Abstract

Homogeneity measurements in a gold-coated integrating sphere at eight wavelengths in the range from 400 to 2000 nm are presented and discussed. The inner sphere wall was scanned with a mirror-based internal sphere scanner at 288 different positions. The spatially resolved measurements show the transition from poor reflectivity, associated with large inhomogeneities at 400 nm, to high reflectivity in the infrared region at 2000 nm, associated with only small deviations. From the measurements the spectrally dependent relative uncertainty of the radiance of the inner sphere wall was deduced. A spectrally dependent sphere homogeneity correction factor F(λ) relative to a specific point within the sphere wall was also derived.

© 2004 Optical Society of America

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References

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  1. W. Budde, “Calibration of reflectance standards,” J. Res. Natl. Bur. Stand. Sect. A 80A, 585–595 (1976).
    [Crossref]
  2. W. Erb, “Requirements for reflection standards and the measurement of their reflection values,” Appl. Opt. 14, 493–499 (1975).
    [Crossref] [PubMed]
  3. W. Budde, C. X. Dodd, “Absolute reflectance measurements in the D/0° geometry,” Die Farbe 19, 94–102 (1970).
  4. W. H. Venable, J. J. Hsia, V. R. Weidner, “Establishing a scale of directional-hemispherical reflectance factor I: The Van den Akker Method,” J. Res. Natl. Bur. Stand. 82, 29–55 (1977).
    [Crossref]
  5. J. A. Van den Akker, L. R. Dearth, W. M. Shillcox, “Evaluation of absolute reflectance for standardization purposes,” J. Opt. Soc. Am. 56, 250–252 (1966).
    [Crossref]
  6. Y. Ohno, “Detector-based luminous-flux calibration using the Absolute Integrating-Sphere Method,” Metrologia 35, 473–478 (1998).
    [Crossref]
  7. L. M. Hansen, S. Kaplan, “Infrared diffuse reflectance instrumentation and standards at NIST,” Anal. Chim. Acta 380, 289–302 (1999).
    [Crossref]
  8. C. H. Sharp, F. W. Little, “Measurement of reflection factors,” Trans. Illum. Eng. Soc. 15, 802–810 (1920).
  9. H. Korte, M. Schmidt, “Über Messungen des Leuchtdichtefaktors an beliebig reflektierenden Proben,” Lichttechnik 19, 135A–137A (1967).
  10. W. Erb, K.-P. Nikolaus, “Untersuchung der Abhängigkeit des Strahldichtefaktors diffus angestrahlter Reflexionsnormale vom Abstrahlungswinke,” PTB—Mitt. 107, 311–316 (1997).
  11. Labsphere, Inc., “Diffuse reflectance coatings and materials,” in Catalog I (Labsphere, North Sutton, N.H., 1997).

1999 (1)

L. M. Hansen, S. Kaplan, “Infrared diffuse reflectance instrumentation and standards at NIST,” Anal. Chim. Acta 380, 289–302 (1999).
[Crossref]

1998 (1)

Y. Ohno, “Detector-based luminous-flux calibration using the Absolute Integrating-Sphere Method,” Metrologia 35, 473–478 (1998).
[Crossref]

1997 (1)

W. Erb, K.-P. Nikolaus, “Untersuchung der Abhängigkeit des Strahldichtefaktors diffus angestrahlter Reflexionsnormale vom Abstrahlungswinke,” PTB—Mitt. 107, 311–316 (1997).

1977 (1)

W. H. Venable, J. J. Hsia, V. R. Weidner, “Establishing a scale of directional-hemispherical reflectance factor I: The Van den Akker Method,” J. Res. Natl. Bur. Stand. 82, 29–55 (1977).
[Crossref]

1976 (1)

W. Budde, “Calibration of reflectance standards,” J. Res. Natl. Bur. Stand. Sect. A 80A, 585–595 (1976).
[Crossref]

1975 (1)

1970 (1)

W. Budde, C. X. Dodd, “Absolute reflectance measurements in the D/0° geometry,” Die Farbe 19, 94–102 (1970).

1967 (1)

H. Korte, M. Schmidt, “Über Messungen des Leuchtdichtefaktors an beliebig reflektierenden Proben,” Lichttechnik 19, 135A–137A (1967).

1966 (1)

1920 (1)

C. H. Sharp, F. W. Little, “Measurement of reflection factors,” Trans. Illum. Eng. Soc. 15, 802–810 (1920).

Budde, W.

W. Budde, “Calibration of reflectance standards,” J. Res. Natl. Bur. Stand. Sect. A 80A, 585–595 (1976).
[Crossref]

W. Budde, C. X. Dodd, “Absolute reflectance measurements in the D/0° geometry,” Die Farbe 19, 94–102 (1970).

Dearth, L. R.

Dodd, C. X.

W. Budde, C. X. Dodd, “Absolute reflectance measurements in the D/0° geometry,” Die Farbe 19, 94–102 (1970).

Erb, W.

W. Erb, K.-P. Nikolaus, “Untersuchung der Abhängigkeit des Strahldichtefaktors diffus angestrahlter Reflexionsnormale vom Abstrahlungswinke,” PTB—Mitt. 107, 311–316 (1997).

W. Erb, “Requirements for reflection standards and the measurement of their reflection values,” Appl. Opt. 14, 493–499 (1975).
[Crossref] [PubMed]

Hansen, L. M.

L. M. Hansen, S. Kaplan, “Infrared diffuse reflectance instrumentation and standards at NIST,” Anal. Chim. Acta 380, 289–302 (1999).
[Crossref]

Hsia, J. J.

W. H. Venable, J. J. Hsia, V. R. Weidner, “Establishing a scale of directional-hemispherical reflectance factor I: The Van den Akker Method,” J. Res. Natl. Bur. Stand. 82, 29–55 (1977).
[Crossref]

Kaplan, S.

L. M. Hansen, S. Kaplan, “Infrared diffuse reflectance instrumentation and standards at NIST,” Anal. Chim. Acta 380, 289–302 (1999).
[Crossref]

Korte, H.

H. Korte, M. Schmidt, “Über Messungen des Leuchtdichtefaktors an beliebig reflektierenden Proben,” Lichttechnik 19, 135A–137A (1967).

Little, F. W.

C. H. Sharp, F. W. Little, “Measurement of reflection factors,” Trans. Illum. Eng. Soc. 15, 802–810 (1920).

Nikolaus, K.-P.

W. Erb, K.-P. Nikolaus, “Untersuchung der Abhängigkeit des Strahldichtefaktors diffus angestrahlter Reflexionsnormale vom Abstrahlungswinke,” PTB—Mitt. 107, 311–316 (1997).

Ohno, Y.

Y. Ohno, “Detector-based luminous-flux calibration using the Absolute Integrating-Sphere Method,” Metrologia 35, 473–478 (1998).
[Crossref]

Schmidt, M.

H. Korte, M. Schmidt, “Über Messungen des Leuchtdichtefaktors an beliebig reflektierenden Proben,” Lichttechnik 19, 135A–137A (1967).

Sharp, C. H.

C. H. Sharp, F. W. Little, “Measurement of reflection factors,” Trans. Illum. Eng. Soc. 15, 802–810 (1920).

Shillcox, W. M.

Van den Akker, J. A.

Venable, W. H.

W. H. Venable, J. J. Hsia, V. R. Weidner, “Establishing a scale of directional-hemispherical reflectance factor I: The Van den Akker Method,” J. Res. Natl. Bur. Stand. 82, 29–55 (1977).
[Crossref]

Weidner, V. R.

W. H. Venable, J. J. Hsia, V. R. Weidner, “Establishing a scale of directional-hemispherical reflectance factor I: The Van den Akker Method,” J. Res. Natl. Bur. Stand. 82, 29–55 (1977).
[Crossref]

Anal. Chim. Acta (1)

L. M. Hansen, S. Kaplan, “Infrared diffuse reflectance instrumentation and standards at NIST,” Anal. Chim. Acta 380, 289–302 (1999).
[Crossref]

Appl. Opt. (1)

Die Farbe (1)

W. Budde, C. X. Dodd, “Absolute reflectance measurements in the D/0° geometry,” Die Farbe 19, 94–102 (1970).

J. Opt. Soc. Am. (1)

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

W. H. Venable, J. J. Hsia, V. R. Weidner, “Establishing a scale of directional-hemispherical reflectance factor I: The Van den Akker Method,” J. Res. Natl. Bur. Stand. 82, 29–55 (1977).
[Crossref]

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

W. Budde, “Calibration of reflectance standards,” J. Res. Natl. Bur. Stand. Sect. A 80A, 585–595 (1976).
[Crossref]

Lichttechnik (1)

H. Korte, M. Schmidt, “Über Messungen des Leuchtdichtefaktors an beliebig reflektierenden Proben,” Lichttechnik 19, 135A–137A (1967).

Metrologia (1)

Y. Ohno, “Detector-based luminous-flux calibration using the Absolute Integrating-Sphere Method,” Metrologia 35, 473–478 (1998).
[Crossref]

PTB—Mitt. (1)

W. Erb, K.-P. Nikolaus, “Untersuchung der Abhängigkeit des Strahldichtefaktors diffus angestrahlter Reflexionsnormale vom Abstrahlungswinke,” PTB—Mitt. 107, 311–316 (1997).

Trans. Illum. Eng. Soc. (1)

C. H. Sharp, F. W. Little, “Measurement of reflection factors,” Trans. Illum. Eng. Soc. 15, 802–810 (1920).

Other (1)

Labsphere, Inc., “Diffuse reflectance coatings and materials,” in Catalog I (Labsphere, North Sutton, N.H., 1997).

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Figures (8)

Fig. 1
Fig. 1

Rotation of the integrating sphere for the calibration of reflectance standards in terms of the radiance factor.

Fig. 2
Fig. 2

Setup for homogeneity measurements in the integrating gold sphere.

Fig. 3
Fig. 3

Two-dimensional sketch of the three-dimensional distribution of the 288 data points within the irradiating inner sphere wall. The hole in the center is the exit port for measuring the radiance.

Fig. 4
Fig. 4

Three repetitive scans (3 × 360°) in the φ direction of the inner sphere wall at ϑ = 45° and λ = 1300 nm (also illustrate reproducibility).

Fig. 5
Fig. 5

Topological homogeneity plots of the irradiating sphere wall at wavelengths of 400, 1000, and 2000 nm (note the different scales).

Fig. 6
Fig. 6

Positions of high- and low-reflecting regions do not change with wavelength. The magnitude of the deviations, however, decrease by a factor of 30 between 400 and 2000 nm.

Fig. 7
Fig. 7

Spectral dependence of the reflectivity of the gold sphere (right) and the relative (Rel.) uncertainty of the measured radiances L i of the inner wall segments (left).

Fig. 8
Fig. 8

Dependence of the homogeneity correction factor F(λ) on the wavelength, on the averaging method, and on the number of considered data points.

Tables (1)

Tables Icon

Table 1 Relative Experimental Standard Deviation of the Radiance of the Inner Sphere Wall

Equations (6)

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x¯=i=1n xifii=1n fi
A=R2φ1φ2dφ ϑ1ϑ2sin ϑdϑ.
d2Φ=L dSo cos ΘdAo cos ΨR2,
E=So L cos Θ cos ψR2dSo.
E=LoR202πdφ ϑ1ϑ2dϑ sin ϑ cos ϑ=const×sin2 ϑϑ1ϑ2.
Q=LMλLWλ=LMλLjWλ Fλ,Fλ=LjWλiLiλfi/i fi, i=1,, 288.

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