Abstract

A sphere arrangement for directional-hemispherical reflectance measurements in the 1–15-μm wavelength range is tested for its accuracy. Comparative measurements with the fundamental PTB sphere reflectometer in the overlapping spectral range between 1.0 and 1.1 μm indicate no systematic measurement uncertainties of the new device. The uncertainty of the reflectance measured by it is therefrom deduced to be ±0.01 for the 1–5.6-μm wavelength range.

© 1987 Optical Society of America

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References

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  1. Bureau Central de la Commission Internationale de l'Eclairage, International Lighting Vocabulary (Paris, 1970), CIE Publication 17 (E-1.1).
  2. R. R. Willey, “Fourier Transform Infrared Spectrophotometer for Transmittance and Diffuse Reflectance Measurements,” Appl. Spectrosc. 30, 593 (1976).
    [Crossref]
  3. W. Richter, “Fourier Transform Reflectance Spectrometry Between 8000 cm−1 (1.25 μm) and 800 cm−1 (12.5 μm) Using an Integrating Sphere,” Appl. Spectrosc. 37, 32 (1983).
    [Crossref]
  4. K. Gindele, M. Köhl, M. Mast, “Spectral Reflectance Measurements Using an Integrating Sphere in the Infrared,” Appl. Opt. 24,1757 (1985).
    [Crossref] [PubMed]
  5. R. R. Willey, “Results of a Round Robin Measurement of Spectral Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, (1987), paper 20.
  6. W. Erb, “Requirements for Reflection Standards and the Measurement of Their Reflection Values,” Appl. Opt. 14, 493 (1975).
    [Crossref] [PubMed]
  7. G. P. Motulevich, A. A. Shubin, “Influence of Fermi Surface Shape in Gold on the Optical Constants and Hall Effect,” Soviet Phys. JETP 20,560 (1965).
  8. W. Erb, “Zur Gültigkeit des Helmholtzchen Reziprozitätstheorems bei diffuser Reflexion,”; Optik 48,425 (1977).
  9. Deutsches Institut fur Normung, “Farbmessung; Weissstandard fur Farbmessung und Photometrie,” DIN 5033, Teil9 (Marz1982).
  10. K. Gindele, M. Köhl, “Measurement of Near-Normal/Hemispherical Reflectance and Directional Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, (1987), paper 22.

1987 (2)

R. R. Willey, “Results of a Round Robin Measurement of Spectral Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, (1987), paper 20.

K. Gindele, M. Köhl, “Measurement of Near-Normal/Hemispherical Reflectance and Directional Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, (1987), paper 22.

1985 (1)

1983 (1)

1977 (1)

W. Erb, “Zur Gültigkeit des Helmholtzchen Reziprozitätstheorems bei diffuser Reflexion,”; Optik 48,425 (1977).

1976 (1)

1975 (1)

1965 (1)

G. P. Motulevich, A. A. Shubin, “Influence of Fermi Surface Shape in Gold on the Optical Constants and Hall Effect,” Soviet Phys. JETP 20,560 (1965).

Erb, W.

W. Erb, “Zur Gültigkeit des Helmholtzchen Reziprozitätstheorems bei diffuser Reflexion,”; Optik 48,425 (1977).

W. Erb, “Requirements for Reflection Standards and the Measurement of Their Reflection Values,” Appl. Opt. 14, 493 (1975).
[Crossref] [PubMed]

Gindele, K.

K. Gindele, M. Köhl, “Measurement of Near-Normal/Hemispherical Reflectance and Directional Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, (1987), paper 22.

K. Gindele, M. Köhl, M. Mast, “Spectral Reflectance Measurements Using an Integrating Sphere in the Infrared,” Appl. Opt. 24,1757 (1985).
[Crossref] [PubMed]

Köhl, M.

K. Gindele, M. Köhl, “Measurement of Near-Normal/Hemispherical Reflectance and Directional Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, (1987), paper 22.

K. Gindele, M. Köhl, M. Mast, “Spectral Reflectance Measurements Using an Integrating Sphere in the Infrared,” Appl. Opt. 24,1757 (1985).
[Crossref] [PubMed]

Mast, M.

Motulevich, G. P.

G. P. Motulevich, A. A. Shubin, “Influence of Fermi Surface Shape in Gold on the Optical Constants and Hall Effect,” Soviet Phys. JETP 20,560 (1965).

Richter, W.

Shubin, A. A.

G. P. Motulevich, A. A. Shubin, “Influence of Fermi Surface Shape in Gold on the Optical Constants and Hall Effect,” Soviet Phys. JETP 20,560 (1965).

Willey, R. R.

R. R. Willey, “Results of a Round Robin Measurement of Spectral Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, (1987), paper 20.

R. R. Willey, “Fourier Transform Infrared Spectrophotometer for Transmittance and Diffuse Reflectance Measurements,” Appl. Spectrosc. 30, 593 (1976).
[Crossref]

Appl. Opt. (2)

Appl. Spectrosc. (2)

Optik (1)

W. Erb, “Zur Gültigkeit des Helmholtzchen Reziprozitätstheorems bei diffuser Reflexion,”; Optik 48,425 (1977).

Proc. Soc. Photo-Opt. Instrum. Eng. (2)

R. R. Willey, “Results of a Round Robin Measurement of Spectral Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, (1987), paper 20.

K. Gindele, M. Köhl, “Measurement of Near-Normal/Hemispherical Reflectance and Directional Emittance in the Mid-Infrared,” Proc. Soc. Photo-Opt. Instrum. Eng. 807, (1987), paper 22.

Soviet Phys. JETP (1)

G. P. Motulevich, A. A. Shubin, “Influence of Fermi Surface Shape in Gold on the Optical Constants and Hall Effect,” Soviet Phys. JETP 20,560 (1965).

Other (2)

Deutsches Institut fur Normung, “Farbmessung; Weissstandard fur Farbmessung und Photometrie,” DIN 5033, Teil9 (Marz1982).

Bureau Central de la Commission Internationale de l'Eclairage, International Lighting Vocabulary (Paris, 1970), CIE Publication 17 (E-1.1).

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Figures (5)

Fig. 1
Fig. 1

Fundamental sphere reflectometer for measuring the spectral radiance factor βd/0(λ). The reflecting surface of sample S is in the equatorial plane of the sphere of 0.5-m diameter. Heating of the sample by lamp L is prevented by a water-cooled shield.

Fig. 2
Fig. 2

Integrating sphere arrangement for measuring the directional–hemispherical reflectance ρ10/d in the infrared spectral range: 1, sample; 2, plane gold mirror of known reflectance; 3, infrared detector. The sample and the gold mirror can be alternately brought into measuring position by turning the rod. The arrow indicates the modulated radiation from the Michelson interferometer.

Fig. 3
Fig. 3

Reflectance factor of powder pressings of (from top): pure sulfur (sublimated sulfur, Merck); a mixture of (as mass fraction) 94.6% S, 5.3% SiO2, 0.1% C; and a mixture of 93.4% S, 5.4% SiO2, 1.2% C. The absorption band around 3.4 μm in the sulfur spectrum is caused by a hydrocarbon residue of ∼0.05%, probably from the fabrication process of the material (also present in sulfur from other sources). The curve for pure sulfur of method II is measured in one single range and smoothed on the high wavelength side to reduce the noise.

Fig. 4
Fig. 4

Reflectance factor in the overlapping range of method I (left curve) and method II (right curve). The noise has been averaged out to show the offset more clearly.

Fig. 5
Fig. 5

Reflectance factor of sulfur (sublimated sulfur, Merck) in the spectral range which altogether with the fundamental sphere reflectometer (method I) and the infrared sphere reflectometer (method II) is accessible. The two methods overlap near 1 μm. The reflectance spectrum of method II is composed of two sections overlapping around 5μm.

Equations (9)

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S s = k L s
S w = k L w ( = k L PRD ) .
β d / 0 = S s / S w .
S s = S s ( 1 + r 2 / R 2 ) = f 1 S s .
S w = 1 / n i = 1 n S w , i .
f 2 = S w , k 1 / n i = 1 n S w , i ( i k ) ,
β d / 0 = f 1 f 2 ( S s / S w , k )
ρ ( λ ) = S ( λ ) S G ( λ ) ρ G ( λ ) f ,
94.6 % S , 5.3 % SiO 2 , 0.1 % C 93.4 % S , 5.4 % SiO 2 , 1.2 % C .

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