Abstract

Though basic problems of the perception of whiteness are as yet unsolved, this paper attempts to survey the present state and the requirements of industrial whiteness measurement. Generic formulas with adjustable parameters for the evaluation of whiteness and tint are presented.

© 1976 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. L. MacAdam, J. Opt. Soc. Am. 24, 188 (1934).
    [CrossRef]
  2. CIBA-GEIGY Rev. 1, 13 (1973).
  3. F. Grum, J. M. Patek, Tappi 48, 357 (1965).
  4. F. W. Billmeyer, Appl. Opt. 13, 1007 (1974).
    [CrossRef] [PubMed]
  5. L. F. C. Friele, Die Farbe 8, 171 (1959).
    [CrossRef]
  6. A. Berger, O. Koch, Die Farbe 9, 259 (1960).
  7. G. Wyszecki, J. Color Appearance 1 (5), 8 (1972).
  8. F. Gärtner, R. Griesser, submitted to Die Farbe.
  9. D. Eitle, E. Ganz, Textilveredlung 3, 389 (1968).
  10. A. Berger, samples and measurements made for CIE TC-1.3 Subcommittee on Whiteness (1972).
  11. F. Grum, R. F. Witzel, P. Stensby, J. Opt. Soc. Am. 64, 210 (1974).
    [CrossRef] [PubMed]
  12. A. Berger, Die Farbe 22, 213 (1973); Colour 73 (London), 331 (1973).
  13. A. Berger, D. Strocka, Die Farbe 21, 131 (1972); Appl. Opt. 12, 338 (1973).
    [PubMed]
  14. E. Ganz, D. Eitle, Die Farbe 19, 103 (1970).
  15. K. Richter, submitted to Die Farbe00, 000 (197?).
  16. A. Berger, D. Strocka, Appl. Opt. 14, 726 (1975).
    [CrossRef] [PubMed]
  17. G. Anders, E. Ganz, to be submitted to Appl. Opt.
  18. F. Grum, in Proceedings of the 17th Session CIE 1971 (CIE, Paris, 1972).
  19. F. T. Simon, J. Color Appearance 1 (4), 5 (1972); Colour 73 (London), 337 (1973).
  20. E. Allen, Appl. Opt. 12, 289 (1973).
    [CrossRef] [PubMed]
  21. G. Wyszecki, Die Farbe 19, 43 (1970); for F(17) see Berger and Strocka.13
  22. D. H. Alman, F. W. Billmeyer, D. G. Phillips, submitted to Proceedings of the 18th Session, CIE, 1975.
  23. E. Allen, J. Opt. Soc. Am. 54, 506 (1964); L. F. C. Friele, Vezelinstituut TNO, Delft, Netherlands, private communication (1968).
    [CrossRef]
  24. E. Ganz, J. Color Appearance 1 (5), 33 (1972).
  25. W. Franke, Thesis, Darmstadt (1966); W. Brecht, W. Franke, Wochenbl. Papierfabr. 95, 829 (1967).
  26. R. Sève, Color 69, (Göttingen), 335 (1970).
  27. Å. S. Stenius, J. Opt. Soc. Am. 65, 213 (1975).
    [CrossRef]
  28. F. Grum, Eastman Kodak; private communication.
  29. S. V. Vaeck, Ann. Sci. Textiles Belges 1, 95 (1966).
  30. D. J. McConnell, Color 69, (Göttingen), 329 (1970).
  31. R. Thielert, G. Schliemann, J. Opt. Soc. Am. 63, 1607 (1973).
    [CrossRef] [PubMed]
  32. K. Honjyo, M. Nonaka, J. Opt. Soc. Am. 60, 1690 (1970).
    [CrossRef] [PubMed]
  33. L. Mori, Acta Chromat. 2, 25 (1969).
  34. L. F. C. Friele, Die Farbe 8, 171 (1959) concluding “The formula is … only given to stimulate further thoughts on whiteness evaluation and cannot be recommended for use, the confusion with respect to this subject being already intolerable.”
    [CrossRef]
  35. G. Anders, Textilveredlung 9, 10 (1974).

1975 (2)

1974 (3)

1973 (4)

CIBA-GEIGY Rev. 1, 13 (1973).

A. Berger, Die Farbe 22, 213 (1973); Colour 73 (London), 331 (1973).

E. Allen, Appl. Opt. 12, 289 (1973).
[CrossRef] [PubMed]

R. Thielert, G. Schliemann, J. Opt. Soc. Am. 63, 1607 (1973).
[CrossRef] [PubMed]

1972 (5)

E. Ganz, J. Color Appearance 1 (5), 33 (1972).

A. Berger, samples and measurements made for CIE TC-1.3 Subcommittee on Whiteness (1972).

F. T. Simon, J. Color Appearance 1 (4), 5 (1972); Colour 73 (London), 337 (1973).

A. Berger, D. Strocka, Die Farbe 21, 131 (1972); Appl. Opt. 12, 338 (1973).
[PubMed]

G. Wyszecki, J. Color Appearance 1 (5), 8 (1972).

1970 (5)

E. Ganz, D. Eitle, Die Farbe 19, 103 (1970).

G. Wyszecki, Die Farbe 19, 43 (1970); for F(17) see Berger and Strocka.13

D. J. McConnell, Color 69, (Göttingen), 329 (1970).

R. Sève, Color 69, (Göttingen), 335 (1970).

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

1969 (1)

L. Mori, Acta Chromat. 2, 25 (1969).

1968 (1)

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

1966 (1)

S. V. Vaeck, Ann. Sci. Textiles Belges 1, 95 (1966).

1965 (1)

F. Grum, J. M. Patek, Tappi 48, 357 (1965).

1964 (1)

1960 (1)

A. Berger, O. Koch, Die Farbe 9, 259 (1960).

1959 (2)

L. F. C. Friele, Die Farbe 8, 171 (1959).
[CrossRef]

L. F. C. Friele, Die Farbe 8, 171 (1959) concluding “The formula is … only given to stimulate further thoughts on whiteness evaluation and cannot be recommended for use, the confusion with respect to this subject being already intolerable.”
[CrossRef]

1934 (1)

Allen, E.

Alman, D. H.

D. H. Alman, F. W. Billmeyer, D. G. Phillips, submitted to Proceedings of the 18th Session, CIE, 1975.

Anders, G.

G. Anders, Textilveredlung 9, 10 (1974).

G. Anders, E. Ganz, to be submitted to Appl. Opt.

Berger, A.

A. Berger, D. Strocka, Appl. Opt. 14, 726 (1975).
[CrossRef] [PubMed]

A. Berger, Die Farbe 22, 213 (1973); Colour 73 (London), 331 (1973).

A. Berger, D. Strocka, Die Farbe 21, 131 (1972); Appl. Opt. 12, 338 (1973).
[PubMed]

A. Berger, samples and measurements made for CIE TC-1.3 Subcommittee on Whiteness (1972).

A. Berger, O. Koch, Die Farbe 9, 259 (1960).

Billmeyer, F. W.

F. W. Billmeyer, Appl. Opt. 13, 1007 (1974).
[CrossRef] [PubMed]

D. H. Alman, F. W. Billmeyer, D. G. Phillips, submitted to Proceedings of the 18th Session, CIE, 1975.

Eitle, D.

E. Ganz, D. Eitle, Die Farbe 19, 103 (1970).

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

Franke, W.

W. Franke, Thesis, Darmstadt (1966); W. Brecht, W. Franke, Wochenbl. Papierfabr. 95, 829 (1967).

Friele, L. F. C.

L. F. C. Friele, Die Farbe 8, 171 (1959).
[CrossRef]

L. F. C. Friele, Die Farbe 8, 171 (1959) concluding “The formula is … only given to stimulate further thoughts on whiteness evaluation and cannot be recommended for use, the confusion with respect to this subject being already intolerable.”
[CrossRef]

Ganz, E.

E. Ganz, J. Color Appearance 1 (5), 33 (1972).

E. Ganz, D. Eitle, Die Farbe 19, 103 (1970).

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

G. Anders, E. Ganz, to be submitted to Appl. Opt.

Gärtner, F.

F. Gärtner, R. Griesser, submitted to Die Farbe.

Griesser, R.

F. Gärtner, R. Griesser, submitted to Die Farbe.

Grum, F.

F. Grum, R. F. Witzel, P. Stensby, J. Opt. Soc. Am. 64, 210 (1974).
[CrossRef] [PubMed]

F. Grum, J. M. Patek, Tappi 48, 357 (1965).

F. Grum, in Proceedings of the 17th Session CIE 1971 (CIE, Paris, 1972).

F. Grum, Eastman Kodak; private communication.

Honjyo, K.

Koch, O.

A. Berger, O. Koch, Die Farbe 9, 259 (1960).

MacAdam, D. L.

McConnell, D. J.

D. J. McConnell, Color 69, (Göttingen), 329 (1970).

Mori, L.

L. Mori, Acta Chromat. 2, 25 (1969).

Nonaka, M.

Patek, J. M.

F. Grum, J. M. Patek, Tappi 48, 357 (1965).

Phillips, D. G.

D. H. Alman, F. W. Billmeyer, D. G. Phillips, submitted to Proceedings of the 18th Session, CIE, 1975.

Richter, K.

K. Richter, submitted to Die Farbe00, 000 (197?).

Schliemann, G.

Sève, R.

R. Sève, Color 69, (Göttingen), 335 (1970).

Simon, F. T.

F. T. Simon, J. Color Appearance 1 (4), 5 (1972); Colour 73 (London), 337 (1973).

Stenius, Å. S.

Stensby, P.

Strocka, D.

A. Berger, D. Strocka, Appl. Opt. 14, 726 (1975).
[CrossRef] [PubMed]

A. Berger, D. Strocka, Die Farbe 21, 131 (1972); Appl. Opt. 12, 338 (1973).
[PubMed]

Thielert, R.

Vaeck, S. V.

S. V. Vaeck, Ann. Sci. Textiles Belges 1, 95 (1966).

Witzel, R. F.

Wyszecki, G.

G. Wyszecki, J. Color Appearance 1 (5), 8 (1972).

G. Wyszecki, Die Farbe 19, 43 (1970); for F(17) see Berger and Strocka.13

Acta Chromat. (1)

L. Mori, Acta Chromat. 2, 25 (1969).

Ann. Sci. Textiles Belges (1)

S. V. Vaeck, Ann. Sci. Textiles Belges 1, 95 (1966).

Appl. Opt. (3)

CIBA-GEIGY Rev. (1)

CIBA-GEIGY Rev. 1, 13 (1973).

Color (2)

R. Sève, Color 69, (Göttingen), 335 (1970).

D. J. McConnell, Color 69, (Göttingen), 329 (1970).

Die Farbe (7)

L. F. C. Friele, Die Farbe 8, 171 (1959) concluding “The formula is … only given to stimulate further thoughts on whiteness evaluation and cannot be recommended for use, the confusion with respect to this subject being already intolerable.”
[CrossRef]

G. Wyszecki, Die Farbe 19, 43 (1970); for F(17) see Berger and Strocka.13

L. F. C. Friele, Die Farbe 8, 171 (1959).
[CrossRef]

A. Berger, O. Koch, Die Farbe 9, 259 (1960).

A. Berger, Die Farbe 22, 213 (1973); Colour 73 (London), 331 (1973).

A. Berger, D. Strocka, Die Farbe 21, 131 (1972); Appl. Opt. 12, 338 (1973).
[PubMed]

E. Ganz, D. Eitle, Die Farbe 19, 103 (1970).

J. Color Appearance (3)

G. Wyszecki, J. Color Appearance 1 (5), 8 (1972).

F. T. Simon, J. Color Appearance 1 (4), 5 (1972); Colour 73 (London), 337 (1973).

E. Ganz, J. Color Appearance 1 (5), 33 (1972).

J. Opt. Soc. Am. (6)

samples and measurements made for CIE TC-1.3 Subcommittee on Whiteness (1)

A. Berger, samples and measurements made for CIE TC-1.3 Subcommittee on Whiteness (1972).

Tappi (1)

F. Grum, J. M. Patek, Tappi 48, 357 (1965).

Textilveredlung (2)

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

G. Anders, Textilveredlung 9, 10 (1974).

Other (7)

D. H. Alman, F. W. Billmeyer, D. G. Phillips, submitted to Proceedings of the 18th Session, CIE, 1975.

F. Grum, Eastman Kodak; private communication.

W. Franke, Thesis, Darmstadt (1966); W. Brecht, W. Franke, Wochenbl. Papierfabr. 95, 829 (1967).

F. Gärtner, R. Griesser, submitted to Die Farbe.

G. Anders, E. Ganz, to be submitted to Appl. Opt.

F. Grum, in Proceedings of the 17th Session CIE 1971 (CIE, Paris, 1972).

K. Richter, submitted to Die Farbe00, 000 (197?).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (14)

Fig. 1
Fig. 1

Sample number 12 (210) of the CIBA-GEIGY Plastic White Scale2 measured with a Zeiss DMC 25 spectrophotometer: (1) spectral radiance factor with xenon lamp(the depressions near 465 nm being due to xenon lines); (2) conventional reflectance with detector for visible range (S10 sensitivity); (3) conventional reflectance with detector for uv range (S5 sensitivity).

Fig. 2
Fig. 2

Apparent D65 chromaticities of sample number 12 (210) of the CIBA-GEIGY Plastic White Scale measured with various instruments: (1) Spectromat SP-3; (2) Zeiss RFC 3 with AGB-filters; (3) Zeiss Elrepho; (4) Spectromat SP-3 with adjustable uv filter8; (5) Zeiss DMC 25; (6) Zeiss DMC 25, but transformed to D65 by the method of Eitle and Ganz.9 All chromaticities of the nonfluorescent substrate for sample 12 lie within the circle 7.

Fig. 3
Fig. 3

Quantum absorption Q(λ′) of the sample by Ganz and Eitle14 (full line) and of the three simulated functions by Berger and Strocka16 (dotted lines).

Fig. 4
Fig. 4

Influence of the spectral power distribution of the irradiance on the effect of FWA’s and of bluing.9 Chromaticities for illuminants D65, and A of a sample: △ untreated, ⊙ treated with FWA, × D75, blued, ⊗ treated with FWA and blued.

Fig. 5
Fig. 5

Lines of intersection of the equiwhiteness surfaces defined by the whiteness formulas of Stensby, Tappi, and Berger with the planes Y = 100 and λd = 470 nm, respectively.24 The whiteness formula W = B was derived from the TAPPI brightness R457. Therefore it is called the Tappi whiteness formula although it is not endorsed by Tappi.

Fig. 6
Fig. 6

Definition of ϕ characterizing hue preference sin(−ϕ) = (ΔWHH); cos(−ϕ) = (ΔWSS).

Fig. 7
Fig. 7

B, G, A whiteness formulas defined by their parameters β, γ, α (with δ = 1) and characterized by ωI and ϕI for dominant wavelength λd = 470 nm (or ψI, respectively).24

Fig. 8
Fig. 8

L, b, a whiteness formulas defined by their parameters ν, μ and characterized by ωI and ϕI for dominant wavelength λd = 470 nm (or ψI, respectively).24 Stensby (SY)ωI = 3.38 × 103 and ϕI = 56°.

Fig. 9
Fig. 9

Graphical method for determining adjusted parameters ρ, σ, and κ3 of Eq. (13) based on measurements of plates 5 to 12 of the CIBA-GEIGY Plastic White Scale with instruments A, B, C of different types and CR with instrument C after reconditioning and replacing the xenon lamp (measurements by Griesser).

Fig. 10
Fig. 10

Equiwhiteness lines and line of the preferred hue corresponding approximately to a dominant wavelength of 472 nm (Illuminant C) presented by Vaeck.29

Fig. 11
Fig. 11

Lines of intersection of the equiwhiteness surfaces defined by the whiteness formulas of Grum et al. (simplified); McConnell; Thielert and Schliemann with the plane Y = 100 and the plane of the preferred hue or of constant dominant wavelength.

Fig. 12
Fig. 12

(a) Relations between the differentials of whiteness and the asymptote cones of the equiwhiteness hyperboloids. (b) Relations between the equiwhiteness point YW on the achromatic axis and the apex of the asymptote cone A and the preferred white P.

Fig. 13
Fig. 13

Lines of intersection of the equiwhiteness surfaces defined by the hyperboloid whiteness Eq. (38) with the plane Y = 100 and the plane of the preferred hue. The parameters of Eq. (38) are those included in function WHYPO as default options.

Fig. 14
Fig. 14

Chromaticities of the paper samples by Berger10 ● and of plates 2 to 12 of the CIBA-GEIGY Plastic White Scale3 × measured by an Elrepho photometer with xenon lamp, computed for D65 illuminant and CIE 1931 standard observer △. The equitint lines are determined by a linear regression analysis of the chromaticity and the visual tint assessments of the samples. The lines separate the tints 5G|4G,3G,2G|1G,N,1R|2R,3R,4R|5R.

Tables (10)

Tables Icon

Table I Chromaticities of Twenty White Papers Measured by Berger with a Filtered Xenon Lamp (Zeiss Elrepho) and by Grum, et al. with a Macbeth D65-Simulator Fluorescent Lamp

Tables Icon

Table II Mean μ and Standard Deviation σ of Computed Differences Between Experimental and True D65 Chromaticity, Luminance, and Whiteness (CIBA-GEIGY units)

Tables Icon

Table III Differences Between Values Measured with Irradiations Indicated and Transformed to D65 by Formula (5) of Berger12 and True D65 Chromaticity Luminance and Whiteness (CIBA-GEIGY units) for CIBA-GEIGY White Scale Samples 210 Plastic (P) and 240 Cotton (C)

Tables Icon

Table IV Factors for Converting AGB in XYZ and Vice Versa

Tables Icon

Table V Ratios of Parameters α/β, μ/ν, ρ/σ as a Function of the Hue Preference Angle ϕI for Reference Dominant Wavelength 470 nm and for the Perfect Diffuser Irradiated by D65 and CIE 1931 2° Observer

Tables Icon

Table VI Luminance Factors Determined by Grum et al.11,28 for a D65-Simulator Fluorescent Lamp and CIE 1964 10° Observer

Tables Icon

Table VII Parameters and Correlation Coefficients Based on Data by Grum et al.11 for Various Whiteness Formulas and Hue Preference Angles ϕI

Tables Icon

Table VIII Calculation of Parameters ρ, σ, and κ3 for Whiteness Eq. (13) Based on Measurements (by Griesser) of Plates 5 to 12 of the CIBA-GEIGY Plastic White Scale with Instruments A, B, C, and CR (see Fig. 9) with = 2, ϕ = 20°, and ρ/σ = 0.2643

Tables Icon

Table IX Means and Standard Deviations of Visual Assessments of Tint of Forty-six Paper Samples by Berger10 vs the CIBA-GEIGY Plastic White Scale by Seven Observers

Tables Icon

Table X Individual Assessments of Tint by Seven Observers of a Set of Forty-six Paper Samples from Berger10 vs the CIBA-GEIGY Plastic White Scale

Equations (62)

Equations on this page are rendered with MathJax. Learn more.

F M ( λ ) = [ β M ( λ ) - β T ( λ ) ] · S M ( λ ) .
Q = k λ [ 1 - β T ( λ ) ] · { 1 - β T ( λ ) · [ 1 - β 0 ( λ ) ] 2 β 0 ( λ ) · [ 1 - β T ( λ ) ] 2 } · S ( λ ) · λ · Δ λ ,
F N ( λ ) = F M ( λ ) · Q N / Q M .
β N ( λ ) = β T ( λ ) + F N ( λ ) / S N ( λ ) = β T ( λ ) + [ β M ( λ ) - β T ( λ ) ] Q N · S M ( λ ) Q M · S N ( λ ) .
T C i = k λ β M ( λ ) S N ( λ ) t ¯ i ( λ ) Δ λ ,
k = 100 / λ S N ( λ ) y ¯ ( λ ) Δ λ .
Δ T i = T C i - T N i = k λ [ β M ( λ ) - β N ( λ ) ] · S N ( λ ) · t ¯ i ( λ ) · Δ λ .
Δ T i = k λ F N ( λ ) · [ Q M · S N ( λ ) Q N · S M ( λ ) - 1 ] · t ¯ i ( λ ) · Δ λ .
S M ( λ ) S N ( λ ) Q M Q N .
W = 100 - [ ( Δ L ) 2 + k ( Δ C ) 2 ] 1 / 2 ,
W = i k i T i .
W = f ( X , Y , Z ) ,
W 1 = β · B + γ · G + α · A + κ 1 ,
W 2 = λ · L + ν · b + μ · a + κ 2 ,
W 3 = · Y + ρ · x + σ · y + κ 3 ,
X = f X A · A + f X B · B , Y = G , Z = f Z B · B ,
A = g A X · X + g A Z · Z , G = Y , B = g B Z · Z ,
g A X = 1 / f X A , g A Z = - f X B / ( f X A · f Z B ) , g B Z = 1 / f Z B .
L = 10.0 · Y 1 / 2 , a = 17.5 · Y - 1 / 2 · [ X / ( f X A + f X B ) - Y ] · 0.01 , b = 7.0 · Y - 1 / 2 · ( Y - Z / f Z B ) · 0.01 ,
Stensby W = L - 3 b + 3 a , TAPPI W = B , Berger W = 3 B + G - 3 A ,
S = [ ( x I - x ) 2 + ( y I - y ) 2 ] 1 / 2 ,
ω = ( W / S ) / ( W / Y ) ,
ϕ = - arctan [ W / H ) / ( W / S ) ] ,
ψ = ϕ + η + π / 2 ,
B , G , A [ Eq · ( 11 ) ] L , b , a [ Eq . ( 12 ) ] ( W 1 / Y ) I = δ ( W 2 / Y ) I = λ / 2 with δ = β + γ + α due to L = 10 Y 1 / 2 κ 1 = 100 ( 1 - δ ) κ 2 = 100 ( 1 - λ ) .
TITAPPI W = B , CR Croes W + B + G - A , ST Stephansen W = 2 B - A , BE Berger W = 3 B + G - 3 A , TA Taube W = 4 B - 3 G ,
HU Hunter W = L - 3 b , SY Stensby W = L - 3 b + 3 a .
W 3 = ( W / Y ) · Y + ( W / S ) · S + κ 3 = ( W / Y ) · ( Y + ω · S ) + κ 3
S = ( x I - x ) · sin ψ - ( y I - y ) · cos ψ sin ( ψ - η ) = ( x I - x ) · cos ( ϕ + η ) + ( y I - y ) · sin ( ϕ + η ) cos ϕ .
= ( W / Y ) , ρ = - ( W / Y ) · ω · cos ( ϕ + η ) / cos ϕ , σ = - ( W / Y ) · ω · sin ( ϕ + η ) / cos ϕ , κ 3 = 100 ( 1 - ) - ρ · x I - σ · y I .
ϕ = arctan ( σ / ρ ) - η , ω = ( cos ϕ ) · ( ρ 2 + σ 2 ) 1 / 2 / .
ω M A = Δ Y / Δ S 10 / 0.017 600.
i { γ · G i + β · [ B i + ( α / β ) ϕ I · A i ] + κ 1 - W i } 2 = Min , i { λ · L i + ν · [ b i + ( μ / ν ) ϕ I · a i ] + κ 2 - W i } 2 = Min , i { · Y i + σ · [ y i + ( ρ / σ ) ϕ · x i ] + κ 3 - W i } 2 = Min .
ρ / σ = tan ( ϕ + η ) ,
S i * = x i · ρ / σ + y i
W i * = W i - · Y i
σ = ( W 1 * - W 2 * ) / ( S 1 * - S 2 * ) , ρ = σ · ( ρ / σ ) , κ 3 = W 1 * - σ · S I * .
W = Y + k · E ( u , v ) ,
W = B - 2 { a 2 + [ b - 0.36 ( 80 - B ) ] 2 } 1 / 2
W = 3.80 Z - 3.647 P ξ , η - 270.1
W = 3.80 · Z - 1201 · S - 270.1
W = Y - 33.3 · p .
W 2 = A L 2 - ( M / b ) 2 - ( S / c ) 2 .
W 2 = 0.298 L 2 - 30.393 K 2 ,
L = 0.53517 X + 0.5487 Y + 0.64468 Z , K = 0.41046 X + 0.49896 Y - 0.76322 Z .
( Y - Y A ) 2 - [ ω ( S - S A ) ] 2 - ( χ H ) 2 = ( Δ Y V ) 2 ,
a = [ ( Δ S / Δ W ) + ( Δ S / Δ W ) ] / 2 , b = [ ( Δ S / Δ W ) - ( Δ S / Δ W ) ] / 2 , c = ( Δ H / Δ W ) , ω = ( Δ Y / Δ S ) yellow = d / b , χ / ω = b / c ; θ = d / a ,
χ = ω ( Δ S / Δ W ) - ( Δ S / Δ W ) 2 ( Δ H / Δ W ) , τ = ω / θ = a / b = ( Δ S / Δ W ) + ( Δ S / Δ W ) ( Δ S / Δ W ) - ( Δ S / Δ W ) .
η = arctan [ ( y I - y P ) / ( x I - x P ) ] .
S = Δ x cos η + Δ y sin η , H = Δ x sin η - Δ y cos η ,
Δ x = x I - x             Δ y = y I - y ,
S A = S P - ( Y P - Y A - Δ Y V ) τ / ω ,
Y W = Y A + [ ( ω S A ) 2 + ( Δ Y V ) 2 ] 1 / 2 , W = ( W / Y ) · Y W + 100 [ 1 - ( W / Y ) ] .
S P = [ ( X I - x P ) 2 + ( y I - y P ) 2 - H I 2 ] 1 / 2 , η = arctan [ ( y I - y P ) / ( x I - x P ) ] - arctan ( H I / S P ) , H = Δ x · sin η - Δ y . cos η + H I , Y W = Y A + [ ( ω S A ) 2 + ( χ H I ) 2 + ( Δ Y V ) 2 ] 1 / 2 .
W = WHYPO ( Y , x , y , Y P , x P , y P , H I , Δ Y V , Y / W , S / W , S / W , H / W , OBS ) ,
Y P = 100 , x P = 0.2899 , y P = 0.2961 , H I = 0 , Δ Y V = 10 , Y / W = 1 , S / W = 5 × 10 - 4 , S / W = - 1.67 × 10 - 4 , H / W = 0.67 × 10 - 4 ,
W / Y = 1 , ω = 2000 , χ = 10 , 000 , τ = 0.50 , S P = 0.0400 , η = 55.1 ° , λ d = 470 nm for 1931 standard observer .
Y P = 100 , x P = 0.3090 , y P = 0.3170 , H I = 0.00448 , Δ Y V = 0 , Y / W = 1 , S / W = 0.0009 , S / W = - 0.0009 , H / W = 0.00027 ,
W / Y = 1 , ω = 1111 , χ = 3704 , τ = 0 , S P = 0.0240 , η = 48 ° .
T = m · x + n · y + k .
m = - 1048 ,             n = 705 ,             k = 95.8 ,
m = - 964 ,             n = 679 ,             k = 78.3.

Metrics