Abstract

Colorimetric matches between light from objects and a three-primary visual colorimeter are generally metameric, not spectral. The amount of difference between the spectral energy distributions from the object and the calorimeter determines the degree of metamerism. Three indexes of metamerism are considered that depend on this difference. One of these indexes is shown to correlate well with the chromaticity spreads found among observers’ settings for a series of metameric matches. This correlation is independent of luminance. The other indexes do not correlate with the spread of chromaticity of matches by observers.

© 1965 Optical Society of America

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References

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  1. W. S. Stiles and G. Wyszecki, J. Opt. Soc. Am. 52, 58 (1962).
    [CrossRef]
  2. I. Nimeroff, J. Opt. Soc. Am. 54, 696 (1964).
    [CrossRef]
  3. D. B. Judd and G. Wyszecki, Color in Business, Science and Industry (John Wiley & Sons, Inc., New York, 1963), 2nd ed., p. 152 ff.
  4. Commission Internationale de l’Eclairage (CIE) Proc. 14th Session A36, Brussels (1959).
  5. D. L. MacAdam, J. Opt. Soc. Am. 27, 294 (1937).
    [CrossRef]
  6. D. L. MacAdam, J. Opt. Soc. Am. 32, 2 (1942).
    [CrossRef]
  7. C. Spearman, Brit. J. Psychol. 2, 89 (1906).
  8. I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Res. Natl. Bur. Std. (U. S.) 65A, 475 (1961); J. Opt. Soc. Am. 52, 685 (1962).
    [CrossRef]
  9. F. J. J. Clarke, PhD. thesis, Imperial College, University of London (1959); Opt. Acta. 7, 355 (1960).
  10. I. Nimeroff, D.I.C. thesis, Imperial College, University of London (1962); J. Opt. Soc. Am. 54, 833 (1964).

1964 (1)

1962 (1)

1961 (1)

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Res. Natl. Bur. Std. (U. S.) 65A, 475 (1961); J. Opt. Soc. Am. 52, 685 (1962).
[CrossRef]

1942 (1)

1937 (1)

1906 (1)

C. Spearman, Brit. J. Psychol. 2, 89 (1906).

Clarke, F. J. J.

F. J. J. Clarke, PhD. thesis, Imperial College, University of London (1959); Opt. Acta. 7, 355 (1960).

Dannemiller, M. C.

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Res. Natl. Bur. Std. (U. S.) 65A, 475 (1961); J. Opt. Soc. Am. 52, 685 (1962).
[CrossRef]

Judd, D. B.

D. B. Judd and G. Wyszecki, Color in Business, Science and Industry (John Wiley & Sons, Inc., New York, 1963), 2nd ed., p. 152 ff.

MacAdam, D. L.

Nimeroff, I.

I. Nimeroff, J. Opt. Soc. Am. 54, 696 (1964).
[CrossRef]

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Res. Natl. Bur. Std. (U. S.) 65A, 475 (1961); J. Opt. Soc. Am. 52, 685 (1962).
[CrossRef]

I. Nimeroff, D.I.C. thesis, Imperial College, University of London (1962); J. Opt. Soc. Am. 54, 833 (1964).

Rosenblatt, J. R.

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Res. Natl. Bur. Std. (U. S.) 65A, 475 (1961); J. Opt. Soc. Am. 52, 685 (1962).
[CrossRef]

Spearman, C.

C. Spearman, Brit. J. Psychol. 2, 89 (1906).

Stiles, W. S.

Wyszecki, G.

W. S. Stiles and G. Wyszecki, J. Opt. Soc. Am. 52, 58 (1962).
[CrossRef]

D. B. Judd and G. Wyszecki, Color in Business, Science and Industry (John Wiley & Sons, Inc., New York, 1963), 2nd ed., p. 152 ff.

Brit. J. Psychol. (1)

C. Spearman, Brit. J. Psychol. 2, 89 (1906).

J. Opt. Soc. Am. (4)

J. Res. Natl. Bur. Std. (U. S.) (1)

I. Nimeroff, J. R. Rosenblatt, and M. C. Dannemiller, J. Res. Natl. Bur. Std. (U. S.) 65A, 475 (1961); J. Opt. Soc. Am. 52, 685 (1962).
[CrossRef]

Other (4)

F. J. J. Clarke, PhD. thesis, Imperial College, University of London (1959); Opt. Acta. 7, 355 (1960).

I. Nimeroff, D.I.C. thesis, Imperial College, University of London (1962); J. Opt. Soc. Am. 54, 833 (1964).

D. B. Judd and G. Wyszecki, Color in Business, Science and Industry (John Wiley & Sons, Inc., New York, 1963), 2nd ed., p. 152 ff.

Commission Internationale de l’Eclairage (CIE) Proc. 14th Session A36, Brussels (1959).

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Figures (8)

Fig. 1
Fig. 1

Spectral irradiance Efl vs trivariate metamerism index, Mi computed by Eq. (3): i=x, l=550 to 650 nm, ●; i=y, l=500 to 600 nm, ○; i=z, l=420 to 460 nm, ○.

Fig. 2
Fig. 2

Predicted chromaticities (·), and observer chromaticity-match boundaries in the NRC (dashed ellipses) and NBS (solid ellipses) field trials of the 10° observer system; NBS observer averages (x).

Fig. 3
Fig. 3

Ellipses of observers’ matches in the (x,y)- and the (u,v)-chromaticity diagrams for trial filter #7.

Fig. 4
Fig. 4

Spectral irradiance distributions for trial filter #7 and range of observers’ matches.

Fig. 5
Fig. 5

Spectral irradiance distributions for trial filter #9 and range of observers’ matches.

Fig. 6
Fig. 6

Spectral irradiance distributions for trial filter #18 and range of observers’ matches.

Fig. 7
Fig. 7

Observer difference δmax in the u,v,w, system and metamerism index computed by method A, in the u,v,w, system.

Fig. 8
Fig. 8

Observer difference δmax in the u, v, w system and metamerism index computed by method B, in the u, v, w system. (Curve shown was visually estimated.)

Tables (3)

Tables Icon

Table I The defining formulas for computing metamerism indexes by Methods A and B in the xyz system and the uvw system.

Tables Icon

Table II Comparison of observer spreads and metamerism indexes for the field trial filters.

Tables Icon

Table III Rank–order correlation between observer spreads and metamerism indexes by methods A and B.

Equations (17)

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0 ( E λ - E λ ) x ¯ ( λ ) d λ = 0 , 0 ( E λ - E λ ) y ¯ ( λ ) d λ = 0 , 0 ( E λ - E λ ) z ¯ ( λ ) d λ = 0 ,
M e = [ λ ( E f λ - E P λ ) 2 ] 1 2 ,
M x 2 = λ [ x ¯ ( λ ) ( E f λ - E P λ ) ] 2 , M y 2 = λ [ y ¯ ( λ ) ( E f λ - E P λ ) ] 2 , M z 2 = λ [ z ¯ ( λ ) ( E f λ - E P λ ) ] 2 .
M i 2 = λ [ i ( λ ) Δ E λ ] 2 ,
M t = [ ( k x M x ) 2 + ( k y M y ) 2 + ( k z M z ) 2 ] 1 2 .
M t = ( M x 2 + M y 2 + M z 2 ) 1 2 .
M i 2 = λ [ ( i ( λ ) Δ E λ ) 2 / i ( λ ) E f λ ] ,
M i 2 = { λ [ i ( λ ) Δ E λ ] 2 } / [ λ i ( λ ) E f λ ] 2 .
λ [ i ( λ ) Δ E λ ] 2 / [ λ i ( λ ) E f λ ] 2 = λ [ i ( λ ) Δ E λ ] 2 / [ λ i ( λ ) E P λ ] 2 ,
U = 2 X / 3 , V = Y , W = ( 3 Y - X + Z ) / 2.
u = 4 x / ( 12 y - 2 x + 3 ) , v = 6 y / ( 12 y - 2 x + 3 ) .
ū ( λ ) = 2 x ¯ ( λ ) / 3 , v ¯ ( λ ) = y ¯ ( λ ) , w ¯ ( λ ) = [ 3 y ¯ ( λ ) - x ¯ ( λ ) + z ¯ ( λ ) ] / 2.
M L t 2 = ( M L i 2 ) .
Δ [ i m ( λ ) E m λ ] ,
Δ E λ = i ( E f λ - E P λ i ) / 11 .
ρ = 6 d 2 / n ( n 2 - 1 ) ,
i t = i + M + 0 + a + ,