Abstract

An empirical formula can express the equivalent luminance of any light as a function of the scotopic and photopic luminances. Tests show the suitability of this standard observer for large-field photometry at any level. A restriction on the use of the term equivalent luminance is suggested.

© 1968 Optical Society of America

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References

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  1. D. A. Palmer, Nature 209, 276 (1966).
    [CrossRef] [PubMed]
  2. D. A. Palmer, Vision Res. 7, 619 (1967).
    [CrossRef] [PubMed]
  3. J. W. Walsh, Photometry (Constable, London, 1962).
  4. G. Wyszecki, J. Opt. Soc. Am. 57, 254 (1967), gives a recent summary of literature on this subject.
    [CrossRef] [PubMed]
  5. CIE Publication 11A, 1964, Proceedings of 1963 meeting, Vienna (CIE Bureau Central, Paris1964) 1st ed.
  6. D. L. MacAdam, J. Soc. Motion Picture Television Engrs. 64, 629 (1955).
  7. J. A. S. Kinney, J. Opt. Soc. Am. 45, 507 (1955).
    [CrossRef] [PubMed]
  8. J. A. S. Kinney, J. Opt. Soc. Am. 48, 185 (1958).
    [CrossRef] [PubMed]
  9. J. A. S. Kinney, J. Opt. Soc. Am. 54, 671 (1964). Dr. Jo Ann S. Kinney is thanked for providing details of the original data.
    [CrossRef] [PubMed]
  10. H. V. Walters and W. D. Wright, Proc. Roy. Soc. (London) B131, 340 (1943).
  11. A. H. Taylor, Illum. Eng. 38, 89 (1943).
  12. C2 in Planck’s formula was taken as 1.438 × 10−2 m °K.

1967 (2)

1966 (1)

D. A. Palmer, Nature 209, 276 (1966).
[CrossRef] [PubMed]

1964 (1)

1958 (1)

1955 (2)

J. A. S. Kinney, J. Opt. Soc. Am. 45, 507 (1955).
[CrossRef] [PubMed]

D. L. MacAdam, J. Soc. Motion Picture Television Engrs. 64, 629 (1955).

1943 (2)

H. V. Walters and W. D. Wright, Proc. Roy. Soc. (London) B131, 340 (1943).

A. H. Taylor, Illum. Eng. 38, 89 (1943).

Kinney, J. A. S.

MacAdam, D. L.

D. L. MacAdam, J. Soc. Motion Picture Television Engrs. 64, 629 (1955).

Palmer, D. A.

D. A. Palmer, Vision Res. 7, 619 (1967).
[CrossRef] [PubMed]

D. A. Palmer, Nature 209, 276 (1966).
[CrossRef] [PubMed]

Taylor, A. H.

A. H. Taylor, Illum. Eng. 38, 89 (1943).

Walsh, J. W.

J. W. Walsh, Photometry (Constable, London, 1962).

Walters, H. V.

H. V. Walters and W. D. Wright, Proc. Roy. Soc. (London) B131, 340 (1943).

Wright, W. D.

H. V. Walters and W. D. Wright, Proc. Roy. Soc. (London) B131, 340 (1943).

Wyszecki, G.

Illum. Eng. (1)

A. H. Taylor, Illum. Eng. 38, 89 (1943).

J. Opt. Soc. Am. (4)

J. Soc. Motion Picture Television Engrs. (1)

D. L. MacAdam, J. Soc. Motion Picture Television Engrs. 64, 629 (1955).

Nature (1)

D. A. Palmer, Nature 209, 276 (1966).
[CrossRef] [PubMed]

Proc. Roy. Soc. (London) (1)

H. V. Walters and W. D. Wright, Proc. Roy. Soc. (London) B131, 340 (1943).

Vision Res. (1)

D. A. Palmer, Vision Res. 7, 619 (1967).
[CrossRef] [PubMed]

Other (3)

J. W. Walsh, Photometry (Constable, London, 1962).

CIE Publication 11A, 1964, Proceedings of 1963 meeting, Vienna (CIE Bureau Central, Paris1964) 1st ed.

C2 in Planck’s formula was taken as 1.438 × 10−2 m °K.

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Figures (5)

Fig. 1
Fig. 1

Loci of constant equivalent luminance in the scotopic and lower mesopic ranges for a 15° field. The coordinates of scotopic and photopic luminance (S,P) are in cd/m2. – – – – – – curves derived from the formula L = (MS+P2)/(M+P) with M = 6.28 × 10−2 cd/m2. +—luminances of the standard radiator to which the loci refer. ○—experimental points.

Fig. 2
Fig. 2

As Fig. 1 but for the higher mesopic and photopic ranges.

Fig. 3
Fig. 3

Kinney’s data plotted in the S,P diagram of Figs. 1 and 2. ■—observer D; ▲—observer K; ●—observer M. – – – – –, representative loci calculated from the formula, not necessarily those best fitting the data. ———, lines separating different sets of points.

Fig. 4
Fig. 4

Tests of the formula with nonmonochromatic lights. – – – – – –, loci derived from the formula as in Figs. 13. ●—experimental points for matches with ten nonmonochromatic lights by 16 observers. ○—points for three such lights reported by the CIE. The numbering is as in the original publications.2,5

Fig. 5
Fig. 5

Suggested photopic V(λ) functions plotted against the wavelength λ in nm. – – – – – –, V10(λ); ———, 0.1079 V′(λ) +0.9972 V2(λ).

Equations (5)

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Σ i { ln [ ( M S i + P i 2 ) / ( M + P i ) ] - ln L i } 2 ,
L = [ M S + ( 1 - n ) S P 2 + n P 2 2 ] / ( M + P 2 )
v 10 ( λ ) 0.0405 v ( λ ) + 0.9595 v 2 ( λ ) ,
P 10 0.0405 S + 0.9595 P 2 ,
V 10 ( λ ) 0.1079 V ( λ ) + 0.9972 V 2 ( λ ) .