Abstract

Gold-plated sandpaper was investigated for use as a Lambertian standard reference reflector for the IR spectrum. Various grit sizes from 3 to 400 μm and material types (i.e., silicon carbide and aluminum oxide) were studied. The different gold-plated sandpaper grit sizes were measured in the same way using three laser wavelengths (0.6328, 3.39, and 10.6 μm) at five angles of incidence of the source (0,10, 20, 30, and 60°). All the scattering measurements were performed in the plane of incidence. The best choices of sandpaper grit sizes were 9-μm Al2O3 for 0.6328- and 3.39-μm radiation and 600 grit by Armak Co. for 10.6-μm radiation. These choices were compared with other commonly used reflectors such as magnesium oxide, halon, sintered bronze, and flowers of sulfur. An attempt was made to correlate surface roughness (size of grit) to the degree of approximation to a good Lambertian reflector, but it was found that grit size is not as important as the filling factor, or density of particles, over a given area. It was found that fairly good approximations to Lambertian behavior result when the angle of incidence is small but not when the angle of incidence is as large as 60°.

© 1981 Optical Society of America

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References

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  1. F. Grum, R. J. Becherer, Optical Radiation Measurements, Vol. 1, Radiometry (Academic, New York, 1979).
  2. M. Kronstein, R. J. Kraushaar, R. E. Deacle, J. Opt. Soc. Am. 53, 458 (1963).
  3. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical Considerations and Nomenclature for Reflectance,” Natl. Bur. Stand. U.S. Monogr.160 (Oct.1977).
  4. F. O. Bartell, E. L. Dereniak, W. L. Wolfe, “The theory and measurement of BRDF and BTDF,” submitted to Appl. Opt. Sept.1981.
  5. D. A. Thomas, “Light Scattering from Reflecting Optical Surfaces,” Ph.D. Dissertation, U. Arizona, Tucson (1980).

1977 (1)

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

1963 (1)

Bartell, F. O.

F. O. Bartell, E. L. Dereniak, W. L. Wolfe, “The theory and measurement of BRDF and BTDF,” submitted to Appl. Opt. Sept.1981.

Becherer, R. J.

F. Grum, R. J. Becherer, Optical Radiation Measurements, Vol. 1, Radiometry (Academic, New York, 1979).

Deacle, R. E.

Dereniak, E. L.

F. O. Bartell, E. L. Dereniak, W. L. Wolfe, “The theory and measurement of BRDF and BTDF,” submitted to Appl. Opt. Sept.1981.

Ginsberg, I. W.

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

Grum, F.

F. Grum, R. J. Becherer, Optical Radiation Measurements, Vol. 1, Radiometry (Academic, New York, 1979).

Hsia, J. J.

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

Kraushaar, R. J.

Kronstein, M.

Limperis, T.

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

Nicodemus, F. E.

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

Richmond, J. C.

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

Thomas, D. A.

D. A. Thomas, “Light Scattering from Reflecting Optical Surfaces,” Ph.D. Dissertation, U. Arizona, Tucson (1980).

Wolfe, W. L.

F. O. Bartell, E. L. Dereniak, W. L. Wolfe, “The theory and measurement of BRDF and BTDF,” submitted to Appl. Opt. Sept.1981.

J. Opt. Soc. Am. (1)

Natl. Bur. Stand. U.S. Monogr. (1)

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

Other (3)

F. O. Bartell, E. L. Dereniak, W. L. Wolfe, “The theory and measurement of BRDF and BTDF,” submitted to Appl. Opt. Sept.1981.

D. A. Thomas, “Light Scattering from Reflecting Optical Surfaces,” Ph.D. Dissertation, U. Arizona, Tucson (1980).

F. Grum, R. J. Becherer, Optical Radiation Measurements, Vol. 1, Radiometry (Academic, New York, 1979).

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Figures (14)

Fig. 1
Fig. 1

Geometry of incident and reflected beams.

Fig. 2
Fig. 2

BRDF instrument.

Fig. 3
Fig. 3

Layout of scattering machine.

Fig. 4
Fig. 4

Typical results of BRDF measurements for various conditions at 3.39 μm for gold-plated sandpapers.

Fig. 5
Fig. 5

Gold-plated sandpaper for various angles of incidence: (a) 9-μm Al2O3 at 0.6328 μm; (b) 9-μm Al2O3 at 3.39 μm; (c) 600-grit Armak at 10.6 μm. These sandpapers were the most nearly Lambertian at each of the three wavelengths.

Fig. 6
Fig. 6

Dependence of BRDF on grit particle size at 10.6 μm. Angle of incidence is 10°.

Fig. 7
Fig. 7

BRDF of two gold-plated sandpapers: (a) 600-grit 3M; (b) 600-grit Armak. 3M sandpaper has the larger grit spacing. Angle of incidence is 10°.

Fig. 8
Fig. 8

BRDF of two gold-plated sandpapers: (a) 9-μm SiC; (b) 9-μm Al2O3. SiC sandpaper has the larger grit spacing. Angle of incidence is 10°.

Fig. 9
Fig. 9

BRDF of gold-plated sandpaper (60 μm) with wide grit spacing. Angle of incidence is 10°.

Fig. 10
Fig. 10

Comparison between gold-plated sandpaper and some other common reflectance standards at 0.6328 μm. Angle of incidence is (a) 0, (b) 30, (c) 60°. Data for sintered bronze are plotted artificially high to assist in comparison of shapes of curves.

Fig. 11
Fig. 11

Comparison between gold-plated sandpaper and sulfur at 3.39 μm. Angle of incidence is (a) 0, (b) 30, (c) 60°. Sulfur data are plotted artificially high to assist in comparison of shapes of curves.

Fig. 12
Fig. 12

Comparison between gold-plated sandpaper and sulfur at 10.6 μm. Angles of incidence are (a) 0, (b) 30, (c) 60°. Sulfur data are plotted artificially high to assist in comparison of shapes of curves.

Fig. 13
Fig. 13

Repeatability of measurements of sandpaper at three time intervals: (a) 9-μm Al2O3 at 0.6328 μm with 3.5-month interval; (b) 600-grit Armak at 3.39 μm with 1-month interval; (c) 600-grit Armak at 10.6 μm with 2.5-month interval. Angle of incidence is 10°.

Fig. 14
Fig. 14

Comparison between uncoated and gold-coated sandpaper at 10.6 μm and 10° angle of incidence: (a) 180-grit 3M; (b) 600-grit 3M. Uncoated sandpaper data are plotted artificially high to assist in comparison of shapes of curves.

Tables (1)

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Table I Types and Grades of Sandpaper

Equations (6)

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f r ( θ i , ϕ i ; θ r , ϕ r ) = d L r ( θ i , ϕ i ; θ r , ϕ r ; E i ) d E i ( θ i , ϕ i ) ,
BRDF s BRDF ref = V s V ref ,
BRDF s ( θ ) = BRDF ref ( θ * ) V s ( θ ) V ref ( θ * ) cos θ * cos θ ,
BRDF ref ( θ * ) = ρ / π ;
V ref ( θ * ) = V s ( θ specular ) ;
BRDF s ( θ ) = ρ π V s ( θ ) V s ( θ specular ) cos θ incidence cos θ .

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