Abstract

The spectral bidirectional scatter distribution function (BSDF) offers a complete description of the spectral and spatial optical characteristics of a material. Any gloss and color measurement can be related to a particular value of the BSDF, while accurate luminaire design with ray tracing software requires the BSDF of reflectors and filters. Many measuring instruments, each having particular advantages and limitations, have been reported in the literature, and an overview of these instruments is included. A measuring instrument that allows for an absolute determination of the spectral BSDF with a full three dimensional spatial coverage in both reflectance and transmittance mode, a broadband spectral coverage, a large dynamic range, a reasonable acquisition time, and a large sample illumination area is presented. The main instrument characteristics are discussed, and the measurement capabilities are illustrated.

© 2008 Optical Society of America

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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  18. P. Apian-Bennewitz and J. von der Hardt, “Enhancing and calibrating a goniophotometer,” Solar Energy Mater. Sol. Cells 54, 309-322 (1998).
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    [CrossRef]
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  28. A. A. Letunov, B. H. Barladian, E. Y. Zueva, V. P. Veshnevetc, and S. A. Soldatov, “CCD-based device for BRDF measurements in computer graphics,” presented at GraphiCon 99--The 9th International Conference on Computer Graphics and Vision, Moscow, Russia, 26 August-1 September, 1999.
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    [CrossRef]
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  32. Commission Internationale de l'Eclairage Technical Report 15:2004, “Colorimetry” (CIE, 2004).
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  35. American Society for Testing and Materials Test Method D523, “Test method for specular gloss” (ASTM, 1999).
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    [CrossRef]
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  38. D. R. White, P. Saunders, S. J. Bonsey, J. van de Ven, and H. Edgar, “Reflectometer for measuring the bidirectional reflectance of rough surfaces,” Appl. Opt. 37, 3450-3454(1998).
    [CrossRef]
  39. T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688-3695 (1999).
    [CrossRef]
  40. G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 241-250 (2005).
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  43. M. R. Pointer, N. J. Barnes, P. J. Clarke, and M. J. Shaw, “A new goniospectrophotometer for measuring gonio-apparent materials,” Color. Technol. 121, 96-103 (2005).
    [CrossRef]
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    [CrossRef]
  47. H. P. A. Lensch, J. Kautz, and M. Goesele, “Image-based reconstruction of spatial appearance and geometric Detail,” ACM Trans. Graph. 22, 234 (2003).
    [CrossRef]
  48. W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759-769(2003).
    [CrossRef]
  49. American Society for Testing and Materials Standard E1392, “Standard practice for angle resolved optical scatter measurements on specular or diffuse surfaces” (ASTM, 1996).
  50. H. J. Kostkowski, “Reliable spectroradiometry” (Spectroradiometry Consulting, 1997).
  51. Y. Ohno, “Spectral colour measurement,” in Colorimetry, Understanding the CIE System, 1st ed., J. Schanda, ed. (CIE Central Bureau, 2006).
  52. Y. Zong, S. W. Brown, K. R. Lykke, and Y. Ohno, “Stray light correction method for array spectrometers,” Appl. Opt. 45, 1111-1119 (2006).
    [CrossRef] [PubMed]
  53. “Chromaflair: thin-film interference color,” Technical Note (JDS Uniphase Corporation, 2006).
  54. Deutsches Institut für Normung Standard 6175-2, “Colour tolerances for automobile lacquer finishes, Part 2: Effect lacquer finishes” (DIN, 2001).
  55. American Society for Testing and Materials Standard E2549-08, “Standard practice for multi-angle measurement of interference pigments” (ASTM, 2008).
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    [CrossRef]
  57. F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of the 10th Congress of the International Color Association, J. L. Nieves and J. Hernández-Andrés, eds. (CIE, 2005), pp. 515-518.

2008

American Society for Testing and Materials Standard E2549-08, “Standard practice for multi-angle measurement of interference pigments” (ASTM, 2008).

2007

A. Ghosh, S. Achutha, W. Heidrich, and M. O'Toole, “BRDF acquisition with basis illumination,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2007).

D. Combes, L. Bousquet, S. Jacquemoud, H. Sinoquet, C. Varlet-Grancher, and I. Moya, “A new spectrogoniophotometer to measure leaf spectral and directional optical properties,” Remote Sens. Environ. 109, 107-117 (2007).
[CrossRef]

2006

M. Andersen, “Validation of the performance of a new bidirectional video-goniophotometer,” Light. Res. Technol. 38, 295-313 (2006).
[CrossRef]

J. Faucheu, K. A. Wood, L.-P. Sung, and J. W. Martin, “Relating gloss loss to topographical features of a PVDF coating,” J. Coat. Technol. 3, 29-39 (2006).
[CrossRef]

Commission Internationale de l'Eclairage Technical Report 176:2006, “Geometric tolerances for colour measurements” (CIE, 2006).

K. Vom Berge, “Compact factored representation for reflectance of complex materials,” Ph.D. dissertation (K.U. Leuven, 2006).

H. Li, S.-C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications”, Opt. Eng. 45, 043605 (2006).
[CrossRef]

Y. Ohno, “Spectral colour measurement,” in Colorimetry, Understanding the CIE System, 1st ed., J. Schanda, ed. (CIE Central Bureau, 2006).

Y. Zong, S. W. Brown, K. R. Lykke, and Y. Ohno, “Stray light correction method for array spectrometers,” Appl. Opt. 45, 1111-1119 (2006).
[CrossRef] [PubMed]

“Chromaflair: thin-film interference color,” Technical Note (JDS Uniphase Corporation, 2006).

2005

M. R. Pointer, N. J. Barnes, P. J. Clarke, and M. J. Shaw, “A new goniospectrophotometer for measuring gonio-apparent materials,” Color. Technol. 121, 96-103 (2005).
[CrossRef]

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 241-250 (2005).

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of the 10th Congress of the International Color Association, J. L. Nieves and J. Hernández-Andrés, eds. (CIE, 2005), pp. 515-518.

J. A. Paterson, D. Claus, and A. W. Fitzgibbon, “BRDF and geometry capture from extended inhomogeneous samples using flash photography,” in Proceedings of the Eurographics Workshop on Rendering Techniques '05 (Springer-Verlag, 2005), Vol. 24(3), pp.383-391.

M. Lindstrand, “An angularly and spatially resolved reflectometer for a perceptually adequate characterization of gloss,” J. Imag. Sci. Technol. 49, 71-84 (2005).

2004

Commission Internationale de l'Eclairage Technical Report 15:2004, “Colorimetry” (CIE, 2004).

J. S. Arney, H. Heo, and P. G. Anderson, “A micro-goniophotometer and the measurement of print gloss,”J. Imag. Sci. Technol. 48, 458-463 (2004).

J. R. Shell, Bidirectional Reflectance: An Overview with Remote Sensing Applications & Measurement Recommendations (Rochester Institute of Technology, 2004).
[PubMed]

2003

H. Granberg, “Optical response from paper. Angle-dependent light scattering: measurements, modelling, and analysis,” Ph.D. dissertation (KTH Royal Institute of Technology, 2003).

H. P. A. Lensch, J. Kautz, and M. Goesele, “Image-based reconstruction of spatial appearance and geometric Detail,” ACM Trans. Graph. 22, 234 (2003).
[CrossRef]

W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759-769(2003).
[CrossRef]

2002

A. Gilchrist, “Characterizing special-effect colours,” Surf. Coat. Intl. B 85, 281-285 (2002).
[CrossRef]

M. E. Nadal and T. A. Germer, “Colorimetric characterization of pearlescent coatings,” Proc. SPIE 4421, 757-760 (2002).
[CrossRef]

D. H. Goldstein and D. B. Chenault, “Spectropolarimetric reflectometer,” Opt. Eng. 41 (5), 1013-1020 (2002).
[CrossRef]

J.-M. Deniel, “Modélisation des luminaires et des BRDF : réalisation, mesure et compression,” Ph.D dissertation (Université de Rennes 1, 2002).

D. K. McAllister, “A generalized surface appearance representation for computer graphics,” Ph.D dissertation (University of North Carolina, 2002).

2001

F. Drago and K. Myszkwski, “Validation proposal for global illumination and rendering techniques,” Comput. Graph. 25, 511-518 (2001).
[CrossRef]

Deutsches Institut für Normung Standard 6175-2, “Colour tolerances for automobile lacquer finishes, Part 2: Effect lacquer finishes” (DIN, 2001).

2000

1999

K. J. Dana, S. Nayar, B. van Ginneken, and J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM Trans. Graph. 18, 1-34 (1999).
[CrossRef]

Y. Boucher, H. Cosnefroy, D. Petit, G. Serrot, and X. Briottet, “Comparison of measured and modeled BRDF of natural targets,” Proc. SPIE 3699, 16-26 (1999).
[CrossRef]

S. R. Sandmeier and K. I. Itten, “A field goniometer system (FIGOS) for acquisition of hyperspectral BRDF data,” IEEE Trans. Geosci. Remote Sens. 37, 978-986 (1999).
[CrossRef]

American Society for Testing and Materials Test Method D523, “Test method for specular gloss” (ASTM, 1999).

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688-3695 (1999).
[CrossRef]

1998

D. R. White, P. Saunders, S. J. Bonsey, J. van de Ven, and H. Edgar, “Reflectometer for measuring the bidirectional reflectance of rough surfaces,” Appl. Opt. 37, 3450-3454(1998).
[CrossRef]

R. Lu, J. J. Koenderink, and A. M. L. Kappers, “Optical properties (bidirectional reflection distribution functions) of velvet,” Appl. Opt. 37, 5974-5984 (1998).
[CrossRef]

W. C. Snyder, “Reciprocity of the bidirectional reflectance distribution function (BRDF) in measurements and models of structured surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 685-691 (1998).
[CrossRef]

B. van Ginneken, M. Stavridi, and J. J. Koenderink, “Diffuse and specular reflectance from rough surfaces,” Appl. Opt. 37, 130-139 (1998).
[CrossRef]

Commission Internationale de l'Eclairage Technical Report 130:1998, “Practical methods for the measurement of reflectance and transmittance” (CIE, 1998).

P. Apian-Bennewitz and J. von der Hardt, “Enhancing and calibrating a goniophotometer,” Solar Energy Mater. Sol. Cells 54, 309-322 (1998).
[CrossRef]

1997

M.-C. Béland and L. Mattsson, “Optical print quality of coated papers,” J. Pulp Pap. Sci. 23, 493-498 (1997).

S. C. Foo, “A gonioreflectometer for measuring the bidirectional reflectance of material for use in illumination computation,” Master's thesis (Cornell University, 1997).

H. J. Kostkowski, “Reliable spectroradiometry” (Spectroradiometry Consulting, 1997).

1996

American Society for Testing and Materials Standard E1392, “Standard practice for angle resolved optical scatter measurements on specular or diffuse surfaces” (ASTM, 1996).

K. F. Karner, H. Mayer, and M. Gervautz, “An image based measurement system for anisotropic reflection,” in Proceedings of the Eurographics Workshop on Rendering Techniques '96 (Springer-Verlag, 1996), Vol. 15(3), pp.119-128.

J.-M. Coulomb and C. Brusque, “Propriétés de réflexion des surfaces. Le gonioréflectomètre du LCPC. Performances et perspectives d'études,” Bull. Lab. Ponts Chaussées 204, 25-35 (1996).

American Society for Testing and Materials Standard E179, “Standard guide for selection of geometric conditions for measurement of reflection and transmission properties of materials” (ASTM, 1996).

1995

J. C. Stover, Optical Scattering: Measurement and Analysis, 2nd ed. (SPIE, 1995).
[CrossRef]

1993

1992

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

1990

J. F. Murray-Coleman and A. M. Smith, “The automated measurement of BRDFs and their application to luminaire modelling,” J. Illum. Eng. Soc. (1990).

1980

1977

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, (1977).

Achutha, S.

A. Ghosh, S. Achutha, W. Heidrich, and M. O'Toole, “BRDF acquisition with basis illumination,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2007).

Andersen, M.

M. Andersen, “Validation of the performance of a new bidirectional video-goniophotometer,” Light. Res. Technol. 38, 295-313 (2006).
[CrossRef]

Anderson, P. G.

J. S. Arney, H. Heo, and P. G. Anderson, “A micro-goniophotometer and the measurement of print gloss,”J. Imag. Sci. Technol. 48, 458-463 (2004).

Apian-Bennewitz, P.

P. Apian-Bennewitz and J. von der Hardt, “Enhancing and calibrating a goniophotometer,” Solar Energy Mater. Sol. Cells 54, 309-322 (1998).
[CrossRef]

Arney, J. S.

J. S. Arney, H. Heo, and P. G. Anderson, “A micro-goniophotometer and the measurement of print gloss,”J. Imag. Sci. Technol. 48, 458-463 (2004).

Asmail, C. C.

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688-3695 (1999).
[CrossRef]

Barladian, B. H.

A. A. Letunov, B. H. Barladian, E. Y. Zueva, V. P. Veshnevetc, and S. A. Soldatov, “CCD-based device for BRDF measurements in computer graphics,” presented at GraphiCon 99--The 9th International Conference on Computer Graphics and Vision, Moscow, Russia, 26 August-1 September, 1999.

Barnes, N. J.

M. R. Pointer, N. J. Barnes, P. J. Clarke, and M. J. Shaw, “A new goniospectrophotometer for measuring gonio-apparent materials,” Color. Technol. 121, 96-103 (2005).
[CrossRef]

Béland, M.-C.

M.-C. Béland and L. Mattsson, “Optical print quality of coated papers,” J. Pulp Pap. Sci. 23, 493-498 (1997).

Bonsey, S. J.

Boucher, Y.

Y. Boucher, H. Cosnefroy, D. Petit, G. Serrot, and X. Briottet, “Comparison of measured and modeled BRDF of natural targets,” Proc. SPIE 3699, 16-26 (1999).
[CrossRef]

Bousquet, L.

D. Combes, L. Bousquet, S. Jacquemoud, H. Sinoquet, C. Varlet-Grancher, and I. Moya, “A new spectrogoniophotometer to measure leaf spectral and directional optical properties,” Remote Sens. Environ. 109, 107-117 (2007).
[CrossRef]

Bousquet, R.

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 241-250 (2005).

Brand, M.

W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759-769(2003).
[CrossRef]

Briottet, X.

Y. Boucher, H. Cosnefroy, D. Petit, G. Serrot, and X. Briottet, “Comparison of measured and modeled BRDF of natural targets,” Proc. SPIE 3699, 16-26 (1999).
[CrossRef]

Brown, S. W.

Brusque, C.

J.-M. Coulomb and C. Brusque, “Propriétés de réflexion des surfaces. Le gonioréflectomètre du LCPC. Performances et perspectives d'études,” Bull. Lab. Ponts Chaussées 204, 25-35 (1996).

Chenault, D. B.

D. H. Goldstein and D. B. Chenault, “Spectropolarimetric reflectometer,” Opt. Eng. 41 (5), 1013-1020 (2002).
[CrossRef]

Clarke, P. J.

M. R. Pointer, N. J. Barnes, P. J. Clarke, and M. J. Shaw, “A new goniospectrophotometer for measuring gonio-apparent materials,” Color. Technol. 121, 96-103 (2005).
[CrossRef]

Claus, D.

J. A. Paterson, D. Claus, and A. W. Fitzgibbon, “BRDF and geometry capture from extended inhomogeneous samples using flash photography,” in Proceedings of the Eurographics Workshop on Rendering Techniques '05 (Springer-Verlag, 2005), Vol. 24(3), pp.383-391.

Combes, D.

D. Combes, L. Bousquet, S. Jacquemoud, H. Sinoquet, C. Varlet-Grancher, and I. Moya, “A new spectrogoniophotometer to measure leaf spectral and directional optical properties,” Remote Sens. Environ. 109, 107-117 (2007).
[CrossRef]

Cosnefroy, H.

Y. Boucher, H. Cosnefroy, D. Petit, G. Serrot, and X. Briottet, “Comparison of measured and modeled BRDF of natural targets,” Proc. SPIE 3699, 16-26 (1999).
[CrossRef]

Coulomb, J.-M.

J.-M. Coulomb and C. Brusque, “Propriétés de réflexion des surfaces. Le gonioréflectomètre du LCPC. Performances et perspectives d'études,” Bull. Lab. Ponts Chaussées 204, 25-35 (1996).

Dana, K. J.

K. J. Dana, S. Nayar, B. van Ginneken, and J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM Trans. Graph. 18, 1-34 (1999).
[CrossRef]

K. J. Dana, “CUReT: Columbia Utrecht reflectance and texture database,” http://www1.cs.columbia.edu/CAVE/software/curet/index.php.

Deniel, J.-M.

J.-M. Deniel, “Modélisation des luminaires et des BRDF : réalisation, mesure et compression,” Ph.D dissertation (Université de Rennes 1, 2002).

Drago, F.

F. Drago and K. Myszkwski, “Validation proposal for global illumination and rendering techniques,” Comput. Graph. 25, 511-518 (2001).
[CrossRef]

Edgar, H.

Erb, W.

Faucheu, J.

J. Faucheu, K. A. Wood, L.-P. Sung, and J. W. Martin, “Relating gloss loss to topographical features of a PVDF coating,” J. Coat. Technol. 3, 29-39 (2006).
[CrossRef]

Feng, X.

Fitzgibbon, A. W.

J. A. Paterson, D. Claus, and A. W. Fitzgibbon, “BRDF and geometry capture from extended inhomogeneous samples using flash photography,” in Proceedings of the Eurographics Workshop on Rendering Techniques '05 (Springer-Verlag, 2005), Vol. 24(3), pp.383-391.

Foo, S. C.

S. C. Foo, “A gonioreflectometer for measuring the bidirectional reflectance of material for use in illumination computation,” Master's thesis (Cornell University, 1997).

Foo, S.-C.

H. Li, S.-C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications”, Opt. Eng. 45, 043605 (2006).
[CrossRef]

Gallagher, T.

Germer, T. A.

M. E. Nadal and T. A. Germer, “Colorimetric characterization of pearlescent coatings,” Proc. SPIE 4421, 757-760 (2002).
[CrossRef]

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688-3695 (1999).
[CrossRef]

Gervautz, M.

K. F. Karner, H. Mayer, and M. Gervautz, “An image based measurement system for anisotropic reflection,” in Proceedings of the Eurographics Workshop on Rendering Techniques '96 (Springer-Verlag, 1996), Vol. 15(3), pp.119-128.

Ghosh, A.

A. Ghosh, S. Achutha, W. Heidrich, and M. O'Toole, “BRDF acquisition with basis illumination,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2007).

Gilchrist, A.

A. Gilchrist, “Characterizing special-effect colours,” Surf. Coat. Intl. B 85, 281-285 (2002).
[CrossRef]

Goesele, M.

H. P. A. Lensch, J. Kautz, and M. Goesele, “Image-based reconstruction of spatial appearance and geometric Detail,” ACM Trans. Graph. 22, 234 (2003).
[CrossRef]

Goldstein, D. H.

D. H. Goldstein and D. B. Chenault, “Spectropolarimetric reflectometer,” Opt. Eng. 41 (5), 1013-1020 (2002).
[CrossRef]

Granberg, H.

H. Granberg, “Optical response from paper. Angle-dependent light scattering: measurements, modelling, and analysis,” Ph.D. dissertation (KTH Royal Institute of Technology, 2003).

Hanselaer, P.

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of the 10th Congress of the International Color Association, J. L. Nieves and J. Hernández-Andrés, eds. (CIE, 2005), pp. 515-518.

Heidrich, W.

A. Ghosh, S. Achutha, W. Heidrich, and M. O'Toole, “BRDF acquisition with basis illumination,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2007).

Heo, H.

J. S. Arney, H. Heo, and P. G. Anderson, “A micro-goniophotometer and the measurement of print gloss,”J. Imag. Sci. Technol. 48, 458-463 (2004).

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, (1977).

Itten, K. I.

S. R. Sandmeier and K. I. Itten, “A field goniometer system (FIGOS) for acquisition of hyperspectral BRDF data,” IEEE Trans. Geosci. Remote Sens. 37, 978-986 (1999).
[CrossRef]

Jacquemoud, S.

D. Combes, L. Bousquet, S. Jacquemoud, H. Sinoquet, C. Varlet-Grancher, and I. Moya, “A new spectrogoniophotometer to measure leaf spectral and directional optical properties,” Remote Sens. Environ. 109, 107-117 (2007).
[CrossRef]

Kappers, A. M. L.

Karner, K. F.

K. F. Karner, H. Mayer, and M. Gervautz, “An image based measurement system for anisotropic reflection,” in Proceedings of the Eurographics Workshop on Rendering Techniques '96 (Springer-Verlag, 1996), Vol. 15(3), pp.119-128.

Kautz, J.

H. P. A. Lensch, J. Kautz, and M. Goesele, “Image-based reconstruction of spatial appearance and geometric Detail,” ACM Trans. Graph. 22, 234 (2003).
[CrossRef]

Knoblauch, K.

G. Obein, T. Leroux, K. Knoblauch, and F. Viénot, “Visually relevant gloss parameters,” presented at the 11th International Metrology Congress, Toulon, France, 20-24 October 2003.

Koenderink, J. J.

Kostkowski, H. J.

H. J. Kostkowski, “Reliable spectroradiometry” (Spectroradiometry Consulting, 1997).

Lafortune, E. P. F.

Leloup, F.

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of the 10th Congress of the International Color Association, J. L. Nieves and J. Hernández-Andrés, eds. (CIE, 2005), pp. 515-518.

Lensch, H. P. A.

H. P. A. Lensch, J. Kautz, and M. Goesele, “Image-based reconstruction of spatial appearance and geometric Detail,” ACM Trans. Graph. 22, 234 (2003).
[CrossRef]

Leroux, T.

G. Obein, T. Leroux, K. Knoblauch, and F. Viénot, “Visually relevant gloss parameters,” presented at the 11th International Metrology Congress, Toulon, France, 20-24 October 2003.

Letunov, A. A.

A. A. Letunov, B. H. Barladian, E. Y. Zueva, V. P. Veshnevetc, and S. A. Soldatov, “CCD-based device for BRDF measurements in computer graphics,” presented at GraphiCon 99--The 9th International Conference on Computer Graphics and Vision, Moscow, Russia, 26 August-1 September, 1999.

Li, H.

H. Li, S.-C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications”, Opt. Eng. 45, 043605 (2006).
[CrossRef]

Lindstrand, M.

M. Lindstrand, “An angularly and spatially resolved reflectometer for a perceptually adequate characterization of gloss,” J. Imag. Sci. Technol. 49, 71-84 (2005).

Lu, R.

Lykke, K. R.

Marschner, S

Martin, J. W.

J. Faucheu, K. A. Wood, L.-P. Sung, and J. W. Martin, “Relating gloss loss to topographical features of a PVDF coating,” J. Coat. Technol. 3, 29-39 (2006).
[CrossRef]

Mattsson, L.

M.-C. Béland and L. Mattsson, “Optical print quality of coated papers,” J. Pulp Pap. Sci. 23, 493-498 (1997).

Matusik, W.

W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759-769(2003).
[CrossRef]

Mayer, H.

K. F. Karner, H. Mayer, and M. Gervautz, “An image based measurement system for anisotropic reflection,” in Proceedings of the Eurographics Workshop on Rendering Techniques '96 (Springer-Verlag, 1996), Vol. 15(3), pp.119-128.

McAllister, D. K.

D. K. McAllister, “A generalized surface appearance representation for computer graphics,” Ph.D dissertation (University of North Carolina, 2002).

McMillan, L.

W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759-769(2003).
[CrossRef]

Moya, I.

D. Combes, L. Bousquet, S. Jacquemoud, H. Sinoquet, C. Varlet-Grancher, and I. Moya, “A new spectrogoniophotometer to measure leaf spectral and directional optical properties,” Remote Sens. Environ. 109, 107-117 (2007).
[CrossRef]

Murray-Coleman, J. F.

J. F. Murray-Coleman and A. M. Smith, “The automated measurement of BRDFs and their application to luminaire modelling,” J. Illum. Eng. Soc. (1990).

Myszkwski, K.

F. Drago and K. Myszkwski, “Validation proposal for global illumination and rendering techniques,” Comput. Graph. 25, 511-518 (2001).
[CrossRef]

Nadal, M. E.

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 241-250 (2005).

M. E. Nadal and T. A. Germer, “Colorimetric characterization of pearlescent coatings,” Proc. SPIE 4421, 757-760 (2002).
[CrossRef]

Nayar, S.

K. J. Dana, S. Nayar, B. van Ginneken, and J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM Trans. Graph. 18, 1-34 (1999).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, (1977).

Obein, G.

G. Obein, T. Leroux, K. Knoblauch, and F. Viénot, “Visually relevant gloss parameters,” presented at the 11th International Metrology Congress, Toulon, France, 20-24 October 2003.

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 241-250 (2005).

Ohno, Y.

Y. Zong, S. W. Brown, K. R. Lykke, and Y. Ohno, “Stray light correction method for array spectrometers,” Appl. Opt. 45, 1111-1119 (2006).
[CrossRef] [PubMed]

Y. Ohno, “Spectral colour measurement,” in Colorimetry, Understanding the CIE System, 1st ed., J. Schanda, ed. (CIE Central Bureau, 2006).

O'Toole, M.

A. Ghosh, S. Achutha, W. Heidrich, and M. O'Toole, “BRDF acquisition with basis illumination,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2007).

Paterson, J. A.

J. A. Paterson, D. Claus, and A. W. Fitzgibbon, “BRDF and geometry capture from extended inhomogeneous samples using flash photography,” in Proceedings of the Eurographics Workshop on Rendering Techniques '05 (Springer-Verlag, 2005), Vol. 24(3), pp.383-391.

Petit, D.

Y. Boucher, H. Cosnefroy, D. Petit, G. Serrot, and X. Briottet, “Comparison of measured and modeled BRDF of natural targets,” Proc. SPIE 3699, 16-26 (1999).
[CrossRef]

Pfister, H.

W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759-769(2003).
[CrossRef]

Pointer, M.

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of the 10th Congress of the International Color Association, J. L. Nieves and J. Hernández-Andrés, eds. (CIE, 2005), pp. 515-518.

Pointer, M. R.

M. R. Pointer, N. J. Barnes, P. J. Clarke, and M. J. Shaw, “A new goniospectrophotometer for measuring gonio-apparent materials,” Color. Technol. 121, 96-103 (2005).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, (1977).

Sandmeier, S. R.

S. R. Sandmeier and K. I. Itten, “A field goniometer system (FIGOS) for acquisition of hyperspectral BRDF data,” IEEE Trans. Geosci. Remote Sens. 37, 978-986 (1999).
[CrossRef]

Saunders, P.

Schott, J. R.

Serrot, G.

Y. Boucher, H. Cosnefroy, D. Petit, G. Serrot, and X. Briottet, “Comparison of measured and modeled BRDF of natural targets,” Proc. SPIE 3699, 16-26 (1999).
[CrossRef]

Shaw, M. J.

M. R. Pointer, N. J. Barnes, P. J. Clarke, and M. J. Shaw, “A new goniospectrophotometer for measuring gonio-apparent materials,” Color. Technol. 121, 96-103 (2005).
[CrossRef]

Shell, J. R.

J. R. Shell, Bidirectional Reflectance: An Overview with Remote Sensing Applications & Measurement Recommendations (Rochester Institute of Technology, 2004).
[PubMed]

Sinoquet, H.

D. Combes, L. Bousquet, S. Jacquemoud, H. Sinoquet, C. Varlet-Grancher, and I. Moya, “A new spectrogoniophotometer to measure leaf spectral and directional optical properties,” Remote Sens. Environ. 109, 107-117 (2007).
[CrossRef]

Smith, A. M.

J. F. Murray-Coleman and A. M. Smith, “The automated measurement of BRDFs and their application to luminaire modelling,” J. Illum. Eng. Soc. (1990).

Snyder, W. C.

W. C. Snyder, “Reciprocity of the bidirectional reflectance distribution function (BRDF) in measurements and models of structured surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 685-691 (1998).
[CrossRef]

Soldatov, S. A.

A. A. Letunov, B. H. Barladian, E. Y. Zueva, V. P. Veshnevetc, and S. A. Soldatov, “CCD-based device for BRDF measurements in computer graphics,” presented at GraphiCon 99--The 9th International Conference on Computer Graphics and Vision, Moscow, Russia, 26 August-1 September, 1999.

Stavridi, M.

Stover, J. C.

J. C. Stover, Optical Scattering: Measurement and Analysis, 2nd ed. (SPIE, 1995).
[CrossRef]

Sung, L.-P.

J. Faucheu, K. A. Wood, L.-P. Sung, and J. W. Martin, “Relating gloss loss to topographical features of a PVDF coating,” J. Coat. Technol. 3, 29-39 (2006).
[CrossRef]

Torrance, K. E.

H. Li, S.-C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications”, Opt. Eng. 45, 043605 (2006).
[CrossRef]

S Marschner, S. H. Westin, E. P. F. Lafortune, and K. E. Torrance, “Image-based bidirectional reflectance distribution function measurement,” Appl. Opt. 39, 2592-2600(2000).
[CrossRef]

van de Ven, J.

van Ginneken, B.

K. J. Dana, S. Nayar, B. van Ginneken, and J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM Trans. Graph. 18, 1-34 (1999).
[CrossRef]

B. van Ginneken, M. Stavridi, and J. J. Koenderink, “Diffuse and specular reflectance from rough surfaces,” Appl. Opt. 37, 130-139 (1998).
[CrossRef]

Varlet-Grancher, C.

D. Combes, L. Bousquet, S. Jacquemoud, H. Sinoquet, C. Varlet-Grancher, and I. Moya, “A new spectrogoniophotometer to measure leaf spectral and directional optical properties,” Remote Sens. Environ. 109, 107-117 (2007).
[CrossRef]

Versluys, J.

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of the 10th Congress of the International Color Association, J. L. Nieves and J. Hernández-Andrés, eds. (CIE, 2005), pp. 515-518.

Veshnevetc, V. P.

A. A. Letunov, B. H. Barladian, E. Y. Zueva, V. P. Veshnevetc, and S. A. Soldatov, “CCD-based device for BRDF measurements in computer graphics,” presented at GraphiCon 99--The 9th International Conference on Computer Graphics and Vision, Moscow, Russia, 26 August-1 September, 1999.

Viénot, F.

G. Obein, T. Leroux, K. Knoblauch, and F. Viénot, “Visually relevant gloss parameters,” presented at the 11th International Metrology Congress, Toulon, France, 20-24 October 2003.

Vom Berge, K.

K. Vom Berge, “Compact factored representation for reflectance of complex materials,” Ph.D. dissertation (K.U. Leuven, 2006).

von der Hardt, J.

P. Apian-Bennewitz and J. von der Hardt, “Enhancing and calibrating a goniophotometer,” Solar Energy Mater. Sol. Cells 54, 309-322 (1998).
[CrossRef]

Ward, G. J.

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

Westin, S. H.

H. Li, S.-C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications”, Opt. Eng. 45, 043605 (2006).
[CrossRef]

S Marschner, S. H. Westin, E. P. F. Lafortune, and K. E. Torrance, “Image-based bidirectional reflectance distribution function measurement,” Appl. Opt. 39, 2592-2600(2000).
[CrossRef]

White, D. R.

Wood, K. A.

J. Faucheu, K. A. Wood, L.-P. Sung, and J. W. Martin, “Relating gloss loss to topographical features of a PVDF coating,” J. Coat. Technol. 3, 29-39 (2006).
[CrossRef]

Zong, Y.

Zueva, E. Y.

A. A. Letunov, B. H. Barladian, E. Y. Zueva, V. P. Veshnevetc, and S. A. Soldatov, “CCD-based device for BRDF measurements in computer graphics,” presented at GraphiCon 99--The 9th International Conference on Computer Graphics and Vision, Moscow, Russia, 26 August-1 September, 1999.

ACM Trans. Graph.

H. P. A. Lensch, J. Kautz, and M. Goesele, “Image-based reconstruction of spatial appearance and geometric Detail,” ACM Trans. Graph. 22, 234 (2003).
[CrossRef]

W. Matusik, H. Pfister, M. Brand, and L. McMillan, “A data-driven reflectance model,” ACM Trans. Graph. 22, 759-769(2003).
[CrossRef]

K. J. Dana, S. Nayar, B. van Ginneken, and J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM Trans. Graph. 18, 1-34 (1999).
[CrossRef]

Appl. Opt.

Bull. Lab. Ponts Chaussées

J.-M. Coulomb and C. Brusque, “Propriétés de réflexion des surfaces. Le gonioréflectomètre du LCPC. Performances et perspectives d'études,” Bull. Lab. Ponts Chaussées 204, 25-35 (1996).

Color. Technol.

M. R. Pointer, N. J. Barnes, P. J. Clarke, and M. J. Shaw, “A new goniospectrophotometer for measuring gonio-apparent materials,” Color. Technol. 121, 96-103 (2005).
[CrossRef]

Comput. Graph.

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

F. Drago and K. Myszkwski, “Validation proposal for global illumination and rendering techniques,” Comput. Graph. 25, 511-518 (2001).
[CrossRef]

IEEE Trans. Geosci. Remote Sens.

W. C. Snyder, “Reciprocity of the bidirectional reflectance distribution function (BRDF) in measurements and models of structured surfaces,” IEEE Trans. Geosci. Remote Sens. 36, 685-691 (1998).
[CrossRef]

S. R. Sandmeier and K. I. Itten, “A field goniometer system (FIGOS) for acquisition of hyperspectral BRDF data,” IEEE Trans. Geosci. Remote Sens. 37, 978-986 (1999).
[CrossRef]

J. Coat. Technol.

J. Faucheu, K. A. Wood, L.-P. Sung, and J. W. Martin, “Relating gloss loss to topographical features of a PVDF coating,” J. Coat. Technol. 3, 29-39 (2006).
[CrossRef]

J. Illum. Eng. Soc.

J. F. Murray-Coleman and A. M. Smith, “The automated measurement of BRDFs and their application to luminaire modelling,” J. Illum. Eng. Soc. (1990).

J. Imag. Sci. Technol.

J. S. Arney, H. Heo, and P. G. Anderson, “A micro-goniophotometer and the measurement of print gloss,”J. Imag. Sci. Technol. 48, 458-463 (2004).

M. Lindstrand, “An angularly and spatially resolved reflectometer for a perceptually adequate characterization of gloss,” J. Imag. Sci. Technol. 49, 71-84 (2005).

J. Pulp Pap. Sci.

M.-C. Béland and L. Mattsson, “Optical print quality of coated papers,” J. Pulp Pap. Sci. 23, 493-498 (1997).

Light. Res. Technol.

M. Andersen, “Validation of the performance of a new bidirectional video-goniophotometer,” Light. Res. Technol. 38, 295-313 (2006).
[CrossRef]

Natl. Bur. Stand. Monogr.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. Monogr. 160, (1977).

Opt. Eng.

D. H. Goldstein and D. B. Chenault, “Spectropolarimetric reflectometer,” Opt. Eng. 41 (5), 1013-1020 (2002).
[CrossRef]

H. Li, S.-C. Foo, K. E. Torrance, and S. H. Westin, “Automated three-axis gonioreflectometer for computer graphics applications”, Opt. Eng. 45, 043605 (2006).
[CrossRef]

Proc. SPIE

Y. Boucher, H. Cosnefroy, D. Petit, G. Serrot, and X. Briottet, “Comparison of measured and modeled BRDF of natural targets,” Proc. SPIE 3699, 16-26 (1999).
[CrossRef]

G. Obein, R. Bousquet, and M. E. Nadal, “New NIST reference goniospectrometer,” Proc. SPIE 5880, 241-250 (2005).

M. E. Nadal and T. A. Germer, “Colorimetric characterization of pearlescent coatings,” Proc. SPIE 4421, 757-760 (2002).
[CrossRef]

Remote Sens. Environ.

D. Combes, L. Bousquet, S. Jacquemoud, H. Sinoquet, C. Varlet-Grancher, and I. Moya, “A new spectrogoniophotometer to measure leaf spectral and directional optical properties,” Remote Sens. Environ. 109, 107-117 (2007).
[CrossRef]

Rev. Sci. Instrum.

T. A. Germer and C. C. Asmail, “Goniometric optical scatter instrument for out-of-plane ellipsometry measurements,” Rev. Sci. Instrum. 70, 3688-3695 (1999).
[CrossRef]

Solar Energy Mater. Sol. Cells

P. Apian-Bennewitz and J. von der Hardt, “Enhancing and calibrating a goniophotometer,” Solar Energy Mater. Sol. Cells 54, 309-322 (1998).
[CrossRef]

Surf. Coat. Intl. B

A. Gilchrist, “Characterizing special-effect colours,” Surf. Coat. Intl. B 85, 281-285 (2002).
[CrossRef]

Other

A. A. Letunov, B. H. Barladian, E. Y. Zueva, V. P. Veshnevetc, and S. A. Soldatov, “CCD-based device for BRDF measurements in computer graphics,” presented at GraphiCon 99--The 9th International Conference on Computer Graphics and Vision, Moscow, Russia, 26 August-1 September, 1999.

J.-M. Deniel, “Modélisation des luminaires et des BRDF : réalisation, mesure et compression,” Ph.D dissertation (Université de Rennes 1, 2002).

Commission Internationale de l'Eclairage Technical Report 130:1998, “Practical methods for the measurement of reflectance and transmittance” (CIE, 1998).

Commission Internationale de l'Eclairage Technical Report 15:2004, “Colorimetry” (CIE, 2004).

Commission Internationale de l'Eclairage Technical Report 176:2006, “Geometric tolerances for colour measurements” (CIE, 2006).

American Society for Testing and Materials Standard E179, “Standard guide for selection of geometric conditions for measurement of reflection and transmission properties of materials” (ASTM, 1996).

American Society for Testing and Materials Test Method D523, “Test method for specular gloss” (ASTM, 1999).

K. J. Dana, “CUReT: Columbia Utrecht reflectance and texture database,” http://www1.cs.columbia.edu/CAVE/software/curet/index.php.

G. Obein, T. Leroux, K. Knoblauch, and F. Viénot, “Visually relevant gloss parameters,” presented at the 11th International Metrology Congress, Toulon, France, 20-24 October 2003.

J. C. Stover, Optical Scattering: Measurement and Analysis, 2nd ed. (SPIE, 1995).
[CrossRef]

K. F. Karner, H. Mayer, and M. Gervautz, “An image based measurement system for anisotropic reflection,” in Proceedings of the Eurographics Workshop on Rendering Techniques '96 (Springer-Verlag, 1996), Vol. 15(3), pp.119-128.

S. C. Foo, “A gonioreflectometer for measuring the bidirectional reflectance of material for use in illumination computation,” Master's thesis (Cornell University, 1997).

H. Granberg, “Optical response from paper. Angle-dependent light scattering: measurements, modelling, and analysis,” Ph.D. dissertation (KTH Royal Institute of Technology, 2003).

J. R. Shell, Bidirectional Reflectance: An Overview with Remote Sensing Applications & Measurement Recommendations (Rochester Institute of Technology, 2004).
[PubMed]

A. Ghosh, S. Achutha, W. Heidrich, and M. O'Toole, “BRDF acquisition with basis illumination,” in Proceedings of IEEE International Conference on Computer Vision (IEEE, 2007).

D. K. McAllister, “A generalized surface appearance representation for computer graphics,” Ph.D dissertation (University of North Carolina, 2002).

J. A. Paterson, D. Claus, and A. W. Fitzgibbon, “BRDF and geometry capture from extended inhomogeneous samples using flash photography,” in Proceedings of the Eurographics Workshop on Rendering Techniques '05 (Springer-Verlag, 2005), Vol. 24(3), pp.383-391.

K. Vom Berge, “Compact factored representation for reflectance of complex materials,” Ph.D. dissertation (K.U. Leuven, 2006).

F. Leloup, P. Hanselaer, M. Pointer, and J. Versluys, “Characterization of gonio-apparent colours,” in Proceedings of the 10th Congress of the International Color Association, J. L. Nieves and J. Hernández-Andrés, eds. (CIE, 2005), pp. 515-518.

American Society for Testing and Materials Standard E1392, “Standard practice for angle resolved optical scatter measurements on specular or diffuse surfaces” (ASTM, 1996).

H. J. Kostkowski, “Reliable spectroradiometry” (Spectroradiometry Consulting, 1997).

Y. Ohno, “Spectral colour measurement,” in Colorimetry, Understanding the CIE System, 1st ed., J. Schanda, ed. (CIE Central Bureau, 2006).

“Chromaflair: thin-film interference color,” Technical Note (JDS Uniphase Corporation, 2006).

Deutsches Institut für Normung Standard 6175-2, “Colour tolerances for automobile lacquer finishes, Part 2: Effect lacquer finishes” (DIN, 2001).

American Society for Testing and Materials Standard E2549-08, “Standard practice for multi-angle measurement of interference pigments” (ASTM, 2008).

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Figures (14)

Fig. 1
Fig. 1

Optical layout of the instrument: (1) xenon discharge source, (2) condenser lens, (3) concave mirror, (4) iris diaphragm, (5) detector head, (6) sample holder, (7) long-wave pass filter, (8) filter wheel, and (9) reference detector.

Fig. 2
Fig. 2

Uniformity of the illumination spot at the sample position, determined by recording the luminance of a white Lambertian sample. Isoluminance regions (expressed in cd / m 2 ) are represented. On the right, luminance values of each pixel on a horizontal cut in the center of the image are displayed on a linear and a log scale (upper and lower figures, respectively).

Fig. 3
Fig. 3

Sample holder with two rotation stages C and D (angles γ and δ) and a translation stage T. The detector bench (1) is mounted on rotation stage B (angle β); this unit is fixed with a bracket (2) onto rotation stage A (angle α). The spectrometer with a CCD detector (3) is mounted onto the detector bench.

Fig. 4
Fig. 4

Representation of the initial (reference) position of the detector head (1), detector bench (2), and sample xyz coordinate system (3) with respect to the global X Y Z coordinate system. The incident light direction (4) and the positive sense of rotation of the four rotation stages A, B, C, and D are also depicted.

Fig. 5
Fig. 5

Instrument signature at 400 nm (dotted curve), 550 nm (dashed curve), and 700 nm (full curve).

Fig. 6
Fig. 6

Instrument signature within a small angular interval of ± 0.2 ° off-axis at three wavelengths: 400 nm (dotted curve), 550 nm (dashed curve), and 700 nm (full curve).

Fig. 7
Fig. 7

Line spread function of the spectroradiometer.

Fig. 8
Fig. 8

Measurement of the absolute reflection of a UV grade fused silica plano-convex lens (dotted curves) compared to the calculated Fresnel reflection (dashed curves) at incidence angles 10 ° (bottom), 30 ° , 40 ° , and 50 ° (top).

Fig. 9
Fig. 9

In-plane (full curve) and out-of-plane (dashed curve) BRDF measurement at 550 nm of a brushed aluminum reflector (MIRO 7 / 5000 from Alanod) in the parallel configuration (incidence plane parallel to the rolling direction).

Fig. 10
Fig. 10

In-plane (full curve) and out-of-plane (dashed curve) BRDF measurement at 550 nm of a brushed aluminum reflector (MIRO 7 / 5000 from Alanod) in the perpendicular configuration (incidence plane perpendicular to the rolling direction).

Fig. 11
Fig. 11

Regular transmittance and sum of both regular transmittance and specular reflectance of a pink dichroic glass filter at incidence angles ranging from 0 ° to 70 ° , with a 10 ° increment.

Fig. 12
Fig. 12

Representation of the CIELAB values in combination with the CIE Standard Illuminant D65 and the CIE 10 ° Standard Observer, as calculated from measurements of the spectral BRDF q e , λ on three ChromaFlair samples. The angle of incidence was fixed at 45 ° from the surface normal. Referring to DIN 6175-2, viewing angles ranged from γ = 40 ° to γ = 125 ° with a 5 ° angle interval in the direction indicated by the arrow.

Fig. 13
Fig. 13

Measurement geometry according to DIN 6175-2. The angle of incidence is fixed at 45 ° from the surface normal. The viewing angle γ is expressed in terms of the “Effektwinkel” or aspecular angle, i.e., the angle referred to the specular reflection angle. γ is taken to be positive toward the incident light direction.

Fig. 14
Fig. 14

Rotation of vector B 0 over a positive angle θ around vector A.

Tables (1)

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Table 1 Neutral Density Filter, Integration Time, and Standard Deviation as a Function of Viewing Angle

Equations (24)

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q e , λ ( θ i , ϕ i , θ s , ϕ s , λ ) = d L e , λ , s ( θ i , ϕ i , θ s , ϕ s , λ ) d E e , λ , i ( θ i , ϕ i , λ ) [ s r 1 ] ,
q e , λ = Φ e , λ , s Φ e , λ , i Ω s | cos θ s | ,
Φ e , λ , s Φ e , λ , i .
r l = r l , ini , r d = R ( Z , α ) . R ( Y , β ) . r d , ini , e x = R ( Z , γ ) . R ( X , δ ) . e x , ini , e x = R ( Z , γ ) . R ( X , δ ) . e y , ini , e z = R ( Z , γ ) . R ( X , δ ) . e z , ini .
r l = ( 1 0 0 ) , r d = ( cos α sin α 0 sin α cos α 0 0 0 1 ) . ( cos β 0 sin β 0 1 0 sin β 0 cos β ) . ( 1 0 0 ) = ( cos α . cos β sin α . cos β sin β ) , e x = ( cos γ sin γ 0 sin γ cos γ 0 0 0 1 ) . ( 1 0 0 0 cos δ sin δ 0 sin δ cos δ ) . ( 0 1 0 ) = ( sin γ . cos δ cos γ . cos δ sin δ ) , e y = ( cos γ sin γ 0 sin γ cos γ 0 0 0 1 ) . ( 1 0 0 0 cos δ sin δ 0 sin δ cos δ ) . ( 0 0 1 ) = ( sin γ . sin δ cos γ . sin δ cos δ ) e z = ( cos γ sin γ 0 sin γ cos γ 0 0 0 1 ) . ( 1 0 0 0 cos δ sin δ 0 sin δ cos δ ) . ( 1 0 0 ) = ( cos γ sin γ 0 ) .
M = ( sin γ . cos δ sin γ . sin δ cos γ cos γ . cos δ cos γ . sin δ sin γ sin δ cos δ 0 ) .
r l ' = M 1 r l = ( sin γ cos δ sin γ sin δ cos γ ) ,
r d ' = M - 1 . r d = ( cos α . cos β . sin γ . cos δ + sin α . cos β . cos γ . cos δ + sin β . sin δ cos α . cos β . sin γ . sin δ sin α . cos β . cos γ . sin δ + sin β . cos δ cos α . cos β . cos γ sin α . cos β . sin γ ) .
sin θ i cos ϕ i = sin γ cos δ , sin θ i sin ϕ i = sin γ sin δ , cos θ i = cos γ ,
sin θ s cos ϕ s = cos α cos β sin γ cos δ + sin α cos β cos γ cos δ + sin β sin δ , sin θ s sin ϕ s = cos α cos β sin γ sin δ sin α cos β cos γ sin δ + sin β cos δ , cos θ s = cos α cos β cos γ sin α cos β sin γ .
Φ d = L A s cos θ s A d d 2 ,
L A s = 0.05 Φ in π .
Φ d Φ in = 0.05 cos θ s A d π d 2 .
C = | B 0 | cos α A | A | ,
D 0 = B 0 C , D 1 = B 1 C .
B 1 A = B 0 A = | B 0 | | A | cos α .
D 1 D 0 = | D 1 | | D 0 | cos θ ,
D 1 ( A × D 0 ) = | D 1 | | A × D 0 | sin θ .
B 1 B 0 | B 0 | 2 cos 2 α = | B 0 | 2 sin 2 α cos θ ,
B 1 B 0 = | B 0 | 2 ( cos θ + ( B 0 A ) 2 | B 0 | 2 | A | 2 ( 1 cos θ ) ) .
B 1 ( A × B 0 ) = | D 0 | | A | | D 0 | sin θ = | A | | B 0 | 2 [ 1 cos 2 α ] sin θ ,
B 1 ( A × B 0 ) = | A | | B 0 | 2 [ 1 ( B 0 . A ) 2 | B 0 | 2 | A | 2 ] sin θ .
( B 1 x B 1 y B 1 z ) = R ( A , θ ) ( B 0 x B 0 y B 0 z ) ,
R ( A , θ ) = 1 | A | ( A x 2 + cos θ ( A y 2 + A z 2 ) A x A y ( 1 cos θ ) A z | A | 1 / 2 sin θ A x A z ( 1 cos θ ) + A y | A | 1 / 2 sin θ A x A y ( 1 cos θ ) + A z | A | 1 / 2 sin θ A y 2 + cos θ ( A x 2 + A z 2 ) A y A z ( 1 cos θ ) A x | A | 1 / 2 sin θ A x A z ( 1 cos θ ) A y | A | 1 / 2 sin θ A y A z ( 1 cos θ ) + A x | A | 1 / 2 sin θ A z 2 + cos θ ( A x 2 + A y 2 ) ) .

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