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References

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  1. P. Moon and D. E. Spencer, J. Opt. Soc. Am. 33, 270 (1943).
    [Crossref]
  2. S. M. Newhall, D. Nickerson, and D. B. Judd, J. Opt. Soc. Am. 33, 385 (1943).
    [Crossref]
  3. W. C. Granville, D. Nickerson, and C. E. Foss, J. Opt. Soc. Am. 33, 376 (1943).
    [Crossref]
  4. K. L. Kelly, K. S. Gibson, and D. Nickerson, J. Opt. Soc. Am. 33, 355 (1943).
    [Crossref]

1943 (4)

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Figures (11)

Fig. 1
Fig. 1

I.C.I. chromaticity diagram showing change in position of the point ω1=ω3=0 for I.C.I. Illuminant C adaptation as a function of α=Y/Y0.

Fig. 2
Fig. 2

Simplified nomographs for making the transformation from X, Y, Z, to ω1, ω2, ω3, and vice versa. Find X on scale A, Y on scale D, and with a straightedge read ω1 on scale E. Find Z on scale A, Y on scale C, and read ω3 on scale F. Find Y on scale A and read ω2 on scale B.

Fig. 3
Fig. 3

Comparison of Eqs. (10) [solid line] and (13) [dotted line], showing deviations from the recommended Munsell value in units of one value step when the recommended Y for Munsell values from 1 to 10 is used in the two equations.

Fig. 4
Fig. 4

Transformation of constant hue lines in the ω1ω3 plane to the I.C.I. chromaticity diagram. Points were calculated for Y=10.

Fig. 5
Fig. 5

The Munsell 100 hue circle plotted in the ω1ω3 plane.

Fig. 6
Fig. 6

Colors of the Munsell 100 hue circle, showing the correlation between the Munsell hue number and the hue angle θ from Fig. 5.

Fig. 7
Fig. 7

The Munsell colors of value 5.

Fig. 8
Fig. 8

The recommended positions of the Munsell colors of value 5.

Fig. 9
Fig. 9

Munsell colors of hue 5R and the recommended positions plotted in a constant hue plane.

Fig. 10
Fig. 10

Munsell colors of hue 5B and the recommended positions.

Fig. 11
Fig. 11

Munsell colors of hue 5GY and the recommended positions.

Equations (20)

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ω 1 = 2 ( p 1 - 0.95 p 2 ) 0.168 ( 1.63 + p 2 ) 1 2 - 0.119 , ω 3 = 2.27 ( p 3 - 1.10 p 2 ) 1.2 0.628 ( 1.80 + p 2 ) 1 2 - 0.521 .
p 1 = X - X 0 Y 0 = Y ( x / y ) - Y 0 ( x 0 / y 0 ) Y 0 , p 2 = Y - Y 0 Y 0 , p 3 = Z - Z 0 Z 0 = Y ( z / y ) - Y 0 ( z 0 / y 0 ) Y 0 .
p 1 - 0.95 p 2 = 0 p 2 - 1.10 p 2 = 0.
x y = [ x 0 y 0 + 0.95 ( α - 1 ) ] 1 α , z y = [ z 0 y 0 + 1.10 ( α - 1 ) ] 1 α .
x = x 0 + 0.95 y 0 ( α - 1 ) 1 + 3.05 y 0 ( α - 1 ) , y = α y 0 1 + 3.05 y 0 ( α - 1 ) , z = z 0 + 1.1 y 0 ( α - 1 ) 1 + 3.05 y 0 ( α - 1 ) ,
x 0 = 0.95 y 0             and         z 0 = 1.1 y 0 .
x 0 = 0.3115 , y 0 = 0.3279 , z 0 = 0.3606.
ω 1 = X - 0.95 Y 0.084 Y 0 ( 0.63 + Y / Y 0 ) 1 2 - 0.0595 Y 0 , ω 3 = ( Z - 1.1 Y ) 1.2 0.2768 Y 0 1.2 ( 0.8 + Y / Y 0 ) 1 2 - 0.2296 Y 0 1.2 .
ω 1 = X - 0.95 Y 0.3757 ( 12.6 + Y ) 1 2 - 1.19 , ω 3 = ( Z - 1.1 Y ) 1.2 2.253 ( 16 + Y ) 1 2 - 8.36 .
Value = 5.0 ( p 2 + 1 ) 0.426 ,
ω 2 = 41.7 ( p 2 + 1 ) 0.426 ,
ω 2 = 11.64 Y 0.426
Value = 6.58 ( p 2 + 1 ) 0.343 - 1.52 ,
Value = 2.357 Y 0.343 - 1.52 ,
ω 2 = 19.62 Y 0.343 - 12.5.
( 1 - x - 2.1 y ) 1.2 x - 0.95 y = β F ( Y ) ( y Y ) 0.2 ,
F ( Y ) = 2.253 ( 16 + Y ) 1 2 - 8.36 0.3757 ( 12.6 + Y ) 1 2 - 1.19 .
1 - x - 2.1 y = 0 ,
x - 0.95 y = 0 ,
ω 3 / ω 1 = tan - 1 θ , ω 1 2 + ω 3 2 = ρ 2 .