Abstract

An uncertainty evaluation is presented for the spectroradiometric measurement of the averaged LED intensity (ALI), which is a standardized photometric quantity of LEDs introduced by the Commission Internationale de l'Éclairage. Using a spectral irradiance standard lamp as a calibration source for the spectroradiometer, 12 uncertainty components are sorted out and their propagation formulated with correlations between the components taken into account. The procedure of uncertainty evaluation is demonstrated for four LED samples of different colors; red, green, blue, and white. The relative uncertainties of the ALI of the test samples are determined to be in a range from 4.1% to 5.5% (k=2), but most of their dominant uncertainty components turn out to be systematic and correlated. In conclusion, correlations between the uncertainty components critically affect the overall uncertainty of the LED measurement using a spectroradiometer.

© 2007 Optical Society of America

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References

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  1. D. G. Pelka and K. Patel, "An overview of LED applications for general illumination," in Design of Efficient Illumination Systems, R. John Koshel, ed., Proc. SPIE 5186, 15-26 (2003).
    [CrossRef]
  2. E. F. Schubert, Light-Emitting Diodes(Cambridge U. Press, 2003), pp. 84-98.
  3. Commision Internationale de l'Éclairage, Measurement of LEDs, CIE publication 127 (CIE, 1999).
  4. Commision Internationale de l'Éclairage, Method of characterizing illuminance meters and luminance meters, CIE Publication 69 (CIE, 1987).
  5. J. L. Gardner, Uncertainties in Photometric Integrals [NMI TR 9] (Commonwealth of Australia, 2005), http://www.measurement.gov.au.
  6. J. H. Walker, R. D. Saunders, J. K. Jackson, and D. A. McSparron, NBS Measurement Service: Spectral Irradiance Calibration, NBS Special Publication 250-20 (U.S. Government Printing Office, 1987), http://www.physics.nist.gov/Divisions/Div844/manual/sp250series.html.
  7. C. E. Gibson and G. T. Fraser, Report of Calibration: Spectral Irradiance Standard, Quartz-Halogen Lamp (Serial # F-522) (NIST, 2001).
  8. J. L. Gardner, "Uncertainty propagation for NIST visible spectral standards," J. Res. Natl. Inst. Stand. Technol. 109, 305-318 (2004).
  9. J. L. Gardner, "Uncertainties in interpolated spectral data," J. Res. Natl. Inst. Stand. Technol. 108, 69-78 (2003).
  10. Y. Ohno, "Photometric standards," in Handbook of Applied Photometry, C. DeCusatis, ed. (Springer-Verlag, 1998), pp. 63-64.
  11. P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 2003), pp. 116-141.
  12. H. Oana, L. Jahreiss, D. Rich, and S. Trost, "Development and characterization of a miniature dual-channel spectrometer for spectrocolorimetry," in Optically Based Methods for Process Analysis, D. S. Bomse, H. Brittain, S. Farquharson, J. M. Lerner, A. J. Rein, C. Sohl, T. R. Todd, and L. Weyer, eds., Proc. SPIE 1681, 12-28 (1992).
    [CrossRef]
  13. D.-J. Shin, D.-H. Lee, C.-W. Park, and S.-N. Park, "A novel linearity tester for optical detectors using high-brightness light emitting diodes," Metrologia 42, 154-158 (2005).
    [CrossRef]
  14. Y. Zong, S. W. Brown, B. C. Johnson, K. R. Lykke, and Y. Ohno, "Simple spectral stray light correction method for array spectroradiometers," Appl. Opt. 45, 1111-1119 (2006).
    [CrossRef] [PubMed]

2006 (1)

2005 (1)

D.-J. Shin, D.-H. Lee, C.-W. Park, and S.-N. Park, "A novel linearity tester for optical detectors using high-brightness light emitting diodes," Metrologia 42, 154-158 (2005).
[CrossRef]

2004 (1)

J. L. Gardner, "Uncertainty propagation for NIST visible spectral standards," J. Res. Natl. Inst. Stand. Technol. 109, 305-318 (2004).

2003 (2)

J. L. Gardner, "Uncertainties in interpolated spectral data," J. Res. Natl. Inst. Stand. Technol. 108, 69-78 (2003).

D. G. Pelka and K. Patel, "An overview of LED applications for general illumination," in Design of Efficient Illumination Systems, R. John Koshel, ed., Proc. SPIE 5186, 15-26 (2003).
[CrossRef]

1992 (1)

H. Oana, L. Jahreiss, D. Rich, and S. Trost, "Development and characterization of a miniature dual-channel spectrometer for spectrocolorimetry," in Optically Based Methods for Process Analysis, D. S. Bomse, H. Brittain, S. Farquharson, J. M. Lerner, A. J. Rein, C. Sohl, T. R. Todd, and L. Weyer, eds., Proc. SPIE 1681, 12-28 (1992).
[CrossRef]

Bevington, P. R.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 2003), pp. 116-141.

Brown, S. W.

Fraser, G. T.

C. E. Gibson and G. T. Fraser, Report of Calibration: Spectral Irradiance Standard, Quartz-Halogen Lamp (Serial # F-522) (NIST, 2001).

Gardner, J. L.

J. L. Gardner, "Uncertainty propagation for NIST visible spectral standards," J. Res. Natl. Inst. Stand. Technol. 109, 305-318 (2004).

J. L. Gardner, "Uncertainties in interpolated spectral data," J. Res. Natl. Inst. Stand. Technol. 108, 69-78 (2003).

J. L. Gardner, Uncertainties in Photometric Integrals [NMI TR 9] (Commonwealth of Australia, 2005), http://www.measurement.gov.au.

Gibson, C. E.

C. E. Gibson and G. T. Fraser, Report of Calibration: Spectral Irradiance Standard, Quartz-Halogen Lamp (Serial # F-522) (NIST, 2001).

Jackson, J. K.

J. H. Walker, R. D. Saunders, J. K. Jackson, and D. A. McSparron, NBS Measurement Service: Spectral Irradiance Calibration, NBS Special Publication 250-20 (U.S. Government Printing Office, 1987), http://www.physics.nist.gov/Divisions/Div844/manual/sp250series.html.

Jahreiss, L.

H. Oana, L. Jahreiss, D. Rich, and S. Trost, "Development and characterization of a miniature dual-channel spectrometer for spectrocolorimetry," in Optically Based Methods for Process Analysis, D. S. Bomse, H. Brittain, S. Farquharson, J. M. Lerner, A. J. Rein, C. Sohl, T. R. Todd, and L. Weyer, eds., Proc. SPIE 1681, 12-28 (1992).
[CrossRef]

Johnson, B. C.

Lee, D.-H.

D.-J. Shin, D.-H. Lee, C.-W. Park, and S.-N. Park, "A novel linearity tester for optical detectors using high-brightness light emitting diodes," Metrologia 42, 154-158 (2005).
[CrossRef]

Lykke, K. R.

McSparron, D. A.

J. H. Walker, R. D. Saunders, J. K. Jackson, and D. A. McSparron, NBS Measurement Service: Spectral Irradiance Calibration, NBS Special Publication 250-20 (U.S. Government Printing Office, 1987), http://www.physics.nist.gov/Divisions/Div844/manual/sp250series.html.

Oana, H.

H. Oana, L. Jahreiss, D. Rich, and S. Trost, "Development and characterization of a miniature dual-channel spectrometer for spectrocolorimetry," in Optically Based Methods for Process Analysis, D. S. Bomse, H. Brittain, S. Farquharson, J. M. Lerner, A. J. Rein, C. Sohl, T. R. Todd, and L. Weyer, eds., Proc. SPIE 1681, 12-28 (1992).
[CrossRef]

Ohno, Y.

Park, C.-W.

D.-J. Shin, D.-H. Lee, C.-W. Park, and S.-N. Park, "A novel linearity tester for optical detectors using high-brightness light emitting diodes," Metrologia 42, 154-158 (2005).
[CrossRef]

Park, S.-N.

D.-J. Shin, D.-H. Lee, C.-W. Park, and S.-N. Park, "A novel linearity tester for optical detectors using high-brightness light emitting diodes," Metrologia 42, 154-158 (2005).
[CrossRef]

Patel, K.

D. G. Pelka and K. Patel, "An overview of LED applications for general illumination," in Design of Efficient Illumination Systems, R. John Koshel, ed., Proc. SPIE 5186, 15-26 (2003).
[CrossRef]

Pelka, D. G.

D. G. Pelka and K. Patel, "An overview of LED applications for general illumination," in Design of Efficient Illumination Systems, R. John Koshel, ed., Proc. SPIE 5186, 15-26 (2003).
[CrossRef]

Rich, D.

H. Oana, L. Jahreiss, D. Rich, and S. Trost, "Development and characterization of a miniature dual-channel spectrometer for spectrocolorimetry," in Optically Based Methods for Process Analysis, D. S. Bomse, H. Brittain, S. Farquharson, J. M. Lerner, A. J. Rein, C. Sohl, T. R. Todd, and L. Weyer, eds., Proc. SPIE 1681, 12-28 (1992).
[CrossRef]

Robinson, D. K.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 2003), pp. 116-141.

Saunders, R. D.

J. H. Walker, R. D. Saunders, J. K. Jackson, and D. A. McSparron, NBS Measurement Service: Spectral Irradiance Calibration, NBS Special Publication 250-20 (U.S. Government Printing Office, 1987), http://www.physics.nist.gov/Divisions/Div844/manual/sp250series.html.

Schubert, E. F.

E. F. Schubert, Light-Emitting Diodes(Cambridge U. Press, 2003), pp. 84-98.

Shin, D.-J.

D.-J. Shin, D.-H. Lee, C.-W. Park, and S.-N. Park, "A novel linearity tester for optical detectors using high-brightness light emitting diodes," Metrologia 42, 154-158 (2005).
[CrossRef]

Trost, S.

H. Oana, L. Jahreiss, D. Rich, and S. Trost, "Development and characterization of a miniature dual-channel spectrometer for spectrocolorimetry," in Optically Based Methods for Process Analysis, D. S. Bomse, H. Brittain, S. Farquharson, J. M. Lerner, A. J. Rein, C. Sohl, T. R. Todd, and L. Weyer, eds., Proc. SPIE 1681, 12-28 (1992).
[CrossRef]

Walker, J. H.

J. H. Walker, R. D. Saunders, J. K. Jackson, and D. A. McSparron, NBS Measurement Service: Spectral Irradiance Calibration, NBS Special Publication 250-20 (U.S. Government Printing Office, 1987), http://www.physics.nist.gov/Divisions/Div844/manual/sp250series.html.

Zong, Y.

Appl. Opt. (1)

J. Res. Natl. Inst. Stand. Technol. (2)

J. L. Gardner, "Uncertainty propagation for NIST visible spectral standards," J. Res. Natl. Inst. Stand. Technol. 109, 305-318 (2004).

J. L. Gardner, "Uncertainties in interpolated spectral data," J. Res. Natl. Inst. Stand. Technol. 108, 69-78 (2003).

Metrologia (1)

D.-J. Shin, D.-H. Lee, C.-W. Park, and S.-N. Park, "A novel linearity tester for optical detectors using high-brightness light emitting diodes," Metrologia 42, 154-158 (2005).
[CrossRef]

Proc. SPIE (2)

H. Oana, L. Jahreiss, D. Rich, and S. Trost, "Development and characterization of a miniature dual-channel spectrometer for spectrocolorimetry," in Optically Based Methods for Process Analysis, D. S. Bomse, H. Brittain, S. Farquharson, J. M. Lerner, A. J. Rein, C. Sohl, T. R. Todd, and L. Weyer, eds., Proc. SPIE 1681, 12-28 (1992).
[CrossRef]

D. G. Pelka and K. Patel, "An overview of LED applications for general illumination," in Design of Efficient Illumination Systems, R. John Koshel, ed., Proc. SPIE 5186, 15-26 (2003).
[CrossRef]

Other (8)

E. F. Schubert, Light-Emitting Diodes(Cambridge U. Press, 2003), pp. 84-98.

Commision Internationale de l'Éclairage, Measurement of LEDs, CIE publication 127 (CIE, 1999).

Commision Internationale de l'Éclairage, Method of characterizing illuminance meters and luminance meters, CIE Publication 69 (CIE, 1987).

J. L. Gardner, Uncertainties in Photometric Integrals [NMI TR 9] (Commonwealth of Australia, 2005), http://www.measurement.gov.au.

J. H. Walker, R. D. Saunders, J. K. Jackson, and D. A. McSparron, NBS Measurement Service: Spectral Irradiance Calibration, NBS Special Publication 250-20 (U.S. Government Printing Office, 1987), http://www.physics.nist.gov/Divisions/Div844/manual/sp250series.html.

C. E. Gibson and G. T. Fraser, Report of Calibration: Spectral Irradiance Standard, Quartz-Halogen Lamp (Serial # F-522) (NIST, 2001).

Y. Ohno, "Photometric standards," in Handbook of Applied Photometry, C. DeCusatis, ed. (Springer-Verlag, 1998), pp. 63-64.

P. R. Bevington and D. K. Robinson, Data Reduction and Error Analysis for the Physical Sciences (McGraw-Hill, 2003), pp. 116-141.

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Figures (7)

Fig. 1
Fig. 1

(Color online) Schematic diagram of the spectroradiometer instrument (a) and the geometric arrangement (b) for calibration and measurement of the ALI.

Fig. 2
Fig. 2

(a) Spectral irradiance reference data, (b) standard uncertainties, and (c) correlation coefficients of the spectral irradiance standard lamp, which are obtained from ten spectral irradiance values (dot symbols) on the NIST calibration report by a cubic spline interpolation.

Fig. 3
Fig. 3

(a) Functional relation between color temperature and feeding current of the FEL standard lamp and (b) spectral irradiance uncertainties caused by the inaccurate lamp current.

Fig. 4
Fig. 4

Calibration result of the wavelength scale of the spectroradiometer using a set of wavelength standard lamps: (a) measured data pairs of the reference wavelengths (cross symbols) and the wavelength calibration curve (line) obtained by third-order polynomial fit, (b) standard uncertainties, and (c) correlation coefficients of the wavelength calibration curve.

Fig. 5
Fig. 5

Linearity measurement of the spectroradiometer's readout on (a) flux level and (b) on exposure time.

Fig. 6
Fig. 6

(a) Normalized response of the spectroradiometer under illumination of a He–Ne laser at 633 nm and (b) stray response function extracted from the measurement.

Fig. 7
Fig. 7

(a) Spectral irradiance and (b), (c) its major uncertainty components of the test blue LED as a function of wavelength.

Tables (2)

Tables Icon

Table 1 Summary of the Symbols used in the Equations

Tables Icon

Table 2 Uncertainty Budget of the ALI Measurement on the Test LEDs: Red, Green, Blue, and White LEDs

Equations (23)

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I L E D = E v d 2 .
E v = K m i V i E i Δ i .
E i = y i y i s y i O D m y i O D n E i s .
u r 2 ( I L E D ) = 2 2 u r 2 ( d ) + X u r 2 ( E v ) | X ,
u 2 ( E v ) | X = 3 = K m 2 [ V i Δ i ] Y [ u ( E i , E j ) ] | Y [ V j Δ j ] T .
u r ( E i , E j ) | Y = 1 = C i j u r ( E i ) u r ( E j ) .
u r ( E i , E j ) | Y = 2 = 2 2 u r 2 ( d s ) .
δ E i s E i s = 1 E i s E i s T T I s δ I s c 2 λ i T 2 T I s δ I s .
u r ( E i ) = c 2 λ i T 2 ( T I s ) I s u r ( I s ) .
u r ( | E i , E j ) | Y = 3 = c 2 2 T 4 ( T I s ) 2 ( I s ) 2 λ i λ j u r 2 ( I s ) .
E i + δ E i = y i + δ y i y i s + δ y i s y i O D m + δ y i O D m y i O D n + δ y i O D n E i s ,
δ E i E i = δ y i y i δ y i s y i s + δ y i O D m y i O D m δ y i O D n y i O D n .
u r ( E i , E j ) | Y = 4 = δ i j [ u r 2 ( y i ) + u r 2 ( y i s ) + u r 2 ( y i O D m ) + u r 2 ( y i O D n ) ] ,
E ( λ ) + δ E ( λ ) = y ( λ + δ λ ) y s ( λ + δ λ ) y O D m ( λ + δ λ ) y O D n ( λ + δ λ ) E s ( λ ) .
δ E E = ( ln E λ ln E s λ ) δ λ ,
u r 2 ( E i ) = ( ln E i λ i ln E i s λ i ) 2 u 2 ( λ i ) f i 2 u 2 ( λ i ) .
u r ( E i , E j ) | Y = 5 = f i f j u ( λ i , λ j ) .
E i + δ E i = y i ( 1 + δ 1 ) y i s ( 1 + δ 2 ) y i O D m ( 1 + δ 3 ) y i O D n ( 1 + δ 4 ) E i s ,
u r ( E i , E j ) | Y = 6 a = 4 δ ϕ δ i j ( on   flux   level ) ,
u r ( E i , E j ) | Y = 6 b = 4 δ τ 2 ( on   exposure   time ) .
u ( y i ) y i stray = j d i j y j ,
u r 2 ( E i ) = u r 2 ( y i ) + [ u r ( y i s ) u r ( y i O D m ) + u r ( y i O D n ) ] 2 .
u r ( E i , E j ) | Y = 7 = u r ( y i ) u r ( y j ) + Π k = i , j [ u r ( y k s ) u r ( y k O D m ) + u r ( y k O D n ) ] .

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