Abstract

We present a new image-based process for measuring a surface’s bidirectional reflectance rapidly, completely, and accurately. Requiring only two cameras, a light source, and a test sample of known shape, our method generates densely spaced samples covering a large domain of illumination and reflection directions. We verified our measurements both by tests of internal consistency and by comparison against measurements made with a gonioreflectometer. The resulting data show accuracy rivaling that of custom-built dedicated instruments.

© 2000 Optical Society of America

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References

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  1. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. Department of Commerce, Washington, D.C., 1977).
  2. J. F. Blinn, “Models of light reflection for computer synthesized pictures,” Comput. Graph. 11, 192–198 (1977).
    [CrossRef]
  3. K. E. Torrance, E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
    [CrossRef]
  4. G. J. Ward, “Measuring and modeling anisotropic reflection,” Comput. Graph. 26, 265–272 (1992).
    [CrossRef]
  5. American Society for Testing and Materials, Standard Practice for Angle Resolved Optical Scatter Measurements on Specular or Diffuse Surfaces (American Society for Testing and Materials, West Conshohocken, Pa., 1996), Standard E 1392–96.
  6. K. E. Torrance, E. M. Sparrow, “Off-specular peaks in the directional distribution of reflected thermal radiation,” ASME J. Heat Transfer 88, 223–230 (1966).
    [CrossRef]
  7. R. J. Castonguay, “New generation high-speed high-resolution hemispherical scatterometer,” in Optical Scattering: Applications, Measurements, and Theory II, J. C. Stover, ed., Proc. SPIE1995, 152–165 (1993).
  8. Z. R. Hatab, J. R. McNeil, S. S. H. Naqvi, “Sixteen-megabit dynamic random access memory trench depth characterization using two-dimensional diffraction analysis,” J. Vac. Sci. Technol. B 13, 174–181 (1995).
    [CrossRef]
  9. J. R. McNeil, S. R. Wilson, “Two-dimensional optical scatterometer apparatus and process,” U.S. patent5,241,369 (31August1993).
  10. K. J. Davis, D. C. Rawlings, “Directional reflectometer for measuring optical bidirectional reflectance,” U.S. patent5,637,873 (10June1997).
  11. K. Ikeuchi, K. Sato, “Determining reflectance properties of an object using range and brightness image,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 1139–1153 (1991).
    [CrossRef]
  12. R. Lu, J. J. Koenderink, A. M. L. Kappers, “Optical properties (BRDF) of velvet,” Appl. Opt. 37, 5974–5984 (1998).
    [CrossRef]
  13. G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, Bellingham, Wash., 1996).
  14. S. S.-F. Chen, J. W.-C. Li, K. E. Torrance, S. N. Pattanaik, “Preliminary calibration of the photometrics PXL1300L CCD camera,” (Cornell University Program of Computer Graphics, Ithaca, N.Y., 1996).
  15. S. N. Pattanaik, K. E. Torrance, “Light measurement using the photometrics PXL1300L CCD camera,” (Cornell University Program of Computer Graphics, Ithaca, N.Y., 1998).
  16. C. S. Fraser, M. R. Shortis, G. Ganci, “Multi-sensor system self-calibration,” in Videometrics IV, S. F. El-Hakim, ed., Proc. SPIE2598, 2–18 (1995).
    [CrossRef]
  17. J. H. Chandler, C. J. Padfield, “Automated digital photogrammetry on a shoestring,” Photogramm. Rec. 15, 545–559 (1996).
    [CrossRef]
  18. J. Fan, I. Gijbels, Local Polynomial Modeling and Its Applications (Chapman & Hall, London, 1996).
  19. S. C. Foo, “A gonioreflectometer for measuring the bidirectional reflectance of material for use in illumination computation,” M.S. thesis (Cornell University, Ithaca, N.Y., 1997).
  20. P. E. Debevec, J. Malik, “Recovering high dynamic range radiance maps from photographs,” Comp. Graph. Proc., Annual Conference Series, 369–378 (1997).

1998 (1)

1997 (1)

P. E. Debevec, J. Malik, “Recovering high dynamic range radiance maps from photographs,” Comp. Graph. Proc., Annual Conference Series, 369–378 (1997).

1996 (1)

J. H. Chandler, C. J. Padfield, “Automated digital photogrammetry on a shoestring,” Photogramm. Rec. 15, 545–559 (1996).
[CrossRef]

1995 (1)

Z. R. Hatab, J. R. McNeil, S. S. H. Naqvi, “Sixteen-megabit dynamic random access memory trench depth characterization using two-dimensional diffraction analysis,” J. Vac. Sci. Technol. B 13, 174–181 (1995).
[CrossRef]

1992 (1)

G. J. Ward, “Measuring and modeling anisotropic reflection,” Comput. Graph. 26, 265–272 (1992).
[CrossRef]

1991 (1)

K. Ikeuchi, K. Sato, “Determining reflectance properties of an object using range and brightness image,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 1139–1153 (1991).
[CrossRef]

1977 (1)

J. F. Blinn, “Models of light reflection for computer synthesized pictures,” Comput. Graph. 11, 192–198 (1977).
[CrossRef]

1967 (1)

1966 (1)

K. E. Torrance, E. M. Sparrow, “Off-specular peaks in the directional distribution of reflected thermal radiation,” ASME J. Heat Transfer 88, 223–230 (1966).
[CrossRef]

Blinn, J. F.

J. F. Blinn, “Models of light reflection for computer synthesized pictures,” Comput. Graph. 11, 192–198 (1977).
[CrossRef]

Castonguay, R. J.

R. J. Castonguay, “New generation high-speed high-resolution hemispherical scatterometer,” in Optical Scattering: Applications, Measurements, and Theory II, J. C. Stover, ed., Proc. SPIE1995, 152–165 (1993).

Chandler, J. H.

J. H. Chandler, C. J. Padfield, “Automated digital photogrammetry on a shoestring,” Photogramm. Rec. 15, 545–559 (1996).
[CrossRef]

Chen, S. S.-F.

S. S.-F. Chen, J. W.-C. Li, K. E. Torrance, S. N. Pattanaik, “Preliminary calibration of the photometrics PXL1300L CCD camera,” (Cornell University Program of Computer Graphics, Ithaca, N.Y., 1996).

Davis, K. J.

K. J. Davis, D. C. Rawlings, “Directional reflectometer for measuring optical bidirectional reflectance,” U.S. patent5,637,873 (10June1997).

Debevec, P. E.

P. E. Debevec, J. Malik, “Recovering high dynamic range radiance maps from photographs,” Comp. Graph. Proc., Annual Conference Series, 369–378 (1997).

Fan, J.

J. Fan, I. Gijbels, Local Polynomial Modeling and Its Applications (Chapman & Hall, London, 1996).

Foo, S. C.

S. C. Foo, “A gonioreflectometer for measuring the bidirectional reflectance of material for use in illumination computation,” M.S. thesis (Cornell University, Ithaca, N.Y., 1997).

Fraser, C. S.

C. S. Fraser, M. R. Shortis, G. Ganci, “Multi-sensor system self-calibration,” in Videometrics IV, S. F. El-Hakim, ed., Proc. SPIE2598, 2–18 (1995).
[CrossRef]

Ganci, G.

C. S. Fraser, M. R. Shortis, G. Ganci, “Multi-sensor system self-calibration,” in Videometrics IV, S. F. El-Hakim, ed., Proc. SPIE2598, 2–18 (1995).
[CrossRef]

Gijbels, I.

J. Fan, I. Gijbels, Local Polynomial Modeling and Its Applications (Chapman & Hall, London, 1996).

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. Department of Commerce, Washington, D.C., 1977).

Hatab, Z. R.

Z. R. Hatab, J. R. McNeil, S. S. H. Naqvi, “Sixteen-megabit dynamic random access memory trench depth characterization using two-dimensional diffraction analysis,” J. Vac. Sci. Technol. B 13, 174–181 (1995).
[CrossRef]

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, Bellingham, Wash., 1996).

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. Department of Commerce, Washington, D.C., 1977).

Ikeuchi, K.

K. Ikeuchi, K. Sato, “Determining reflectance properties of an object using range and brightness image,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 1139–1153 (1991).
[CrossRef]

Kappers, A. M. L.

Koenderink, J. J.

Li, J. W.-C.

S. S.-F. Chen, J. W.-C. Li, K. E. Torrance, S. N. Pattanaik, “Preliminary calibration of the photometrics PXL1300L CCD camera,” (Cornell University Program of Computer Graphics, Ithaca, N.Y., 1996).

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. Department of Commerce, Washington, D.C., 1977).

Lu, R.

Malik, J.

P. E. Debevec, J. Malik, “Recovering high dynamic range radiance maps from photographs,” Comp. Graph. Proc., Annual Conference Series, 369–378 (1997).

McNeil, J. R.

Z. R. Hatab, J. R. McNeil, S. S. H. Naqvi, “Sixteen-megabit dynamic random access memory trench depth characterization using two-dimensional diffraction analysis,” J. Vac. Sci. Technol. B 13, 174–181 (1995).
[CrossRef]

J. R. McNeil, S. R. Wilson, “Two-dimensional optical scatterometer apparatus and process,” U.S. patent5,241,369 (31August1993).

Naqvi, S. S. H.

Z. R. Hatab, J. R. McNeil, S. S. H. Naqvi, “Sixteen-megabit dynamic random access memory trench depth characterization using two-dimensional diffraction analysis,” J. Vac. Sci. Technol. B 13, 174–181 (1995).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. Department of Commerce, Washington, D.C., 1977).

Padfield, C. J.

J. H. Chandler, C. J. Padfield, “Automated digital photogrammetry on a shoestring,” Photogramm. Rec. 15, 545–559 (1996).
[CrossRef]

Pattanaik, S. N.

S. S.-F. Chen, J. W.-C. Li, K. E. Torrance, S. N. Pattanaik, “Preliminary calibration of the photometrics PXL1300L CCD camera,” (Cornell University Program of Computer Graphics, Ithaca, N.Y., 1996).

S. N. Pattanaik, K. E. Torrance, “Light measurement using the photometrics PXL1300L CCD camera,” (Cornell University Program of Computer Graphics, Ithaca, N.Y., 1998).

Rawlings, D. C.

K. J. Davis, D. C. Rawlings, “Directional reflectometer for measuring optical bidirectional reflectance,” U.S. patent5,637,873 (10June1997).

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. Department of Commerce, Washington, D.C., 1977).

Sato, K.

K. Ikeuchi, K. Sato, “Determining reflectance properties of an object using range and brightness image,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 1139–1153 (1991).
[CrossRef]

Shortis, M. R.

C. S. Fraser, M. R. Shortis, G. Ganci, “Multi-sensor system self-calibration,” in Videometrics IV, S. F. El-Hakim, ed., Proc. SPIE2598, 2–18 (1995).
[CrossRef]

Sparrow, E. M.

K. E. Torrance, E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
[CrossRef]

K. E. Torrance, E. M. Sparrow, “Off-specular peaks in the directional distribution of reflected thermal radiation,” ASME J. Heat Transfer 88, 223–230 (1966).
[CrossRef]

Torrance, K. E.

K. E. Torrance, E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
[CrossRef]

K. E. Torrance, E. M. Sparrow, “Off-specular peaks in the directional distribution of reflected thermal radiation,” ASME J. Heat Transfer 88, 223–230 (1966).
[CrossRef]

S. N. Pattanaik, K. E. Torrance, “Light measurement using the photometrics PXL1300L CCD camera,” (Cornell University Program of Computer Graphics, Ithaca, N.Y., 1998).

S. S.-F. Chen, J. W.-C. Li, K. E. Torrance, S. N. Pattanaik, “Preliminary calibration of the photometrics PXL1300L CCD camera,” (Cornell University Program of Computer Graphics, Ithaca, N.Y., 1996).

Ward, G. J.

G. J. Ward, “Measuring and modeling anisotropic reflection,” Comput. Graph. 26, 265–272 (1992).
[CrossRef]

Wilson, S. R.

J. R. McNeil, S. R. Wilson, “Two-dimensional optical scatterometer apparatus and process,” U.S. patent5,241,369 (31August1993).

Appl. Opt. (1)

ASME J. Heat Transfer (1)

K. E. Torrance, E. M. Sparrow, “Off-specular peaks in the directional distribution of reflected thermal radiation,” ASME J. Heat Transfer 88, 223–230 (1966).
[CrossRef]

Comp. Graph. Proc. (1)

P. E. Debevec, J. Malik, “Recovering high dynamic range radiance maps from photographs,” Comp. Graph. Proc., Annual Conference Series, 369–378 (1997).

Comput. Graph. (2)

J. F. Blinn, “Models of light reflection for computer synthesized pictures,” Comput. Graph. 11, 192–198 (1977).
[CrossRef]

G. J. Ward, “Measuring and modeling anisotropic reflection,” Comput. Graph. 26, 265–272 (1992).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

K. Ikeuchi, K. Sato, “Determining reflectance properties of an object using range and brightness image,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 1139–1153 (1991).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Vac. Sci. Technol. B (1)

Z. R. Hatab, J. R. McNeil, S. S. H. Naqvi, “Sixteen-megabit dynamic random access memory trench depth characterization using two-dimensional diffraction analysis,” J. Vac. Sci. Technol. B 13, 174–181 (1995).
[CrossRef]

Photogramm. Rec. (1)

J. H. Chandler, C. J. Padfield, “Automated digital photogrammetry on a shoestring,” Photogramm. Rec. 15, 545–559 (1996).
[CrossRef]

Other (11)

J. Fan, I. Gijbels, Local Polynomial Modeling and Its Applications (Chapman & Hall, London, 1996).

S. C. Foo, “A gonioreflectometer for measuring the bidirectional reflectance of material for use in illumination computation,” M.S. thesis (Cornell University, Ithaca, N.Y., 1997).

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr.160 (U.S. Department of Commerce, Washington, D.C., 1977).

G. C. Holst, CCD Arrays, Cameras, and Displays (SPIE, Bellingham, Wash., 1996).

S. S.-F. Chen, J. W.-C. Li, K. E. Torrance, S. N. Pattanaik, “Preliminary calibration of the photometrics PXL1300L CCD camera,” (Cornell University Program of Computer Graphics, Ithaca, N.Y., 1996).

S. N. Pattanaik, K. E. Torrance, “Light measurement using the photometrics PXL1300L CCD camera,” (Cornell University Program of Computer Graphics, Ithaca, N.Y., 1998).

C. S. Fraser, M. R. Shortis, G. Ganci, “Multi-sensor system self-calibration,” in Videometrics IV, S. F. El-Hakim, ed., Proc. SPIE2598, 2–18 (1995).
[CrossRef]

J. R. McNeil, S. R. Wilson, “Two-dimensional optical scatterometer apparatus and process,” U.S. patent5,241,369 (31August1993).

K. J. Davis, D. C. Rawlings, “Directional reflectometer for measuring optical bidirectional reflectance,” U.S. patent5,637,873 (10June1997).

R. J. Castonguay, “New generation high-speed high-resolution hemispherical scatterometer,” in Optical Scattering: Applications, Measurements, and Theory II, J. C. Stover, ed., Proc. SPIE1995, 152–165 (1993).

American Society for Testing and Materials, Standard Practice for Angle Resolved Optical Scatter Measurements on Specular or Diffuse Surfaces (American Society for Testing and Materials, West Conshohocken, Pa., 1996), Standard E 1392–96.

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Figures (17)

Fig. 1
Fig. 1

Measurement setup.

Fig. 2
Fig. 2

Schematic of the measurement setup.

Fig. 3
Fig. 3

Mapping from the surface to the BRDF parameter space in the incidence plane. If both camera and source were at an infinite distance from the sample, θ e - θ i would be constant and the diagonal lines would be straight as shown; in our measurements, they are slightly curved.

Fig. 4
Fig. 4

Examples of photogrammetric targets.

Fig. 5
Fig. 5

Field flatness of camera: normalized pixel response versus radius for image area used.

Fig. 6
Fig. 6

Contour plot of relative flash irradiance: contour lines at ±2.5% mean irradiance of center region.

Fig. 7
Fig. 7

Repeatability of flash with 30-s cycle time.

Fig. 8
Fig. 8

Radiance across face of flash (nonlinear mapping).

Fig. 9
Fig. 9

Incidence-plane BRDF measurements plotted against incident and exitant angles.

Fig. 10
Fig. 10

Reciprocity comparison for white paper. BRDF measurements plotted for three fixed incident and exitant angles. Dashed curves are the fixed incident angles; solid curves are fixed exitant angles.

Fig. 11
Fig. 11

Gonioreflectometer comparison for white paper. Image-based BRDF measurements (solid curves) and gonioreflectometer measurements of the same material (dashed curves).

Fig. 12
Fig. 12

Reciprocity comparison for gray primer. BRDF measurements are plotted for three fixed incident and exitant angles. Dashed curves are fixed incident angles; solid curves are fixed exitant angles.

Fig. 13
Fig. 13

Photographs of actual test samples used.

Fig. 14
Fig. 14

BRDF sampling pattern for a single incident direction. Each ring is derived from a single digital image.

Fig. 15
Fig. 15

Scattering diagram for the gray primer at θ = 45°. The scale is double that used for the red and blue paints.

Fig. 16
Fig. 16

Resampled scattering diagrams of the BRDF measurements of two paints: a blue enamel (top row) and a red automotive lacquer (bottom row). The RGB color measurements are shown from left to right.

Fig. 17
Fig. 17

Image-based measurements of the red paint (top row; identical to bottom row of Fig. 16) with the corresponding measurements from the gonioreflectometer (bottom row). The gonioreflectometer data were triangulated directly from the sample points, whereas the image-based data, which do not come in sets of fixed θ, were resampled.

Equations (4)

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

Ωmin=π 0.0282221.32=3.0×10-6 sr,
Ωmax=π 0.0281121.32=1.2×10-5 sr.
Ωmin=π 0.050×0.0132.62=3.0×10-4 sr,
Ωmax=π 0.050×0.0131.32=1.2×10-3 sr.

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