Abstract

This paper proposes a three-component bidirectional reflectance distribution function (3C BRDF) model consisting of diffuse, quasi-specular, and glossy components for calculation of effective emissivities of blackbody cavities and then investigates the properties of the new reflection model. The particle swarm optimization method is applied for fitting a 3C BRDF model to measured BRDFs. The model is incorporated into the Monte Carlo ray-tracing algorithm for isothermal cavities. Finally, the paper compares the results obtained using the 3C model and the conventional specular-diffuse model of reflection.

© 2012 Optical Society of America

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  1. J. Hollandt, J. Seidel, R. Klein, G. Ulm, A. Migdall, and M. Ware, “Primary sources for use in radiometry,” Optical Radiometry, A. C. Parr, R. U. Datla, and J. L. Gardner, eds. (Academic, 2005), pp. 213–290.
  2. J. Hartmann, J. Hollandt, B. Khlevnoy, S. Morozova, S. Ogarev, and F. Sakuma, “Blackbody and other calibration sources,” Radiometric Temperature Measurements. I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), pp. 241–295.
  3. F. J. Kelly, “On Kirchhoff’s law and its generalized application to absorption and emission by cavities,” J. Res. Natl. Bur. Stand. B 69, 165–171 (1965).
  4. R. E. Bedford, “Calculation of effective emissivities of cavity sources of thermal radiation,” Theory and Practice if Radiation Thermometry, D. P. DeWitt and G. D. Nutter, eds. (Wiley, 1988), pp. 653–772.
  5. A. V. Prokhorov, L. M. Hanssen, and S. N. Mekhontsev, “Calculation of the radiation characteristics of blackbody radiation sources,” in Radiometric Temperature Measurements: I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), Vol. 42, pp. 181–240.
  6. A. Ono, “Calculation of the directional emissivities of the cavities by the Monte Carlo method,” J. Opt. Soc. Am. 70, 547–554 (1980).
    [CrossRef]
  7. M. J. Ballico, “Modeling of the effective emissivity of a graphite tube black body,” Metrologia 32, 259–265 (1995).
    [CrossRef]
  8. K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996).
    [CrossRef]
  9. M. J. Persky, “Review of black surfaces for space-borne infrared systems,” Rev. Sci. Instrum. 70, 2193–2217 (1999).
    [CrossRef]
  10. S. R. Meier, “Characterization of highly absorbing black appliqués in the infrared,” Appl. Opt. 40, 2788–2795 (2001).
    [CrossRef]
  11. S. R. Meier, “Reflectance and scattering properties of highly absorbing black appliqués over a broadband spectral region,” Appl. Opt. 40, 6260–6264 (2001).
    [CrossRef]
  12. J. Hartmann, “High-temperature measurement techniques for the application in photometry, radiometry and thermometry,” Phys. Rep. 469, 205–269 (2009).
    [CrossRef]
  13. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (U.S. Department of Commerce, National Bureau of Standards, 1977).
  14. A. S. Glassner, Principles of Digital Image Synthesis (Morgan Kaufmann, 1995), Vol. II.
  15. P. Shirley, Fundamentals of Computer Graphics (A K Peters, 2002).
  16. P. Dutré, P. Bekaert, and K. Bala, Advanced Global Illumination (A K Peters, 2003).
  17. M. Pharr and C. Humphreys, Physically Based Rendering: from Theory to Implementation (Morgan Kaufmann, 2010).
  18. M. Kurt and D. Edwards, “A survey of BRDF models for computer graphics,” Comput. Graphics43, 4 (2009).
  19. K. Schwenk, “A survey of shading models for real-time rendering,” http://www.karsten-schwenk.de/downloads/a_survey_of_shading_models.pdf (2011).
  20. O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, “Parametric bidirectional reflectance factor models: evaluation, improvements and applications” (Space Applications Institute, Joint Research Centre, European Commission, ECSC-EC-EAEC, 1996).
  21. S. Liang, Quantitative Remote Sensing of Land Surfaces(Wiley, 2004).
  22. D. L. B. Jupp, “A compendium of kernel and other (semi-)empirical BRDF models” (CSIRO Office of Space Science Applications—Earth Observation Centre, 2000), http://www.eoc.csiro.au/tasks/brdf/k_summ.pdf .
  23. A. F. Sarofim and H. C. Hottel, “Radiation exchange among non-Lambert surfaces,” J. Heat Transfer 88C, 37–44 (1964).
  24. J. Zeng and L. Hanssen, “Development of an infrared optical scattering instrument from 1 μm to 5 μm,” Proc. SPIE 7453, 7453Q1 (2009).
    [CrossRef]
  25. L. M. Hanssen and A. V. Prokhorov, “Stochastic modeling of non-Lambertian surfaces for Monte Carlo computations in optical radiometry,” Proc. SPIE 7427, 742707 (2009).
    [CrossRef]
  26. L. M. Hanssen, S. N. Mekhontsev, J. Zeng, and A. V. Prokhorov, “Evaluation of blackbody cavity emissivity in the infrared using total integrated scatter measurements,” Int. J. Thermophys. 29, 352–369 (2008).
    [CrossRef]
  27. J. S. Liu, Monte Carlo Strategies in Scientific Computing (Springer, 2001).
  28. D. Geisler-Moroder and A. Dür, “A new ward BRDF model with bounded albedo,” Comput. Graph. Forum 29, 1391–1398 (2010).
    [CrossRef]
  29. K. E. Torrance and E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
    [CrossRef]
  30. C. Schlick, “An inexpensive BRDF model for physically based rendering,” Comput. Graph. Forum 13, 233–246(1994).
    [CrossRef]
  31. P. van Dooren and L. de Ridder, “An adaptive algorithm for numerical integration over an n-dimensional cube,” J. Comp. Appl. Math. 2, 207–217 (1976).
    [CrossRef]
  32. M. Clerc, Particle Swarm Optimization (ISTE, 2006).
  33. M. Clerc and J. Kennedy, “The particle swarm—explosion, stability, and convergence in a multidimensional complex space,” IEEE Trans. Evol. Comput. 6, 58–73 (2002).
    [CrossRef]
  34. A. S. Glassner, “An overview of ray tracing,” in An Introduction to Ray TracingA. S. Glassner, ed. (Academic, 1993), pp. 1–32.
  35. E. M. Sparrow and R. D. Cess, Radiation Heat Transfer(Hemisphere, 1978).

2010 (1)

D. Geisler-Moroder and A. Dür, “A new ward BRDF model with bounded albedo,” Comput. Graph. Forum 29, 1391–1398 (2010).
[CrossRef]

2009 (3)

J. Zeng and L. Hanssen, “Development of an infrared optical scattering instrument from 1 μm to 5 μm,” Proc. SPIE 7453, 7453Q1 (2009).
[CrossRef]

L. M. Hanssen and A. V. Prokhorov, “Stochastic modeling of non-Lambertian surfaces for Monte Carlo computations in optical radiometry,” Proc. SPIE 7427, 742707 (2009).
[CrossRef]

J. Hartmann, “High-temperature measurement techniques for the application in photometry, radiometry and thermometry,” Phys. Rep. 469, 205–269 (2009).
[CrossRef]

2008 (1)

L. M. Hanssen, S. N. Mekhontsev, J. Zeng, and A. V. Prokhorov, “Evaluation of blackbody cavity emissivity in the infrared using total integrated scatter measurements,” Int. J. Thermophys. 29, 352–369 (2008).
[CrossRef]

2002 (1)

M. Clerc and J. Kennedy, “The particle swarm—explosion, stability, and convergence in a multidimensional complex space,” IEEE Trans. Evol. Comput. 6, 58–73 (2002).
[CrossRef]

2001 (2)

1999 (1)

M. J. Persky, “Review of black surfaces for space-borne infrared systems,” Rev. Sci. Instrum. 70, 2193–2217 (1999).
[CrossRef]

1996 (1)

K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996).
[CrossRef]

1995 (1)

M. J. Ballico, “Modeling of the effective emissivity of a graphite tube black body,” Metrologia 32, 259–265 (1995).
[CrossRef]

1994 (1)

C. Schlick, “An inexpensive BRDF model for physically based rendering,” Comput. Graph. Forum 13, 233–246(1994).
[CrossRef]

1980 (1)

1976 (1)

P. van Dooren and L. de Ridder, “An adaptive algorithm for numerical integration over an n-dimensional cube,” J. Comp. Appl. Math. 2, 207–217 (1976).
[CrossRef]

1967 (1)

1965 (1)

F. J. Kelly, “On Kirchhoff’s law and its generalized application to absorption and emission by cavities,” J. Res. Natl. Bur. Stand. B 69, 165–171 (1965).

1964 (1)

A. F. Sarofim and H. C. Hottel, “Radiation exchange among non-Lambert surfaces,” J. Heat Transfer 88C, 37–44 (1964).

Bala, K.

P. Dutré, P. Bekaert, and K. Bala, Advanced Global Illumination (A K Peters, 2003).

Ballico, M. J.

M. J. Ballico, “Modeling of the effective emissivity of a graphite tube black body,” Metrologia 32, 259–265 (1995).
[CrossRef]

Bedford, R. E.

R. E. Bedford, “Calculation of effective emissivities of cavity sources of thermal radiation,” Theory and Practice if Radiation Thermometry, D. P. DeWitt and G. D. Nutter, eds. (Wiley, 1988), pp. 653–772.

Bekaert, P.

P. Dutré, P. Bekaert, and K. Bala, Advanced Global Illumination (A K Peters, 2003).

Brown, D. P.

K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996).
[CrossRef]

Cess, R. D.

E. M. Sparrow and R. D. Cess, Radiation Heat Transfer(Hemisphere, 1978).

Clerc, M.

M. Clerc and J. Kennedy, “The particle swarm—explosion, stability, and convergence in a multidimensional complex space,” IEEE Trans. Evol. Comput. 6, 58–73 (2002).
[CrossRef]

M. Clerc, Particle Swarm Optimization (ISTE, 2006).

Costantino, J. P.

K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996).
[CrossRef]

de Ridder, L.

P. van Dooren and L. de Ridder, “An adaptive algorithm for numerical integration over an n-dimensional cube,” J. Comp. Appl. Math. 2, 207–217 (1976).
[CrossRef]

Dür, A.

D. Geisler-Moroder and A. Dür, “A new ward BRDF model with bounded albedo,” Comput. Graph. Forum 29, 1391–1398 (2010).
[CrossRef]

Dutré, P.

P. Dutré, P. Bekaert, and K. Bala, Advanced Global Illumination (A K Peters, 2003).

Edwards, D.

M. Kurt and D. Edwards, “A survey of BRDF models for computer graphics,” Comput. Graphics43, 4 (2009).

Engelsen, O.

O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, “Parametric bidirectional reflectance factor models: evaluation, improvements and applications” (Space Applications Institute, Joint Research Centre, European Commission, ECSC-EC-EAEC, 1996).

Geisler-Moroder, D.

D. Geisler-Moroder and A. Dür, “A new ward BRDF model with bounded albedo,” Comput. Graph. Forum 29, 1391–1398 (2010).
[CrossRef]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (U.S. Department of Commerce, National Bureau of Standards, 1977).

Glassner, A. S.

A. S. Glassner, Principles of Digital Image Synthesis (Morgan Kaufmann, 1995), Vol. II.

A. S. Glassner, “An overview of ray tracing,” in An Introduction to Ray TracingA. S. Glassner, ed. (Academic, 1993), pp. 1–32.

Hanssen, L.

J. Zeng and L. Hanssen, “Development of an infrared optical scattering instrument from 1 μm to 5 μm,” Proc. SPIE 7453, 7453Q1 (2009).
[CrossRef]

Hanssen, L. M.

L. M. Hanssen and A. V. Prokhorov, “Stochastic modeling of non-Lambertian surfaces for Monte Carlo computations in optical radiometry,” Proc. SPIE 7427, 742707 (2009).
[CrossRef]

L. M. Hanssen, S. N. Mekhontsev, J. Zeng, and A. V. Prokhorov, “Evaluation of blackbody cavity emissivity in the infrared using total integrated scatter measurements,” Int. J. Thermophys. 29, 352–369 (2008).
[CrossRef]

A. V. Prokhorov, L. M. Hanssen, and S. N. Mekhontsev, “Calculation of the radiation characteristics of blackbody radiation sources,” in Radiometric Temperature Measurements: I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), Vol. 42, pp. 181–240.

Hartmann, J.

J. Hartmann, “High-temperature measurement techniques for the application in photometry, radiometry and thermometry,” Phys. Rep. 469, 205–269 (2009).
[CrossRef]

J. Hartmann, J. Hollandt, B. Khlevnoy, S. Morozova, S. Ogarev, and F. Sakuma, “Blackbody and other calibration sources,” Radiometric Temperature Measurements. I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), pp. 241–295.

Hollandt, J.

J. Hartmann, J. Hollandt, B. Khlevnoy, S. Morozova, S. Ogarev, and F. Sakuma, “Blackbody and other calibration sources,” Radiometric Temperature Measurements. I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), pp. 241–295.

J. Hollandt, J. Seidel, R. Klein, G. Ulm, A. Migdall, and M. Ware, “Primary sources for use in radiometry,” Optical Radiometry, A. C. Parr, R. U. Datla, and J. L. Gardner, eds. (Academic, 2005), pp. 213–290.

Hottel, H. C.

A. F. Sarofim and H. C. Hottel, “Radiation exchange among non-Lambert surfaces,” J. Heat Transfer 88C, 37–44 (1964).

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (U.S. Department of Commerce, National Bureau of Standards, 1977).

Humphreys, C.

M. Pharr and C. Humphreys, Physically Based Rendering: from Theory to Implementation (Morgan Kaufmann, 2010).

Kelly, F. J.

F. J. Kelly, “On Kirchhoff’s law and its generalized application to absorption and emission by cavities,” J. Res. Natl. Bur. Stand. B 69, 165–171 (1965).

Kennedy, J.

M. Clerc and J. Kennedy, “The particle swarm—explosion, stability, and convergence in a multidimensional complex space,” IEEE Trans. Evol. Comput. 6, 58–73 (2002).
[CrossRef]

Khlevnoy, B.

J. Hartmann, J. Hollandt, B. Khlevnoy, S. Morozova, S. Ogarev, and F. Sakuma, “Blackbody and other calibration sources,” Radiometric Temperature Measurements. I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), pp. 241–295.

Klein, R.

J. Hollandt, J. Seidel, R. Klein, G. Ulm, A. Migdall, and M. Ware, “Primary sources for use in radiometry,” Optical Radiometry, A. C. Parr, R. U. Datla, and J. L. Gardner, eds. (Academic, 2005), pp. 213–290.

Knowles, T. R.

K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996).
[CrossRef]

Kurt, M.

M. Kurt and D. Edwards, “A survey of BRDF models for computer graphics,” Comput. Graphics43, 4 (2009).

Liang, S.

S. Liang, Quantitative Remote Sensing of Land Surfaces(Wiley, 2004).

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (U.S. Department of Commerce, National Bureau of Standards, 1977).

Liu, J. S.

J. S. Liu, Monte Carlo Strategies in Scientific Computing (Springer, 2001).

Lynn, W. F.

K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996).
[CrossRef]

Martonchik, J. V.

O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, “Parametric bidirectional reflectance factor models: evaluation, improvements and applications” (Space Applications Institute, Joint Research Centre, European Commission, ECSC-EC-EAEC, 1996).

Meier, S. R.

Mekhontsev, S. N.

L. M. Hanssen, S. N. Mekhontsev, J. Zeng, and A. V. Prokhorov, “Evaluation of blackbody cavity emissivity in the infrared using total integrated scatter measurements,” Int. J. Thermophys. 29, 352–369 (2008).
[CrossRef]

A. V. Prokhorov, L. M. Hanssen, and S. N. Mekhontsev, “Calculation of the radiation characteristics of blackbody radiation sources,” in Radiometric Temperature Measurements: I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), Vol. 42, pp. 181–240.

Migdall, A.

J. Hollandt, J. Seidel, R. Klein, G. Ulm, A. Migdall, and M. Ware, “Primary sources for use in radiometry,” Optical Radiometry, A. C. Parr, R. U. Datla, and J. L. Gardner, eds. (Academic, 2005), pp. 213–290.

Morozova, S.

J. Hartmann, J. Hollandt, B. Khlevnoy, S. Morozova, S. Ogarev, and F. Sakuma, “Blackbody and other calibration sources,” Radiometric Temperature Measurements. I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), pp. 241–295.

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (U.S. Department of Commerce, National Bureau of Standards, 1977).

Ogarev, S.

J. Hartmann, J. Hollandt, B. Khlevnoy, S. Morozova, S. Ogarev, and F. Sakuma, “Blackbody and other calibration sources,” Radiometric Temperature Measurements. I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), pp. 241–295.

Ono, A.

Persky, M. J.

M. J. Persky, “Review of black surfaces for space-borne infrared systems,” Rev. Sci. Instrum. 70, 2193–2217 (1999).
[CrossRef]

Pharr, M.

M. Pharr and C. Humphreys, Physically Based Rendering: from Theory to Implementation (Morgan Kaufmann, 2010).

Pinty, B.

O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, “Parametric bidirectional reflectance factor models: evaluation, improvements and applications” (Space Applications Institute, Joint Research Centre, European Commission, ECSC-EC-EAEC, 1996).

Prokhorov, A. V.

L. M. Hanssen and A. V. Prokhorov, “Stochastic modeling of non-Lambertian surfaces for Monte Carlo computations in optical radiometry,” Proc. SPIE 7427, 742707 (2009).
[CrossRef]

L. M. Hanssen, S. N. Mekhontsev, J. Zeng, and A. V. Prokhorov, “Evaluation of blackbody cavity emissivity in the infrared using total integrated scatter measurements,” Int. J. Thermophys. 29, 352–369 (2008).
[CrossRef]

A. V. Prokhorov, L. M. Hanssen, and S. N. Mekhontsev, “Calculation of the radiation characteristics of blackbody radiation sources,” in Radiometric Temperature Measurements: I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), Vol. 42, pp. 181–240.

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (U.S. Department of Commerce, National Bureau of Standards, 1977).

Sakuma, F.

J. Hartmann, J. Hollandt, B. Khlevnoy, S. Morozova, S. Ogarev, and F. Sakuma, “Blackbody and other calibration sources,” Radiometric Temperature Measurements. I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), pp. 241–295.

Sarofim, A. F.

A. F. Sarofim and H. C. Hottel, “Radiation exchange among non-Lambert surfaces,” J. Heat Transfer 88C, 37–44 (1964).

Schlick, C.

C. Schlick, “An inexpensive BRDF model for physically based rendering,” Comput. Graph. Forum 13, 233–246(1994).
[CrossRef]

Schmidt, C. W.

K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996).
[CrossRef]

Seaman, C. L.

K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996).
[CrossRef]

Seidel, J.

J. Hollandt, J. Seidel, R. Klein, G. Ulm, A. Migdall, and M. Ware, “Primary sources for use in radiometry,” Optical Radiometry, A. C. Parr, R. U. Datla, and J. L. Gardner, eds. (Academic, 2005), pp. 213–290.

Shemano, W. C.

K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996).
[CrossRef]

Shirley, P.

P. Shirley, Fundamentals of Computer Graphics (A K Peters, 2002).

Snail, K. A.

K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996).
[CrossRef]

Sparrow, E. M.

Torrance, K. E.

Ulm, G.

J. Hollandt, J. Seidel, R. Klein, G. Ulm, A. Migdall, and M. Ware, “Primary sources for use in radiometry,” Optical Radiometry, A. C. Parr, R. U. Datla, and J. L. Gardner, eds. (Academic, 2005), pp. 213–290.

van Dooren, P.

P. van Dooren and L. de Ridder, “An adaptive algorithm for numerical integration over an n-dimensional cube,” J. Comp. Appl. Math. 2, 207–217 (1976).
[CrossRef]

Verstraete, M. M.

O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, “Parametric bidirectional reflectance factor models: evaluation, improvements and applications” (Space Applications Institute, Joint Research Centre, European Commission, ECSC-EC-EAEC, 1996).

Ware, M.

J. Hollandt, J. Seidel, R. Klein, G. Ulm, A. Migdall, and M. Ware, “Primary sources for use in radiometry,” Optical Radiometry, A. C. Parr, R. U. Datla, and J. L. Gardner, eds. (Academic, 2005), pp. 213–290.

Zeng, J.

J. Zeng and L. Hanssen, “Development of an infrared optical scattering instrument from 1 μm to 5 μm,” Proc. SPIE 7453, 7453Q1 (2009).
[CrossRef]

L. M. Hanssen, S. N. Mekhontsev, J. Zeng, and A. V. Prokhorov, “Evaluation of blackbody cavity emissivity in the infrared using total integrated scatter measurements,” Int. J. Thermophys. 29, 352–369 (2008).
[CrossRef]

Appl. Opt. (2)

Comput. Graph. Forum (2)

D. Geisler-Moroder and A. Dür, “A new ward BRDF model with bounded albedo,” Comput. Graph. Forum 29, 1391–1398 (2010).
[CrossRef]

C. Schlick, “An inexpensive BRDF model for physically based rendering,” Comput. Graph. Forum 13, 233–246(1994).
[CrossRef]

IEEE Trans. Evol. Comput. (1)

M. Clerc and J. Kennedy, “The particle swarm—explosion, stability, and convergence in a multidimensional complex space,” IEEE Trans. Evol. Comput. 6, 58–73 (2002).
[CrossRef]

Int. J. Thermophys. (1)

L. M. Hanssen, S. N. Mekhontsev, J. Zeng, and A. V. Prokhorov, “Evaluation of blackbody cavity emissivity in the infrared using total integrated scatter measurements,” Int. J. Thermophys. 29, 352–369 (2008).
[CrossRef]

J. Comp. Appl. Math. (1)

P. van Dooren and L. de Ridder, “An adaptive algorithm for numerical integration over an n-dimensional cube,” J. Comp. Appl. Math. 2, 207–217 (1976).
[CrossRef]

J. Heat Transfer (1)

A. F. Sarofim and H. C. Hottel, “Radiation exchange among non-Lambert surfaces,” J. Heat Transfer 88C, 37–44 (1964).

J. Opt. Soc. Am. (2)

J. Res. Natl. Bur. Stand. B (1)

F. J. Kelly, “On Kirchhoff’s law and its generalized application to absorption and emission by cavities,” J. Res. Natl. Bur. Stand. B 69, 165–171 (1965).

Metrologia (1)

M. J. Ballico, “Modeling of the effective emissivity of a graphite tube black body,” Metrologia 32, 259–265 (1995).
[CrossRef]

Phys. Rep. (1)

J. Hartmann, “High-temperature measurement techniques for the application in photometry, radiometry and thermometry,” Phys. Rep. 469, 205–269 (2009).
[CrossRef]

Proc. SPIE (3)

K. A. Snail, D. P. Brown, J. P. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, and T. R. Knowles, “Optical characterization of black appliqués,” Proc. SPIE 2864, 465–474 (1996).
[CrossRef]

J. Zeng and L. Hanssen, “Development of an infrared optical scattering instrument from 1 μm to 5 μm,” Proc. SPIE 7453, 7453Q1 (2009).
[CrossRef]

L. M. Hanssen and A. V. Prokhorov, “Stochastic modeling of non-Lambertian surfaces for Monte Carlo computations in optical radiometry,” Proc. SPIE 7427, 742707 (2009).
[CrossRef]

Rev. Sci. Instrum. (1)

M. J. Persky, “Review of black surfaces for space-borne infrared systems,” Rev. Sci. Instrum. 70, 2193–2217 (1999).
[CrossRef]

Other (18)

R. E. Bedford, “Calculation of effective emissivities of cavity sources of thermal radiation,” Theory and Practice if Radiation Thermometry, D. P. DeWitt and G. D. Nutter, eds. (Wiley, 1988), pp. 653–772.

A. V. Prokhorov, L. M. Hanssen, and S. N. Mekhontsev, “Calculation of the radiation characteristics of blackbody radiation sources,” in Radiometric Temperature Measurements: I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), Vol. 42, pp. 181–240.

J. Hollandt, J. Seidel, R. Klein, G. Ulm, A. Migdall, and M. Ware, “Primary sources for use in radiometry,” Optical Radiometry, A. C. Parr, R. U. Datla, and J. L. Gardner, eds. (Academic, 2005), pp. 213–290.

J. Hartmann, J. Hollandt, B. Khlevnoy, S. Morozova, S. Ogarev, and F. Sakuma, “Blackbody and other calibration sources,” Radiometric Temperature Measurements. I. Fundamentals, Z. M. Zhang, B. K. Tsai, and G. Machin, eds. (Academic, 2010), pp. 241–295.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, and T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (U.S. Department of Commerce, National Bureau of Standards, 1977).

A. S. Glassner, Principles of Digital Image Synthesis (Morgan Kaufmann, 1995), Vol. II.

P. Shirley, Fundamentals of Computer Graphics (A K Peters, 2002).

P. Dutré, P. Bekaert, and K. Bala, Advanced Global Illumination (A K Peters, 2003).

M. Pharr and C. Humphreys, Physically Based Rendering: from Theory to Implementation (Morgan Kaufmann, 2010).

M. Kurt and D. Edwards, “A survey of BRDF models for computer graphics,” Comput. Graphics43, 4 (2009).

K. Schwenk, “A survey of shading models for real-time rendering,” http://www.karsten-schwenk.de/downloads/a_survey_of_shading_models.pdf (2011).

O. Engelsen, B. Pinty, M. M. Verstraete, and J. V. Martonchik, “Parametric bidirectional reflectance factor models: evaluation, improvements and applications” (Space Applications Institute, Joint Research Centre, European Commission, ECSC-EC-EAEC, 1996).

S. Liang, Quantitative Remote Sensing of Land Surfaces(Wiley, 2004).

D. L. B. Jupp, “A compendium of kernel and other (semi-)empirical BRDF models” (CSIRO Office of Space Science Applications—Earth Observation Centre, 2000), http://www.eoc.csiro.au/tasks/brdf/k_summ.pdf .

J. S. Liu, Monte Carlo Strategies in Scientific Computing (Springer, 2001).

M. Clerc, Particle Swarm Optimization (ISTE, 2006).

A. S. Glassner, “An overview of ray tracing,” in An Introduction to Ray TracingA. S. Glassner, ed. (Academic, 1993), pp. 1–32.

E. M. Sparrow and R. D. Cess, Radiation Heat Transfer(Hemisphere, 1978).

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Figures (12)

Fig. 1.
Fig. 1.

Schematic for the BRDF definition.

Fig. 2.
Fig. 2.

Dependences of the DHR on the incidence angle computed for the Geisler-Moroder and Dür BRDF model for R=1 and σ=0.0001, 0.005, 0.01, 0.05, 0.1, and 0.2 (see legend).

Fig. 3.
Fig. 3.

In-plane Cartesian plots for the Geisler-Moroder and Dür BRDF model with R=0.1, σ=0.1, and six incidence angles shown in legend. The negative values of viewing angles correspond to backscattering.

Fig. 4.
Fig. 4.

3D plots in spherical coordinates for the Geisler-Moroder and Dür BRDF at the incidence angle of 45°; R=0.1, σ=0.05, 0.1, and 0.2.

Fig. 5.
Fig. 5.

Results for the 3C BRDF model (lines) fitted to the Chemglaze Z302 black paint BRDFs measured at 10.6 µm (symbols).

Fig. 6.
Fig. 6.

Dependences of the DHR on the incidence angle for 3C BRDF model (and its components, see the legend) fitted to the measured at 10.6 µm BRDFs for the Chemglaze Z302 black paint.

Fig. 7.
Fig. 7.

Schematics of the cavities and viewing conditions used for numerical experiments.

Fig. 8.
Fig. 8.

Average normal effective emissivities versus viewing beam radius for the cylindro-conical cavity with quasi-specular walls; Rqs=0.2; σqs=0.002, 0.005, 0.007, and 0.01 (see the legend; PS denotes perfectly specular case with the reflectance of 0.2)

Fig. 9.
Fig. 9.

Dependences of the conical effective emissivities on the viewing cone angle computed for cylindrical cavity with glossy walls; Rg=0.1, σg=0.2, 0.3, 0.4, and 0.5 (see legend). Curve for diffuse cavity at ρ=0.1 is shown for comparison.

Fig. 10.
Fig. 10.

In-plane Cartesian plots of BRDFs for the 3C model used in numerical experiments. The negative values of viewing angles correspond to the backscattering.

Fig. 11.
Fig. 11.

Dependences of DHR on the incidence angle for the 3C BRDF model and its components (see legend) used in numerical experiments.

Fig. 12.
Fig. 12.

Dependences of the conical effective emissivities on the viewing cone angle A computed for cylindro-conical cavity for the 3C BRDF model with kd=0.2, kqs=0.3, kg=0.5, Rd=Rqs=Rg=0.2 σqs=0.003, σg=0.03 and for the USD model (in the legend: the first number bracketed denotes ρ, the second denotes D).

Equations (28)

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εe(λ,ξ,ω)=1ρe(λ,ξ,ω),
fr(λ,θi,ϕi,θv,ϕv)=dLλ,v(λ,θi,ϕi,θv,ϕv)dEλ,i(λ,θi,ϕi),
fr(θi,ϕi,θv,ϕv)=fr(θv,ϕv,θi,ϕi).
ρ(θi)=ϕv=02πθv=0π/2fr(θi,ϕi,θv,ϕv)sinθvcosθvdθvdϕv
fr=kdfr,d+kqsfr,qs+kgfr,g,
kd+kqs+kg=1.
fr,d=Rdπ,
fr(θi,θv,ϕ)=R(θh)πσexp[(tanθhσ)2]2[1+cosθicosθvsinθisinθvcosϕ](cosθicosθv)4,
R(θh)=Rqs+(1Rqs)(1cosθh)5,
ρ(θi)=ρd+ρqs(θi)+ρg(θi),
ρd=kdϕv=02πθv=0π/2fr,d(Rd,θi,ϕi,θv,ϕv)sinθvcosθvdθvdϕv=kdRd,
ρqs(θi)=kqsϕv=02πθv=0π/2fr,qs(Rqs,σqs,θi,ϕi,θv,ϕv)sinθvcosθvdθvdϕv,
ρg(θi)=kgϕv=02πθv=0π/2fr,g(Rg,σg,θi,ϕi,θv,ϕv)sinθvcosθvdθvdϕv.
0kd,Rd,Kqs,Rqs,kg,Rg1,
0.0001σqs0.001,
0.001<σg0.5.
F=k=1nij=1nv,k[fr,m(θi,k,θv,jk)fr(θi,k,θv,jk)]2,
F={0,iffr,m(θi,k,θv,jk)=fr(θi,k,θv,jk)=0maxk=1,,nimaxj=1,,nv,k{|fr,m(θi,k,θv,jk)fr(θi,k,θv,jk)|fr,m(θi,k,θv,jk)+fr(θi,k,θv,jk)}otherwise.
F=k=1nij=1nv,k|fr,m(θi,k,θv,jk)fr(θi,k,θv,jk)|.
sin2θv=uθ,
ϕv=2πuϕ,
{ωx=2ux1ωy=2uy1ωz=+1ωx2ωy2.
θh=tan1(σlnuθ)
ϕh=2πuϕ.
{hx=sinθhcosϕhhy=sinθhsinϕhhz=cosθh.
{ωvx=ωix2(ωi·h)hxωvy=ωiy2(ωi·h)hyωvz=ωiz2(ωi·h)hz.
w=2R(θh)1ωiz/ωvz
εe=11nk=1nj=1mkwjk,

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