Abstract

Gonioreflectometric determination of reflectance factors that involves hemispherical collection of reflected flux, which is an alternative to integrating sphere-based methods, is discussed. A detailed description of a gonioreflectometer built at the Helsinki University of Technology is presented. The instrument is used to establish an absolute scale of total diffuse reflectance factors throughout the spectral range 360–830 nm. The hemispherical reflectance factors are obtained through integration of the gonioreflectometric measurement results. The reflectance factors of white high-quality artifacts can be determined with a combined standard uncertainty of 0.20%. Results of test measurements were found to be in agreement with values traceable to other absolute scales based on integrating-sphere methods.

© 2004 Optical Society of America

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References

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  1. Commission Internationale de l’Eclairage, Absolute Methods for Reflection Measurements, Publ. CIE 44 (CIE, Vienna, 1979).
  2. W. Budde, C. X. Dodd, “Absolute reflectance measurements in the d/0° geometry,” Farbe 19, 94–102 (1970).
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    [CrossRef] [PubMed]
  4. W. H. Venable, J. J. Hsia, V. R. Weidner, “Establishing a scale of directional-hemispherical reflectance factor: the Van den Akker method,” J. Res. Natl. Bur. Stand. 82, 29–55 (1977).
    [CrossRef]
  5. C. J. Chunnilall, A. J. Deadman, L. Crane, E. Usadi, “NPL scales for radiance factor and total diffuse reflectance,” Metrologia 40, S192–S195 (2003).
    [CrossRef]
  6. International Bureau of Weights and Measures, “The BIPM key comparison data base. Appendix C, Calibration and measurement capabilities of National Metrology Institutes,” http://kcdb.bipm.org/appendixC/ .
  7. L. Morren, “Mesure absolue des facteurs de luminance et de réflexion,” Lux 45, 448–453 (1967).
  8. D. C. Williams, “Establishment of absolute diffuse reflectance scales using the NPL reference reflectometer,” Anal. Chim. Acta 380, 165–172 (1999).
    [CrossRef]
  9. W. Erb, “Computer-controlled gonioreflectometer for the measurement of spectral reflection characteristics,” Appl. Opt. 19, 3789–3794 (1980).
    [CrossRef] [PubMed]
  10. J. E. Proctor, P. Y. Barnes, “NIST high accuracy reference reflectometer-spectrometer,” J. Res. Natl. Inst. Stand. Technol. 101, 619–627 (1996).
    [CrossRef]
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    [CrossRef] [PubMed]
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  13. R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Taylor & Francis, London, 1992).
  14. DTMc300 Monochromator, Bentham Instruments, Ltd., Berkshire, England.
  15. J. L. Gardner, “Astigmatism cancellation in spectroradiometry,” Metrologia 28, 251–254 (1991).
    [CrossRef]
  16. One-circle goniometer 420, Huber Diffraktionstechnik GmbH & Co. KG, Rimsting, Germany.
  17. International Organization for Standardization, Guide to the Expression of Uncertainty in Measurement (ISO, Geneva, 1993).
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    [CrossRef] [PubMed]
  19. W. Möller, K. P. Nikolaus, A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212–S215 (2003).
    [CrossRef]

2003 (2)

C. J. Chunnilall, A. J. Deadman, L. Crane, E. Usadi, “NPL scales for radiance factor and total diffuse reflectance,” Metrologia 40, S192–S195 (2003).
[CrossRef]

W. Möller, K. P. Nikolaus, A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212–S215 (2003).
[CrossRef]

1999 (1)

D. C. Williams, “Establishment of absolute diffuse reflectance scales using the NPL reference reflectometer,” Anal. Chim. Acta 380, 165–172 (1999).
[CrossRef]

1996 (1)

J. E. Proctor, P. Y. Barnes, “NIST high accuracy reference reflectometer-spectrometer,” J. Res. Natl. Inst. Stand. Technol. 101, 619–627 (1996).
[CrossRef]

1995 (1)

1991 (1)

J. L. Gardner, “Astigmatism cancellation in spectroradiometry,” Metrologia 28, 251–254 (1991).
[CrossRef]

1980 (1)

1977 (1)

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

1975 (2)

1970 (1)

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

1967 (1)

L. Morren, “Mesure absolue des facteurs de luminance et de réflexion,” Lux 45, 448–453 (1967).

Barnes, P. Y.

J. E. Proctor, P. Y. Barnes, “NIST high accuracy reference reflectometer-spectrometer,” J. Res. Natl. Inst. Stand. Technol. 101, 619–627 (1996).
[CrossRef]

Budde, W.

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

Chunnilall, C. J.

C. J. Chunnilall, A. J. Deadman, L. Crane, E. Usadi, “NPL scales for radiance factor and total diffuse reflectance,” Metrologia 40, S192–S195 (2003).
[CrossRef]

Crane, L.

C. J. Chunnilall, A. J. Deadman, L. Crane, E. Usadi, “NPL scales for radiance factor and total diffuse reflectance,” Metrologia 40, S192–S195 (2003).
[CrossRef]

Deadman, A. J.

C. J. Chunnilall, A. J. Deadman, L. Crane, E. Usadi, “NPL scales for radiance factor and total diffuse reflectance,” Metrologia 40, S192–S195 (2003).
[CrossRef]

Dodd, C. X.

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

Erb, W.

Gardner, J. L.

J. L. Gardner, “Astigmatism cancellation in spectroradiometry,” Metrologia 28, 251–254 (1991).
[CrossRef]

Höpe, A.

W. Möller, K. P. Nikolaus, A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212–S215 (2003).
[CrossRef]

Howell, J. R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Taylor & Francis, London, 1992).

Hsia, J. J.

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

Ikonen, E.

Kartachevskaya, V. E.

Korte, H.

Manoochehri, F.

Möller, W.

W. Möller, K. P. Nikolaus, A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212–S215 (2003).
[CrossRef]

Morren, L.

L. Morren, “Mesure absolue des facteurs de luminance et de réflexion,” Lux 45, 448–453 (1967).

Nikolaus, K. P.

W. Möller, K. P. Nikolaus, A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212–S215 (2003).
[CrossRef]

Proctor, J. E.

J. E. Proctor, P. Y. Barnes, “NIST high accuracy reference reflectometer-spectrometer,” J. Res. Natl. Inst. Stand. Technol. 101, 619–627 (1996).
[CrossRef]

Robertson, A. R.

Siegel, R.

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Taylor & Francis, London, 1992).

Usadi, E.

C. J. Chunnilall, A. J. Deadman, L. Crane, E. Usadi, “NPL scales for radiance factor and total diffuse reflectance,” Metrologia 40, S192–S195 (2003).
[CrossRef]

Venable, W. H.

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

Williams, D. C.

D. C. Williams, “Establishment of absolute diffuse reflectance scales using the NPL reference reflectometer,” Anal. Chim. Acta 380, 165–172 (1999).
[CrossRef]

Anal. Chim. Acta (1)

D. C. Williams, “Establishment of absolute diffuse reflectance scales using the NPL reference reflectometer,” Anal. Chim. Acta 380, 165–172 (1999).
[CrossRef]

Appl. Opt. (4)

Farbe (1)

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

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

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

J. Res. Natl. Inst. Stand. Technol. (1)

J. E. Proctor, P. Y. Barnes, “NIST high accuracy reference reflectometer-spectrometer,” J. Res. Natl. Inst. Stand. Technol. 101, 619–627 (1996).
[CrossRef]

Lux (1)

L. Morren, “Mesure absolue des facteurs de luminance et de réflexion,” Lux 45, 448–453 (1967).

Metrologia (3)

W. Möller, K. P. Nikolaus, A. Höpe, “Degradation of the diffuse reflectance of Spectralon under low-level irradiation,” Metrologia 40, S212–S215 (2003).
[CrossRef]

J. L. Gardner, “Astigmatism cancellation in spectroradiometry,” Metrologia 28, 251–254 (1991).
[CrossRef]

C. J. Chunnilall, A. J. Deadman, L. Crane, E. Usadi, “NPL scales for radiance factor and total diffuse reflectance,” Metrologia 40, S192–S195 (2003).
[CrossRef]

Other (7)

International Bureau of Weights and Measures, “The BIPM key comparison data base. Appendix C, Calibration and measurement capabilities of National Metrology Institutes,” http://kcdb.bipm.org/appendixC/ .

Commission Internationale de l’Eclairage, Absolute Methods for Reflection Measurements, Publ. CIE 44 (CIE, Vienna, 1979).

Commission International de l’Eclairage, International Lighting Vocabulary, Publ. CIE 17.4 (CIE, Vienna, 1987).

R. Siegel, J. R. Howell, Thermal Radiation Heat Transfer, 3rd ed. (Taylor & Francis, London, 1992).

DTMc300 Monochromator, Bentham Instruments, Ltd., Berkshire, England.

One-circle goniometer 420, Huber Diffraktionstechnik GmbH & Co. KG, Rimsting, Germany.

International Organization for Standardization, Guide to the Expression of Uncertainty in Measurement (ISO, Geneva, 1993).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the gonioreflectometer setup: QTH, quartz–tungsten–halogen lamp; SPMs, spherical mirrors; GT1, GT2, grating turrets; OSF, order-sorting filter; M1, M2, flat mirrors; A, aperture; OPM, off-axis parabolic mirror; DP, dichroic polarizer; MD, monitor detector;L, distance between sample and detector.

Fig. 2
Fig. 2

Schematic drawing of the detection system at its cross section. The movements of the linear translator are perpendicular to the plane of the drawing. The horizontal slide moves in the plane of the drawing. The transimpedance amplifier (C-V) acts as a current-to-voltage converter.

Fig. 3
Fig. 3

Relative difference between the radiance factors measured with s- and p-polarized beams as a function of viewing angle. The measurements were carried out on a gray Spectralon sample at 0° incidence and 600-nm wavelength.

Fig. 4
Fig. 4

Recorded detector output signal as a function of time. The relative percentage change is plotted. The straight line represents a linear fit to the data points.

Fig. 5
Fig. 5

Correction factor for the scattered light. Measured values and a third-order polynomial fit to the data points are shown.

Fig. 6
Fig. 6

Radiance factors measured for a Spectralon and a mate opal-glass sample. The measurements were made at a 0-deg incidence angle and 560-nm wavelength.

Fig. 7
Fig. 7

0/d reflectance of an opal-glass sample: (a) gonioreflectometer results and values from the relative scale of the HUT, (b) discrepancy between the two sets of values. The error bars represent the combined standard uncertainty of the discrepancy.

Fig. 8
Fig. 8

0/d reflectance for a Spectralon sample: (a) comparison of gonioreflectometer results and values from the relative scale, (b) discrepancy between the two results. The error bars represent the combined standard uncertainty of the two measurements.

Fig. 9
Fig. 9

0/d reflectance for a gray Spectralon sample: (a) gonioreflectometer results compared with the relative scale of the HUT, (b) discrepancy between the absolute and the relative scales. The error bars represent the combined standard uncertainty of the two data sets.

Tables (1)

Tables Icon

Table 1 Relative Standard Uncertainties in Gonioreflectometric Measurements

Equations (5)

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

ρ=Φr/Φi.
Φr=2π 0π/2 Φθsinθdθ,
Φr=0π/2 Φθ4L2D2 cosθsin2θdθ.
ΦL=π 0π/2 I0 sin2θdθ=Φi,
R=0π/2 βθsin2θdθ,

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