Abstract

Optical roughness was introduced into the bidirectional reflectance distribution function (BRDF) model to simulate the reflectance characteristics of thermal radiation. The optical roughness BRDF model stemmed from the influence of surface roughness and wavelength on the ray reflectance calculation. This model was adopted to simulate real metal emissivity. The reverse Monte Carlo method was used to display the distribution of reflectance rays. The numerical simulations showed that the optical roughness BRDF model can calculate the wavelength effect on emissivity and simulate the real metal emissivity variance with incidence angles.

© 2014 Optical Society of America

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References

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  1. A. Prokhorov, “Effective emissivities of isothermal blackbody cavities calculated by the Monte Carlo method using the three-component bidirectional reflectance distribution function model,” Appl. Opt. 51, 2322–2332 (2012).
    [CrossRef]
  2. R. Montes and C. Ureña, “An overview of BRDF models,” (University of Granada).
  3. D. Geisler-Moroder and A. Dür, “A new Ward BRDF model with bounded albedo,” Comput. Graph. Forum 29, 1391–1398 (2010).
    [CrossRef]
  4. A. V. Prokhorov and L. M. Hanssen, “Algorithmic model of microfacet BRDF for Monte Carlo calculation of optical radiation transfer,” Proc. SPIE 5192, 141–157 (2003).
    [CrossRef]
  5. G. J. Ward, “Measuring and modeling anisotropic reflection,” SIGGRAPH Comput. Graph. 26, 265–272 (1992).
    [CrossRef]
  6. M. Matsumoto and T. Nishimura, “A 623 dimensionally equidistributed uniform pseudo random number generator,” ACM Trans. Model. Comput. Simul. 8, 3–30 (1998).
    [CrossRef]
  7. A. Dür, “An improved normalization for the Ward reflectance model,” J. Graph. GPU Game Tool. 11, 51–59 (2006).
    [CrossRef]
  8. L. Neumann, A. Neumann, and L. Szirmay-Kalos, “Compact metallic reflectance models,” Comput. Graph. Forum 18, 161–172 (1999).
    [CrossRef]
  9. C. Sun, Y. Yuan, X. Zhang, and Q. Wang, “Research on the model of spectral BRDF for space target surface material,” International Symposium on Optomechatronic Technologies (ISOT), 2010.
  10. A. Prokhorov and N. I. Prokhorova, “Application of the three-component bidirectional reflectance distribution function model to Monte Carlo calculation of spectral effective emissivities of nonisothermal blackbody cavities,” Appl. Opt. 51, 8003–8012 (2012).
    [CrossRef]
  11. M. F. Modest, Radiative Heat Transfer, 2nd ed. (Academic, 2003).

2012 (2)

2010 (1)

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

2006 (1)

A. Dür, “An improved normalization for the Ward reflectance model,” J. Graph. GPU Game Tool. 11, 51–59 (2006).
[CrossRef]

2003 (1)

A. V. Prokhorov and L. M. Hanssen, “Algorithmic model of microfacet BRDF for Monte Carlo calculation of optical radiation transfer,” Proc. SPIE 5192, 141–157 (2003).
[CrossRef]

1999 (1)

L. Neumann, A. Neumann, and L. Szirmay-Kalos, “Compact metallic reflectance models,” Comput. Graph. Forum 18, 161–172 (1999).
[CrossRef]

1998 (1)

M. Matsumoto and T. Nishimura, “A 623 dimensionally equidistributed uniform pseudo random number generator,” ACM Trans. Model. Comput. Simul. 8, 3–30 (1998).
[CrossRef]

1992 (1)

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

A. Dür, “An improved normalization for the Ward reflectance model,” J. Graph. GPU Game Tool. 11, 51–59 (2006).
[CrossRef]

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]

Hanssen, L. M.

A. V. Prokhorov and L. M. Hanssen, “Algorithmic model of microfacet BRDF for Monte Carlo calculation of optical radiation transfer,” Proc. SPIE 5192, 141–157 (2003).
[CrossRef]

Matsumoto, M.

M. Matsumoto and T. Nishimura, “A 623 dimensionally equidistributed uniform pseudo random number generator,” ACM Trans. Model. Comput. Simul. 8, 3–30 (1998).
[CrossRef]

Modest, M. F.

M. F. Modest, Radiative Heat Transfer, 2nd ed. (Academic, 2003).

Montes, R.

R. Montes and C. Ureña, “An overview of BRDF models,” (University of Granada).

Neumann, A.

L. Neumann, A. Neumann, and L. Szirmay-Kalos, “Compact metallic reflectance models,” Comput. Graph. Forum 18, 161–172 (1999).
[CrossRef]

Neumann, L.

L. Neumann, A. Neumann, and L. Szirmay-Kalos, “Compact metallic reflectance models,” Comput. Graph. Forum 18, 161–172 (1999).
[CrossRef]

Nishimura, T.

M. Matsumoto and T. Nishimura, “A 623 dimensionally equidistributed uniform pseudo random number generator,” ACM Trans. Model. Comput. Simul. 8, 3–30 (1998).
[CrossRef]

Prokhorov, A.

Prokhorov, A. V.

A. V. Prokhorov and L. M. Hanssen, “Algorithmic model of microfacet BRDF for Monte Carlo calculation of optical radiation transfer,” Proc. SPIE 5192, 141–157 (2003).
[CrossRef]

Prokhorova, N. I.

Sun, C.

C. Sun, Y. Yuan, X. Zhang, and Q. Wang, “Research on the model of spectral BRDF for space target surface material,” International Symposium on Optomechatronic Technologies (ISOT), 2010.

Szirmay-Kalos, L.

L. Neumann, A. Neumann, and L. Szirmay-Kalos, “Compact metallic reflectance models,” Comput. Graph. Forum 18, 161–172 (1999).
[CrossRef]

Ureña, C.

R. Montes and C. Ureña, “An overview of BRDF models,” (University of Granada).

Wang, Q.

C. Sun, Y. Yuan, X. Zhang, and Q. Wang, “Research on the model of spectral BRDF for space target surface material,” International Symposium on Optomechatronic Technologies (ISOT), 2010.

Ward, G. J.

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

Yuan, Y.

C. Sun, Y. Yuan, X. Zhang, and Q. Wang, “Research on the model of spectral BRDF for space target surface material,” International Symposium on Optomechatronic Technologies (ISOT), 2010.

Zhang, X.

C. Sun, Y. Yuan, X. Zhang, and Q. Wang, “Research on the model of spectral BRDF for space target surface material,” International Symposium on Optomechatronic Technologies (ISOT), 2010.

ACM Trans. Model. Comput. Simul. (1)

M. Matsumoto and T. Nishimura, “A 623 dimensionally equidistributed uniform pseudo random number generator,” ACM Trans. Model. Comput. Simul. 8, 3–30 (1998).
[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]

L. Neumann, A. Neumann, and L. Szirmay-Kalos, “Compact metallic reflectance models,” Comput. Graph. Forum 18, 161–172 (1999).
[CrossRef]

J. Graph. GPU Game Tool. (1)

A. Dür, “An improved normalization for the Ward reflectance model,” J. Graph. GPU Game Tool. 11, 51–59 (2006).
[CrossRef]

Proc. SPIE (1)

A. V. Prokhorov and L. M. Hanssen, “Algorithmic model of microfacet BRDF for Monte Carlo calculation of optical radiation transfer,” Proc. SPIE 5192, 141–157 (2003).
[CrossRef]

SIGGRAPH Comput. Graph. (1)

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

Other (3)

R. Montes and C. Ureña, “An overview of BRDF models,” (University of Granada).

C. Sun, Y. Yuan, X. Zhang, and Q. Wang, “Research on the model of spectral BRDF for space target surface material,” International Symposium on Optomechatronic Technologies (ISOT), 2010.

M. F. Modest, Radiative Heat Transfer, 2nd ed. (Academic, 2003).

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Figures (9)

Fig. 1.
Fig. 1.

Schematic of the BRDF definition.

Fig. 2.
Fig. 2.

In-plane Cartesian plots for the BRDF model with optical roughness 0.1, 0.2, 0.3, and five incidence angles shown in the legend.

Fig. 3.
Fig. 3.

Stability comparison of four integration forms.

Fig. 4.
Fig. 4.

DHR functions of the optical roughness BRDF for ρd=0, ρs=1.

Fig. 5.
Fig. 5.

Reflectance ray distribution of the BRDF model determined by the RMC method for optical roughness 0.1, 0.2, and 0.3 at a 45° incidence angle with ρd=0, ρs=1.

Fig. 6.
Fig. 6.

Reflectance ray distribution of the BRDF model determined by the RMC method for optical roughness 0.1, 0.2, and 0.3 at a 45° incidence angle with ρd=0.5, ρs=0.5.

Fig. 7.
Fig. 7.

Direction spectral emissivity of platinum at wavelength λ=2

Fig. 8.
Fig. 8.

Hemisphere spectral reflectivity at room temperature for aluminum, copper, and silver.

Fig. 9.
Fig. 9.

Effect of surface roughness on bidirectional reflectivity in the specular direction for ground nickel specimens.

Equations (18)

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xk+nxk+m(xku|xk+1l)A,(k=0,1,),
φ=2πRφ.
θ=sin1(Rθsinθmax),
fr(λ,θi,φi,θv,φv)=dLλ,v(λ,θi,φi,θv,φv)dEλ,i(λ,θi,φi).
fward(θi,φi,θv,φv)=ρdπ+ρscosθicosθvetan2(θh)/α24πα2,
fWD(θi,φi,θv,φv)=ρdπ+ρsπαv2etan2(θh)/α24cosθicosθ.
fGM(θi,φi,θv,φv)=ρsπαβ·exp(tan2θh(cos2φα2+sin2φβ2))·2(1+cosθicosθv+sinθisinθvcos(φvφi))(cosθi+cosθv)4
fGM(θi,θv,φv)=R(θh)πσ·exp((tanθhσ2)2)·2(1+cosθicosθvsinθisinθvcosφ)(cosθicosθv)4
fGM(θi,φi,θv,φv)=fGM(θv,φv,θi,φi),
φv=02πθv=0π/2fGM(θi,φi,θv,φv)sinθvcosθvdθvdφv1.
fGM(θi,φi,θv,φv)=ρsπα2·exp((tan2θhα2))·2(1+cosθicosθv+sinθisinθvcos(φvφi))(cosθi+cosθv)4.
σopt=σ0/λ.
fopt(λ,θi,φi,θv,φv)=ρsπ(σ0/λ)2·exp((tan2θh(σ0/λ)2))·2(1+cosθicosθv+sinθisinθvcos(φvφi))(cosθi+cosθv)4.
fopt(λ,θi,φi,θv,φv)=ρdπ+ρsπ(σ0/λ)2·exp((tan2θh(σ0/λ)2))·2(1+cosθicosθv+sinθisinθvcos(φvφi))(cosθi+cosθv)4.
ρ(θi)=φv=02πθv=0π/2fGM(θi,φi,θv,φv)sinθvcosθvdθvdφv.
ελ(λ,θ,φ,T)=1ρλ(λ,θ,φ,T).
ελ(λ,θ,φ)=1ρλ(λ,θ,φ).
ρλ(λ,θi,φi)=φv=02πθv=0π/2fopt(λ,θi,φi,θv,φv)sinθvcosθvdθvdφv.

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