Abstract

In this study, the spectral scattering characteristics of a space target are calculated in the near-UV to visible bands on the basis of measured data of spectral hemispheric reflectivity in the upper half space. Further, the bidirectional reflection distribution function (BRDF) model proposed by Davies is modified to describe the light scattering properties of a target surface. This modification aims to improve the characteristics identifying ability for different space targets. By using this modified Davies spectrum BRDF model, the spectral scattering characteristics of each subsurface can be obtained. A mathematical model of spectral scattering properties of the space target is built by summing all the contributing surface grid reflection scattering components, considering the impact of surface shadow effect.Moreover, the spectral scattering characteristics of the space target calculated with both the traditional and modified Davies BRDF models are compared. The results show that in the fixed and modified cases, the hemispheric reflectivity significantly affects the spectral scattering irradiance of the target.

© 2014 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012

2009

W. H. Yuan, Z. Wei, W. Z. Le, “Ultraviolet dynamic characteristics of space satellites based on bidirectional reflection distribution function,” J. Appl. Opt. 30, 410–416 (2009).

2008

Y. Q. Zhang, Z. S. Wu, “Character of light scattering of spatial dynamic objects at direrent stations and analysis of relativity,” J. Electromagn. Waves Appl. 22(8-9), 1071–1080 (2008).
[CrossRef]

Y. H. Cao, Z. S. Wu, H. L. Zhang, Q. N. Wei, S. M. Wang, “Research on visible light scattering of spatial targets based on spectral BRDF of target samples,” Acta Photonica Sinica 37, 2264–2268 (2008).

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

I. G. E. Renhorn, G. D. Boreman, “Analytical fitting model for rough-surface BRDF,” Opt. Express 16(17), 12892–12898 (2008).
[CrossRef] [PubMed]

2007

2006

2003

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

2002

Z. S. Wu, A. A. Liu, “Scattering of solar and atmospheric background radiation from a target,” Int. J. Infrared Millim. Waves 23(6), 907–917 (2002).
[CrossRef]

2001

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

2000

C. Y. Hsieh, “Polarization of optic wave backscattering from dielectric rough surfaces,” Journal of Microwaves and Optoelectronics 2, 14–30 (2000).

1999

W. C. Shemano, W. F. Lynn, D. Shemano, T. A. Davis, “Modification of the Maxwell-Beard bidirectional reflectance distribution function,” Proc. SPIE 3784, 240–248 (1999).
[CrossRef]

1997

1995

M. P. Newell, L. A. Whitlock, R. A. M. Keski-Kuha, J. L. Jackson, “Extreme ultraviolet scatter from particulate contaminated mirrors,” Proc. SPIE 2541, 174–185 (1995).
[CrossRef]

T. Zurbuchen, P. Bochsler, F. Scholze, “Reflection of ultraviolet light at 121.6 nm from rough surfaces,” Opt. Eng. 34(5), 1303–1315 (1995).
[CrossRef]

1993

Y. Barnes, J. J. Hsia, “UV bidirectional reflectance distribution function measurements for diffusers,” Proc. SPIE 1764, 285–288 (1993).
[CrossRef]

1992

J. L. Roujean, M. Leroy, P. Y. Deschamps, “A bidirectional reflectance model of the earth’s surface for the correction of remote sensing data,” J. Geophys. Res. 97(D18), 20455–20468 (1992).
[CrossRef]

X. Li, A. H. Strahler, “Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: effect of crown shape and mutual shadowing,” IEEE Trans. Geosci. Rem. Sens. 30(2), 276–292 (1992).
[CrossRef]

1985

1973

J. R. Maxwell, J. Beard, “Bidirectional reflectance model validation and utilization,” Appl. Opt. 5, 521–528 (1973).

1941

M. Minnaert, “The reciprocity principle of linear photometry,” Astrophys. J. 93, 403–410 (1941).
[CrossRef]

Bai, L.

Barnes, Y.

Y. Barnes, J. J. Hsia, “UV bidirectional reflectance distribution function measurements for diffusers,” Proc. SPIE 1764, 285–288 (1993).
[CrossRef]

Beard, J.

J. R. Maxwell, J. Beard, “Bidirectional reflectance model validation and utilization,” Appl. Opt. 5, 521–528 (1973).

Blad, B. L.

Bochsler, P.

T. Zurbuchen, P. Bochsler, F. Scholze, “Reflection of ultraviolet light at 121.6 nm from rough surfaces,” Opt. Eng. 34(5), 1303–1315 (1995).
[CrossRef]

Boreman, G. D.

Campbell, G.

Cao, Y. H.

L. Bai, Z. S. Wu, X. R. Zou, Y. H. Cao, “Seven-parameter statistical model for BRDF in the UV band,” Opt. Express 20(11), 12085–12094 (2012).
[CrossRef] [PubMed]

Y. H. Cao, Z. S. Wu, H. L. Zhang, Q. N. Wei, S. M. Wang, “Research on visible light scattering of spatial targets based on spectral BRDF of target samples,” Acta Photonica Sinica 37, 2264–2268 (2008).

Davis, T. A.

W. C. Shemano, W. F. Lynn, D. Shemano, T. A. Davis, “Modification of the Maxwell-Beard bidirectional reflectance distribution function,” Proc. SPIE 3784, 240–248 (1999).
[CrossRef]

Deschamps, P. Y.

J. L. Roujean, M. Leroy, P. Y. Deschamps, “A bidirectional reflectance model of the earth’s surface for the correction of remote sensing data,” J. Geophys. Res. 97(D18), 20455–20468 (1992).
[CrossRef]

Dong, A.

Dou, Y. H.

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

Gamiz, V. L.

Hoover, B. G.

Hsia, J. J.

Y. Barnes, J. J. Hsia, “UV bidirectional reflectance distribution function measurements for diffusers,” Proc. SPIE 1764, 285–288 (1993).
[CrossRef]

Hsieh, C. Y.

C. Y. Hsieh, “Polarization of optic wave backscattering from dielectric rough surfaces,” Journal of Microwaves and Optoelectronics 2, 14–30 (2000).

Jackson, J. L.

M. P. Newell, L. A. Whitlock, R. A. M. Keski-Kuha, J. L. Jackson, “Extreme ultraviolet scatter from particulate contaminated mirrors,” Proc. SPIE 2541, 174–185 (1995).
[CrossRef]

Keski-Kuha, R. A. M.

M. P. Newell, R. A. M. Keski-Kuha, “Bidirectional reflectance distribution function of diffuse extreme ultraviolet scatterers and extreme ultraviolet baffle materials,” Appl. Opt. 36(22), 5471–5475 (1997).
[CrossRef] [PubMed]

M. P. Newell, L. A. Whitlock, R. A. M. Keski-Kuha, J. L. Jackson, “Extreme ultraviolet scatter from particulate contaminated mirrors,” Proc. SPIE 2541, 174–185 (1995).
[CrossRef]

Le, W. Z.

W. H. Yuan, Z. Wei, W. Z. Le, “Ultraviolet dynamic characteristics of space satellites based on bidirectional reflection distribution function,” J. Appl. Opt. 30, 410–416 (2009).

Leroy, M.

J. L. Roujean, M. Leroy, P. Y. Deschamps, “A bidirectional reflectance model of the earth’s surface for the correction of remote sensing data,” J. Geophys. Res. 97(D18), 20455–20468 (1992).
[CrossRef]

Li, X.

X. Li, A. H. Strahler, “Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: effect of crown shape and mutual shadowing,” IEEE Trans. Geosci. Rem. Sens. 30(2), 276–292 (1992).
[CrossRef]

Liu, A. A.

Z. S. Wu, A. A. Liu, “Scattering of solar and atmospheric background radiation from a target,” Int. J. Infrared Millim. Waves 23(6), 907–917 (2002).
[CrossRef]

Lynn, W. F.

W. C. Shemano, W. F. Lynn, D. Shemano, T. A. Davis, “Modification of the Maxwell-Beard bidirectional reflectance distribution function,” Proc. SPIE 3784, 240–248 (1999).
[CrossRef]

Maxwell, J. R.

J. R. Maxwell, J. Beard, “Bidirectional reflectance model validation and utilization,” Appl. Opt. 5, 521–528 (1973).

Minnaert, M.

M. Minnaert, “The reciprocity principle of linear photometry,” Astrophys. J. 93, 403–410 (1941).
[CrossRef]

Newell, M. P.

M. P. Newell, R. A. M. Keski-Kuha, “Bidirectional reflectance distribution function of diffuse extreme ultraviolet scatterers and extreme ultraviolet baffle materials,” Appl. Opt. 36(22), 5471–5475 (1997).
[CrossRef] [PubMed]

M. P. Newell, L. A. Whitlock, R. A. M. Keski-Kuha, J. L. Jackson, “Extreme ultraviolet scatter from particulate contaminated mirrors,” Proc. SPIE 2541, 174–185 (1995).
[CrossRef]

Norman, J. M.

Raven, P.

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

Renhorn, I. G. E.

Roujean, J. L.

J. L. Roujean, M. Leroy, P. Y. Deschamps, “A bidirectional reflectance model of the earth’s surface for the correction of remote sensing data,” J. Geophys. Res. 97(D18), 20455–20468 (1992).
[CrossRef]

Scholze, F.

T. Zurbuchen, P. Bochsler, F. Scholze, “Reflection of ultraviolet light at 121.6 nm from rough surfaces,” Opt. Eng. 34(5), 1303–1315 (1995).
[CrossRef]

Shemano, D.

W. C. Shemano, W. F. Lynn, D. Shemano, T. A. Davis, “Modification of the Maxwell-Beard bidirectional reflectance distribution function,” Proc. SPIE 3784, 240–248 (1999).
[CrossRef]

Shemano, W. C.

W. C. Shemano, W. F. Lynn, D. Shemano, T. A. Davis, “Modification of the Maxwell-Beard bidirectional reflectance distribution function,” Proc. SPIE 3784, 240–248 (1999).
[CrossRef]

Strahler, A. H.

X. Li, A. H. Strahler, “Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: effect of crown shape and mutual shadowing,” IEEE Trans. Geosci. Rem. Sens. 30(2), 276–292 (1992).
[CrossRef]

Sun, C. M.

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

Sun, Y. L.

Walthall, C. L.

Wang, H. Y.

H. Y. Wang, W. Zhang, A. Dong, “Modeling and validation of photometric characteristics of space targets oriented to space-based observation,” Appl. Opt. 51(32), 7810–7819 (2012).
[CrossRef] [PubMed]

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

Wang, S. M.

Y. H. Cao, Z. S. Wu, H. L. Zhang, Q. N. Wei, S. M. Wang, “Research on visible light scattering of spatial targets based on spectral BRDF of target samples,” Acta Photonica Sinica 37, 2264–2268 (2008).

Wang, Z. L.

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

Watson, R.

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

Wei, Q. N.

Y. H. Cao, Z. S. Wu, H. L. Zhang, Q. N. Wei, S. M. Wang, “Research on visible light scattering of spatial targets based on spectral BRDF of target samples,” Acta Photonica Sinica 37, 2264–2268 (2008).

Wei, Z.

W. H. Yuan, Z. Wei, W. Z. Le, “Ultraviolet dynamic characteristics of space satellites based on bidirectional reflection distribution function,” J. Appl. Opt. 30, 410–416 (2009).

Welles, J. M.

Whitlock, L. A.

M. P. Newell, L. A. Whitlock, R. A. M. Keski-Kuha, J. L. Jackson, “Extreme ultraviolet scatter from particulate contaminated mirrors,” Proc. SPIE 2541, 174–185 (1995).
[CrossRef]

Wu, Z. S.

L. Bai, Z. S. Wu, X. R. Zou, Y. H. Cao, “Seven-parameter statistical model for BRDF in the UV band,” Opt. Express 20(11), 12085–12094 (2012).
[CrossRef] [PubMed]

Y. Q. Zhang, Z. S. Wu, “Character of light scattering of spatial dynamic objects at direrent stations and analysis of relativity,” J. Electromagn. Waves Appl. 22(8-9), 1071–1080 (2008).
[CrossRef]

Y. H. Cao, Z. S. Wu, H. L. Zhang, Q. N. Wei, S. M. Wang, “Research on visible light scattering of spatial targets based on spectral BRDF of target samples,” Acta Photonica Sinica 37, 2264–2268 (2008).

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

Z. S. Wu, A. A. Liu, “Scattering of solar and atmospheric background radiation from a target,” Int. J. Infrared Millim. Waves 23(6), 907–917 (2002).
[CrossRef]

Yuan, W. H.

W. H. Yuan, Z. Wei, W. Z. Le, “Ultraviolet dynamic characteristics of space satellites based on bidirectional reflection distribution function,” J. Appl. Opt. 30, 410–416 (2009).

Zhang, H. L.

Y. H. Cao, Z. S. Wu, H. L. Zhang, Q. N. Wei, S. M. Wang, “Research on visible light scattering of spatial targets based on spectral BRDF of target samples,” Acta Photonica Sinica 37, 2264–2268 (2008).

Zhang, W.

H. Y. Wang, W. Zhang, A. Dong, “Modeling and validation of photometric characteristics of space targets oriented to space-based observation,” Appl. Opt. 51(32), 7810–7819 (2012).
[CrossRef] [PubMed]

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

Zhang, Y. Q.

Y. Q. Zhang, Z. S. Wu, “Character of light scattering of spatial dynamic objects at direrent stations and analysis of relativity,” J. Electromagn. Waves Appl. 22(8-9), 1071–1080 (2008).
[CrossRef]

Zou, X. R.

Zurbuchen, T.

T. Zurbuchen, P. Bochsler, F. Scholze, “Reflection of ultraviolet light at 121.6 nm from rough surfaces,” Opt. Eng. 34(5), 1303–1315 (1995).
[CrossRef]

Acta Opt. Sin.

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

Acta Photonica Sinica

Y. H. Cao, Z. S. Wu, H. L. Zhang, Q. N. Wei, S. M. Wang, “Research on visible light scattering of spatial targets based on spectral BRDF of target samples,” Acta Photonica Sinica 37, 2264–2268 (2008).

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

Appl. Opt.

Astrophys. J.

M. Minnaert, “The reciprocity principle of linear photometry,” Astrophys. J. 93, 403–410 (1941).
[CrossRef]

IEEE Trans. Geosci. Rem. Sens.

X. Li, A. H. Strahler, “Geometric-optical bidirectional reflectance modeling of the discrete crown vegetation canopy: effect of crown shape and mutual shadowing,” IEEE Trans. Geosci. Rem. Sens. 30(2), 276–292 (1992).
[CrossRef]

Int. J. Infrared Millim. Waves

Z. S. Wu, A. A. Liu, “Scattering of solar and atmospheric background radiation from a target,” Int. J. Infrared Millim. Waves 23(6), 907–917 (2002).
[CrossRef]

J. Appl. Opt.

W. H. Yuan, Z. Wei, W. Z. Le, “Ultraviolet dynamic characteristics of space satellites based on bidirectional reflection distribution function,” J. Appl. Opt. 30, 410–416 (2009).

J. Electromagn. Waves Appl.

Y. Q. Zhang, Z. S. Wu, “Character of light scattering of spatial dynamic objects at direrent stations and analysis of relativity,” J. Electromagn. Waves Appl. 22(8-9), 1071–1080 (2008).
[CrossRef]

J. Geophys. Res.

J. L. Roujean, M. Leroy, P. Y. Deschamps, “A bidirectional reflectance model of the earth’s surface for the correction of remote sensing data,” J. Geophys. Res. 97(D18), 20455–20468 (1992).
[CrossRef]

J. Opt. Soc. Am. A

Journal of Microwaves and Optoelectronics

C. Y. Hsieh, “Polarization of optic wave backscattering from dielectric rough surfaces,” Journal of Microwaves and Optoelectronics 2, 14–30 (2000).

Opt. Eng.

T. Zurbuchen, P. Bochsler, F. Scholze, “Reflection of ultraviolet light at 121.6 nm from rough surfaces,” Opt. Eng. 34(5), 1303–1315 (1995).
[CrossRef]

Opt. Express

Proc. SPIE

Y. Barnes, J. J. Hsia, “UV bidirectional reflectance distribution function measurements for diffusers,” Proc. SPIE 1764, 285–288 (1993).
[CrossRef]

M. P. Newell, L. A. Whitlock, R. A. M. Keski-Kuha, J. L. Jackson, “Extreme ultraviolet scatter from particulate contaminated mirrors,” Proc. SPIE 2541, 174–185 (1995).
[CrossRef]

W. C. Shemano, W. F. Lynn, D. Shemano, T. A. Davis, “Modification of the Maxwell-Beard bidirectional reflectance distribution function,” Proc. SPIE 3784, 240–248 (1999).
[CrossRef]

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

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Figures (9)

Fig. 1
Fig. 1

Geometric model of a space target. (a) 3-D model with the triangular surface mesh. (b) Side view.

Fig. 2
Fig. 2

Space target model for different incident cases (a) 1, (b) 2, and (c) 3.

Fig. 3
Fig. 3

Spectral reflectance of typical samples used in a space target.

Fig. 4
Fig. 4

Spectral BRDF Davies model of yellow Kapton materials at incident angles of (a) 20°, (b) 30°, (c) 45°, and (d) 60°.

Fig. 5
Fig. 5

Spectral radiance of the satellite in different incident cases.

Fig. 6
Fig. 6

Spectral radiance of a satellite at different scattering angles with the space target in case 1 position.

Fig. 7
Fig. 7

Spectral radiance of a satellite at different scattering angles with the space target in case 2 position.

Fig. 8
Fig. 8

Spectral radiance of a satellite at different scattering angles with the space target in case 3 position.

Fig. 9
Fig. 9

Spectral radiance of a satellite at different scattering angles with fixed hemispherical reflectance.

Tables (1)

Tables Icon

Table 1 Characteristic parameters of some rough surfaces

Equations (5)

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

f r ( θ i , φ i , θ r , φ r ,λ )= d L r ( θ i , φ i , θ r , φ r ,λ ) d E i ( θ i , φ i )
f r = P s P i cos θ r 1 Ω s
f r ( θ i , φ i , θ r , φ r )= 132ρ πcos θ i exp[ ( 4π σ λ cos θ i ) 2 ] + ρ cos θ i cos θ r π 3 (cos θ i +cos θ r ) 4 ( ε λ ) 2 ( σ λ ) 2 exp[ ( πε λ ) 2 ( sin 2 θ i + sin 2 θ r +2sin θ i sin θ r cos( φ i φ r ) ) ]
d L r = E i (λ) f r ( θ i , φ i , θ r , φ r ,λ)cos θ i cos θ r dA/ R 2
L r = E i (λ) j f rj ( θ ij , φ ij , θ rj , φ rj ,λ)cos θ ij cos θ rj d A j / R j 2

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