Abstract

A study on the variation of the spectral bidirectional reflectance distribution function (BRDF) of four diffuse reflectance standards (matte ceramic, BaSO4, Spectralon, and white Russian opal glass) is accomplished through this work. Spectral BRDF measurements were carried out and, using principal components analysis, its spectral and geometrical variation respect to a reference geometry was assessed from the experimental data. Several descriptors were defined in order to compare the spectral BRDF variation of the four materials.

© 2012 Optical Society of America

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References

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  1. A. Pons, J. Campos, J. A. Méndez, and J. Martín, “Reflectance changes in white reflectance standards measured in different instruments with 0/d geometry,” Proceedings of 26th Session of the CIE, CIE 1.178:2007 (CIE, 2007), Vol. 1, pp. D2-46–D2-49.
  2. W. Budde, “Standards of reflectance,” J. Opt. Soc. Am. 50, 217–220 (1960).
    [CrossRef]
  3. F. W. Billmeyer, D. L. Lewis, and J. G. Davidson, “Goniophotometry of pressed barium sulfate,” Color Eng. 9, 31–36 (1971).
  4. W. Erb, “Requirements for reflection standards and the measurement of their reflection values,” Appl. Opt. 14, 493–499 (1975).
    [CrossRef]
  5. Subcommittee “Standards and Techniques”, “CIE 046-1979, A review of publications on properties and reflection values of material reflection standards” (CIE, 1979).
  6. S. Holopainen, F. Manoocheri, E. Ikonen, K.-O. Hauer, and A. Höpe, “Comparison measurements of 0:45 radiance factor and goniometrically determined diffuse reflectance,” Appl. Opt. 48, 2946–2956 (2009).
    [CrossRef]
  7. V. R. Weidner and Jack J. Hsia, “Reflection properties of pressed polytetrafluoroethylene powder,” J. Opt. Soc. Am. 71, 856–861 (1981).
    [CrossRef]
  8. J. C. Zwinkels and W. Erb, “Comparison of absolute d/0diffuse reflectance factor scales of the NRC and the PTB,” Metrologia 34, 357–363 (1997).
    [CrossRef]
  9. E. A. Early, P. Y. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. S. Spyak, and M. M. Pavlov, “Bidirectional reflectance round-robin in support of the earth observing system program,” J. Atmos. Ocean. Technol. 17, 1077–1091 (2000).
    [CrossRef]
  10. A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio–spectrophotometer for the absolute measurement of the spectral BRDF at in&out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
    [CrossRef]
  11. 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]
  12. D. Hünerhoff, U. Grusemann, and A. Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection,” Metrologia 43, S11–S16 (2006).
    [CrossRef]
  13. F. B. Leloup, S. Forment, P. Dutré, M. R. Pointer, and P. Hanselaer, “Design of an instrument for measuring the spectral bidirectional scatter distribution function,” Appl. Opt. 47, 5454–5467 (2008).
    [CrossRef]
  14. R. Baribeau, W. S. Neil, and E. Côté, “Development of a robot-based gonioreflectometer for spectral BRDF measurement,” J. Mod. Opt. 56, 1497–1503 (2009).
    [CrossRef]
  15. F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” National Bureau of Standards Monograph 160 (U.S. Department of Commerce, 1977), 3–7.
  16. A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards,” Opt. Express 19, 19199–19211 (2011).
    [CrossRef]
  17. A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Geometrical representation of the spectral bidirectional reflectance distribution function (BRDF) of pearlescent samples,” J. Opt. Soc. Am. A 29, 842–847 (2012).
    [CrossRef]
  18. A. Springsteen, “Standards for the measurement of diffuse reflectance—an overview of available materials and measurement laboratories,” Anal. Chim. Acta 380, 379–390 (1999).
    [CrossRef]
  19. A. Höpe and K.-O. Hauer, “Three-dimensional appearance characterization of diffuse standard reflection materials,” Metrologia 47, 295–304 (2010).
    [CrossRef]

2012 (2)

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio–spectrophotometer for the absolute measurement of the spectral BRDF at in&out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Geometrical representation of the spectral bidirectional reflectance distribution function (BRDF) of pearlescent samples,” J. Opt. Soc. Am. A 29, 842–847 (2012).
[CrossRef]

2011 (1)

2010 (1)

A. Höpe and K.-O. Hauer, “Three-dimensional appearance characterization of diffuse standard reflection materials,” Metrologia 47, 295–304 (2010).
[CrossRef]

2009 (2)

R. Baribeau, W. S. Neil, and E. Côté, “Development of a robot-based gonioreflectometer for spectral BRDF measurement,” J. Mod. Opt. 56, 1497–1503 (2009).
[CrossRef]

S. Holopainen, F. Manoocheri, E. Ikonen, K.-O. Hauer, and A. Höpe, “Comparison measurements of 0:45 radiance factor and goniometrically determined diffuse reflectance,” Appl. Opt. 48, 2946–2956 (2009).
[CrossRef]

2008 (1)

2006 (1)

D. Hünerhoff, U. Grusemann, and A. Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection,” Metrologia 43, S11–S16 (2006).
[CrossRef]

2000 (1)

E. A. Early, P. Y. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. S. Spyak, and M. M. Pavlov, “Bidirectional reflectance round-robin in support of the earth observing system program,” J. Atmos. Ocean. Technol. 17, 1077–1091 (2000).
[CrossRef]

1999 (2)

A. Springsteen, “Standards for the measurement of diffuse reflectance—an overview of available materials and measurement laboratories,” Anal. Chim. Acta 380, 379–390 (1999).
[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]

1997 (1)

J. C. Zwinkels and W. Erb, “Comparison of absolute d/0diffuse reflectance factor scales of the NRC and the PTB,” Metrologia 34, 357–363 (1997).
[CrossRef]

1981 (1)

1975 (1)

1971 (1)

F. W. Billmeyer, D. L. Lewis, and J. G. Davidson, “Goniophotometry of pressed barium sulfate,” Color Eng. 9, 31–36 (1971).

1960 (1)

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]

Baribeau, R.

R. Baribeau, W. S. Neil, and E. Côté, “Development of a robot-based gonioreflectometer for spectral BRDF measurement,” J. Mod. Opt. 56, 1497–1503 (2009).
[CrossRef]

Barnes, P. Y.

E. A. Early, P. Y. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. S. Spyak, and M. M. Pavlov, “Bidirectional reflectance round-robin in support of the earth observing system program,” J. Atmos. Ocean. Technol. 17, 1077–1091 (2000).
[CrossRef]

Biggar, S. F.

E. A. Early, P. Y. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. S. Spyak, and M. M. Pavlov, “Bidirectional reflectance round-robin in support of the earth observing system program,” J. Atmos. Ocean. Technol. 17, 1077–1091 (2000).
[CrossRef]

Billmeyer, F. W.

F. W. Billmeyer, D. L. Lewis, and J. G. Davidson, “Goniophotometry of pressed barium sulfate,” Color Eng. 9, 31–36 (1971).

Bruegge, C. J.

E. A. Early, P. Y. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. S. Spyak, and M. M. Pavlov, “Bidirectional reflectance round-robin in support of the earth observing system program,” J. Atmos. Ocean. Technol. 17, 1077–1091 (2000).
[CrossRef]

Budde, W.

Butler, J. J.

E. A. Early, P. Y. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. S. Spyak, and M. M. Pavlov, “Bidirectional reflectance round-robin in support of the earth observing system program,” J. Atmos. Ocean. Technol. 17, 1077–1091 (2000).
[CrossRef]

Campos, J.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio–spectrophotometer for the absolute measurement of the spectral BRDF at in&out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Geometrical representation of the spectral bidirectional reflectance distribution function (BRDF) of pearlescent samples,” J. Opt. Soc. Am. A 29, 842–847 (2012).
[CrossRef]

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards,” Opt. Express 19, 19199–19211 (2011).
[CrossRef]

A. Pons, J. Campos, J. A. Méndez, and J. Martín, “Reflectance changes in white reflectance standards measured in different instruments with 0/d geometry,” Proceedings of 26th Session of the CIE, CIE 1.178:2007 (CIE, 2007), Vol. 1, pp. D2-46–D2-49.

Corróns, A.

Côté, E.

R. Baribeau, W. S. Neil, and E. Côté, “Development of a robot-based gonioreflectometer for spectral BRDF measurement,” J. Mod. Opt. 56, 1497–1503 (2009).
[CrossRef]

Davidson, J. G.

F. W. Billmeyer, D. L. Lewis, and J. G. Davidson, “Goniophotometry of pressed barium sulfate,” Color Eng. 9, 31–36 (1971).

Dutré, P.

Early, E. A.

E. A. Early, P. Y. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. S. Spyak, and M. M. Pavlov, “Bidirectional reflectance round-robin in support of the earth observing system program,” J. Atmos. Ocean. Technol. 17, 1077–1091 (2000).
[CrossRef]

Erb, W.

J. C. Zwinkels and W. Erb, “Comparison of absolute d/0diffuse reflectance factor scales of the NRC and the PTB,” Metrologia 34, 357–363 (1997).
[CrossRef]

W. Erb, “Requirements for reflection standards and the measurement of their reflection values,” Appl. Opt. 14, 493–499 (1975).
[CrossRef]

Ferrero, A.

Fontecha, J. L.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio–spectrophotometer for the absolute measurement of the spectral BRDF at in&out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Forment, S.

Germer, T. A.

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]

Grusemann, U.

D. Hünerhoff, U. Grusemann, and A. Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection,” Metrologia 43, S11–S16 (2006).
[CrossRef]

Hanselaer, P.

Hauer, K.-O.

A. Höpe and K.-O. Hauer, “Three-dimensional appearance characterization of diffuse standard reflection materials,” Metrologia 47, 295–304 (2010).
[CrossRef]

S. Holopainen, F. Manoocheri, E. Ikonen, K.-O. Hauer, and A. Höpe, “Comparison measurements of 0:45 radiance factor and goniometrically determined diffuse reflectance,” Appl. Opt. 48, 2946–2956 (2009).
[CrossRef]

Hernanz, M. L.

Holopainen, S.

Höpe, A.

A. Höpe and K.-O. Hauer, “Three-dimensional appearance characterization of diffuse standard reflection materials,” Metrologia 47, 295–304 (2010).
[CrossRef]

S. Holopainen, F. Manoocheri, E. Ikonen, K.-O. Hauer, and A. Höpe, “Comparison measurements of 0:45 radiance factor and goniometrically determined diffuse reflectance,” Appl. Opt. 48, 2946–2956 (2009).
[CrossRef]

D. Hünerhoff, U. Grusemann, and A. Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection,” Metrologia 43, S11–S16 (2006).
[CrossRef]

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” National Bureau of Standards Monograph 160 (U.S. Department of Commerce, 1977), 3–7.

Hsia, Jack J.

Hünerhoff, D.

D. Hünerhoff, U. Grusemann, and A. Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection,” Metrologia 43, S11–S16 (2006).
[CrossRef]

Ikonen, E.

Johnson, B. C.

E. A. Early, P. Y. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. S. Spyak, and M. M. Pavlov, “Bidirectional reflectance round-robin in support of the earth observing system program,” J. Atmos. Ocean. Technol. 17, 1077–1091 (2000).
[CrossRef]

Leloup, F. B.

Lewis, D. L.

F. W. Billmeyer, D. L. Lewis, and J. G. Davidson, “Goniophotometry of pressed barium sulfate,” Color Eng. 9, 31–36 (1971).

Manoocheri, F.

Martín, J.

A. Pons, J. Campos, J. A. Méndez, and J. Martín, “Reflectance changes in white reflectance standards measured in different instruments with 0/d geometry,” Proceedings of 26th Session of the CIE, CIE 1.178:2007 (CIE, 2007), Vol. 1, pp. D2-46–D2-49.

Méndez, J. A.

A. Pons, J. Campos, J. A. Méndez, and J. Martín, “Reflectance changes in white reflectance standards measured in different instruments with 0/d geometry,” Proceedings of 26th Session of the CIE, CIE 1.178:2007 (CIE, 2007), Vol. 1, pp. D2-46–D2-49.

Neil, W. S.

R. Baribeau, W. S. Neil, and E. Côté, “Development of a robot-based gonioreflectometer for spectral BRDF measurement,” J. Mod. Opt. 56, 1497–1503 (2009).
[CrossRef]

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” National Bureau of Standards Monograph 160 (U.S. Department of Commerce, 1977), 3–7.

Pavlov, M. M.

E. A. Early, P. Y. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. S. Spyak, and M. M. Pavlov, “Bidirectional reflectance round-robin in support of the earth observing system program,” J. Atmos. Ocean. Technol. 17, 1077–1091 (2000).
[CrossRef]

Pointer, M. R.

Pons, A.

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Geometrical representation of the spectral bidirectional reflectance distribution function (BRDF) of pearlescent samples,” J. Opt. Soc. Am. A 29, 842–847 (2012).
[CrossRef]

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio–spectrophotometer for the absolute measurement of the spectral BRDF at in&out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

A. Ferrero, J. Campos, A. M. Rabal, A. Pons, M. L. Hernanz, and A. Corróns, “Principal components analysis on the spectral bidirectional reflectance distribution function of ceramic colour standards,” Opt. Express 19, 19199–19211 (2011).
[CrossRef]

A. Pons, J. Campos, J. A. Méndez, and J. Martín, “Reflectance changes in white reflectance standards measured in different instruments with 0/d geometry,” Proceedings of 26th Session of the CIE, CIE 1.178:2007 (CIE, 2007), Vol. 1, pp. D2-46–D2-49.

Rabal, A. M.

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” National Bureau of Standards Monograph 160 (U.S. Department of Commerce, 1977), 3–7.

Rubiño, A. M.

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio–spectrophotometer for the absolute measurement of the spectral BRDF at in&out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

Springsteen, A.

A. Springsteen, “Standards for the measurement of diffuse reflectance—an overview of available materials and measurement laboratories,” Anal. Chim. Acta 380, 379–390 (1999).
[CrossRef]

Spyak, P. S.

E. A. Early, P. Y. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. S. Spyak, and M. M. Pavlov, “Bidirectional reflectance round-robin in support of the earth observing system program,” J. Atmos. Ocean. Technol. 17, 1077–1091 (2000).
[CrossRef]

Weidner, V. R.

Zwinkels, J. C.

J. C. Zwinkels and W. Erb, “Comparison of absolute d/0diffuse reflectance factor scales of the NRC and the PTB,” Metrologia 34, 357–363 (1997).
[CrossRef]

Anal. Chim. Acta (1)

A. Springsteen, “Standards for the measurement of diffuse reflectance—an overview of available materials and measurement laboratories,” Anal. Chim. Acta 380, 379–390 (1999).
[CrossRef]

Appl. Opt. (3)

Color Eng. (1)

F. W. Billmeyer, D. L. Lewis, and J. G. Davidson, “Goniophotometry of pressed barium sulfate,” Color Eng. 9, 31–36 (1971).

J. Atmos. Ocean. Technol. (1)

E. A. Early, P. Y. Barnes, B. C. Johnson, J. J. Butler, C. J. Bruegge, S. F. Biggar, P. S. Spyak, and M. M. Pavlov, “Bidirectional reflectance round-robin in support of the earth observing system program,” J. Atmos. Ocean. Technol. 17, 1077–1091 (2000).
[CrossRef]

J. Mod. Opt. (1)

R. Baribeau, W. S. Neil, and E. Côté, “Development of a robot-based gonioreflectometer for spectral BRDF measurement,” J. Mod. Opt. 56, 1497–1503 (2009).
[CrossRef]

J. Opt. Soc. Am. (2)

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

Metrologia (4)

A. Höpe and K.-O. Hauer, “Three-dimensional appearance characterization of diffuse standard reflection materials,” Metrologia 47, 295–304 (2010).
[CrossRef]

D. Hünerhoff, U. Grusemann, and A. Höpe, “New robot-based gonioreflectometer for measuring spectral diffuse reflection,” Metrologia 43, S11–S16 (2006).
[CrossRef]

A. M. Rabal, A. Ferrero, J. Campos, J. L. Fontecha, A. Pons, A. M. Rubiño, and A. Corróns, “Automatic gonio–spectrophotometer for the absolute measurement of the spectral BRDF at in&out-of-plane and retroreflection geometries,” Metrologia 49, 213–223 (2012).
[CrossRef]

J. C. Zwinkels and W. Erb, “Comparison of absolute d/0diffuse reflectance factor scales of the NRC and the PTB,” Metrologia 34, 357–363 (1997).
[CrossRef]

Opt. Express (1)

Rev. Sci. Instrum. (1)

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]

Other (3)

A. Pons, J. Campos, J. A. Méndez, and J. Martín, “Reflectance changes in white reflectance standards measured in different instruments with 0/d geometry,” Proceedings of 26th Session of the CIE, CIE 1.178:2007 (CIE, 2007), Vol. 1, pp. D2-46–D2-49.

F. E. Nicodemus, J. C. Richmond, and J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” National Bureau of Standards Monograph 160 (U.S. Department of Commerce, 1977), 3–7.

Subcommittee “Standards and Techniques”, “CIE 046-1979, A review of publications on properties and reflection values of material reflection standards” (CIE, 1979).

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Figures (5)

Fig. 1.
Fig. 1.

Sample coordinate system showing spherical coordinates for illumination (θi, ϕi) and viewing directions (θs, ϕs).

Fig. 2.
Fig. 2.

Results on matte ceramic reflection standard from CSS series.

Fig. 3.
Fig. 3.

Results on barium sulphate, BaSO4.

Fig. 4.
Fig. 4.

Results on Spectralon.

Fig. 5.
Fig. 5.

Results on polished white Russian opal glass.

Tables (2)

Tables Icon

Table 1. Definition of the Descriptors of the Spectral BRDF Relative Variation

Tables Icon

Table 2. Descriptors of the Spectral BRDF Relative Variation for the White Reflectance Standards Matte Ceramic, BaSO4, Spectralon, and White Russian Opal Glass

Equations (2)

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

fr,rel(θi,ϕi;θs,ϕs;λ)=fr(θi,ϕi;θs,ϕs;λ)fr(0°,0°;45°,180°;λ).
fr,rel(θi,ϕi;θs,ϕs;λ)=fr,rel(θi,ϕi;θs,ϕs;λ)λ[1+Σj=1Mcj(θi,ϕi;θs,ϕs)Hj(λ)].

Metrics