Abstract

A novel approach is proposed for measuring a surface’s bidirectional reflectance distribution function rapidly and accurately. By using a hemi-parabolic mirror, the angular distribution of a surface’s reflectance in three-dimensional space can be transformed into a two-dimensional planar image, which is collected by a CCD camera and goes through a followed coordinate mapping. It is shown that, using this method and apparatus, measurement of in plane and out of plane reflectance distributions may be realized within two minutes.

© 2010 Optical Society of America

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References

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  1. F. E. Nicodemus, Appl. Opt. 4, 767 (1965).
    [CrossRef]
  2. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Natl. Bur. Stand. (U.S.) Monogr. 160, 3 (1977).
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    [CrossRef]
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    [CrossRef]
  6. A. L. Lay, Proc. SPIE 5965, 596527 (2005).
    [CrossRef]
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  9. K. J. Dana and J. Wang, J. Opt. Soc. Am. A 21, 1 (2004).
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  11. C. Hahlweg and H. Rothe, Proc. SPIE 6396, 63960F (2006).
    [CrossRef]
  12. J. C. Stover, Proc. SPIE 1165, 2 (1989).
  13. W. Q. Jin and W. J. Hu, Radiometry, Photometry and Colorimetry (in Chinese) (Beijing Institute of Technology Press, 2006).

2007 (1)

Z. H. Gu and A. T. Wang, Proc. SPIE 6672, 66720H (2007).
[CrossRef]

2006 (1)

C. Hahlweg and H. Rothe, Proc. SPIE 6396, 63960F (2006).
[CrossRef]

2005 (4)

C. Hahlweg and H. Rothe, Proc. SPIE 5965, 59650G (2005).
[CrossRef]

A. L. Lay, Proc. SPIE 5965, 596527 (2005).
[CrossRef]

M. Barilli and A. Mazzoni, Proc. SPIE 5962, 59620L (2005).
[CrossRef]

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, Proc. SPIE 5878, 58780S (2005).
[CrossRef]

2004 (1)

1994 (1)

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Muller, Proc. SPIE 2260, 83 (1994).
[CrossRef]

1992 (1)

G. J. Ward, Comput. Graph. 92, 265 (1992).

1989 (1)

J. C. Stover, Proc. SPIE 1165, 2 (1989).

1977 (1)

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Natl. Bur. Stand. (U.S.) Monogr. 160, 3 (1977).

1965 (1)

Barilli, M.

M. Barilli and A. Mazzoni, Proc. SPIE 5962, 59620L (2005).
[CrossRef]

Dana, K. J.

Foo, S. C.

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, Proc. SPIE 5878, 58780S (2005).
[CrossRef]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Natl. Bur. Stand. (U.S.) Monogr. 160, 3 (1977).

Gu, Z. H.

Z. H. Gu and A. T. Wang, Proc. SPIE 6672, 66720H (2007).
[CrossRef]

Hahlweg, C.

C. Hahlweg and H. Rothe, Proc. SPIE 6396, 63960F (2006).
[CrossRef]

C. Hahlweg and H. Rothe, Proc. SPIE 5965, 59650G (2005).
[CrossRef]

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Natl. Bur. Stand. (U.S.) Monogr. 160, 3 (1977).

Hu, W. J.

W. Q. Jin and W. J. Hu, Radiometry, Photometry and Colorimetry (in Chinese) (Beijing Institute of Technology Press, 2006).

Jin, W. Q.

W. Q. Jin and W. J. Hu, Radiometry, Photometry and Colorimetry (in Chinese) (Beijing Institute of Technology Press, 2006).

Kasper, A.

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Muller, Proc. SPIE 2260, 83 (1994).
[CrossRef]

Lay, A. L.

A. L. Lay, Proc. SPIE 5965, 596527 (2005).
[CrossRef]

Li, H. S.

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, Proc. SPIE 5878, 58780S (2005).
[CrossRef]

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Natl. Bur. Stand. (U.S.) Monogr. 160, 3 (1977).

Mazzoni, A.

M. Barilli and A. Mazzoni, Proc. SPIE 5962, 59620L (2005).
[CrossRef]

Muller, W.

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Muller, Proc. SPIE 2260, 83 (1994).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Natl. Bur. Stand. (U.S.) Monogr. 160, 3 (1977).

F. E. Nicodemus, Appl. Opt. 4, 767 (1965).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Natl. Bur. Stand. (U.S.) Monogr. 160, 3 (1977).

Riedel, P.

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Muller, Proc. SPIE 2260, 83 (1994).
[CrossRef]

Rothe, H.

C. Hahlweg and H. Rothe, Proc. SPIE 6396, 63960F (2006).
[CrossRef]

C. Hahlweg and H. Rothe, Proc. SPIE 5965, 59650G (2005).
[CrossRef]

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Muller, Proc. SPIE 2260, 83 (1994).
[CrossRef]

Specht, O.

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Muller, Proc. SPIE 2260, 83 (1994).
[CrossRef]

Stover, J. C.

J. C. Stover, Proc. SPIE 1165, 2 (1989).

Torrance, K. E.

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, Proc. SPIE 5878, 58780S (2005).
[CrossRef]

Wang, A. T.

Z. H. Gu and A. T. Wang, Proc. SPIE 6672, 66720H (2007).
[CrossRef]

Wang, J.

Ward, G. J.

G. J. Ward, Comput. Graph. 92, 265 (1992).

Westin, S. H.

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, Proc. SPIE 5878, 58780S (2005).
[CrossRef]

Appl. Opt. (1)

Comput. Graph. (1)

G. J. Ward, Comput. Graph. 92, 265 (1992).

J. Opt. Soc. Am. A (1)

Natl. Bur. Stand. (U.S.) Monogr. (1)

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, Natl. Bur. Stand. (U.S.) Monogr. 160, 3 (1977).

Proc. SPIE (8)

M. Barilli and A. Mazzoni, Proc. SPIE 5962, 59620L (2005).
[CrossRef]

H. S. Li, S. C. Foo, K. E. Torrance, and S. H. Westin, Proc. SPIE 5878, 58780S (2005).
[CrossRef]

Z. H. Gu and A. T. Wang, Proc. SPIE 6672, 66720H (2007).
[CrossRef]

A. L. Lay, Proc. SPIE 5965, 596527 (2005).
[CrossRef]

C. Hahlweg and H. Rothe, Proc. SPIE 5965, 59650G (2005).
[CrossRef]

C. Hahlweg and H. Rothe, Proc. SPIE 6396, 63960F (2006).
[CrossRef]

J. C. Stover, Proc. SPIE 1165, 2 (1989).

H. Rothe, A. Kasper, P. Riedel, O. Specht, and W. Muller, Proc. SPIE 2260, 83 (1994).
[CrossRef]

Other (1)

W. Q. Jin and W. J. Hu, Radiometry, Photometry and Colorimetry (in Chinese) (Beijing Institute of Technology Press, 2006).

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Figures (3)

Fig. 1
Fig. 1

Diagrammatic layout of the instrument for BRDF measurement based on a hemi-parabolic mirror.

Fig. 2
Fig. 2

Schematic representation of the coordinate inverse mapping of the parabolic mirror.

Fig. 3
Fig. 3

Polar plot of BRDF shown in grayscale. Polar plot of BRDF. Top to bottom: polished aluminum, unpolished aluminum, and white manifold paper, respectively; Left to right: incident angles equal to 30°, 60°, and 80°, respectively.

Equations (6)

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f r ( θ i , ϕ i ; θ r , ϕ r ) = d L r ( θ i , ϕ i ; θ r , ϕ r ; E i ) d E i ( θ i , ϕ i ) ,
f r ( θ i , ϕ i ; θ r , ϕ r ) 1 π Φ r ( θ i , ϕ i ; θ r , ϕ r ; E i ) Φ r 0 ( θ i , ϕ i ; θ r , ϕ r ; E i ) .
θ = arccos 4 f r cos α 4 f 2 + r 2 ,
ϕ = { arctan 4 f 2 r 2 4 f r sin α , α > 0 arctan 4 f 2 r 2 4 f r sin α + π , α < 0 π 2 , α = 0 , r < f π 2 , α = 0 , r > f } .
Φ r ( θ i , ϕ i ; θ r , ϕ r ; E i ) = A Φ r ( θ i , ϕ i ; θ r , ϕ r ; E i ) + Φ 0 ,
Φ r 0 ( θ i , ϕ i ; θ r , ϕ r ; E i ) = A Φ r 0 ( θ i , ϕ i ; θ r , ϕ r ; E i ) + Φ 0 .

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