Color Tolerance Specifications for Paint

Thomas F. Boyd

doi:10.1364/JOSA.41.000552

Journal of the Optical Society of America
Vol. 41,
Issue 8,
pp. 552-557
(1951)
•https://doi.org/10.1364/JOSA.41.000552

Color Tolerance Specifications for Paint

Thomas F. Boyd

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Thomas F. Boyd, "Color Tolerance Specifications for Paint," J. Opt. Soc. Am. 41, 552-557 (1951)

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Abstract

As a basis for preparing color specifications for paints, a study was made of observers and conditions in relation to grading color differences and selecting tolerances for a green paint. Simple color difference formulas gave correlation with visual observations as good as or better than complicated formulas. There was no appreciable difference between results under north daylight and an artificial source of north daylight. Color requirement limits determined by inexperienced observers were about the same order as for experienced observers. The study indicates that in many cases it may not be necessary to prepare a very large number of colors in the preparation of color specifications. Time was saved in the present study by the use of one-dimensional color series to determine color requirement limits.

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Series	Number of samples		Dominant wavelength (mμ)	Excitation purity (%)	Reflectance (%)	Δ E NBS units from standard
1. Reflectance increased	16	Standard	554	33.5	28.0	—
		First sample W-1	554	32.1	28.5	1.1
		Last sample W-14	555	31.0	33.4	6.6
2. Reflectance decreased	14	Standard	554	33.5	28.0	—
		First sample B-1	554	33.0	27.7	0.5
		Last sample B-13	555	25.8	22.4	11.1
3. Dominant wavelength increased	17	Standard	554	32.0	29.1	—
		First sample Y-1	555	32.5	29.1	0.9
		Last sample Y-16	562	39.0	27.9	11.6
4. Dominant wavelength decreased	16	Standard	554	31.9	28.7	—
		First sample Bu-1	554	31.8	28.6	0.1
		Last sample Bu-15	543	23.0	23.9	9.6

	Series 1 reflectance increased set 1^a		Series 2 reflectance decreased set 1		Series 3 dominant wavelength increased set 1		Series 4 dominant wavelength decreased set 1
	Sample number	Δ E NBS units	Sample number	Δ E NBS units	Sample number	Δ E NBS units	Sample number	Δ E NBS units
	W-1	1.1	B-1	0.5	Y-1	0.9	Bu-1	0.1
	W-2	1.9	B-2	1.0	Y-2	1.6	Bu-2	0.3
	W-3	2.2	B-3	1.1	Y-3	2.1	Bu-3	1.3
	W-4	2.8	B-4	1.2	Y-4	2.2	Bu-4	2.4
	W-5	3.0	B-5	1.9	Y-5	3.0	Bu-5	2.6
	W-6	3.7	B-6	2.0	Y-6	3.4	Bu-6	3.4
	W-7	3.9	B-7	2.7	Y-7	4.2	Bu-7	3.6
					Y-8	4.5
Rank correlation “Analyte” north daylight		1.00, 0.89, 0.96		0.82		1.00		1.00
Rank correlation north daylight		0.86, 0.92, 0.96		0.89		1.00		1.00

	Series 1 reflectance increased set 2^a		Series 2 reflectance decreased set 2		Series 3 dominant wavelength increased set 2		Series 4 dominant wavelength decreased set 2
	Sample number	Δ E NBS units	Sample number	Δ E NBS units	Sample number	Δ E NBS units	Sample number	Δ E NBS units

	W-8	4.0	B-8	5.0	Y-9	5.7	Bu-8	4.2
	W-9	4.1	B-9	6.1	Y-10	6.5	Bu-9	4.6
	W-10	4.5	B-10	7.4	Y-11	7.4	BU-10	5.4
	W-11	4.6	B-11	8.2	Y-12	8.2	Bu-11	6.2
	W-12	5.6	B-12	10.6	Y-13	9.8	Bu-12	7.2
	W-13	5.8	B-13	11.1	Y-14	10.1	Bu-13	7.9
	W-14	6.6			Y-15	11.1	Bu-14	8.9
					Y-16	11.6	Bu-15	9.6
Rank correlation “Analyte” north daylight		0.96, 0.96, 0.96		1.00		1.00		1.00
Rank correlation north daylight		0.96, 0.99, 1.00		1.00		1.00		1.00

	Chromaticity coordinates		Dominant wavelength (mμ)	Excitation purity (%)	Diffuse reflectance (%)	Δ E NBS units	Munsell renotations
Sample	x	y	Dominant wavelength (mμ)	Excitation purity (%)	Diffuse reflectance (%)	Δ E NBS units	H	V/C
Std.	0.3162	0.4280	554	31.9	27.8	—	9.5GY	5.8/6.3
B-2	0.3156	0.4269	554	31.2	27.1	0.8	9.5GY	5.7/6.3
Bu-3	0.3140	0.4234	553	30.0	27.5	1.4	9.8GY	5.8/6.2
Y-3	0.3196	0.4270	555	32.5	27.9	2.0	9.1GY	5.8/6.2
W-4	0.3162	0.4221	554	30.2	28.9	2.3	9.7GY	5.9/6.1
Bu-8	0.3091	0.4191	551	27.9	26.2	3.6	0.3G	5.7/6.0
B-8	0.3165	0.4173	554	29.0	25.5	4.5	9.8GY	5.7/5.6
W-12	0.3180	0.4215	555	30.5	32.0	4.9	9.3GY	6.2/6.2
Y-8	0.3262	0.4292	558	34.8	27.6	5.1	8.6GY	5.8/6.0

			Color difference formulas
	Visual^a		Judd		Judd-Hunter-Schofield		Nickerson		Nickerson-Balinkin		Saunderson-Milner
Sample	Analyte North daylight	North daylight	Color units	Rank	Color units	Rank	Color units	Rank	Color units	Rank	Color units	Rank
B-2	1	1	0.8	1	1.2	1.5	1.4	1	1.0	1	0.3	1
W-4	2	2	2.3	4	1.7	4	1.7	4	1.5	2	0.4	3
Bu-3	3	3	1.4	2	1.2	1.5	1.6	2.5	1.6	3.5	0.4	3
Y-3	4	4	2.0	3	1.5	3	1.6	2.5	1.6	3.5	0.4	3
W-12	5	5	4.9	7	3.9	7	3.2	6	2.5	5	0.7	5
B-8	6	7.5	4.5	6	4.0	8	3.4	7.5	4.6	8	1.7	8
Y-8	7	6	5.1	8	3.8	6	3.1	5	2.9	7	1.1	7
Bu-8	8	7.5	3.6	5	2.5	5	3.4	7.5	2.8	6	0.9	6
Rank correlation “Analyte” north daylight				0.76		0.70		0.83		0.89		0.82
Rank correlation north daylight				0.73		0.79		0.89		0.94		0.93

Author		Type of color space on which formula is based
Judd	$\begin{array}{c} Δ E_{J} = f_{g} {[7 Y^{\frac{1}{4}} [{(Δ α)}^{2} + {(Δ β)}^{2} {]^{\frac{1}{2}} 10^{2}]}^{2} + [k Δ (Y^{\frac{1}{2}})]^{2}}^{\frac{1}{2}} \\ α = \frac{2.4266 x - 1.3631 y - 0.3214}{1.0000 x + 2.2633 y + 1.1054} \\ β = \frac{0.5710 x + 1.2447 y - 0.5708}{1.0000 x + 2.2633 y + 1.1054} \\ f_{g} = 1.0 for matte surfaces \\ k = 100 \end{array}$	3-dimensional concept combining Judd UCS diagram with a scale of lightness $L = Y^{\frac{1}{2}}$ .
Judd-Hunter-Schofield	$\begin{array}{c} Δ E_{H - S} = [{(L_{1} - L_{0})}^{2} + {(a_{1} - a_{0})}^{2} + {(b_{1} - b_{0})}^{2}]^{\frac{1}{2}} \\ L = 100 Y^{\frac{1}{2}} \\ a = 7 L α \\ b = 7 L β \end{array}$	3-dimensional concept combining Judd UCS diagram with a scale of lightness $L = Y^{\frac{1}{2}}$ .
Nickerson	$I = \frac{C}{5} (2 Δ H) + 6 Δ V + 3 Δ C$	Munsell 3-dimensional concept of hue, value, and chroma.
Nickerson-Balinkin	$I^{'} = {[{(\frac{C}{5} 2 Δ H)}^{2} + {(6 Δ V)}^{2} + {(\frac{20}{π} Δ C)}^{2}]}^{\frac{1}{2}}$	Munsell 3-dimensional concept of hue, value, and chroma.
Saunderson-Milner	$\begin{array}{c} Δ E_{S - M} = Δ ζ_{1} + Δ ζ_{2} + Δ ζ_{3} \\ ζ_{1} = (V_{X} - V_{Y}) (9.37 + 0.79 cos θ) \\ ζ_{3} = (V_{Z} - V_{Y}) (3.33 + 0.87 sin θ) \\ tan θ = \frac{V_{X} - V_{Y}}{V_{Z} - V_{Y}} \\ ζ_{2} = k Δ V_{Y} \end{array}$	3-dimensional concept in which the coordinates are ζ₁, ζ₂, and ζ₃. V_X, V_Y, and V_Z are Munsell values corresponding to X_C, Y, and Z_C.
	k may vary from 2 to 10 depending on the conditions of viewing

	Analyte north light
Sample	Average for 3 trials by 6 inexperienced observers	Average for 3 trials by 4 experienced observers	Natural north daylight 4 experienced observers. Resubmission
W-1	6	4	4
W-2	5.7	4	4
W-3	5.7	4	4
W-5	5	3.7	2
W-7	2.7	1.7	1
W-9	2.3	2.3	0
W-11	2.3	0.7	—
W-12	1.3	0	—
B-1	6	4	4
B-2	5.7	4	4
B-3	5.3	3.7	4
B-4	5.7	3.7	4
B-5	5	3.3	4
B-6	4	2.3	1
B-7	1.7	2.0	1
B-8	0	0	—
Y-1	6	4	4
Y-2	5.7	4	4
Y-3	4	2.3	4
Y-4	1.0	1	1
Y-5	0	0	—
Y-6	0	0	—
Y-7	0	0	—
Y-8	0	0	—
Bu-1	5.7	4	4
Bu-2	4.7	3.3	4
Bu-3	3	3.3	4
Bu-4	1.3	0.7	1
Bu-5	1.7	0.7	—
Bu-6	0.3	0	—
Bu-7	0.3	0	—
Bu-8	0	0	—

Sample	Chromaticity coordinates		Dominant length (mμ)	Excitation purity (%)	Diffuse reflectance (%)	NBS units from standard
Sample	x	y	Dominant length (mμ)	Excitation purity (%)	Diffuse reflectance (%)	NBS units from standard
W-3	0.3167	0.4230	554	30.7	28.3	2.0
W-11	0.3188	0.4228	555	31.0	31.1	4.3
B-2	0.3156	0.4269	554	31.2	27.1	0.8
B-7	0.3172	0.4234	554	30.8	26.6	2.3
Y-2	0.3196	0.4272	555	32.4	27.9	1.7
Y-4	0.3209	0.4279	556	32.9	28.0	2.6
Bu-1	0.3160	0.4249	553	30.1	27.7	1.1
Bu-5	0.3108	0.4225	551	29.6	26.8	2.5

	I.C.I. system					Munsell renotations			NBS color unit Units from standard in any color direction
	Chromaticity coordinates		Dominant wavelengh (mμ)	Excitation purity (%)	Diffuse reflectance (%) Y	Munsell renotations
	x	y	Dominant wavelengh (mμ)	Excitation purity (%)	Diffuse reflectance (%) Y	H	V	C
Minimum	0.3140	0.4230	553	30.0	26.8	9.1GY	5.7	6.1	2.1
Standard	0.3162	0.4280	554	30.9	27.8	9.5GY	5.8	6.3
Maximum	0.3209	0.4330	555	32.5	29.5	9.8GY	6.0	6.5
Efficiency			87.8%				85.9%		85.4%

Abstract

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Tables (9)

Equations (2)

Journal of the Optical Society of America