Abstract

Experience in assessing whiteness and industrial requirements is considered in the selection of whiteness formulas. The problems set by the photometry of fluorescent samples and the calorimetric prerequisites delimit the choice. A standard whiteness formula of neutral hue preference is proposed. Two supplementary whiteness formulas of green and red hue preference, respectively, are added. The feasibility of a complete characterization of white samples by whiteness, tint, and luminance factor is discussed.

© 1979 Optical Society of America

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References

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  1. D. Eitle, E. Ganz, Textilveredlung 3, 389 (1968).
  2. F. Grum, “Use of True Reflectance and Fluorescence for Color Evaluation of Achromatic and Chromatic Fluorescent Materials,” in Proceedings of the Seventeenth Session CIE (Bureau Central de la CIE, Paris, 1972), p. 71.22.
  3. D. H. Alman, F. W. Billmeyer, Color Res. Appl. 2, 19 (1977).
  4. F. Gärtner, R. Griesser, Farbe 24, 199 (1975).
  5. E. Ganz, Appl. Opt. 15, 2039 (1976).
    [CrossRef] [PubMed]
  6. R. Levene, A. Knoll, ISDC 94, 144 (1978).
  7. L. F. C. Friele, Farbe 8, 171 (1959).
  8. K. Honjyo, M. Nonaka, J. Opt. Soc. Am. 60, 1690 (1970).
    [CrossRef] [PubMed]
  9. R. Thielert, G. Schliemann, J. Opt. Soc. Am. 63, 1607 (1973).
    [CrossRef] [PubMed]
  10. S. V. Vaeck, Ann. Sci. Text. Belg. 2, 184 (1975).
  11. E. Ganz, J. Color Appearance 1, 33 (1972).
  12. A. S. Stenius, Farbe26, in press.
  13. A. Berger, Farbe26, in press.
  14. G. Anders, C. Daul, Textilveredlung 5, 211 (1970).

1978 (1)

R. Levene, A. Knoll, ISDC 94, 144 (1978).

1977 (1)

D. H. Alman, F. W. Billmeyer, Color Res. Appl. 2, 19 (1977).

1976 (1)

1975 (2)

S. V. Vaeck, Ann. Sci. Text. Belg. 2, 184 (1975).

F. Gärtner, R. Griesser, Farbe 24, 199 (1975).

1973 (1)

1972 (1)

E. Ganz, J. Color Appearance 1, 33 (1972).

1970 (2)

G. Anders, C. Daul, Textilveredlung 5, 211 (1970).

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

1968 (1)

D. Eitle, E. Ganz, Textilveredlung 3, 389 (1968).

1959 (1)

L. F. C. Friele, Farbe 8, 171 (1959).

Alman, D. H.

D. H. Alman, F. W. Billmeyer, Color Res. Appl. 2, 19 (1977).

Anders, G.

G. Anders, C. Daul, Textilveredlung 5, 211 (1970).

Berger, A.

A. Berger, Farbe26, in press.

Billmeyer, F. W.

D. H. Alman, F. W. Billmeyer, Color Res. Appl. 2, 19 (1977).

Daul, C.

G. Anders, C. Daul, Textilveredlung 5, 211 (1970).

Eitle, D.

D. Eitle, E. Ganz, Textilveredlung 3, 389 (1968).

Friele, L. F. C.

L. F. C. Friele, Farbe 8, 171 (1959).

Ganz, E.

E. Ganz, Appl. Opt. 15, 2039 (1976).
[CrossRef] [PubMed]

E. Ganz, J. Color Appearance 1, 33 (1972).

D. Eitle, E. Ganz, Textilveredlung 3, 389 (1968).

Gärtner, F.

F. Gärtner, R. Griesser, Farbe 24, 199 (1975).

Griesser, R.

F. Gärtner, R. Griesser, Farbe 24, 199 (1975).

Grum, F.

F. Grum, “Use of True Reflectance and Fluorescence for Color Evaluation of Achromatic and Chromatic Fluorescent Materials,” in Proceedings of the Seventeenth Session CIE (Bureau Central de la CIE, Paris, 1972), p. 71.22.

Honjyo, K.

Knoll, A.

R. Levene, A. Knoll, ISDC 94, 144 (1978).

Levene, R.

R. Levene, A. Knoll, ISDC 94, 144 (1978).

Nonaka, M.

Schliemann, G.

Stenius, A. S.

A. S. Stenius, Farbe26, in press.

Thielert, R.

Vaeck, S. V.

S. V. Vaeck, Ann. Sci. Text. Belg. 2, 184 (1975).

Ann. Sci. Text. Belg. (1)

S. V. Vaeck, Ann. Sci. Text. Belg. 2, 184 (1975).

Appl. Opt. (1)

Color Res. Appl. (1)

D. H. Alman, F. W. Billmeyer, Color Res. Appl. 2, 19 (1977).

Farbe (2)

F. Gärtner, R. Griesser, Farbe 24, 199 (1975).

L. F. C. Friele, Farbe 8, 171 (1959).

ISDC (1)

R. Levene, A. Knoll, ISDC 94, 144 (1978).

J. Color Appearance (1)

E. Ganz, J. Color Appearance 1, 33 (1972).

J. Opt. Soc. Am. (2)

Textilveredlung (2)

G. Anders, C. Daul, Textilveredlung 5, 211 (1970).

D. Eitle, E. Ganz, Textilveredlung 3, 389 (1968).

Other (3)

F. Grum, “Use of True Reflectance and Fluorescence for Color Evaluation of Achromatic and Chromatic Fluorescent Materials,” in Proceedings of the Seventeenth Session CIE (Bureau Central de la CIE, Paris, 1972), p. 71.22.

A. S. Stenius, Farbe26, in press.

A. Berger, Farbe26, in press.

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Figures (4)

Fig. 1
Fig. 1

Definition of calorimetric saturation s, colorimetric tint f, and hue preference angle ϕ.

Fig. 2
Fig. 2

Correlation of the parameters ωPD and ϕ with the factors α, β, and γ = 1 − αβ of BGA type whiteness formulas (1). The selected formulas 1.3, 2.3, 3.7, and 3.8 are marked ⊙; formula 2.4 is marked ○.

Fig. 3
Fig. 3

Correlation of the parameters ωPD and ϕ with the factors αT, βT, and γT = 100 − αTβT of Z/Z0, Y/Y0, and X/X0 type whiteness formulas (3). The selected formulas 1.2, 2.2, and 3.4 are marked 0.

Fig. 4
Fig. 4

Correlation of the parameters ω and ϕ with the factors ρ and σ of Yxy type whiteness formulas (5). The selected formulas 1.1, 2.1, and 3.1 are marked ⊙.

Tables (3)

Tables Icon

Table I Characteristic Parameters of Some Well-Known Whiteness Formulas, Illuminant D65 and CIE 1931 2° Standard Observer

Tables Icon

Table II Characteristic Parameters of Some Selected Whiteness and Tint Formulas for a Representative Fluorescent White (Y = 90.00, s = 0.0300, and λd = 470 nm) and for the Perfect Diffuser (Y = 100.00 and s = 0.0000), which Yields W = 100.0 and (∂W/∂Y) = 1.000 with All Formulas (Standard Illuminant D65)

Tables Icon

Table III Whiteness W1.1 of the Samples of the CIBA-GEIGY Plastic White Scale, Computed with Whiteness Formula 1.1 for Illuminant D65, Rounded to the Next Even Integer

Equations (20)

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W = β · B + γ · G + α · A ,
B = 100 · Z / Z 0 , G = 100 · Y / Y 0 , A = ( 1 + g ) · 100 · X / X 0 - g · 100 · Z / Z 0 g = 0.234 for illuminant D 65 , and
β + γ + α = 1
W = β T · Z / Z 0 + γ T · Y / Y 0 + α T · X / X 0 ,
β T + γ T + α T = 100 ,
W = 100 · Y / Y 0 + ρ ( x - x 0 ) + σ ( y - y 0 ) ,
W = Y + ρ · x + σ · y - C W ;             C W = ρ · x 0 + σ · y 0
s = ( x 0 - x ) cos η + ( y 0 - y ) sin η ,
f = ( x 0 - x ) sin η - ( y 0 - y ) cos η .
ω = ( W / s ) / ( W / Y ) ,
ϕ = - arctan [ ( W / f ) / ( W / s ) ]
T = μ ( x - x 0 ) + ν ( y - y 0 )
T = μ · x + ν · y - C T ;             C T = μ · x 0 + ν · y 0 ,
C = W - Y = ρ ( x - x 0 ) + σ ( y - y 0 ) ,
Y > 70 , W > 40 , - 6 < T < 6.
W = Y - 800 ( x - x o ) - 1700 ( y - y 0 )
W = Y - 1700 ( x - x 0 ) - 900 ( y - y 0 ) ,
W = Y + 800 ( x - x 0 ) - 3000 ( y - y 0 ) ,
T = - 1000 ( x - x 0 ) + 700 ( y - y 0 ) ,
T = - 900 ( x - x 0 ) + 800 ( y - y 0 ) .

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