FMC Color-Difference Formulas: Clarification Concerning Usage

K. D. Chickering

doi:10.1364/JOSA.61.000118

Journal of the Optical Society of America
Vol. 61,
Issue 1,
pp. 118-122
(1971)
•https://doi.org/10.1364/JOSA.61.000118

FMC Color-Difference Formulas: Clarification Concerning Usage

K. D. Chickering

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K. D. Chickering, "FMC Color-Difference Formulas: Clarification Concerning Usage," J. Opt. Soc. Am. 61, 118-122 (1971)

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Abstract

There are two distinct versions of the FMC color-difference formula. The FMC-2 version, now recommended for study by the CIE, was developed to reproduce certain features of the Simon–Goodwin graphical technique and is intended only for use with non-self-luminous stimulus objects. Color-difference ellipsoids computed from the two versions always differ. However, when the luminous reflectance is 10.69, the FMC-2 version fits the Nutting chromaticity-discrimination ellipse data with a mean-square error of color difference equal to 0.0306. Formulas for color-metric coefficients for the FMC-2 version are given.

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Chromaticity coordinates		Ratios of color-metric coefficients			Angular differences of inclinations of semimajor axes (degrees)	Ratios of semimajor and semiminor ellipse axes

x	y	R₁₁	R₁₂	R₂₂	θ₁−θ₂	R_a	R_b
0.160	0.057	1.000	0.979	1.301	−0.234	0.805	1.000
0.187	0.118	1.000	0.998	1.051	−0.108	0.944	1.000
0.253	0.125	1.005	1.016	1.039	−0.441	0.959	0.993
0.150	0.680	1.004	1.006	1.001	0.016	1.000	0.998
0.131	0.521	1.005	1.011	1.002	0.053	1.000	0.997
0.212	0.550	1.002	1.042	1.001	0.042	1.000	0.999
0.258	0.450	1.000	0.997	1.002	0.025	0.999	1.000
0.152	0.365	1.004	1.057	1.005	0.121	0.998	0.998
0.280	0.385	1.000	1.000	1.003	−0.010	0.998	1.000
0.380	0.498	1.000	1.002	1.003	−0.040	0.999	1.000
0.160	0.200	1.003	0.961	1.023	0.174	0.986	0.999
0.228	0.250	1.000	0.999	1.009	−0.014	0.992	1.000
0.305	0.323	1.000	1.003	1.006	−0.068	0.996	0.999
0.385	0.393	1.002	1.005	1.007	−0.091	0.998	0.998
0.472	0.399	1.006	1.013	1.012	−0.146	0.999	0.995
0.527	0.350	1.014	1.031	1.023	−0.197	1.000	0.988
0.475	0.300	1.015	1.030	1.026	−0.214	0.999	0.988
0.510	0.236	1.032	1.072	1.058	−0.227	1.000	0.972
0.596	0.283	1.029	1.108	1.054	0.206	1.000	0.970
0.344	0.284	1.003	1.008	1.012	−0.143	0.996	0.997
0.390	0.237	1.013	1.023	1.027	−0.255	0.996	0.990
0.441	0.198	1.032	1.058	1.059	−0.369	0.998	0.974
0.278	0.223	1.001	1.005	1.014	−0.144	0.989	0.998
0.300	0.163	1.009	1.019	1.032	−0.353	0.983	0.991
0.365	0.153	1.028	1.049	1.062	−0.512	0.991	0.976

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Journal of the Optical Society of America