retroflective BRDF peak exhibited by several surfaces relevant to ladar applications,” Proc. SPIE 6682, 66820E (2007).
[CrossRef]

Watson, R. M. J.

R. M. J. Watson and P. N. Raven, “Comparison of measured BRDF data with parameterized reflectance models,” Proc. SPIE 4370, 159–168 (2001).
[CrossRef]

Wolff, L. B.

Wu, Z.

H. Zhang, Z. Wu, Y. Cao, and G. Zhang, “Measurement and statistical modeling of BRDF of various samples,” Opt. Appl. 40, 197–208 (2010).

Y. Li and Z. Wu, “Targets recognition using subnanosecond pulse laser range profiles,” Opt. Express 18, 16788–16796 (2010).
[CrossRef]

Wu, Z. S.

Y. H. Li, Z. S. Wu, and Y. J. Gong, “Ultra-short pulse laser one-dimensional range profile of a cone,” Nucl. Instr. Meth. A 637 (Suppl.), S149–S152 (2011).
[CrossRef]

Y. Q. Zhang and Z. S. Wu, “Character of light scattering of spatial dynamic objects at different stations and analysis of relativity,” J. Electromagn. Waves Appl. 22, 1071–1080 (2008).
[CrossRef]

Yang, S.

H. Li and S. Yang, “Using range profiles as feature vectors to identify aerospace objects,” IEEE Trans. Antennas Propag. 41, 261–268 (1993).
[CrossRef]

Zhang, G.

H. Zhang, Z. Wu, Y. Cao, and G. Zhang, “Measurement and statistical modeling of BRDF of various samples,” Opt. Appl. 40, 197–208 (2010).

Zhang, H.

H. Zhang, Z. Wu, Y. Cao, and G. Zhang, “Measurement and statistical modeling of BRDF of various samples,” Opt. Appl. 40, 197–208 (2010).

Zhang, H.

Zhang, Y. Q.

Y. Q. Zhang and Z. S. Wu, “Character of light scattering of spatial dynamic objects at different stations and analysis of relativity,” J. Electromagn. Waves Appl. 22, 1071–1080 (2008).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Antennas Propag. (2)

D. Barrick, “Rough surface scattering based on the specular point theory,” IEEE Trans. Antennas Propag. 16, 449–454 (1968).
[CrossRef]

H. Li and S. Yang, “Using range profiles as feature vectors to identify aerospace objects,” IEEE Trans. Antennas Propag. 41, 261–268 (1993).
[CrossRef]

IEEE Trans. Geosci. Remote Sens. (1)

R. Latifovic, J. Cihlar, and J. Chen, “A comparison of BRDF models for the normalization of satellite optical data to a standard sun-target-sensor geometry,” IEEE Trans. Geosci. Remote Sens. 41, 1889–1898 (2003).
[CrossRef]

J. Electromagn. Waves Appl. (2)

Y. Q. Zhang and Z. S. Wu, “Character of light scattering of spatial dynamic objects at different stations and analysis of relativity,” J. Electromagn. Waves Appl. 22, 1071–1080 (2008).
[CrossRef]

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

J. Opt. Soc. Am. A (1)

Nucl. Instr. Meth. A (1)

Y. H. Li, Z. S. Wu, and Y. J. Gong, “Ultra-short pulse laser one-dimensional range profile of a cone,” Nucl. Instr. Meth. A 637 (Suppl.), S149–S152 (2011).
[CrossRef]

Opt. Appl. (1)

H. Zhang, Z. Wu, Y. Cao, and G. Zhang, “Measurement and statistical modeling of BRDF of various samples,” Opt. Appl. 40, 197–208 (2010).

Opt. Express (1)

Proc. SPIE (4)

T. J. Papetti, W. E. Walker, C. E. Keffer, and B. E. Johnson, “Coherent backscatter: measurement of the retroflective BRDF peak exhibited by several surfaces relevant to ladar applications,” Proc. SPIE 6682, 66820E (2007).
[CrossRef]

R. M. J. Watson and P. N. Raven, “Comparison of measured BRDF data with parameterized reflectance models,” Proc. SPIE 4370, 159–168 (2001).
[CrossRef]

G. J. Kunz, H. H. P. T. Bekman, K. W. Benoist, L. H. Coen, J. C. van den Heuvel, and F. J. M. van Putten, “Detection of small targets in a marine environment using laser radar,” Proc. SPIE 5885, 128–139 (2005).
[CrossRef]

R. Schoemaker and K. Benoist, “Characterisation of small targets in a maritime environment by means of laser range profiling,” Proc. SPIE 8037, 803705 (2011).
[CrossRef]

Other (5)

L. G. Shirley and G. R. Hallerman, Applications of Tunable Lasers to Laser Radar and 3D Imaging (Lincoln Laboratory, 1996).

B. Jutzi and U. Stilla, “Precise range estimation on known surfaces by analysis of full-waveform laser,” in Proceedings of the Symposium of ISPRS Commission III: Photogrammetric Computer Vision (PCV06) (International Archives of Photogrammetry, Remote Sensing, and Spatial Information Sciences 36, Part 3, 2006), pp. 234–239.

C. G. Bachman, Laser Radar Systems and Techniques (Artech House, 1979).

A. V. Jelalian, Laser Radar Systems (Artech House, 1992).

D. Mensa, High Resolution Radar Imaging (Artech House, 1981).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1.
Fig. 1.

Convex quadric body of revolution in a coordinate axis used for the analytical model.

Fig. 2.
Fig. 2.

LRPs of theoretical simulation compared with those of the experimental results in [8].

Fig. 3.
Fig. 3.

Cylinder, cone, sphere, and spheroid at the same height (h=0.5m) in the coordinate axis used for the model. (a) Cylinder with a radius of 0.1 m, (b) cone with a base radius of 0.1 m, (c) sphere with a radius of 0.25 m, (d) spheroid with semiminor axis of 0.1 m.

Fig. 4.
Fig. 4.

LRPs for the targets with Lambertian reflectance at the same height (h=0.5m) and pulse width (T0=0.1ns), but different aspect angles (θ=0°, 10°, 20°, 30° and 45°). (a) Cylinder, (b) cone, (c) sphere, (d) spheroid.

Fig. 5.
Fig. 5.

LRPs for a cylinder, cone, sphere, and spheroid with diffuse Gaussian and exponential reflectance at the same height (h=0.5m), pulse width (T0=0.1ns) and aspect angle (θ=45°). (a) Cylinder, (b) cone, (c) sphere, (d) spheroid.

Fig. 6.
Fig. 6.

LRPs for a cylinder, cone, sphere, and spheroid with diffuse five-parameter BRDF model reflectance at the same height (h=0.5m), pulse width (T0=0.1ns), and aspect angle (θ=30°). (a) Cylinder, (b) cone, (c) sphere, (d) spheroid.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

Ps=Pt4πRt2σ4πRr2ArGr,
ΔPs(β,t)=GrAr4πRt2Rr2P(t)fr(β)ΔAcos2β,
x2+y2=Az2+2Bz+Cz0zz0+h,
(xyz)=(1000cosθsinθ0sinθcosθ)(XYZ).
X2+(YcosθZsinθ)2=A(Zcosθ+Ysinθ)2+2B(Zcosθ+Ysinθ)+C.
ΔPs(β,t)=GrAr4πRt2Rr2P(t)ΔXΔYfr(β)cosβ.
cosβ=sinθ(YcosθZsinθ)+cosθ(AYsinθ+AZcosθ+B)X2+(YcosθZsinθ)2+(AYsinθ+AZcosθ+B)2.
Z=cosθ(Ysinθ+AYsinθ+B)Acos2θsin2θ±AY2+2BYsinθ+sin2θ(CX2)+cos2θ(B2AC+AX2)Acos2θsin2θ.
Z=Y2(Asin2θcos2θ)+2BYsinθ+CX22cosθ(Ysinθ+AYsinθ+B).
ΔPs(X,Y,t)=GrAr4πRt2Rr2P(t)ΔXΔYfr(β)cosβ.
Ps(t)=GrAr4πRt2Rr2zCP(t)fr(β)cosβdXdY,
C:cosβ=sinθ(YcosθZsinθ)+cosθ(AYsinθ+AZcosθ+B)X2+(YcosθZsinθ)2+(AYsinθ+AZcosθ+B)2>0z0Ysinθ+Zcosθz0+h}.
Ps(zt)=GrAr4πRt2Rr2zCP(2zt/c2Z/c)fr(β)cosβdXdY.
P(t)=P0exp(2t2/T02),
fr(β)=ρ/π,
fr(β)=sec6β4πs2exp(tan2βs2)|R(0)|2,
fr(β)=3sec6β4πs2exp(6tanβs)|R(0)|2.
fr(β)=kbkr2cosα1+(kr21)cosαexp[b(1cosγ)a]G(β)cosβ+kd,

Metrics