Abstract

The General V(λ) Mismatch Index, f1 , was defined for a general description of the photometric performance of photometers. This index is widely-used in photometry, and it is very relevant for selecting photometers for low-uncertainty photometric measurements. It quantifies the spectral mismatch between the relative spectral responsivity of a photometer and the luminous efficiency function for photopic vision, V(λ). The linear correlation between the real general photometric measurement error and f1  of 77 photometers was studied for four sets of light sources: R, G and B LEDs (narrowband spectral power distributions, SPDs), blackbodies at different colour temperatures (broadband SPDs), phosphor-based LEDs at different correlated color temperatures (SPDs with narrow- and broad-band features), and a mixture of blackbodies and phosphor-based LED sources. This article shows that it can be defined an alternative index which is notably better correlated with the real general photometric measurement error of the photometers under light sources with broadband features in their SPDs, adequate for general lighting. This index is based on filtering the high spectral frequencies variations between the relative spectral responsivity of the photometer and V(λ). The use of this new index for the assessment of the general photometric performance of photometers would improve the selection of high quality photometers and, consequently, would contribute to the general improvement of photometric measurements.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. “Photometry - The CIE system of physical photometry,” (ISO Standard: ISO 23539:2005(E)/CIE S010/E:2004, 2004).
  2. R. Rattunde and P. Blattner, “Characterization of the Performance of Illuminance Meters and Luminance Meters,” (ISO/CIE 19476:2014 (CIE S 023 E:2013), 2013).
  3. P. Csuti, B. Kránicz, and J. Schanda, “Comparison of the goodness of fit of photometers to the V(λ) function using real LED spectra,” in CIE LED Symposium, (2004).
  4. P. Csuti and B. Kránicz, “Description of a partial f′1 error index recommended for LED photometry,” Light. Eng. 14, 28–34 (2006).
  5. R. Young, K. Muray, and C. Jones, “Quantifying photometric spectral mismatch uncertainties in LED measurements,” in Proceedings of the 2nd CIE Expert Symposium on LED Measurement, CIE x022: 2001,(2001).
  6. U. Krüger and P. Blatter, “Spectral mismatch correction factor estimation for white LED spectra based on the photometer’s f1 ′ value,” in Proc. of the CIE Centenary Conference “Towards a New Century of Light”,(2013), pp. 300–307.
  7. K. Muray., “Publ. CIE127.2 (Revision of CIE127-1997) Draft No. 4, Dec. 2003,” in Measurement of LEDs, (Comission Internationale de l’Eclairage, 2003).
  8. “Specifications for the Chromaticity of Solid-state Lighting Products,” (NEMA, ANSI C78.377-2015, American National Standard for Electric Lamps, 2015).
  9. R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, inc., New York, 1958).
  10. T. Dönsberg, T. Pulli, M. Sildoja, T. Poikonen, H. Baumgartner, F. Manoocheri, P. Kärhä, and E. Ikonen, “Methods for decreasing uncertainties in LED photometry,” in 17th International Congress of Metrology, (EDP Sciences, 2015), p. 11001.

2006 (1)

P. Csuti and B. Kránicz, “Description of a partial f′1 error index recommended for LED photometry,” Light. Eng. 14, 28–34 (2006).

Baumgartner, H.

T. Dönsberg, T. Pulli, M. Sildoja, T. Poikonen, H. Baumgartner, F. Manoocheri, P. Kärhä, and E. Ikonen, “Methods for decreasing uncertainties in LED photometry,” in 17th International Congress of Metrology, (EDP Sciences, 2015), p. 11001.

Blackman, R. B.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, inc., New York, 1958).

Blatter, P.

U. Krüger and P. Blatter, “Spectral mismatch correction factor estimation for white LED spectra based on the photometer’s f1 ′ value,” in Proc. of the CIE Centenary Conference “Towards a New Century of Light”,(2013), pp. 300–307.

Blattner, P.

R. Rattunde and P. Blattner, “Characterization of the Performance of Illuminance Meters and Luminance Meters,” (ISO/CIE 19476:2014 (CIE S 023 E:2013), 2013).

Csuti, P.

P. Csuti and B. Kránicz, “Description of a partial f′1 error index recommended for LED photometry,” Light. Eng. 14, 28–34 (2006).

P. Csuti, B. Kránicz, and J. Schanda, “Comparison of the goodness of fit of photometers to the V(λ) function using real LED spectra,” in CIE LED Symposium, (2004).

Dönsberg, T.

T. Dönsberg, T. Pulli, M. Sildoja, T. Poikonen, H. Baumgartner, F. Manoocheri, P. Kärhä, and E. Ikonen, “Methods for decreasing uncertainties in LED photometry,” in 17th International Congress of Metrology, (EDP Sciences, 2015), p. 11001.

Ikonen, E.

T. Dönsberg, T. Pulli, M. Sildoja, T. Poikonen, H. Baumgartner, F. Manoocheri, P. Kärhä, and E. Ikonen, “Methods for decreasing uncertainties in LED photometry,” in 17th International Congress of Metrology, (EDP Sciences, 2015), p. 11001.

Jones, C.

R. Young, K. Muray, and C. Jones, “Quantifying photometric spectral mismatch uncertainties in LED measurements,” in Proceedings of the 2nd CIE Expert Symposium on LED Measurement, CIE x022: 2001,(2001).

Kärhä, P.

T. Dönsberg, T. Pulli, M. Sildoja, T. Poikonen, H. Baumgartner, F. Manoocheri, P. Kärhä, and E. Ikonen, “Methods for decreasing uncertainties in LED photometry,” in 17th International Congress of Metrology, (EDP Sciences, 2015), p. 11001.

Kránicz, B.

P. Csuti and B. Kránicz, “Description of a partial f′1 error index recommended for LED photometry,” Light. Eng. 14, 28–34 (2006).

P. Csuti, B. Kránicz, and J. Schanda, “Comparison of the goodness of fit of photometers to the V(λ) function using real LED spectra,” in CIE LED Symposium, (2004).

Krüger, U.

U. Krüger and P. Blatter, “Spectral mismatch correction factor estimation for white LED spectra based on the photometer’s f1 ′ value,” in Proc. of the CIE Centenary Conference “Towards a New Century of Light”,(2013), pp. 300–307.

Manoocheri, F.

T. Dönsberg, T. Pulli, M. Sildoja, T. Poikonen, H. Baumgartner, F. Manoocheri, P. Kärhä, and E. Ikonen, “Methods for decreasing uncertainties in LED photometry,” in 17th International Congress of Metrology, (EDP Sciences, 2015), p. 11001.

Muray, K.

K. Muray., “Publ. CIE127.2 (Revision of CIE127-1997) Draft No. 4, Dec. 2003,” in Measurement of LEDs, (Comission Internationale de l’Eclairage, 2003).

R. Young, K. Muray, and C. Jones, “Quantifying photometric spectral mismatch uncertainties in LED measurements,” in Proceedings of the 2nd CIE Expert Symposium on LED Measurement, CIE x022: 2001,(2001).

Poikonen, T.

T. Dönsberg, T. Pulli, M. Sildoja, T. Poikonen, H. Baumgartner, F. Manoocheri, P. Kärhä, and E. Ikonen, “Methods for decreasing uncertainties in LED photometry,” in 17th International Congress of Metrology, (EDP Sciences, 2015), p. 11001.

Pulli, T.

T. Dönsberg, T. Pulli, M. Sildoja, T. Poikonen, H. Baumgartner, F. Manoocheri, P. Kärhä, and E. Ikonen, “Methods for decreasing uncertainties in LED photometry,” in 17th International Congress of Metrology, (EDP Sciences, 2015), p. 11001.

Rattunde, R.

R. Rattunde and P. Blattner, “Characterization of the Performance of Illuminance Meters and Luminance Meters,” (ISO/CIE 19476:2014 (CIE S 023 E:2013), 2013).

Schanda, J.

P. Csuti, B. Kránicz, and J. Schanda, “Comparison of the goodness of fit of photometers to the V(λ) function using real LED spectra,” in CIE LED Symposium, (2004).

Sildoja, M.

T. Dönsberg, T. Pulli, M. Sildoja, T. Poikonen, H. Baumgartner, F. Manoocheri, P. Kärhä, and E. Ikonen, “Methods for decreasing uncertainties in LED photometry,” in 17th International Congress of Metrology, (EDP Sciences, 2015), p. 11001.

Tukey, J. W.

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, inc., New York, 1958).

Young, R.

R. Young, K. Muray, and C. Jones, “Quantifying photometric spectral mismatch uncertainties in LED measurements,” in Proceedings of the 2nd CIE Expert Symposium on LED Measurement, CIE x022: 2001,(2001).

Light. Eng. (1)

P. Csuti and B. Kránicz, “Description of a partial f′1 error index recommended for LED photometry,” Light. Eng. 14, 28–34 (2006).

Other (9)

R. Young, K. Muray, and C. Jones, “Quantifying photometric spectral mismatch uncertainties in LED measurements,” in Proceedings of the 2nd CIE Expert Symposium on LED Measurement, CIE x022: 2001,(2001).

U. Krüger and P. Blatter, “Spectral mismatch correction factor estimation for white LED spectra based on the photometer’s f1 ′ value,” in Proc. of the CIE Centenary Conference “Towards a New Century of Light”,(2013), pp. 300–307.

K. Muray., “Publ. CIE127.2 (Revision of CIE127-1997) Draft No. 4, Dec. 2003,” in Measurement of LEDs, (Comission Internationale de l’Eclairage, 2003).

“Specifications for the Chromaticity of Solid-state Lighting Products,” (NEMA, ANSI C78.377-2015, American National Standard for Electric Lamps, 2015).

R. B. Blackman and J. W. Tukey, The Measurement of Power Spectra (Dover Publications, inc., New York, 1958).

T. Dönsberg, T. Pulli, M. Sildoja, T. Poikonen, H. Baumgartner, F. Manoocheri, P. Kärhä, and E. Ikonen, “Methods for decreasing uncertainties in LED photometry,” in 17th International Congress of Metrology, (EDP Sciences, 2015), p. 11001.

“Photometry - The CIE system of physical photometry,” (ISO Standard: ISO 23539:2005(E)/CIE S010/E:2004, 2004).

R. Rattunde and P. Blattner, “Characterization of the Performance of Illuminance Meters and Luminance Meters,” (ISO/CIE 19476:2014 (CIE S 023 E:2013), 2013).

P. Csuti, B. Kránicz, and J. Schanda, “Comparison of the goodness of fit of photometers to the V(λ) function using real LED spectra,” in CIE LED Symposium, (2004).

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Figures (5)

Fig. 1
Fig. 1 (Top) RGB LED set: Spectral power distributions of the blue, red and green LEDs. (Middle) BB set: Spectral power distributions of the blackbody sources with color temperatures of 2500 K, 2700 K, 3000 K, 3500 K, 4000 K, 4500 K, 5000 K, 5700 K and 6500 K. (Bottom) Ph LED set: Spectral power distributions of the phosphor-based LEDs with CCTs of 2500 K, 2700 K, 3000 K, 3500 K, 4000 K, 4500 K, 5000 K, 5700 K and 6500 K.
Fig. 2
Fig. 2 Relationships between f 1   and the general photometric measurement error, 〈ϵP〉, when the latter was calculated using one red, one green and one blue LEDs (upper left), 9 blackbody sources (upper right), 9 phosphor-based white LEDs (lower left), and 9 blackbody sources together with 9 phosphor-based LEDs (lower right).
Fig. 3
Fig. 3 Determination of the cutoff spectral frequency, νλ,c in the definition of f 1   . The figure shows the correlation coefficients of 〈ϵP〉 with f 1   for the four sets of light sources when the latter were calculated for νλ,c = 2 × 10−3 nm−1, 3 × 10−3 nm−1, 4 × 10−3 nm−1, 5 × 10−3 nm−1, and 6 × 10−3 nm−1. For comparison, the correlation coefficients for f 1   are shown in the graph too. Every position at the X-axis identifies different indexes, from the conventional f 1   to the indexes obtained from our analysis at different cutoff spectral frequencies.
Fig. 4
Fig. 4 Relationships between f 1   and the general photometric measurement error, 〈ϵP〉, when the latter was calculated using one red, one green and one blue LEDs (upper left), 9 blackbody sources (upper right), 9 phosphor-based LEDs (lower left), and 9 blackbody sources together with 9 phosphor-based LEDs (lower right).
Fig. 5
Fig. 5 Relationships between f 1   (left plot) and f 1   (right plot) and the averaged |1 – F*| across the SPDs in the W set.

Equations (9)

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f 1   = 380 nm 780 nm | s rel ( λ ) V ( λ ) | d λ 380 nm 780 nm V ( λ ) d λ
s rel ( λ ) = s rel ( λ ) 380 nm 780 nm S A ( λ ) V ( λ ) d λ 380 n m 780 n m S A ( λ ) s rel ( λ ) d λ
ϵ P ( Z ) = | λ min λ max S Z ( λ ) [ s ¯ rel ( λ ) V ( λ ) d λ ] 360 nm 830 nm S Z ( λ ) V ( λ ) d λ | ,
s ¯ rel ( λ ) = s rel ( λ ) 380 nm 780 nm V ( λ ) d λ 380 nm 780 nm s rel ( λ ) d λ ,
ϵ P = 1 N Z = 1 N ϵ P ( Z ) = 1 N Z = 1 N | λ min λ max S Z ( λ ) [ s ¯ rel ( λ ) V ( λ ) d λ ] 360 nm 830 nm S Z ( λ ) V ( λ ) d λ |
δ s ( λ ) = s ¯ rel ( λ ) V ( λ ) 360 nm 830 nm V ( λ ) d λ ,
f 1   = 2 0 ν λ , c | δ ^ s | 2 d ν λ
V a r ( δ s ) = 2 0 + D PSD ( ν λ ) d ν λ .
F = s C s Z = 360 nm 830 nm S Z ( λ ) V ( λ ) d λ λ min λ max S C ( λ ) s rel ( λ ) d λ 360 nm 830 nm S C ( λ ) V ( λ ) d λ λ min λ max S Z ( λ ) s rel ( λ ) d λ ,

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