Abstract

A surface bidirectional reflectance distribution function (BRDF) depends on both the optical properties of the material and the microstructure of the surface and appears as combination of these factors. We propose a method for modeling the BRDF based on a separate optical-property (refractive-index) estimation by polarization measurement. Because the BRDF and the refractive index for precisely the same place can be determined, errors cased by individual difference or spatial dependence can be eliminated. Our BRDF model treats the surface as an aggregation of microfacets, and the diffractive effect is negligible because of randomness. An example model of a painted aluminum plate is presented.

© 2005 Optical Society of America

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References

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  1. J. M. Bennett, “Polarization,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. I, pp. 5.4–5.13.
  2. C. Deumie, H. Giovannini, C. Arma, “Angle-resolved ellipsometry of light scattering: discrimination of surface and bulk effects in substrates and optical coatings,” Appl. Opt. 41, 3362–3369 (2002).
    [CrossRef] [PubMed]
  3. F. Cremer, P. B. W. Schwering, W. Jong, K. Scutte, A. N. Jong, “Infrared polarization measurements of targets and background marine environment,” in Targets and Backgrounds VII, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4370, 169–179 (2001).
  4. F. A. Sadjadi, C. S. L. Chun, “Automatic detection of small objects from their infrared state-of-polarization vectors,” Opt. Lett. 28, 531–533 (2003).
    [CrossRef] [PubMed]
  5. P. L. Walker, W. J. Lentz, A. W. Cooper, “Atmospheric and sea state dependence of polarized infrared contrast,” in Targets and Backgrounds, W. R. Watkins, D. Clement, eds., Proc. SPIE2469, 393–403 (1995).
    [CrossRef]
  6. M. A. Culpepper, “Empirical bidirectional reflectivity model,” in Targets and Backgrounds, W. R. Watkins, D. Clement, eds., Proc. SPIE2469, 208–219 (1995).
    [CrossRef]
  7. Y. Boucher, C. Deumie, C. Arma, L. Pinard, J. Mackowski, S. Mainguy, L. Hespel, J. Perelgritz, “Round robin of painted targets BRDF measurements,” in Targets and Backgrounds VI, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4029, 148–159 (2000).
  8. L. Claustres, Y. Boucher, M. Paulin, “Spectral BRDF modeling using wavelets,” in Wavelet and Independent Component Analysis Applications IX, H. H. Szu, J. R. Buss, eds., Proc. SPIE4738, 33–43 (2002).
    [CrossRef]
  9. J. E. Harvey, “Surface scatter phenomena: a linear, shift-invariant process,” in Scatter from Optical Components, J. C. Stover, ed., Proc. SPIE1165, 87–99 (1989).
    [CrossRef]
  10. W. W. Barkas, “Analysis of light scattered from a surface of low gloss into its specular and diffuse components,” Proc. Phys. Soc. 51, 274–295 (1939).
    [CrossRef]
  11. R. L. Cook, K. E. Torrance, “A reflectance model for computer graphics,” Comput. Graph. 15, 307–316 (1981).
    [CrossRef]
  12. G. Obein, T. Leroux, F. Vienot, “Bi-directional reflectance distribution factor and gloss scales,” in Human Vision and Electronic Imaging VI, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE4299, 279–290 (2001).
    [CrossRef]
  13. D. D. Duncan, D. V. Hahn, M. E. Thomas, “Physics-based polarimetric BRDF models,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 129–140 (2003).
    [CrossRef]
  14. M. E. Thomas, D. W. Blodgett, D. V. Hahn, “Analysis and representation of BSDF and BRDF measurements,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 158–167 (2003).
    [CrossRef]
  15. P. N. Raven, R. M. J. Watson, J. W. Williams, P. E. Y. Milne, “Bidirectional reflectance from pigmented coatings,” in Rough Surface Scattering and Contamination, P. T. Chen, Z. Gu, A. A. Maradudin, eds., Proc. SPIE3784, 262–273 (1999).
    [CrossRef]
  16. C. Schlick, “An inexpensive BRDF model for physically-based rendering,” Eurographics 13, C233–C246 (1994).
  17. N. Destouches, C. Deumie, H. Giovannini, C. Arma, “Determination of refractive indices of opaque rough surfaces,” Appl. Opt. 43, 756–765 (2004).
    [CrossRef] [PubMed]
  18. C. Deumie, H. Giovannini, C. Arma, “Ellipsometry of light scattering from multilayer coatings,” Appl. Opt. 35, 5600–5608 (1996).
    [CrossRef] [PubMed]
  19. C. Arma, “From light scattering to the microstructure of thin-film multilayers,” Appl. Opt. 32, 5481–5491 (1993).
    [CrossRef]
  20. H. Giovannini, C. Arma, “Scattering reduction effect with overcoated rough surfaces: theory and experiment,” Appl. Opt. 36, 5574–5579 (1997).
    [CrossRef] [PubMed]
  21. R. A. Chipman, “Polarimetry,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. II, pp. 22–29.

2004

2003

2002

1997

1996

1994

C. Schlick, “An inexpensive BRDF model for physically-based rendering,” Eurographics 13, C233–C246 (1994).

1993

1981

R. L. Cook, K. E. Torrance, “A reflectance model for computer graphics,” Comput. Graph. 15, 307–316 (1981).
[CrossRef]

1939

W. W. Barkas, “Analysis of light scattered from a surface of low gloss into its specular and diffuse components,” Proc. Phys. Soc. 51, 274–295 (1939).
[CrossRef]

Arma, C.

Barkas, W. W.

W. W. Barkas, “Analysis of light scattered from a surface of low gloss into its specular and diffuse components,” Proc. Phys. Soc. 51, 274–295 (1939).
[CrossRef]

Bennett, J. M.

J. M. Bennett, “Polarization,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. I, pp. 5.4–5.13.

Blodgett, D. W.

M. E. Thomas, D. W. Blodgett, D. V. Hahn, “Analysis and representation of BSDF and BRDF measurements,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 158–167 (2003).
[CrossRef]

Boucher, Y.

Y. Boucher, C. Deumie, C. Arma, L. Pinard, J. Mackowski, S. Mainguy, L. Hespel, J. Perelgritz, “Round robin of painted targets BRDF measurements,” in Targets and Backgrounds VI, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4029, 148–159 (2000).

L. Claustres, Y. Boucher, M. Paulin, “Spectral BRDF modeling using wavelets,” in Wavelet and Independent Component Analysis Applications IX, H. H. Szu, J. R. Buss, eds., Proc. SPIE4738, 33–43 (2002).
[CrossRef]

Chipman, R. A.

R. A. Chipman, “Polarimetry,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. II, pp. 22–29.

Chun, C. S. L.

Claustres, L.

L. Claustres, Y. Boucher, M. Paulin, “Spectral BRDF modeling using wavelets,” in Wavelet and Independent Component Analysis Applications IX, H. H. Szu, J. R. Buss, eds., Proc. SPIE4738, 33–43 (2002).
[CrossRef]

Cook, R. L.

R. L. Cook, K. E. Torrance, “A reflectance model for computer graphics,” Comput. Graph. 15, 307–316 (1981).
[CrossRef]

Cooper, A. W.

P. L. Walker, W. J. Lentz, A. W. Cooper, “Atmospheric and sea state dependence of polarized infrared contrast,” in Targets and Backgrounds, W. R. Watkins, D. Clement, eds., Proc. SPIE2469, 393–403 (1995).
[CrossRef]

Cremer, F.

F. Cremer, P. B. W. Schwering, W. Jong, K. Scutte, A. N. Jong, “Infrared polarization measurements of targets and background marine environment,” in Targets and Backgrounds VII, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4370, 169–179 (2001).

Culpepper, M. A.

M. A. Culpepper, “Empirical bidirectional reflectivity model,” in Targets and Backgrounds, W. R. Watkins, D. Clement, eds., Proc. SPIE2469, 208–219 (1995).
[CrossRef]

Destouches, N.

Deumie, C.

Duncan, D. D.

D. D. Duncan, D. V. Hahn, M. E. Thomas, “Physics-based polarimetric BRDF models,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 129–140 (2003).
[CrossRef]

Giovannini, H.

Hahn, D. V.

M. E. Thomas, D. W. Blodgett, D. V. Hahn, “Analysis and representation of BSDF and BRDF measurements,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 158–167 (2003).
[CrossRef]

D. D. Duncan, D. V. Hahn, M. E. Thomas, “Physics-based polarimetric BRDF models,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 129–140 (2003).
[CrossRef]

Harvey, J. E.

J. E. Harvey, “Surface scatter phenomena: a linear, shift-invariant process,” in Scatter from Optical Components, J. C. Stover, ed., Proc. SPIE1165, 87–99 (1989).
[CrossRef]

Hespel, L.

Y. Boucher, C. Deumie, C. Arma, L. Pinard, J. Mackowski, S. Mainguy, L. Hespel, J. Perelgritz, “Round robin of painted targets BRDF measurements,” in Targets and Backgrounds VI, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4029, 148–159 (2000).

Jong, A. N.

F. Cremer, P. B. W. Schwering, W. Jong, K. Scutte, A. N. Jong, “Infrared polarization measurements of targets and background marine environment,” in Targets and Backgrounds VII, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4370, 169–179 (2001).

Jong, W.

F. Cremer, P. B. W. Schwering, W. Jong, K. Scutte, A. N. Jong, “Infrared polarization measurements of targets and background marine environment,” in Targets and Backgrounds VII, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4370, 169–179 (2001).

Lentz, W. J.

P. L. Walker, W. J. Lentz, A. W. Cooper, “Atmospheric and sea state dependence of polarized infrared contrast,” in Targets and Backgrounds, W. R. Watkins, D. Clement, eds., Proc. SPIE2469, 393–403 (1995).
[CrossRef]

Leroux, T.

G. Obein, T. Leroux, F. Vienot, “Bi-directional reflectance distribution factor and gloss scales,” in Human Vision and Electronic Imaging VI, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE4299, 279–290 (2001).
[CrossRef]

Mackowski, J.

Y. Boucher, C. Deumie, C. Arma, L. Pinard, J. Mackowski, S. Mainguy, L. Hespel, J. Perelgritz, “Round robin of painted targets BRDF measurements,” in Targets and Backgrounds VI, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4029, 148–159 (2000).

Mainguy, S.

Y. Boucher, C. Deumie, C. Arma, L. Pinard, J. Mackowski, S. Mainguy, L. Hespel, J. Perelgritz, “Round robin of painted targets BRDF measurements,” in Targets and Backgrounds VI, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4029, 148–159 (2000).

Milne, P. E. Y.

P. N. Raven, R. M. J. Watson, J. W. Williams, P. E. Y. Milne, “Bidirectional reflectance from pigmented coatings,” in Rough Surface Scattering and Contamination, P. T. Chen, Z. Gu, A. A. Maradudin, eds., Proc. SPIE3784, 262–273 (1999).
[CrossRef]

Obein, G.

G. Obein, T. Leroux, F. Vienot, “Bi-directional reflectance distribution factor and gloss scales,” in Human Vision and Electronic Imaging VI, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE4299, 279–290 (2001).
[CrossRef]

Paulin, M.

L. Claustres, Y. Boucher, M. Paulin, “Spectral BRDF modeling using wavelets,” in Wavelet and Independent Component Analysis Applications IX, H. H. Szu, J. R. Buss, eds., Proc. SPIE4738, 33–43 (2002).
[CrossRef]

Perelgritz, J.

Y. Boucher, C. Deumie, C. Arma, L. Pinard, J. Mackowski, S. Mainguy, L. Hespel, J. Perelgritz, “Round robin of painted targets BRDF measurements,” in Targets and Backgrounds VI, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4029, 148–159 (2000).

Pinard, L.

Y. Boucher, C. Deumie, C. Arma, L. Pinard, J. Mackowski, S. Mainguy, L. Hespel, J. Perelgritz, “Round robin of painted targets BRDF measurements,” in Targets and Backgrounds VI, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4029, 148–159 (2000).

Raven, P. N.

P. N. Raven, R. M. J. Watson, J. W. Williams, P. E. Y. Milne, “Bidirectional reflectance from pigmented coatings,” in Rough Surface Scattering and Contamination, P. T. Chen, Z. Gu, A. A. Maradudin, eds., Proc. SPIE3784, 262–273 (1999).
[CrossRef]

Sadjadi, F. A.

Schlick, C.

C. Schlick, “An inexpensive BRDF model for physically-based rendering,” Eurographics 13, C233–C246 (1994).

Schwering, P. B. W.

F. Cremer, P. B. W. Schwering, W. Jong, K. Scutte, A. N. Jong, “Infrared polarization measurements of targets and background marine environment,” in Targets and Backgrounds VII, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4370, 169–179 (2001).

Scutte, K.

F. Cremer, P. B. W. Schwering, W. Jong, K. Scutte, A. N. Jong, “Infrared polarization measurements of targets and background marine environment,” in Targets and Backgrounds VII, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4370, 169–179 (2001).

Thomas, M. E.

M. E. Thomas, D. W. Blodgett, D. V. Hahn, “Analysis and representation of BSDF and BRDF measurements,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 158–167 (2003).
[CrossRef]

D. D. Duncan, D. V. Hahn, M. E. Thomas, “Physics-based polarimetric BRDF models,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 129–140 (2003).
[CrossRef]

Torrance, K. E.

R. L. Cook, K. E. Torrance, “A reflectance model for computer graphics,” Comput. Graph. 15, 307–316 (1981).
[CrossRef]

Vienot, F.

G. Obein, T. Leroux, F. Vienot, “Bi-directional reflectance distribution factor and gloss scales,” in Human Vision and Electronic Imaging VI, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE4299, 279–290 (2001).
[CrossRef]

Walker, P. L.

P. L. Walker, W. J. Lentz, A. W. Cooper, “Atmospheric and sea state dependence of polarized infrared contrast,” in Targets and Backgrounds, W. R. Watkins, D. Clement, eds., Proc. SPIE2469, 393–403 (1995).
[CrossRef]

Watson, R. M. J.

P. N. Raven, R. M. J. Watson, J. W. Williams, P. E. Y. Milne, “Bidirectional reflectance from pigmented coatings,” in Rough Surface Scattering and Contamination, P. T. Chen, Z. Gu, A. A. Maradudin, eds., Proc. SPIE3784, 262–273 (1999).
[CrossRef]

Williams, J. W.

P. N. Raven, R. M. J. Watson, J. W. Williams, P. E. Y. Milne, “Bidirectional reflectance from pigmented coatings,” in Rough Surface Scattering and Contamination, P. T. Chen, Z. Gu, A. A. Maradudin, eds., Proc. SPIE3784, 262–273 (1999).
[CrossRef]

Appl. Opt.

Comput. Graph.

R. L. Cook, K. E. Torrance, “A reflectance model for computer graphics,” Comput. Graph. 15, 307–316 (1981).
[CrossRef]

Eurographics

C. Schlick, “An inexpensive BRDF model for physically-based rendering,” Eurographics 13, C233–C246 (1994).

Opt. Lett.

Proc. Phys. Soc.

W. W. Barkas, “Analysis of light scattered from a surface of low gloss into its specular and diffuse components,” Proc. Phys. Soc. 51, 274–295 (1939).
[CrossRef]

Other

J. M. Bennett, “Polarization,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. I, pp. 5.4–5.13.

F. Cremer, P. B. W. Schwering, W. Jong, K. Scutte, A. N. Jong, “Infrared polarization measurements of targets and background marine environment,” in Targets and Backgrounds VII, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4370, 169–179 (2001).

R. A. Chipman, “Polarimetry,” in Handbook of Optics, M. Bass, E. W. Van Stryland, D. R. Williams, W. L. Wolfe, eds. (McGraw-Hill, New York, 1995), Vol. II, pp. 22–29.

G. Obein, T. Leroux, F. Vienot, “Bi-directional reflectance distribution factor and gloss scales,” in Human Vision and Electronic Imaging VI, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE4299, 279–290 (2001).
[CrossRef]

D. D. Duncan, D. V. Hahn, M. E. Thomas, “Physics-based polarimetric BRDF models,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 129–140 (2003).
[CrossRef]

M. E. Thomas, D. W. Blodgett, D. V. Hahn, “Analysis and representation of BSDF and BRDF measurements,” in Optical Diagnostic Methods for Inorganic Materials III, L. M. Hanssen, ed., Proc. SPIE5192, 158–167 (2003).
[CrossRef]

P. N. Raven, R. M. J. Watson, J. W. Williams, P. E. Y. Milne, “Bidirectional reflectance from pigmented coatings,” in Rough Surface Scattering and Contamination, P. T. Chen, Z. Gu, A. A. Maradudin, eds., Proc. SPIE3784, 262–273 (1999).
[CrossRef]

P. L. Walker, W. J. Lentz, A. W. Cooper, “Atmospheric and sea state dependence of polarized infrared contrast,” in Targets and Backgrounds, W. R. Watkins, D. Clement, eds., Proc. SPIE2469, 393–403 (1995).
[CrossRef]

M. A. Culpepper, “Empirical bidirectional reflectivity model,” in Targets and Backgrounds, W. R. Watkins, D. Clement, eds., Proc. SPIE2469, 208–219 (1995).
[CrossRef]

Y. Boucher, C. Deumie, C. Arma, L. Pinard, J. Mackowski, S. Mainguy, L. Hespel, J. Perelgritz, “Round robin of painted targets BRDF measurements,” in Targets and Backgrounds VI, W. R. Watkins, D. Clement, W. R. Reynolds, eds., Proc. SPIE4029, 148–159 (2000).

L. Claustres, Y. Boucher, M. Paulin, “Spectral BRDF modeling using wavelets,” in Wavelet and Independent Component Analysis Applications IX, H. H. Szu, J. R. Buss, eds., Proc. SPIE4738, 33–43 (2002).
[CrossRef]

J. E. Harvey, “Surface scatter phenomena: a linear, shift-invariant process,” in Scatter from Optical Components, J. C. Stover, ed., Proc. SPIE1165, 87–99 (1989).
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Illustration of the material structure composed of micro-facets that reflect the incident light in accordance with Fresnel reflection.

Fig. 2
Fig. 2

Geometric illustration of angle variables for description of a BRDF.

Fig. 3
Fig. 3

Instrument setup for measurement of the polarization properties of a BRDF. Here the parabolic reflector is illustrated as a lens for simplicity.

Fig. 4
Fig. 4

Polarization P of the single-reflection components. The open circles are the experimental data and the solid line is the theoretical model, which has the complex refractive index 1.5 − i0.2.

Fig. 5
Fig. 5

Measured data and proposed BRDF model. The BRDF shows a slight asymmetry caused by Fresnel reflection.

Fig. 6
Fig. 6

Measured data and proposed BRDF model in polarized states. The p-polarized component is parallel to the incident plane, and the s-polarized component is perpendicular.

Equations (7)

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

cos α = cos θ i + cos θ r { 2 [ 1 sin θ i sin θ r cos ( ϕ r ϕ i ) + cos θ i cos θ r ] ,
tan β = sin θ i sin ( ϕ r ϕ i ) sin θ r cos ( ϕ r ϕ i ) sin θ i ,
cos 2 ω = sin θ i sin θ r cos ( ϕ r ϕ i ) + cos θ i cos θ r .
f ( θ i , ϕ i , θ r , ϕ r ) = ρ single R ( ñ , ω ) g ( α , β ) + ρ multi / π ,
f m ( θ i , ϕ i , θ r , ϕ r ) = ρ single R m ( ñ , ω ) g ( α , β ) + ρ multi / π ,
P ( ñ , ω ) = R s ( ñ , ω ) R p ( ñ , ω ) R s ( ñ , ω ) + R p ( ñ , ω ) .
P ( ñ , ω ) = f s ( θ i , ϕ i , θ r , ϕ r ) f p ( θ i , ϕ i , θ r , ϕ r ) f s ( θ i , ϕ i , θ r , ϕ r ) + f p ( θ i , ϕ i , θ r , ϕ r ) 2 ρ multi / π .

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