Abstract

This paper utilizes the optical cross section (OCS) to characterize the optical scattering characteristics of a space target under the conditions of Sun lighting. We derive the mathematical expression of OCS according to the radiometric theory, and put forward a fast visualization calculation method of complex space targets’ OCS based on an OpenGL and 3D model. Through the OCS simulation of Lambert bodies (cylinder and sphere), the computational accuracy and speed of the algorithm were verified. By using this method, the relative error for OCS will not exceed 0.1%, and it only takes 0.05 s to complete a complex calculation. Additionally, we calculated the OCS of three actual satellites with bidirectional reflectance distribution function model parameters in visible bands, and results indicate that it is easy to distinguish the three targets by comparing their OCS curves. This work is helpful for the identification and classification of unresolved space target based on photometric characteristics.

© 2013 Optical Society of America

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Corrections

Yi Han, Huayan Sun, Yingchun Li, and Huichao Guo, "Fast calculation method of complex space targets’ optical cross section: erratum," Appl. Opt. 53, 1142-1142 (2014)
https://www.osapublishing.org/ao/abstract.cfm?uri=ao-53-6-1142

References

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  1. F. Daniel, K. Katharine, and C. Francis, “Optimizing site locations for determining shape from photometric light curves,” in Proceedings of Advanced Maui Optical and Space Surveillance Technologies Conference (The Maui Economic Development Board, 2009), pp. 1–11.
  2. K. Bush, G. A. Crockett, and C. Barnard, “Satellite discrimination from active and passive polarization signatures: simulation predictions using the TASAT satellite model,” Proc. SPIE 4481, 46–57 (2002).
    [CrossRef]
  3. P. W. Kervin, J. L. Africano, P. F. Sydney, and D. Hall, “Small satellite characterization technologies applied to orbital debris,” Adv. Space Res. 35, 1214–1225 (2005).
    [CrossRef]
  4. R. A. Mark, T. M. John, B. M. Jeffrey, and C. Z. Peter, “Blind search for micro satellites in LEO: optical signatures and search strategies,” in AMOS (The Maui Economic Development Board, 2003), pp. 1–24.
  5. Y. Han and H. Sun, “Advances in space target optical scattering character research,” Infrared Laser Eng. 42, 1–10 (2013).
  6. J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional reflectance model validation and utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).
  7. O. Steinvall, “Effects of target shape and reflection on laser radar cross sections,” Appl. Opt. 39, 4381–4391 (2000).
    [CrossRef]
  8. K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
    [CrossRef]
  9. H. Doyle, “Surface material characterization from multi-band optical observations,” in AMOS (The Maui Economic Development Board, 2010), pp. 1–15.
  10. B. David and W. David, “Broadband spectral-polarimetric BRDF scan system and data for spacecraft materials,” in AMOS (The Maui Economic Development Board, 2011), pp. 1–9.
  11. D. B. Major, L. Martin, and W. Brad, “Measurement of the photometric and spectral BRDF of small Canadian satellites in a controlled environment,” in AMOS (The Maui Economic Development Board, 2011), pp. 1–10.
  12. D. F. Alistair, Daytime Detection of Space Objects (Air Force Institute of Technology, 2005), pp. 1–65.
  13. W. David and B. David, “Laboratory imaging of satellites and orbital appearance estimation,” in AMOS (The Maui Economic Development Board, 2007), pp. 1–12.
  14. S. Cody and C. Francis, “Simulating complex satellite and a space-based surveillance sensor simulation,” in AMOS (The Maui Economic Development Board, 2009), pp. 1–10.
  15. Y. Han, H. Sun, Y. Li, and L. Tang, “Simulation of space object laser radar cross section,” Infrared Laser Eng. 39, 819–823 (2010).
  16. Y. Yuan, C. Sun, X. Zhang, H. Zhao, and Q. Wang, “Analysis of influence of attitude variation on visible characteristics of space target,” Acta Opt. Sin. 30, 2748–2752 (2010).
    [CrossRef]
  17. J. M. Rius, M. Ferrando, and L. Jofre, “GRECO: graphical electromagnetic computing for RCS prediction in real time,” IEEE Antennas Propag. Mag. 35, 7–17 (1993).
    [CrossRef]
  18. Y. Han, H. Sun, and H. Guo, “Research on rocket target laser scattering characteristic simulation software,” Laser Physics 23, 056007 (2013).
    [CrossRef]
  19. B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
    [CrossRef]

2013 (2)

Y. Han and H. Sun, “Advances in space target optical scattering character research,” Infrared Laser Eng. 42, 1–10 (2013).

Y. Han, H. Sun, and H. Guo, “Research on rocket target laser scattering characteristic simulation software,” Laser Physics 23, 056007 (2013).
[CrossRef]

2010 (2)

Y. Han, H. Sun, Y. Li, and L. Tang, “Simulation of space object laser radar cross section,” Infrared Laser Eng. 39, 819–823 (2010).

Y. Yuan, C. Sun, X. Zhang, H. Zhao, and Q. Wang, “Analysis of influence of attitude variation on visible characteristics of space target,” Acta Opt. Sin. 30, 2748–2752 (2010).
[CrossRef]

2005 (1)

P. W. Kervin, J. L. Africano, P. F. Sydney, and D. Hall, “Small satellite characterization technologies applied to orbital debris,” Adv. Space Res. 35, 1214–1225 (2005).
[CrossRef]

2002 (1)

K. Bush, G. A. Crockett, and C. Barnard, “Satellite discrimination from active and passive polarization signatures: simulation predictions using the TASAT satellite model,” Proc. SPIE 4481, 46–57 (2002).
[CrossRef]

2000 (1)

1993 (1)

J. M. Rius, M. Ferrando, and L. Jofre, “GRECO: graphical electromagnetic computing for RCS prediction in real time,” IEEE Antennas Propag. Mag. 35, 7–17 (1993).
[CrossRef]

1975 (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[CrossRef]

1967 (1)

Africano, J. L.

P. W. Kervin, J. L. Africano, P. F. Sydney, and D. Hall, “Small satellite characterization technologies applied to orbital debris,” Adv. Space Res. 35, 1214–1225 (2005).
[CrossRef]

Alistair, D. F.

D. F. Alistair, Daytime Detection of Space Objects (Air Force Institute of Technology, 2005), pp. 1–65.

Barnard, C.

K. Bush, G. A. Crockett, and C. Barnard, “Satellite discrimination from active and passive polarization signatures: simulation predictions using the TASAT satellite model,” Proc. SPIE 4481, 46–57 (2002).
[CrossRef]

Beard, J.

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional reflectance model validation and utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

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 AMOS (The Maui Economic Development Board, 2011), pp. 1–10.

Bush, K.

K. Bush, G. A. Crockett, and C. Barnard, “Satellite discrimination from active and passive polarization signatures: simulation predictions using the TASAT satellite model,” Proc. SPIE 4481, 46–57 (2002).
[CrossRef]

Cody, S.

S. Cody and C. Francis, “Simulating complex satellite and a space-based surveillance sensor simulation,” in AMOS (The Maui Economic Development Board, 2009), pp. 1–10.

Crockett, G. A.

K. Bush, G. A. Crockett, and C. Barnard, “Satellite discrimination from active and passive polarization signatures: simulation predictions using the TASAT satellite model,” Proc. SPIE 4481, 46–57 (2002).
[CrossRef]

Daniel, F.

F. Daniel, K. Katharine, and C. Francis, “Optimizing site locations for determining shape from photometric light curves,” in Proceedings of Advanced Maui Optical and Space Surveillance Technologies Conference (The Maui Economic Development Board, 2009), pp. 1–11.

David, B.

B. David and W. David, “Broadband spectral-polarimetric BRDF scan system and data for spacecraft materials,” in AMOS (The Maui Economic Development Board, 2011), pp. 1–9.

W. David and B. David, “Laboratory imaging of satellites and orbital appearance estimation,” in AMOS (The Maui Economic Development Board, 2007), pp. 1–12.

David, W.

B. David and W. David, “Broadband spectral-polarimetric BRDF scan system and data for spacecraft materials,” in AMOS (The Maui Economic Development Board, 2011), pp. 1–9.

W. David and B. David, “Laboratory imaging of satellites and orbital appearance estimation,” in AMOS (The Maui Economic Development Board, 2007), pp. 1–12.

Doyle, H.

H. Doyle, “Surface material characterization from multi-band optical observations,” in AMOS (The Maui Economic Development Board, 2010), pp. 1–15.

Ferrando, M.

J. M. Rius, M. Ferrando, and L. Jofre, “GRECO: graphical electromagnetic computing for RCS prediction in real time,” IEEE Antennas Propag. Mag. 35, 7–17 (1993).
[CrossRef]

Francis, C.

S. Cody and C. Francis, “Simulating complex satellite and a space-based surveillance sensor simulation,” in AMOS (The Maui Economic Development Board, 2009), pp. 1–10.

F. Daniel, K. Katharine, and C. Francis, “Optimizing site locations for determining shape from photometric light curves,” in Proceedings of Advanced Maui Optical and Space Surveillance Technologies Conference (The Maui Economic Development Board, 2009), pp. 1–11.

Guo, H.

Y. Han, H. Sun, and H. Guo, “Research on rocket target laser scattering characteristic simulation software,” Laser Physics 23, 056007 (2013).
[CrossRef]

Hall, D.

P. W. Kervin, J. L. Africano, P. F. Sydney, and D. Hall, “Small satellite characterization technologies applied to orbital debris,” Adv. Space Res. 35, 1214–1225 (2005).
[CrossRef]

Han, Y.

Y. Han and H. Sun, “Advances in space target optical scattering character research,” Infrared Laser Eng. 42, 1–10 (2013).

Y. Han, H. Sun, and H. Guo, “Research on rocket target laser scattering characteristic simulation software,” Laser Physics 23, 056007 (2013).
[CrossRef]

Y. Han, H. Sun, Y. Li, and L. Tang, “Simulation of space object laser radar cross section,” Infrared Laser Eng. 39, 819–823 (2010).

Jeffrey, B. M.

R. A. Mark, T. M. John, B. M. Jeffrey, and C. Z. Peter, “Blind search for micro satellites in LEO: optical signatures and search strategies,” in AMOS (The Maui Economic Development Board, 2003), pp. 1–24.

Jofre, L.

J. M. Rius, M. Ferrando, and L. Jofre, “GRECO: graphical electromagnetic computing for RCS prediction in real time,” IEEE Antennas Propag. Mag. 35, 7–17 (1993).
[CrossRef]

John, T. M.

R. A. Mark, T. M. John, B. M. Jeffrey, and C. Z. Peter, “Blind search for micro satellites in LEO: optical signatures and search strategies,” in AMOS (The Maui Economic Development Board, 2003), pp. 1–24.

Katharine, K.

F. Daniel, K. Katharine, and C. Francis, “Optimizing site locations for determining shape from photometric light curves,” in Proceedings of Advanced Maui Optical and Space Surveillance Technologies Conference (The Maui Economic Development Board, 2009), pp. 1–11.

Kervin, P. W.

P. W. Kervin, J. L. Africano, P. F. Sydney, and D. Hall, “Small satellite characterization technologies applied to orbital debris,” Adv. Space Res. 35, 1214–1225 (2005).
[CrossRef]

Ladd, D.

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional reflectance model validation and utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

Ladd, S.

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional reflectance model validation and utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

Li, Y.

Y. Han, H. Sun, Y. Li, and L. Tang, “Simulation of space object laser radar cross section,” Infrared Laser Eng. 39, 819–823 (2010).

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 AMOS (The Maui Economic Development Board, 2011), pp. 1–10.

Mark, R. A.

R. A. Mark, T. M. John, B. M. Jeffrey, and C. Z. Peter, “Blind search for micro satellites in LEO: optical signatures and search strategies,” in AMOS (The Maui Economic Development Board, 2003), pp. 1–24.

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 AMOS (The Maui Economic Development Board, 2011), pp. 1–10.

Maxwell, J. R.

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional reflectance model validation and utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

Peter, C. Z.

R. A. Mark, T. M. John, B. M. Jeffrey, and C. Z. Peter, “Blind search for micro satellites in LEO: optical signatures and search strategies,” in AMOS (The Maui Economic Development Board, 2003), pp. 1–24.

Phong, B. T.

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[CrossRef]

Rius, J. M.

J. M. Rius, M. Ferrando, and L. Jofre, “GRECO: graphical electromagnetic computing for RCS prediction in real time,” IEEE Antennas Propag. Mag. 35, 7–17 (1993).
[CrossRef]

Sparrow, E. M.

Steinvall, O.

Sun, C.

Y. Yuan, C. Sun, X. Zhang, H. Zhao, and Q. Wang, “Analysis of influence of attitude variation on visible characteristics of space target,” Acta Opt. Sin. 30, 2748–2752 (2010).
[CrossRef]

Sun, H.

Y. Han, H. Sun, and H. Guo, “Research on rocket target laser scattering characteristic simulation software,” Laser Physics 23, 056007 (2013).
[CrossRef]

Y. Han and H. Sun, “Advances in space target optical scattering character research,” Infrared Laser Eng. 42, 1–10 (2013).

Y. Han, H. Sun, Y. Li, and L. Tang, “Simulation of space object laser radar cross section,” Infrared Laser Eng. 39, 819–823 (2010).

Sydney, P. F.

P. W. Kervin, J. L. Africano, P. F. Sydney, and D. Hall, “Small satellite characterization technologies applied to orbital debris,” Adv. Space Res. 35, 1214–1225 (2005).
[CrossRef]

Tang, L.

Y. Han, H. Sun, Y. Li, and L. Tang, “Simulation of space object laser radar cross section,” Infrared Laser Eng. 39, 819–823 (2010).

Torrance, K. E.

Wang, Q.

Y. Yuan, C. Sun, X. Zhang, H. Zhao, and Q. Wang, “Analysis of influence of attitude variation on visible characteristics of space target,” Acta Opt. Sin. 30, 2748–2752 (2010).
[CrossRef]

Weiner, S.

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional reflectance model validation and utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

Yuan, Y.

Y. Yuan, C. Sun, X. Zhang, H. Zhao, and Q. Wang, “Analysis of influence of attitude variation on visible characteristics of space target,” Acta Opt. Sin. 30, 2748–2752 (2010).
[CrossRef]

Zhang, X.

Y. Yuan, C. Sun, X. Zhang, H. Zhao, and Q. Wang, “Analysis of influence of attitude variation on visible characteristics of space target,” Acta Opt. Sin. 30, 2748–2752 (2010).
[CrossRef]

Zhao, H.

Y. Yuan, C. Sun, X. Zhang, H. Zhao, and Q. Wang, “Analysis of influence of attitude variation on visible characteristics of space target,” Acta Opt. Sin. 30, 2748–2752 (2010).
[CrossRef]

Acta Opt. Sin. (1)

Y. Yuan, C. Sun, X. Zhang, H. Zhao, and Q. Wang, “Analysis of influence of attitude variation on visible characteristics of space target,” Acta Opt. Sin. 30, 2748–2752 (2010).
[CrossRef]

Adv. Space Res. (1)

P. W. Kervin, J. L. Africano, P. F. Sydney, and D. Hall, “Small satellite characterization technologies applied to orbital debris,” Adv. Space Res. 35, 1214–1225 (2005).
[CrossRef]

Appl. Opt. (1)

Commun. ACM (1)

B. T. Phong, “Illumination for computer generated pictures,” Commun. ACM 18, 311–317 (1975).
[CrossRef]

IEEE Antennas Propag. Mag. (1)

J. M. Rius, M. Ferrando, and L. Jofre, “GRECO: graphical electromagnetic computing for RCS prediction in real time,” IEEE Antennas Propag. Mag. 35, 7–17 (1993).
[CrossRef]

Infrared Laser Eng. (2)

Y. Han and H. Sun, “Advances in space target optical scattering character research,” Infrared Laser Eng. 42, 1–10 (2013).

Y. Han, H. Sun, Y. Li, and L. Tang, “Simulation of space object laser radar cross section,” Infrared Laser Eng. 39, 819–823 (2010).

J. Opt. Soc. Am. (1)

Laser Physics (1)

Y. Han, H. Sun, and H. Guo, “Research on rocket target laser scattering characteristic simulation software,” Laser Physics 23, 056007 (2013).
[CrossRef]

Proc. SPIE (1)

K. Bush, G. A. Crockett, and C. Barnard, “Satellite discrimination from active and passive polarization signatures: simulation predictions using the TASAT satellite model,” Proc. SPIE 4481, 46–57 (2002).
[CrossRef]

Other (9)

F. Daniel, K. Katharine, and C. Francis, “Optimizing site locations for determining shape from photometric light curves,” in Proceedings of Advanced Maui Optical and Space Surveillance Technologies Conference (The Maui Economic Development Board, 2009), pp. 1–11.

R. A. Mark, T. M. John, B. M. Jeffrey, and C. Z. Peter, “Blind search for micro satellites in LEO: optical signatures and search strategies,” in AMOS (The Maui Economic Development Board, 2003), pp. 1–24.

J. R. Maxwell, J. Beard, S. Weiner, D. Ladd, and S. Ladd, “Bidirectional reflectance model validation and utilization,” Tech. Rep. AFAL-TR-73-303, Air Force Avionics Laboratory, Wright-Patterson Air Force Base, OH (1973).

H. Doyle, “Surface material characterization from multi-band optical observations,” in AMOS (The Maui Economic Development Board, 2010), pp. 1–15.

B. David and W. David, “Broadband spectral-polarimetric BRDF scan system and data for spacecraft materials,” in AMOS (The Maui Economic Development Board, 2011), pp. 1–9.

D. B. Major, L. Martin, and W. Brad, “Measurement of the photometric and spectral BRDF of small Canadian satellites in a controlled environment,” in AMOS (The Maui Economic Development Board, 2011), pp. 1–10.

D. F. Alistair, Daytime Detection of Space Objects (Air Force Institute of Technology, 2005), pp. 1–65.

W. David and B. David, “Laboratory imaging of satellites and orbital appearance estimation,” in AMOS (The Maui Economic Development Board, 2007), pp. 1–12.

S. Cody and C. Francis, “Simulating complex satellite and a space-based surveillance sensor simulation,” in AMOS (The Maui Economic Development Board, 2009), pp. 1–10.

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Figures (9)

Fig. 1.
Fig. 1.

Geometric relationship between the Sun, the target, and the detector.

Fig. 2.
Fig. 2.

Illustration of the coordinate systems and corresponding angles.

Fig. 3.
Fig. 3.

Process illustration of calculating the complex space target’s OCS.

Fig. 4.
Fig. 4.

Illustration of coordinate systems of Lambert sphere and cylinder.

Fig. 5.
Fig. 5.

Comparison of theoretical OCS and simulated OCS of sphere.

Fig. 6.
Fig. 6.

Comparison of theoretical OCS and simulated OCS of cylinder.

Fig. 7.
Fig. 7.

Three satellite models, the left is Jason, the middle is Aura, and the right is Cloud.

Fig. 8.
Fig. 8.

OCS variation curves of three satellites changing with angle α.

Fig. 9.
Fig. 9.

OCS variation curves of three satellites changing with angle φ.

Tables (1)

Tables Icon

Table 1. BRDF Parameters of Satellite Surface Materials

Equations (16)

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

Esun=MsunRsun2/R02,
Ir=dLrdAcosθr=Esunfr(θi,θr)cosθicosθrdA.
Φd=S0IrdΩ=S0AIrdAdsπ·R12,
Ed=ΦdS0=EsunπR12·(Afr(θi,θr)cosθicosθrdA).
OCS=Afr(θi,θr)cosθicosθrdA.
m=26.742.5·lg(EdEsun)=26.742.5·lg(OCSπR2),
Iout=Iaka+Idkdcosθi+Iskscosgϕ,
BRDF=fr(θi,φ)=kdcosθi+kscosgφπcosθi.
L⃗=(cosηsinφ,sinη,cosηcosφ)S⃗=(0,0,1).
Imn=L⃗·N⃗mn·Cmn=cosθimn·Cmn.
N⃗mn=(IR1IR2,IG1IG2,IB1).
OCSmn=fr(θimn,ϕmn)cosθimncosθrmnSmn,
OCSs=2ρsR12[sinβ1+(πβ1)cosβ1]/3π.
O1=ρ1R2Lsinηsinγ[sinβ2+(πβ2)cosβ2]/2π.
O2=ρ2R22cosηcosγ.
OCSc=O1+O2·max{cosηcosγ,0}.

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