Abstract

Comprehensive measurements of the bidirectional reflectance factor of BaSO4 paint vs both viewing and illumination angles are presented as contour plots. Contours resulting from several surfacing techniques are compared to demonstrate that a machined surface on a thick BaSO4 deposit gives the most reproducible diffuse reflectivity. It is also shown that a spray deposit of BaSO4 gives a much less diffuse reflectivity. We also show that the contours of bidirectional reflectance of either machined BaSO4 or smoked MgO may be described by a three-parameter fit, which automatically obeys the Helmholtz reciprocity theorem and is simply related to the efficiency of total reflectance.

© 1980 Optical Society of America

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References

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  1. D. C. Carmer, M. E. Bair, Appl. Opt. 8, 1597 (1969).
    [CrossRef] [PubMed]
  2. D. K. Edwards, “Measurement of Thermal Radiation Characteristics,” in Institute of Environmental Sciences. Proceedings, 1963, Los Angeles, p. 417.
  3. D. K. Edwards, J. T. Bevans, “Thermal Radiation Characteristics of Imperfectly Diffuse Materials I: Emission, Absorption, Reflection, and Transmission, Space Technology Laboratories report 9990-6343-RU-000.
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    [CrossRef]
  5. H. J. McNicholas, J. Res. Natl. Bur. Stand. 1, 29 (1928).
    [CrossRef]
  6. W. M. Brandenberg, J. T. Neu, J. Opt. Soc. Am. 56, 97 (1966).
    [CrossRef]
  7. P. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. monograph 160 (Oct.1977).
  8. H. von Hemholtz, Physiological Optics (1909), translated by J. P. C. Southall (Optical Society of America, Washington, D.C., 1924), Vol. 1, p. 231.
  9. W. Budde, J. Opt. Soc. Am. 50, 217 (1960).
    [CrossRef]
  10. F. Grum, G. W. Luckey, Appl. Opt. 7, 2289 (1968).
    [CrossRef] [PubMed]
  11. D. Blet-Talbot, Rev. Opt. 34, 579 (1955).
  12. V. G. W. Harrison, Proc. Phys. Soc. London 58, 408 (1946).
    [CrossRef]
  13. H. H. Blau, E. L. Gray, G. M. B. Bourioius, Appl. Opt. 6, 1899 (1967).
    [CrossRef] [PubMed]
  14. G. Kortum, Reflectance Spectroscopy: Principles, Methods, Applications (Springer, New York, 1969), p. 38.
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    [CrossRef]
  16. J. R. Schutt, J. F. Arens, C. M. Shal, E. Stromberg, Appl. Opt. 13, 2218 (1974).
    [CrossRef] [PubMed]
  17. F. Grum, L. F. Costa, Appl. Opt. 13, 2228 (1974).
    [CrossRef] [PubMed]
  18. Kodak publication JJ-32.
  19. S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), p. 124.
  20. E. Young, R. B. Bennett, T. L. Houk, Eos 57, 311 (1976).

1976 (1)

E. Young, R. B. Bennett, T. L. Houk, Eos 57, 311 (1976).

1974 (2)

1969 (1)

1968 (1)

1967 (1)

1966 (2)

1965 (1)

1960 (1)

1955 (1)

D. Blet-Talbot, Rev. Opt. 34, 579 (1955).

1946 (1)

V. G. W. Harrison, Proc. Phys. Soc. London 58, 408 (1946).
[CrossRef]

1928 (1)

H. J. McNicholas, J. Res. Natl. Bur. Stand. 1, 29 (1928).
[CrossRef]

Arens, J. F.

Bair, M. E.

Bennett, R. B.

E. Young, R. B. Bennett, T. L. Houk, Eos 57, 311 (1976).

Bevans, J. T.

D. K. Edwards, J. T. Bevans, “Thermal Radiation Characteristics of Imperfectly Diffuse Materials I: Emission, Absorption, Reflection, and Transmission, Space Technology Laboratories report 9990-6343-RU-000.

Blau, H. H.

Blet-Talbot, D.

D. Blet-Talbot, Rev. Opt. 34, 579 (1955).

Bourioius, G. M. B.

Brandenberg, W. M.

Budde, W.

Caldwell, B. P.

Carmer, D. C.

Chandrasekhar, S.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), p. 124.

Costa, L. F.

Edwards, D. K.

D. K. Edwards, “Measurement of Thermal Radiation Characteristics,” in Institute of Environmental Sciences. Proceedings, 1963, Los Angeles, p. 417.

D. K. Edwards, J. T. Bevans, “Thermal Radiation Characteristics of Imperfectly Diffuse Materials I: Emission, Absorption, Reflection, and Transmission, Space Technology Laboratories report 9990-6343-RU-000.

Ginsberg, I. W.

P. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. monograph 160 (Oct.1977).

Goebel, D. G.

Gray, E. L.

Grum, F.

Hammond, H. K.

Harrison, V. G. W.

V. G. W. Harrison, Proc. Phys. Soc. London 58, 408 (1946).
[CrossRef]

Houk, T. L.

E. Young, R. B. Bennett, T. L. Houk, Eos 57, 311 (1976).

Hsia, J. J.

P. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. monograph 160 (Oct.1977).

Kortum, G.

G. Kortum, Reflectance Spectroscopy: Principles, Methods, Applications (Springer, New York, 1969), p. 38.

Limperis, T.

P. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. monograph 160 (Oct.1977).

Luckey, G. W.

McNicholas, H. J.

H. J. McNicholas, J. Res. Natl. Bur. Stand. 1, 29 (1928).
[CrossRef]

Neu, J. T.

Nicodemus, F. E.

Nicodemus, P. E.

P. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. monograph 160 (Oct.1977).

Richmond, J. C.

P. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. monograph 160 (Oct.1977).

Schutt, J. R.

Shal, C. M.

Stromberg, E.

von Hemholtz, H.

H. von Hemholtz, Physiological Optics (1909), translated by J. P. C. Southall (Optical Society of America, Washington, D.C., 1924), Vol. 1, p. 231.

Young, E.

E. Young, R. B. Bennett, T. L. Houk, Eos 57, 311 (1976).

Appl. Opt. (6)

Eos (1)

E. Young, R. B. Bennett, T. L. Houk, Eos 57, 311 (1976).

J. Opt. Soc. Am. (3)

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

H. J. McNicholas, J. Res. Natl. Bur. Stand. 1, 29 (1928).
[CrossRef]

Proc. Phys. Soc. London (1)

V. G. W. Harrison, Proc. Phys. Soc. London 58, 408 (1946).
[CrossRef]

Rev. Opt. (1)

D. Blet-Talbot, Rev. Opt. 34, 579 (1955).

Other (7)

P. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. monograph 160 (Oct.1977).

H. von Hemholtz, Physiological Optics (1909), translated by J. P. C. Southall (Optical Society of America, Washington, D.C., 1924), Vol. 1, p. 231.

D. K. Edwards, “Measurement of Thermal Radiation Characteristics,” in Institute of Environmental Sciences. Proceedings, 1963, Los Angeles, p. 417.

D. K. Edwards, J. T. Bevans, “Thermal Radiation Characteristics of Imperfectly Diffuse Materials I: Emission, Absorption, Reflection, and Transmission, Space Technology Laboratories report 9990-6343-RU-000.

G. Kortum, Reflectance Spectroscopy: Principles, Methods, Applications (Springer, New York, 1969), p. 38.

Kodak publication JJ-32.

S. Chandrasekhar, Radiative Transfer (Dover, New York, 1960), p. 124.

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Figures (7)

Fig. 1
Fig. 1

Bidirectional reflectance factor and related quantities: ′, Incident and scattering angles are unembellished and primed, respectively; θ,θ′, angle from the normal; ϕ,ϕ′, azimuthal angles; and dΩ,dΩ′, element of solid angle.

Fig. 2
Fig. 2

Goniophotometer. Both the viewing and the illumination beams are collimated in our goniophotometer to provide accurate angular response and to detect any specular component. Viewed portion of the sample always completely includes the smaller illuminated portion at the angles we recorded, thus eliminating clumsy compound geometrical factors. Normal operation sets the angles of the viewing and illumination telescopes relative to each other and then tilts the sample over a wide range of angles about an axis perpendicular to the plane including the two telescopes.

Fig. 3
Fig. 3

Bidirectional reflectance factor of MgO. Contours proportional to bidirectional reflectance factor are plotted with respect to the two angles θ (incident) and θ′ (viewing). Bidirectional reflectance factor at θ = θ′ = 0 is taken as 1.0 in these plots.

Fig. 4
Fig. 4

Bidirectional reflectance factor of poured machined BaSO4 (sample A). Axes are the same as in Fig. 6. Results are also similar to those for smoked MgO except there is notably less reflectance near the specular axis at grazing angles and slightly more scattering into near perpendicular viewing angles from grazing incidence.

Fig. 5
Fig. 5

Bidirectional reflectance factor of poured machined BaSO4 (sample B). These results are highly similar to those of Fig. 4, demonstrating the repeatability of our process. Measured reflectances of sample B are in general within 2% of those of sample A at the same illumination and viewing angles.

Fig. 6
Fig. 6

Sprayed BaSO4 paint. Greatly enhanced backscatter of sprayed BaSO4 is shown by the maximal contours along the θ′ = θ axis. Conversely, the minimal values along the θ′ = −θ axis show that specular reflection is reduced except at very grazing angles.

Fig. 7
Fig. 7

Poured machined BaSO4 topped by a sprayed layer. At moderate angles of incidence and viewing, this sample exhibits the increased backscatter and reduced specular component of the final sprayed layer. At grazing angles, however, the increased specular reflection of poured machined BaSO4 appears.

Tables (1)

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Table I Parameters a, b, and c Fitted to MgO for the Equation R = a + b(cosθc)(cosθ′ − c)

Equations (8)

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Φ = L ( θ ϕ ) cos θ d A d Ω ,
Φ = L ( θ ϕ ) cos θ d A d Ω .
R ( θ ϕ ; θ ϕ ) = π L ( θ ϕ ) L ( θ ϕ ) cos θ d Ω .
L ( θ ϕ ) = 1 π L ( θ ϕ ) R ( θ ϕ ; θ ϕ ) cos θ d Ω .
R ( θ ϕ ; θ ϕ ) = R ( θ ϕ ; θ ϕ ) .
Φ ( θ ϕ ) = 1 π Φ ( θ ϕ ) R ( θ ϕ ; θ ϕ ) cos θ d Ω ,
R ( θ ; θ ) = a + b ( cos θ c ) ( cos θ c ) .
R ( θ / θ ) = 2 a b 2 / ( a 2 sin 2 θ + b 2 cos 2 θ ) ,

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