Abstract

A modeling and validation method of photometric characteristics of the space target was presented in order to track and identify different satellites effectively. The background radiation characteristics models of the target were built based on blackbody radiation theory. The geometry characteristics of the target were illustrated by the surface equations based on its body coordinate system. The material characteristics of the target surface were described by a bidirectional reflectance distribution function model, which considers the character of surface Gauss statistics and microscale self-shadow and is obtained by measurement and modeling in advance. The contributing surfaces of the target to observation system were determined by coordinate transformation according to the relative position of the space-based target, the background radiation sources, and the observation platform. Then a mathematical model on photometric characteristics of the space target was built by summing reflection components of all the surfaces. Photometric characteristics simulation of the space-based target was achieved according to its given geometrical dimensions, physical parameters, and orbital parameters. Experimental validation was made based on the scale model of the satellite. The calculated results fit well with the measured results, which indicates the modeling method of photometric characteristics of the space target is correct.

© 2012 Optical Society of America

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References

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  1. M. A. Cauquy, “Approaches for processing spectral measurements of reflected sunlight for space object detection and identification,” Ph.D. dissertation (Michigan Technological University, 2004).
  2. E. W. Rork, S. S. Lin, and A. J. Yakutis, “Ground-based electro-optical detection of artificial satellites in daylight from reflected sunlight,” Report no. ETS-63, ADA117413 (MIT Lincoln Laboratory, 1982), pp. 5–33.
  3. J. D. Rask, “Modeling of diffuse photometric signatures of satellites for space object identification,” Master’s thesis (Air Force Institute of Technology, 1982).
  4. H. Ragheb and E. R. Hancock, “Lambertian reflectance correction for rough and shiny surface,” in International Conference on Image Processing (IEEE Signal Processing Society, 2002), Vol. 2, pp. 553–556.
  5. K. Green, L. Lamberg, and K. Lumme, “Stochastic modeling of paper structure and Monte Carlo simulation of light scattering,” Appl. Opt. 39, 4669–4683 (2000).
    [CrossRef]
  6. M. M. Pharr, “Monte Carlo solution of scattering equations for computer graphics,” Ph.D. dissertation (Stanford University, 2005).
  7. S. Mazumder, “Methods to accelerate ray tracing in the Monte Carlo method for surface-to-surface radiation transport,” J. Heat Transfer 128, 945–952 (2006).
    [CrossRef]
  8. M. D. Hejduk, “Specular and diffuse components in spherical satellite photometric modeling,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference (Maui Economic Development Board, 2011), p. E15.
  9. Z. S. Wu and A. A. Liu, “Scattering of solar and atmospheric background radiation from a target,” Int. J. Infrared Millim. Waves 23, 907–917 (2002).
    [CrossRef]
  10. Z. S. Wu and Y. H. Dou, “Visible light scattering and infrared radiation of spatial object,” Acta Opt. Sin. 23, 1250–1254 (2003).
  11. H. Y. Wang, W. Zhang, and Z. L. Wang, “Visible characteristics of space satellite based on nth cosine scattering distribution,” Acta Opt. Sin. 28, 593–598 (2008).
    [CrossRef]
  12. W. Zhang, H. Y. Wang, Z. L. Wang, and C. M. Sun, “Modeling method for visible scattering properties of space target,” Acta Photonica Sin. 37, 2462–2467 (2008).
  13. D. B. Major, L. Martin, and W. Brad, “Measurement of the photometric and spectral BRDF of small Canadian satellites in a controlled environment,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference (Maui Economic Development Board, 2011), p. E16.
  14. W. Zhang, H. Y. Wang, and Z. L. Wang, “Measurement of bidirectional reflection distribution function on material surface,” Chin. Opt. Lett. 7, 88–91 (2009).
    [CrossRef]
  15. M. Ashikhmin, S. Premoze, and P. Shirley, “A microfacet-based BRDF generator,” in SIGGRAPH’00 Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley, 2000), pp. 65–74.
  16. D. S. Chen, “A long arc approach to GPS satellite orbit improvement,” Thesis (The University of New Brunswick, (1991), pp. 12–26.
  17. F. Sauceda, “International space station program: space station reference coordinate systems,” 3-2, 3-12, 4-4 (2001).

2009 (1)

2008 (2)

H. Y. Wang, W. Zhang, and Z. L. Wang, “Visible characteristics of space satellite based on nth cosine scattering distribution,” Acta Opt. Sin. 28, 593–598 (2008).
[CrossRef]

W. Zhang, H. Y. Wang, Z. L. Wang, and C. M. Sun, “Modeling method for visible scattering properties of space target,” Acta Photonica Sin. 37, 2462–2467 (2008).

2006 (1)

S. Mazumder, “Methods to accelerate ray tracing in the Monte Carlo method for surface-to-surface radiation transport,” J. Heat Transfer 128, 945–952 (2006).
[CrossRef]

2003 (1)

Z. S. Wu and Y. H. Dou, “Visible light scattering and infrared radiation of spatial object,” Acta Opt. Sin. 23, 1250–1254 (2003).

2002 (1)

Z. S. Wu and A. A. Liu, “Scattering of solar and atmospheric background radiation from a target,” Int. J. Infrared Millim. Waves 23, 907–917 (2002).
[CrossRef]

2000 (1)

Ashikhmin, M.

M. Ashikhmin, S. Premoze, and P. Shirley, “A microfacet-based BRDF generator,” in SIGGRAPH’00 Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley, 2000), pp. 65–74.

Brad, W.

D. B. Major, L. Martin, and W. Brad, “Measurement of the photometric and spectral BRDF of small Canadian satellites in a controlled environment,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference (Maui Economic Development Board, 2011), p. E16.

Cauquy, M. A.

M. A. Cauquy, “Approaches for processing spectral measurements of reflected sunlight for space object detection and identification,” Ph.D. dissertation (Michigan Technological University, 2004).

Chen, D. S.

D. S. Chen, “A long arc approach to GPS satellite orbit improvement,” Thesis (The University of New Brunswick, (1991), pp. 12–26.

Dou, Y. H.

Z. S. Wu and Y. H. Dou, “Visible light scattering and infrared radiation of spatial object,” Acta Opt. Sin. 23, 1250–1254 (2003).

Green, K.

Hancock, E. R.

H. Ragheb and E. R. Hancock, “Lambertian reflectance correction for rough and shiny surface,” in International Conference on Image Processing (IEEE Signal Processing Society, 2002), Vol. 2, pp. 553–556.

Hejduk, M. D.

M. D. Hejduk, “Specular and diffuse components in spherical satellite photometric modeling,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference (Maui Economic Development Board, 2011), p. E15.

Lamberg, L.

Lin, S. S.

E. W. Rork, S. S. Lin, and A. J. Yakutis, “Ground-based electro-optical detection of artificial satellites in daylight from reflected sunlight,” Report no. ETS-63, ADA117413 (MIT Lincoln Laboratory, 1982), pp. 5–33.

Liu, A. A.

Z. S. Wu and A. A. Liu, “Scattering of solar and atmospheric background radiation from a target,” Int. J. Infrared Millim. Waves 23, 907–917 (2002).
[CrossRef]

Lumme, K.

Major, D. B.

D. B. Major, L. Martin, and W. Brad, “Measurement of the photometric and spectral BRDF of small Canadian satellites in a controlled environment,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference (Maui Economic Development Board, 2011), p. E16.

Martin, L.

D. B. Major, L. Martin, and W. Brad, “Measurement of the photometric and spectral BRDF of small Canadian satellites in a controlled environment,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference (Maui Economic Development Board, 2011), p. E16.

Mazumder, S.

S. Mazumder, “Methods to accelerate ray tracing in the Monte Carlo method for surface-to-surface radiation transport,” J. Heat Transfer 128, 945–952 (2006).
[CrossRef]

Pharr, M. M.

M. M. Pharr, “Monte Carlo solution of scattering equations for computer graphics,” Ph.D. dissertation (Stanford University, 2005).

Premoze, S.

M. Ashikhmin, S. Premoze, and P. Shirley, “A microfacet-based BRDF generator,” in SIGGRAPH’00 Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley, 2000), pp. 65–74.

Ragheb, H.

H. Ragheb and E. R. Hancock, “Lambertian reflectance correction for rough and shiny surface,” in International Conference on Image Processing (IEEE Signal Processing Society, 2002), Vol. 2, pp. 553–556.

Rask, J. D.

J. D. Rask, “Modeling of diffuse photometric signatures of satellites for space object identification,” Master’s thesis (Air Force Institute of Technology, 1982).

Rork, E. W.

E. W. Rork, S. S. Lin, and A. J. Yakutis, “Ground-based electro-optical detection of artificial satellites in daylight from reflected sunlight,” Report no. ETS-63, ADA117413 (MIT Lincoln Laboratory, 1982), pp. 5–33.

Sauceda, F.

F. Sauceda, “International space station program: space station reference coordinate systems,” 3-2, 3-12, 4-4 (2001).

Shirley, P.

M. Ashikhmin, S. Premoze, and P. Shirley, “A microfacet-based BRDF generator,” in SIGGRAPH’00 Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley, 2000), pp. 65–74.

Sun, C. M.

W. Zhang, H. Y. Wang, Z. L. Wang, and C. M. Sun, “Modeling method for visible scattering properties of space target,” Acta Photonica Sin. 37, 2462–2467 (2008).

Wang, H. Y.

W. Zhang, H. Y. Wang, and Z. L. Wang, “Measurement of bidirectional reflection distribution function on material surface,” Chin. Opt. Lett. 7, 88–91 (2009).
[CrossRef]

W. Zhang, H. Y. Wang, Z. L. Wang, and C. M. Sun, “Modeling method for visible scattering properties of space target,” Acta Photonica Sin. 37, 2462–2467 (2008).

H. Y. Wang, W. Zhang, and Z. L. Wang, “Visible characteristics of space satellite based on nth cosine scattering distribution,” Acta Opt. Sin. 28, 593–598 (2008).
[CrossRef]

Wang, Z. L.

W. Zhang, H. Y. Wang, and Z. L. Wang, “Measurement of bidirectional reflection distribution function on material surface,” Chin. Opt. Lett. 7, 88–91 (2009).
[CrossRef]

H. Y. Wang, W. Zhang, and Z. L. Wang, “Visible characteristics of space satellite based on nth cosine scattering distribution,” Acta Opt. Sin. 28, 593–598 (2008).
[CrossRef]

W. Zhang, H. Y. Wang, Z. L. Wang, and C. M. Sun, “Modeling method for visible scattering properties of space target,” Acta Photonica Sin. 37, 2462–2467 (2008).

Wu, Z. S.

Z. S. Wu and Y. H. Dou, “Visible light scattering and infrared radiation of spatial object,” Acta Opt. Sin. 23, 1250–1254 (2003).

Z. S. Wu and A. A. Liu, “Scattering of solar and atmospheric background radiation from a target,” Int. J. Infrared Millim. Waves 23, 907–917 (2002).
[CrossRef]

Yakutis, A. J.

E. W. Rork, S. S. Lin, and A. J. Yakutis, “Ground-based electro-optical detection of artificial satellites in daylight from reflected sunlight,” Report no. ETS-63, ADA117413 (MIT Lincoln Laboratory, 1982), pp. 5–33.

Zhang, W.

W. Zhang, H. Y. Wang, and Z. L. Wang, “Measurement of bidirectional reflection distribution function on material surface,” Chin. Opt. Lett. 7, 88–91 (2009).
[CrossRef]

W. Zhang, H. Y. Wang, Z. L. Wang, and C. M. Sun, “Modeling method for visible scattering properties of space target,” Acta Photonica Sin. 37, 2462–2467 (2008).

H. Y. Wang, W. Zhang, and Z. L. Wang, “Visible characteristics of space satellite based on nth cosine scattering distribution,” Acta Opt. Sin. 28, 593–598 (2008).
[CrossRef]

Acta Opt. Sin. (2)

Z. S. Wu and Y. H. Dou, “Visible light scattering and infrared radiation of spatial object,” Acta Opt. Sin. 23, 1250–1254 (2003).

H. Y. Wang, W. Zhang, and Z. L. Wang, “Visible characteristics of space satellite based on nth cosine scattering distribution,” Acta Opt. Sin. 28, 593–598 (2008).
[CrossRef]

Acta Photonica Sin. (1)

W. Zhang, H. Y. Wang, Z. L. Wang, and C. M. Sun, “Modeling method for visible scattering properties of space target,” Acta Photonica Sin. 37, 2462–2467 (2008).

Appl. Opt. (1)

Chin. Opt. Lett. (1)

Int. J. Infrared Millim. Waves (1)

Z. S. Wu and A. A. Liu, “Scattering of solar and atmospheric background radiation from a target,” Int. J. Infrared Millim. Waves 23, 907–917 (2002).
[CrossRef]

J. Heat Transfer (1)

S. Mazumder, “Methods to accelerate ray tracing in the Monte Carlo method for surface-to-surface radiation transport,” J. Heat Transfer 128, 945–952 (2006).
[CrossRef]

Other (10)

M. D. Hejduk, “Specular and diffuse components in spherical satellite photometric modeling,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference (Maui Economic Development Board, 2011), p. E15.

M. M. Pharr, “Monte Carlo solution of scattering equations for computer graphics,” Ph.D. dissertation (Stanford University, 2005).

D. B. Major, L. Martin, and W. Brad, “Measurement of the photometric and spectral BRDF of small Canadian satellites in a controlled environment,” in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference (Maui Economic Development Board, 2011), p. E16.

M. A. Cauquy, “Approaches for processing spectral measurements of reflected sunlight for space object detection and identification,” Ph.D. dissertation (Michigan Technological University, 2004).

E. W. Rork, S. S. Lin, and A. J. Yakutis, “Ground-based electro-optical detection of artificial satellites in daylight from reflected sunlight,” Report no. ETS-63, ADA117413 (MIT Lincoln Laboratory, 1982), pp. 5–33.

J. D. Rask, “Modeling of diffuse photometric signatures of satellites for space object identification,” Master’s thesis (Air Force Institute of Technology, 1982).

H. Ragheb and E. R. Hancock, “Lambertian reflectance correction for rough and shiny surface,” in International Conference on Image Processing (IEEE Signal Processing Society, 2002), Vol. 2, pp. 553–556.

M. Ashikhmin, S. Premoze, and P. Shirley, “A microfacet-based BRDF generator,” in SIGGRAPH’00 Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (ACM/Addison-Wesley, 2000), pp. 65–74.

D. S. Chen, “A long arc approach to GPS satellite orbit improvement,” Thesis (The University of New Brunswick, (1991), pp. 12–26.

F. Sauceda, “International space station program: space station reference coordinate systems,” 3-2, 3-12, 4-4 (2001).

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Figures (10)

Fig. 1.
Fig. 1.

Background radiation of space-based targets.

Fig. 2.
Fig. 2.

Sketch of geometric modeling of the space target.

Fig. 3.
Fig. 3.

Sketch of material surface characteristics. (a) Object with a marked grid area ΔA. (b) Surface profile of ΔA and a marked macrofacet dA. (c) Enlarged view of dA.

Fig. 4.
Fig. 4.

Geometrical model for optical characteristics of the space target.

Fig. 5.
Fig. 5.

Relationship of the target’s irradiance on entrance pupil of the optical detection system and observation time at 00:00 to 24:00 on June 5, 2008. (a)–(c) are the results based on Lambertian model, while (d)–(f) are the results based on BRDF model.

Fig. 6.
Fig. 6.

Relationship of the target’s equivalent apparent magnitude and observation time at 00:00 to 24:00 on June 5, 2008. (a)–(c) are the results based on Lambertian model, while (d)–(f) are the results based on BRDF model.

Fig. 7.
Fig. 7.

Detection range of the targets.

Fig. 8.
Fig. 8.

Experimental scheme for measuring optical characteristics of the target.

Fig. 9.
Fig. 9.

Comparison between calculated and measured results at lighting angle 30°.

Fig. 10.
Fig. 10.

Comparison between calculated and measured results at lighting angle 60°.

Tables (3)

Tables Icon

Table 1. BRDF Model Parameters of the Surface Material

Tables Icon

Table 2. Physical Dimension and Material Type of the Target

Tables Icon

Table 3. Orbital Parameters

Equations (23)

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

ESun(λ)=2πhc2λ5[exp(ch/λkT)]·RS2RSE2,
EEarth(λ)=ESun(λ)·ρ·RE2(RE+RTE)2,
fr(θi,φi,θr,φr,λ)=dLr(θr,φr,λ)dEi(θi,φi,λ)=dLr(θr,φr,λ)Li(θi,φi,λ)cosθidωi,
fr(θi,φi,θr,φr,λ)=ksDGF(θi,λ)πcosθicosθr+kdπ,
p=Rz(Ω)Rx(i)Rz(ω)p0,
Rz(Ω)=[cosΩsinΩ0sinΩcosΩ0001]Rx(i)=[1000cosisini0sinicosi]Rz(ω)=[cosωsinω0sinωcosω0001],
r=a(1e2)1+ecosv,
v=M+e(2e2/4+5e4/96)sinM+e2(5/411e2/24)sin2M+e3(13/1243e2/64)sin3M+103e4sin4M/96+1097e5sin5M/960,
M=(tτ)μ/a3,
qo=L001Rz(ω+v)Rx(i)Rz(Ω)p,
L001=[010001100].
q=Hqo,
Hzxz=Rz(Ψ)Rx(Θ)Rz(Ψ).
Hzxy=Ry(φ)Rx(Θ)Rz(Ψ),
Φpupili(λ)=AtargetiΩLr(θr,φr,λ)cosθrdω,
Φpupili(λ)=Atargeti(π4)(DRtarget)2cosθrcos3αLr(θr,φr,λ),
Epupili(λ)=AtargetiRtarget2cosθrcos3αLr(θr,φr,λ).
Lr(θr,φr,λ)=ρ(λ)Ei(θi,φi,λ)π,
Epupili=AtargetiRtarget2cosθrcos3αλ1λ2ρ(λ)Ei(θi,φi,λ)πdλ.
Epupili=AtargetiRtarget2cosθrcos3αλ1λ2fr(θi,φi,θr,φr,λ)Ei(θi,φi,λ)dλ.
Epupili=Epupil-Suni+Epupil-Earthi,
Epupiltotal=i=1n(Epupil-Suni+Epupil-Earthi).
Mv=26.742.5log10(Epupiltotal/Es),

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