Abstract

A method is described which allows a quick evaluation of a large number of spectral reflectance (transmittance) curves which with respect to a given light source and the 1931 C.I.E. standard observer produce metameric colors. The method is based on a precalculated set of linearly independent metameric blacks and demonstrated by a numerical example.

© 1958 Optical Society of America

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References

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  1. Committee on Colorimetry of the Optical Society of America, The Science of Color (Thomas Y. Crowell Company, New York, 1953), p. 385.
  2. R. H. Bingham and H. Hoerlin, J. Opt. Soc. Am. 37, 199 (1947).
    [CrossRef] [PubMed]
  3. R. H. Morris, J. Opt. Soc. Am. 37, 669 (1947).
    [CrossRef]
  4. W. L. Brewer and F. R. Holly, J. Opt. Soc. Am. 38, 858 (1948).
    [CrossRef] [PubMed]
  5. E. Hellmig, Farbe 4, 3 (1955).
  6. F. R. Güntsch, Farbe 4, 313 (1955).
  7. G. Wyszecki, Farbe 2, 39 (1953).
  8. D. L. MacAdam, J. Opt. Soc. Am. 44, 713 (1954).
    [CrossRef]
  9. E. Hellmig, Farbe 3, 165 (1955).

1955 (3)

E. Hellmig, Farbe 4, 3 (1955).

F. R. Güntsch, Farbe 4, 313 (1955).

E. Hellmig, Farbe 3, 165 (1955).

1954 (1)

1953 (1)

G. Wyszecki, Farbe 2, 39 (1953).

1948 (1)

1947 (2)

Farbe (4)

E. Hellmig, Farbe 4, 3 (1955).

F. R. Güntsch, Farbe 4, 313 (1955).

G. Wyszecki, Farbe 2, 39 (1953).

E. Hellmig, Farbe 3, 165 (1955).

J. Opt. Soc. Am. (4)

Other (1)

Committee on Colorimetry of the Optical Society of America, The Science of Color (Thomas Y. Crowell Company, New York, 1953), p. 385.

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Figures (1)

Fig. 1
Fig. 1

Example of spectral reflectance curves rλ(p) and rλ which produce metameric neutrals with respect to C.I.E. standard source C and the 1931 C.I.E. standard observer.

Tables (2)

Tables Icon

Table I Spectral reflectances rλ(hi) of 27 linearly independent metameric blacks with respect to C.I.E. standard source C and the 1931 C.I.E. standard observer over the spectral range of λ=400 mμ to λ=690 mμ. Each metameric black contains only four reflectance values different from zero. Three of them are located always at 450 mμ, 520 mμ, and 600 mμ, respectively; the fourth one which is always equal to 1.0 varies its position in the spectrum from one metameric black to the other.

Tables Icon

Table II Spectral reflectances rλ(hi) of 27 orthogonal metameric blacks with respect to C.I.E. standard source C and the 1931 C.I.E. standard observer over the spectral range of λ=400 mμ to λ=690 mμ. Empty spaces denote zeros.

Equations (6)

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X ( 1 ) = k S L r ( 1 ) ( λ ) H ( λ ) x ¯ ( λ ) d λ , Y ( 1 ) = k S L r ( 1 ) ( λ ) H ( λ ) y ¯ ( λ ) d λ , Z ( 1 ) = k S L r ( 1 ) ( λ ) H ( λ ) z ¯ ( λ ) d λ .
X = λ = S λ = L r λ H λ x ¯ λ Y = λ = S λ = L r λ H λ y ¯ λ Z = λ = S λ = L r λ H λ z ¯ λ .
λ r λ H λ x ¯ λ = 0 λ r λ H λ y ¯ λ = 0 λ r λ H λ z ¯ λ = 0.
r λ ( i ) = r λ ( p ) + r λ ( h i ) ,
X = X ( i ) = λ r λ ( i ) H λ x ¯ λ ,
λ r λ ( h s ) r λ ( h t ) = 0.