Abstract

I present angle-dependent directional hemispherical reflectance (DHR) and bidirectional reflectance distribution function (BRDF) measurements of three highly absorbing black appliqués in the 250–2000-nm broadband spectral region. DHR measurements of Energy Science Laboratories, Inc. (ESLI), Rippey, and Rodel appliqués were obtained at incidence angles of 8°, 50°, and 70°. For an incidence angle of 8°, the ESLI appliqué exhibited the lowest DHR value of 0.3% across this entire spectral region, whereas the Rippey and Rodel had DHR values of 1.5% and 2.0–2.5%, respectively. In-plane BRDF measurements of the appliqués, obtained at a wavelength of 633 nm and incidence angle of 10°, yielded Lambertian profiles from -80° to +80° with values ranging from ∼10-3 sr-1 for the ESLI, 6 × 10-3 sr-1 for the Rippey, and 9 × 10-3 sr-1 for the Rodel appliqué. In addition, rms surface roughness and correlation lengths for the Rippey and the Rodel appliqués were determined. The in-plane BRDF data were used to estimate the reflected specular component from Beckmann’s scattering theory, and excellent agreement was found.

© 2001 Optical Society of America

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References

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  1. S. R. Meier, “Characterization of highly absorbing black appliqué in the infrared,” Appl. Opt. 40, 2788–2795 (2001).
    [CrossRef]
  2. S. R. Meier, M. L. Korwin, C. I. Merzbacher, “Carbon aerogel: a new nonreflective material for the infrared,” Appl. Opt. 39, 3940–3944 (2000).
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  3. K. A. Snail, D. P. Brown, J. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, T. R. Knowles, “Optical characterization of black appliqués,” in Optical System Contamination V and Stray Light and System Optimization, A. P. M. Glassford, R. P. Breault, S. M. Pompea, eds., Proc. SPIE2864, 465–474 (1996).
    [CrossRef]
  4. H. Kaplan, “Black coatings are critical in optical design,” Photonics Spectra 31, 48–50 (1997).
  5. Direct inquiries to Tim Knowles, Energy Science Laboratories, 6888 Nancy Ridge Road, San Diego, Calif. 92121.
  6. Direct inquiries to Chris Bhaten, Rippey Corporation, 5000 Hillsdale Circle, El Dorado Hills, Calif. 95762.
  7. Direct inquiries to Tara MacDonald, Rodel, 9495 E. San Salvador Drive, Scottsdale, Ariz. 85258.
  8. The mention of manufacturers and model names is intended solely for the purpose of technical information to the reader and should not be construed as an endorsement of the named manufacturer or product.
  9. Labsphere, Inc.A Guide to Integrating Sphere Photometry and Radiometry (North Sutton, N.H., 1994), pp. 5–6.
  10. D. K. Edwards, J. T. Gier, K. E. Nelson, R. D. Roddick, “Integrating sphere for imperfectly diffuse samples,” J. Opt. Soc. Am. 51, 1279–1288 (1961).
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  11. J. C. Stover, ed., Optical Scattering: Measurement and Analysis, Vol. PM24 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1995), p. 21.
  12. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, 3–9 (1977).
  13. P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), Part I, p. 86.

2001

2000

1997

H. Kaplan, “Black coatings are critical in optical design,” Photonics Spectra 31, 48–50 (1997).

1977

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, 3–9 (1977).

1961

Beckmann, P.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), Part I, p. 86.

Brown, D. P.

K. A. Snail, D. P. Brown, J. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, T. R. Knowles, “Optical characterization of black appliqués,” in Optical System Contamination V and Stray Light and System Optimization, A. P. M. Glassford, R. P. Breault, S. M. Pompea, eds., Proc. SPIE2864, 465–474 (1996).
[CrossRef]

Costantino, J.

K. A. Snail, D. P. Brown, J. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, T. R. Knowles, “Optical characterization of black appliqués,” in Optical System Contamination V and Stray Light and System Optimization, A. P. M. Glassford, R. P. Breault, S. M. Pompea, eds., Proc. SPIE2864, 465–474 (1996).
[CrossRef]

Edwards, D. K.

Gier, J. T.

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, 3–9 (1977).

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, 3–9 (1977).

Kaplan, H.

H. Kaplan, “Black coatings are critical in optical design,” Photonics Spectra 31, 48–50 (1997).

Knowles, T. R.

K. A. Snail, D. P. Brown, J. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, T. R. Knowles, “Optical characterization of black appliqués,” in Optical System Contamination V and Stray Light and System Optimization, A. P. M. Glassford, R. P. Breault, S. M. Pompea, eds., Proc. SPIE2864, 465–474 (1996).
[CrossRef]

Korwin, M. L.

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, 3–9 (1977).

Lynn, W. F.

K. A. Snail, D. P. Brown, J. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, T. R. Knowles, “Optical characterization of black appliqués,” in Optical System Contamination V and Stray Light and System Optimization, A. P. M. Glassford, R. P. Breault, S. M. Pompea, eds., Proc. SPIE2864, 465–474 (1996).
[CrossRef]

Meier, S. R.

Merzbacher, C. I.

Nelson, K. E.

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, 3–9 (1977).

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, 3–9 (1977).

Roddick, R. D.

Schmidt, C. W.

K. A. Snail, D. P. Brown, J. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, T. R. Knowles, “Optical characterization of black appliqués,” in Optical System Contamination V and Stray Light and System Optimization, A. P. M. Glassford, R. P. Breault, S. M. Pompea, eds., Proc. SPIE2864, 465–474 (1996).
[CrossRef]

Seaman, C. L.

K. A. Snail, D. P. Brown, J. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, T. R. Knowles, “Optical characterization of black appliqués,” in Optical System Contamination V and Stray Light and System Optimization, A. P. M. Glassford, R. P. Breault, S. M. Pompea, eds., Proc. SPIE2864, 465–474 (1996).
[CrossRef]

Shemano, W. C.

K. A. Snail, D. P. Brown, J. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, T. R. Knowles, “Optical characterization of black appliqués,” in Optical System Contamination V and Stray Light and System Optimization, A. P. M. Glassford, R. P. Breault, S. M. Pompea, eds., Proc. SPIE2864, 465–474 (1996).
[CrossRef]

Snail, K. A.

K. A. Snail, D. P. Brown, J. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, T. R. Knowles, “Optical characterization of black appliqués,” in Optical System Contamination V and Stray Light and System Optimization, A. P. M. Glassford, R. P. Breault, S. M. Pompea, eds., Proc. SPIE2864, 465–474 (1996).
[CrossRef]

Spizzichino, A.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), Part I, p. 86.

Appl. Opt.

J. Opt. Soc. Am.

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

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometric considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160, 3–9 (1977).

Photonics Spectra

H. Kaplan, “Black coatings are critical in optical design,” Photonics Spectra 31, 48–50 (1997).

Other

Direct inquiries to Tim Knowles, Energy Science Laboratories, 6888 Nancy Ridge Road, San Diego, Calif. 92121.

Direct inquiries to Chris Bhaten, Rippey Corporation, 5000 Hillsdale Circle, El Dorado Hills, Calif. 95762.

Direct inquiries to Tara MacDonald, Rodel, 9495 E. San Salvador Drive, Scottsdale, Ariz. 85258.

The mention of manufacturers and model names is intended solely for the purpose of technical information to the reader and should not be construed as an endorsement of the named manufacturer or product.

Labsphere, Inc.A Guide to Integrating Sphere Photometry and Radiometry (North Sutton, N.H., 1994), pp. 5–6.

J. C. Stover, ed., Optical Scattering: Measurement and Analysis, Vol. PM24 of the SPIE Press Monographs (SPIE, Bellingham, Wash., 1995), p. 21.

P. Beckmann, A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963), Part I, p. 86.

K. A. Snail, D. P. Brown, J. Costantino, W. C. Shemano, C. W. Schmidt, W. F. Lynn, C. L. Seaman, T. R. Knowles, “Optical characterization of black appliqués,” in Optical System Contamination V and Stray Light and System Optimization, A. P. M. Glassford, R. P. Breault, S. M. Pompea, eds., Proc. SPIE2864, 465–474 (1996).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

DHR measurements of the ESLI, Rippey, and Rodel appliqués in the 250–2000-nm wavelength region obtained at incidence angles of (a) 8° off normal, (b) 50° off normal, (c) 70° off normal.

Fig. 2
Fig. 2

BRDF measurements of the ESLI, Rippey, and Rodel appliqués obtained at an incidence angle of -10° and a wavelength of 633 nm.

Equations (6)

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

DHRsamθi, ϕi; 2π=Isam×ρsamθi, ϕi; 2π×τsamsphθi, ϕi/Iref×τrefsphθi, ϕiIsam×τsamsphθi, ϕi/Iref×τrefsphθi, ϕi,
BRDFθi, θs; ϕs, ϕi=Ps/ΩsPi cos θs,
DHRθi, ϕi; 2π= BRDFθi, ϕi; θs, ϕsdΩ,
Cx=-11NkN-1 hxexpi2πx/Nk2.
Rspec=R0 exp-g+πT2ΔΩλ2m=1gmm!m,
Rspec=R0 exp-g+πT2ΔΩλ2g.

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