Abstract

Scale values D of whiteness have been determined visually by the method of paired comparisons of a number of white samples that differed in hue, saturation, and lightness. Each sample was also specified by use of a newly developed whiteness formula W = Y − 33.33p. W is the whiteness, Y is the luminous reflectance of the sample, and p is the ratio of two distances in the 1931 CIE chromaticity diagram, p = <O F>/<O E>. <O F> is the distance between the chromaticity point F of the sample and a point O with the chromaticity coordinates xo = 0.3090, yo = 0.3170. Point O is the center of an ellipse with a major semiaxis a = 0.030 and a minor semiaxis b = 0.009. The angle of inclination of the major axis with respect to the positive direction of the x axis of the chromaticity diagram is θ = 48.0°. <O E> is the distance between point O and the intersection E of the ellipse with the straight line through the points O and F. Good correlation between D and W was obtained in all cases, even if samples were compared that differed considerably in hue. This demonstrates the greater range of validity of the newly developed formula in comparison with current whiteness formulas.

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References

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  1. G. Wyszecki and W. S. Stiles, Color Science (Wiley, NewYork, 1967), pp. 468–469.
  2. H. Loof (private communication).
  3. Reference 1, p. 289. In this reference, the illuminant to which we refer is denoted as D6000. We use, however, the denotation D60 because this is in accordance with the denotations now in use with the CIE standard illuminants D.
  4. H. A. David, The Method of Paired Comparisons (Griffin, London, 1963).
  5. S. Ishihara, Tests for Colour-Blindness, 38 plates Edition(Kanehara Shuppan Co., Tokyo, 1967).
  6. U. Schultz and R. Lehmann, in Proceedings of the International Color Meeting "Color 69," Stockholm 1969 (Muster-Schmidt, Göttingen, 1970), Vol. 2, p. 845.
  7. H.-G. Frühling, W. Münch, and M. Richter, Farbe 5, 41(1956).
  8. R. Thielert and G. Schliemann, Farbe 21, 113 (1972).
  9. R. Thielert and G. Schliemann, J. Opt. Soc. Am. 62, 137 (1972).
    [CrossRef] [PubMed]
  10. A. Berger, Farbe 8, 187 (1959).
  11. R. S. Hunter, J. Opt. Soc. Am. 50, 44 (1960).
    [CrossRef]
  12. P. S. Stensby, J. Am. Oil Chem. Soc. 45, 497 (1968).
    [CrossRef]
  13. G. Hansen, Zellstoff Papier 18, 393 (1938).
  14. SCAN-P3: 62, Brightness of Paper and Paperboard (Scandinavian Pulp, Paper, and Board Testing Committee, Stockholm, 1962).
  15. S. V. Vaeck and F. van Lierde, Ann. Textiles Beiges No.3-9/64, 7 (Sept. 1964).
  16. K. Honjyo and M. Nonaka, J. Opt. Soc. Am. 60, 1690 (1970).
    [CrossRef] [PubMed]
  17. We are very much indebted to Dr. Kazuo Honjyo of Central Research Laboratory, Hitachi, Ltd., Tokyo, for communication of these data.

1972 (2)

R. Thielert and G. Schliemann, Farbe 21, 113 (1972).

R. Thielert and G. Schliemann, J. Opt. Soc. Am. 62, 137 (1972).
[CrossRef] [PubMed]

1970 (1)

K. Honjyo and M. Nonaka, J. Opt. Soc. Am. 60, 1690 (1970).
[CrossRef] [PubMed]

1968 (1)

P. S. Stensby, J. Am. Oil Chem. Soc. 45, 497 (1968).
[CrossRef]

1960 (1)

R. S. Hunter, J. Opt. Soc. Am. 50, 44 (1960).
[CrossRef]

1959 (1)

A. Berger, Farbe 8, 187 (1959).

1956 (1)

H.-G. Frühling, W. Münch, and M. Richter, Farbe 5, 41(1956).

1938 (1)

G. Hansen, Zellstoff Papier 18, 393 (1938).

Berger, A.

A. Berger, Farbe 8, 187 (1959).

David, H. A.

H. A. David, The Method of Paired Comparisons (Griffin, London, 1963).

Frühling, H.-G.

H.-G. Frühling, W. Münch, and M. Richter, Farbe 5, 41(1956).

Hansen, G.

G. Hansen, Zellstoff Papier 18, 393 (1938).

Honjyo, K.

K. Honjyo and M. Nonaka, J. Opt. Soc. Am. 60, 1690 (1970).
[CrossRef] [PubMed]

Hunter, R. S.

R. S. Hunter, J. Opt. Soc. Am. 50, 44 (1960).
[CrossRef]

Ishihara, S.

S. Ishihara, Tests for Colour-Blindness, 38 plates Edition(Kanehara Shuppan Co., Tokyo, 1967).

Lehmann, R.

U. Schultz and R. Lehmann, in Proceedings of the International Color Meeting "Color 69," Stockholm 1969 (Muster-Schmidt, Göttingen, 1970), Vol. 2, p. 845.

Loof, H.

H. Loof (private communication).

Münch, W.

H.-G. Frühling, W. Münch, and M. Richter, Farbe 5, 41(1956).

Nonaka, M.

K. Honjyo and M. Nonaka, J. Opt. Soc. Am. 60, 1690 (1970).
[CrossRef] [PubMed]

Richter, M.

H.-G. Frühling, W. Münch, and M. Richter, Farbe 5, 41(1956).

Schliemann, G.

R. Thielert and G. Schliemann, J. Opt. Soc. Am. 62, 137 (1972).
[CrossRef] [PubMed]

R. Thielert and G. Schliemann, Farbe 21, 113 (1972).

Schultz, U.

U. Schultz and R. Lehmann, in Proceedings of the International Color Meeting "Color 69," Stockholm 1969 (Muster-Schmidt, Göttingen, 1970), Vol. 2, p. 845.

Stensby, P. S.

P. S. Stensby, J. Am. Oil Chem. Soc. 45, 497 (1968).
[CrossRef]

Stiles, W. S.

G. Wyszecki and W. S. Stiles, Color Science (Wiley, NewYork, 1967), pp. 468–469.

Thielert, R.

R. Thielert and G. Schliemann, J. Opt. Soc. Am. 62, 137 (1972).
[CrossRef] [PubMed]

R. Thielert and G. Schliemann, Farbe 21, 113 (1972).

Vaeck, S. V.

S. V. Vaeck and F. van Lierde, Ann. Textiles Beiges No.3-9/64, 7 (Sept. 1964).

van Lierde, F.

S. V. Vaeck and F. van Lierde, Ann. Textiles Beiges No.3-9/64, 7 (Sept. 1964).

Wyszecki, G.

G. Wyszecki and W. S. Stiles, Color Science (Wiley, NewYork, 1967), pp. 468–469.

Other (17)

G. Wyszecki and W. S. Stiles, Color Science (Wiley, NewYork, 1967), pp. 468–469.

H. Loof (private communication).

Reference 1, p. 289. In this reference, the illuminant to which we refer is denoted as D6000. We use, however, the denotation D60 because this is in accordance with the denotations now in use with the CIE standard illuminants D.

H. A. David, The Method of Paired Comparisons (Griffin, London, 1963).

S. Ishihara, Tests for Colour-Blindness, 38 plates Edition(Kanehara Shuppan Co., Tokyo, 1967).

U. Schultz and R. Lehmann, in Proceedings of the International Color Meeting "Color 69," Stockholm 1969 (Muster-Schmidt, Göttingen, 1970), Vol. 2, p. 845.

H.-G. Frühling, W. Münch, and M. Richter, Farbe 5, 41(1956).

R. Thielert and G. Schliemann, Farbe 21, 113 (1972).

R. Thielert and G. Schliemann, J. Opt. Soc. Am. 62, 137 (1972).
[CrossRef] [PubMed]

A. Berger, Farbe 8, 187 (1959).

R. S. Hunter, J. Opt. Soc. Am. 50, 44 (1960).
[CrossRef]

P. S. Stensby, J. Am. Oil Chem. Soc. 45, 497 (1968).
[CrossRef]

G. Hansen, Zellstoff Papier 18, 393 (1938).

SCAN-P3: 62, Brightness of Paper and Paperboard (Scandinavian Pulp, Paper, and Board Testing Committee, Stockholm, 1962).

S. V. Vaeck and F. van Lierde, Ann. Textiles Beiges No.3-9/64, 7 (Sept. 1964).

K. Honjyo and M. Nonaka, J. Opt. Soc. Am. 60, 1690 (1970).
[CrossRef] [PubMed]

We are very much indebted to Dr. Kazuo Honjyo of Central Research Laboratory, Hitachi, Ltd., Tokyo, for communication of these data.

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Figures (5)

Fig. 1
Fig. 1

Chromaticity coordinates of samples B1–B10 (○), B11–B20 (×), and V1–V10 (●).

Fig. 2
Fig. 2

Chromaticity coordinates of samples RG1–RG10 (●) and F1–F12 (○).

Fig. 3
Fig. 3

Chromaticity coordinates of samples H1–H10 (○) and H11–H20 (●).

Fig. 4
Fig. 4

Tolerance ellipse and definition of p.

Fig. 5
Fig. 5

Relationship between visually determined scale values D of whiteness and colorimetrically evaluated whiteness W.

Tables (2)

Tables Icon

Table I Tristimulus values, visually determined scale values of whiteness, and colorimetrically evaluated whiteness.

Tables Icon

Table II Correlation coefficients.

Equations (7)

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P λ = ρ λ + f λ .
r ( D , d ) = i ( D i D ¯ ) ( d i d ¯ ) / [ i ( D i D ¯ ) 2 i ( d i d ¯ ) 2 ] 1 2 ,
W 7 = Y + 5000 Δ B 7000 Δ E ,
υ = 2.9042 ( u 0.2014 ) + 0.3072.
q = P F P G ,
p = O F O E
W = Y c ( 100 p ) ,