Colorimetry/Chapter 2

by I. Nimeroff

2. The 1931 CIE Standard Colorimetric System and 1964 Supplement

2.1. General Principles

Fig. 2.Spectral tristimulus values according to the 1931 CIE standard observer.

In 1931, the Commission Internationale de l'Eclairage (CIE)^[1] recommended that all subsequent color data be expressed in terms of the same tristimulus system so that the results would be immediately comparable. The standard observer and coordinate system recommended [49, 65, 135, 143] is defined by the tristimulus values of the spectrum colors given in table 1a and plotted in figure 2. The supplementary observer for large fields, adopted by the CIE in 1964 [59] is given in table 1b. It will be noted that the primaries chosen are such that none of these tristimulus values is less than zero. It is further true that the green primary chosen, whose amounts are designated by y, is such as to carry all of the luminosity, the other two primaries (red, blue) whose amounts are designated by $X$ and $Z$, respectively, being unassociated with luminosity. Therefore, the values of ${\overline {y}}$ for the spectrum correspond to the standard luminosity function, and it is convenient and customary to express the $Y$ value of a luminous area as its luminance (photometric brightness) in terms of some recognized unit (such as candles per square meter, milli-lambert, or foot-lambert). The $Y$ value of an opaque specimen may be conveniently expressed as its luminous reflectance (ratio of reflected to incident luminous flux); and the $Y$ value of a transmitting specimen is customarily put in terms of luminous transmittance (ratio of transmitted to incident luminous flux).

Table 1(a). The 1931 CIE standard observer (2°)

Wave­length, nm	Spectral tristimulus values of equal-energy
	${\overline {x_{2}}}$	${\overline {y_{2}}}$	${\overline {z_{2}}}$
380	0.0014	0.0000	0.0065
385	.0022	.0001	.0106
390	.0042	.0001	.0201
395	.0076	.0002	.0362
400	.0143	.0004	.0679
405	.0232	.0006	.1102
410	.0435	.0012	.2074
415	.0776	.0022	.3713
420	.1344	.0040	.6456
425	.2148	.0073	1.0391
430	.2839	.0116	1.3856
435	.8285	.0168	1.6230
440	.3483	.0230	1.7471
445	.3481	.0298	1.7826
450	.3362	.0380	.7721
455	.3187	.0480	1.7441
460	.2908	.0600	1.6692
465	.2511	.0739	1.5281
470	.1954	.0910	1.2876
475	.1421	.1126	1.0419
480	.0956	.1390	0.8130
485	.0580	.1693	.6162
490	.0320	.2080	.4652
495	.0147	.2586	.3533
500	.0049	.3230	.2720
505	.0024	.4073	.2123
510	.0093	.5030	.1582
515	.0291	.6082	.1117
520	.0633	.7100	.0782
525	.1096	.7932	.0573
530	.1655	.8620	.0422
535	.2257	.9149	.0298
540	.2904	.9540	.0203
545	.3597	.9803	.0134
550	.4334	.9950	.0087
555	.5121	1.0002	.0057
560	.5945	0.9950	.0039
565	.6784	.9786	.0027
570	.7621	.9520	.0021
575	.8425	.9154	.0018
580	.9163	.8700	.0017
585	.9786	.8163	.0014
590	1.0263	.7570	.0011
595	1.0567	.6949	.0010
600	1.0622	.6310	.0008
605	1.0456	.5668	.0006
610	1.0026	.5030	.0003
615	0.9384	.4412	.0002
620	.8544	.3810	.0002
625	.7514	.3210	.0001
630	.6424	.2650	.0000
635	.5419	.2170	.0000
640	.4479	.1750	.0000
645	.3608	.1382	.0000
650	.2835	.1070	.0000
655	.2187	.0816	.0000
660	.1649	.0610	.0000
665	.1212	.0446	.0000
670	.0874	.0320	.0000
675	.0636	.0232	.0000
680	.0468	.0170	.0000
685	.0329	.0119	.0000
690	.0227	.0082	.0000
695	.0158	.0057	.0000
700	.0114	.0041	.0000
705	.0081	.0029	.0000
710	.0058	.0021	.0000
715	.0041	.0015	.0000
720	.0029	.0010	.0000
725	.0020	.0007	.0000
730	.0014	.0005	.0000
735	.0010	.0004	.0000
740	.0007	.0003	.0000
745	.0005	.0002	.0000
750	.0003	.0001	.0000
755	.0002	.0001	.0000
760	.0002	.0001	.0000
765	.0001	.0000	.0000
770	.0001	.0000	.0000
775	.0000	.0000	.0000
780	.0000	.0000	.0000
Totals	21.3713	21.3714	21.3715

Table 1(b). The 1964 CIE supplementary observer (10°)

Wave­length, nm	Spectral tristimulus values of equal-energy
	${\overline {x_{10}}}$	${\overline {y_{10}}}$	${\overline {z_{10}}}$
380	0.0002	0.0000	0.0007
385	0.0007	0.0001	.0029
390	.0024	.0003	.0105
395	.0072	.0008	.0323
400	.0191	.0020	.0860
405	.0434	.1140	.1971
410	.0847	.0008	.0323
415	.1406	.0145	.6568
420	.0245	0.214	.9725
425	.2647	.0295	1.2825
430	.3147	.0387	1.5535
435	.3577	.0496	1.7985
440	.3837	.0621	1.9673
445	.3867	.0747	.20273
450	.3707	.0895	1.9948
455	.3430	.1063	1.9007
460	.3023	.1282	1.7454
465	.2541	.1528	1.5549
470	.1956	.1852	1.3176
475	.1323	.2199	1.0302
480	.0805	.2536	0.7721
485	.0411	.2977	.5701
490	.0162	.3391	.4153
495	.0051	.3954	.3024
500	.0038	.4608	.2185
505	.0154	.5314	.1592
510	.0375	.6067	.1120
515	.0714	.6857	.0822
520	.1177	.7618	.0607
525	.1730	.8233	.0431
530	.2365	.8752	.0305
535	.3042	.9238	.0206
540	.3768	.9620	.0137
545	.4516	.9822	.0079
550	.5298	.9918	.0040
555	.6161	.9991	.0011
560	.7052	.9973	.0000
565	.7938	.9824	.0000
570	.8787	.9555	.0000
575	.9512	.9152	.0000
580	1.0142	.8689	.0000
585	1.0743	.8256	.0000
590	1.1185	.7774	.0000
595	1.1343	.7204	.0000
600	1.1240	.6583	.0000
605	1.0891	.5939	.0000
610	1.0305	.5280	.0000
615	0.9507	.4618	.0000
620	.8563	.3981	.0000
625	.7549	.3396	.0000
630	.6475	.2835	.0000
635	.5351	.2283	.0000
640	.4316	.1798	.0000
645	.3437	.1402	.0000
650	.2683	.1076	.0000
655	.2043	.0812	.0000
660	.1526	.0603	.0000
665	.1122	.0441	.0000
670	.0813	.0318	.0000
675	.0579	.0226	.0000
680	.0409	.0159	.0000
685	.0286	.0111	.0000
690	.0199	.0077	.0000
695	.0138	.0054	.0000
700	.0096	.0037	.0000
705	.0066	.0026	.0000
710	.0046	.0018	.0000
715	.0031	.0012	.0000
720	.0022	.0008	.0000
725	.0015	.0006	.0000
730	.0010	.0004	.0000
735	.0007	.0003	.0000
740	.0005	.0002	.0000
745	.0004	.0001	.0000
750	.0003	.0001	.0000
755	.0002	.0001	.0000
760	.0001	.0000	.0000
765	.0001	.0000	.0000
770	.0001	.0000	.0000
775	.0000	.0000	.0000
780	.0000	.0000	.0000
Totals	23.3294	23.3323	23.3343

Table 2(a). Chromaticity coordinates of the spectrum colors (2°)

Wave­length, nm	Chromaticity coordinates
	$x_{2}$	$y_{2}$	$z_{2}$
380	0.1741	0.0050	0.8209
385	.1740	.0050	.8210
390	.1738	.0049	.8213
395	.1736	.0049	.8215
400	.1733	.0048	.8219
405	.1730	.0048	.8222
410	.1726	.0048	.8226
415	.1721	.0048	.8231
420	.1714	.0051	.8235
425	.1703	.0058	.8239
430	.1689	.0069	.8242
435	.1669	.0086	.8245
440	.1644	.0109	.8247
445	.1611	.0138	.8251
450	.1566	.0177	.8257
455	.1510	.0227	.8263
460	.1440	.0297	.8263
465	.1355	.0399	.8246
470	.1241	.0578	.8181
475	.1096	.0868	.8036
480	.0913	.1327	.7760
485	.0687	.2007	.7306
490	.0454	.2950	.6596
495	.0235	.4127	.5638
500	.0082	.5384	.4534
505	.0039	.6548	.3413
510	.0139	.7502	.2359
515	.0389	.8120	.1491
520	.0743	.8338	.0919
525	.1142	.8262	.0596
530	.1547	.8059	.0394
535	.1929	.7816	.0255
540	.2296	.7543	.0161
545	.2658	.7243	0099
550	.3016	.6923	.0061
555	.3373	.6589	.0038
560	.3731	.6245	.0024
565	.4087	.5896	.0017
570	.4441	.5547	.0012
575	.4788	.5202	.0010
580	.5125	.4866	.0009
585	.5448	.4544	.0008
590	.5752	.4242	.0006
595	.6029	.3965	.0006
600	.6270	.3725	.0005
605	.6482	.3514	.0004
610	.6658	.3340	.0002
615	.6801	.3197	.0002
620	.6915	.3083	.0002
625	.7006	.2993	.0001
630	.7079	.2920	.0001
635	.7140	.2859	.0001
640	.7190	.2809	.0001
645	.7230	.2770	.0000
650	.7260	.2740	.0000
655	.7283	.2717	.0000
660	.7300	.2700	.0000
665	.7311	.2689	.0000
670	.7320	.2680	.0000
675	.7327	.2673	.0000
680	.7334	.2666	.0000
685	.7340	.2660	.0000
690	.7344	.2656	.0000
695	.7346	.2654	.0000
700	.7347	.2653	.0000
705	.7347	.2653	.0000
710	.7347	.2653	.0000
715	.7347	.2653	.0000
720	.7347	.2653	.0000
725	.7347	.2653	.0000
730	.7347	.2653	.0000
735	.7347	.2653	.0000
740	.7347	.2653	.0000
745	.7347	.2653	.0000
750	.7347	.2653	.0000
755	.7347	.2653	.0000
760	.7347	.2653	.0000
765	.7347	.2653	.0000
770	.7347	.2653	.0000
775	.7347	.2653	.0000
780	.7347	.2653	.0000

Table 2(b). Chromaticity coordinates of the spectrum colors (10°)

Wave­length, nm	Chromaticity coordinates
	$x_{1}0$	$y_{1}0$	$z_{1}0$
0.380	0.1813	0.0197	0.7990
.385	.1809	.0195	.7996
.390	.1803	.0194	.8003
.395	.1795	.0190	.8015
.400	1784	0187	.8029
.405	.1771	.0184	.8045
.410	.1755	.0181	.8064
.415	.1732	.0178	.8090
.420	.1706	.0179	.8115
.425	.1679	.0187	.8134
.430	.1650	.0203	.8147
.435	.1622	.0225	.8153
.440	.1590	.0257	.8153
.445	.1554	.0300	.8146
.450	.1510	.0364	.8126
.455	.1459	.0452	.8088
.460	.1389	.0589	.8022
.465	.1295	.0779	.7926
.470	.1152	.1090	.7758
.475	.0957	.1591	.7452
.480	.0728	.2292	.6980
.485	.0452	.3275	.6273
.490	.0210	.4401	.5389
.495	.0073	.5625	.4302
.500	.0056	.6745	.3199
.505	.0219	.7526	.2256
.510	.0495	.8023	.1482
.515	.0850	.8170	.0980
.520	.1252	.8102	.0646
.525	.1664	.7922	.0414
.530	.2071	.7663	.0267
.535	.2436	.7399	.0165
.540	.2786	.7113	.0101
.545	.3132	.6813	.0055
.550	.3473	.6501	.0026
.555	.3812	.6182	.0007
.560	.4142	.5858	.0000
.565	.4469	.5531	.0000
.570	.4790	.5210	.0000
.575	.5096	.4904	.0000
.580	.5386	.4614	.0000
.585	.5654	.4346	.0000
.590	.5900	.4100	.0000
.595	.6116	.3884	.0000
.600	.6306	.3694	.0000
.605	.6471	.3529	.0000
.610	.6612	.3388	.0000
.615	.6731	.3269	.0000
.620	.6827	.3173	.0000
.625	.6898	.3102	.0000
.630	.6955	.3045	.0000
.635	.7010	.2990	.0000
.640	.7059	.2941	.0000
.645	.7103	.2898	.0000
.650	.7137	.2863	.0000
.655	.7156	.2844	.0000
.660	.7168	.2832	.0000
.665	.7179	.2821	.0000
.670	.7187	.2813	.0000
.675	.7193	.2807	.0000
.680	.7198	.2802	.0000
.685	.7200	.2800	.0000
.690	.7202	.2798	.0000
.695	.7203	.2797	.0000
.700	.7204	.2796	.0000
.705	.7203	.2797	.0000
.710	.7202	.2798	.0000
.715	.7201	.2799	.0000
.720	.7199	.2801	.0000
.725	.7197	.2803	.0000
.730	.7195	.2806	.0000
.735	.7192	.2808	.0000
.740	.7189	.2811	.0000
.745	.7186	.2814	.0000
.750	.7183	.2817	.0000
.755	.7180	.2820	.0000
.760	.7176	.2824	.0000
.765	.7172	.2828	.0000
.770	.7169	.2831	.0000
.775	.7165	.2835	.0000
.780	.7161	.2839	.0000

If, as is usual, light combinations are not the chief interest, it is convenient to substitute for the tristimulus values, $X,Y,Z,$ the two ratios, $X/(X+Y+Z)$ and $Y/(X+Y+Z)$, combined with the luminous value, $Y$. The two ratios are known as chromaticity coordinates, $x,y$, because they serve to Fig. 3.The (x,y) chromaticitiy diagram, showing the spectrum locus and the purple boundary.Wavelength is indicated in millimicrons. The hue names are those proposed by Kelly (77). specify the chromatic aspect of the light. The analogous ratio, $Z/(X+Y+Z)$, is also known as a chromaticity coordinate, $z$, but only two of the three coordinates, $x,y,z$, give independent information since by definition the sum of all three is unity. Table 2a gives the chromaticity coordinates, $x,y,x,$ of the spectrum colors for 2° and table 2b for 10° fields [59]. Figure 3 shows the points representing the spectrum colors in the ($x,y$)-chromaticity diagram. This diagram is also known as a Maxwell triangle because of Maxwell's first use of such a diagram [98]. Furthermore, it has aptly been called a mixture diagram because it indicates in a very simple way the chromaticity of the color resulting from the additive combination of any two lights. The point representing this chromaticity is found on the straight line connecting the points representing two lights. The primary lights are represented by points at the corners of a triangle, and every point within the triangle represents the chromaticity of a mixture of the primary lights whose proportions are indicated by the chromaticity coordinates, $x,y,z$. The spectrum colors are shown by a smooth curve known as the spectrum locus. A few points on this locus are identified by wavelength in nanometers. It will be noted from figure 3 that the spectrum locus is substantially straight from 540 nm to the long-wave extreme. This means that the standard observer would find binary mixtures of, say, 540 nm with 640 nm, closely equivalent to some intermediate portion of the spectrum. But the spectrum locus from 540 nm to the short-wave extreme is curved outward. This means that for the standard observer a binary mixture of 540 nm with, say, 440 nm would differ importantly in chromaticity from the intermediate parts of the spectrum. By drawing straight lines through any central point (such as x = y = ⅓, representing the so-called equal-energy stimulus) and extending them until they cut the spectrum locus, we may find the spectral complementaries relative to a stimulus represented by that point; that is, we may find the two parts of the spectrum that, when combined in proper proportions, will for the standard observer be equivalent to the central stimulus.

The straight line in figure 3 joining the extremes of the spectrum locus represents the chromaticities of the mixtures of the two extremes of the visible spectrum. The area bounded by the closed curve made up of the spectrum locus and this straight line is the locus of all physically realizable chromaticities. Note that the points representing the primaries of the CIE coordinate system, the apices of the triangle ($x=1,y=z=0$; $y=1,x=z=0$; $z=1,x=y=0$), all fall outside this area; that is, the primaries are imaginary. Note also that both the $X$ and $Z$ primaries fall on the line $y=0$, which is unassociated with luminosity and is known as the alychne or lightless line. The short-wave extreme of the spectrum locus comes close to this line; this means that, although it has the power to elicit in the standard observer a considerable $X$ and $Z$ response, resulting in a vivid bluish purple color, radiant flux of wavelength 380 to 420 nm is almost unassociated with luminosity. The areas in figure 3 corresponding to common color designations for lights are those proposed by Kelly [77] and will be discussed later.

2.2. Standard Sources

At the time of setting up the standard observer and coordinate system, the International Commission on Illumination [135], Commission International de I'Eclairage (CIE), recommended use of three standard sovirces for colorimetry; source A, representative of gas-filled incandescent lamps; source B, representative of noon sunlight; and source C, representative of average daylight such as that from a completely overcast sky. Source A is an incandescent lamp operated at a color temperature of 2854 °K, on the international temperature scale ($c_{2}$ = 14,380). Source B is obtained by using this same lamp in combination with a two-cell Davis-Gibson liquid filter designed to give a color temperature of about 5000 °K. Source C is obtained similarly and results in a source of correlated color temperature about 6800 °K. These sources are recommended for general use, or whenever there is no special reason for using some other source. Table 3 gives the relative spectral irradiance of Sources A, B, C, D₅₅₀₀, D₆₅₀₀, and D₇₅₀₀. Sources D₅₅₀₀, D₆₅₀₀, D₇₅₀₀ represent several phases of daylight, closely represented by the subscripted correlated color temperatures. Tables 4a and 4b give computation forms for evaluation of the colors of non-self-luminous specimens that transmit, scatter, or reflect incident light for the 2° standard observer. Table 4a refers to Source A; table 4b, to Source C. Source B is relatively little used except in Great Britain. Table 4c gives corresponding values for the 10° observer.

Table 3. Relative spectral irradiance E of the six standard sources, A, B, C, D₅₅₀₀,D₆₅₀₀ and D₇₅₀₀

Wave­length nm	EA	EB	EC	E5500	E6500	E7500
380	9.79	22.40	33.00	32.60	50.00	66.70
385	10.90	26.85	39.92	33.35	52.30	68.35
390	12.09	31.30	47.40	38.10	54.60	70.00
395	13.36	36.18	55.17	49.50	68.70	85.95
400	14.71	41.30	63.30	60.90	82.80	101.90
405	16.15	46.62	71.81	64.75	87.15	106.90
410	17.68	52.10	80.60	68.60	91.50	111.90
415	19.29	57.70	89.53	70.10	92.45	112.35
420	21.00	63.20	98.10	71.60	93.40	112.80
425	22.79	68.37	105.80	69.75	90.05	107.95
430	24.67	73.10	112.40	(illegible text)	86.70	(illegible text)
435	26.64	77.31	117.75	76.75	95.80	112.15
440	28.70	80.80	121.50	85.60	104.90	(illegible text)
445	30.85	83.44	123.45	91.80	110.95	127.25
450	33.09	85.40	124.00	98.00	117.00	133.30
455	35.41	86.88	123.60	99.25	114.40	132.85
460	37.82	88.30	123.10	100.50	117.80	132.40
465	40.30	90.08	123.30	100.20	116.35	129.85
470	42.87	92.00	123.80	99.90	114.90	127.30
475	45.52	93.75	124.09	101.30	115.40	127.05
480	48.25	95.20	123.90	102.70	115.90	126.80
485	51.04	96.23	122.92	100.40	112.35	122.30
490	53.91	96.50	120.70	98.10	108.80	117.80
495	56.85	95.71	116.90	99.40	109.10	117.20
500	59.86	94.20	112.10	100.70	109.40	116.60
505	62.93	92.37	106.98	100.70	108.60	115.15
510	66.06	90.70	102.30	100.70	107.80	113.70
515	69.25	89.65	98.81	100.35	106.30	111.20
520	72.50	89.50	96.90	100.00	104.80	108.70
525	75.79	90.43	96.78	102.10	106.25	109.55
530	79.13	92.20	98.00	104.20	107.70	110.40
535	82.52	94.46	99.94	103.15	106.05	108.35
540	85.95	96.90	102.10	102.10	104.40	106.30
545	89.41	99.16	103.95	102.55	104.20	105.60
550	92.91	101.00	105.20	103.00	104.00	104.90
555	96.44	102.20	105.67	101.50	102.00	102.45
560	100.00	102.80	105.30	100.00	100.00	100.00
565	103.58	102.92	104.11	98.60	98.15	97.80
570	107.18	102.60	102.30	97.20	96.30	95.60
575	110.80	101.90	100.15	97.45	96.05	94.90
580	114.44	101.00	97.80	97.70	95.80	94.20
585	118.08	100.07	95.43	94.55	92.25	90.60
590	121.73	99.20	93.20	91.40	88.70	87.00
595	125.39	98.44	91.22	92.90	89.35	87.10
600	129.04	98.00	89.70	94.40	90.00	87.20
605	132.70	98.08	88.83	94.75	89.80	86.65
610	136.34	98.50	88.40	95.10	89.60	86.10
615	139.99	99.06	88.19	94.65	88.65	64.85
620	143.62	99.70	88.10	94.20	87.70	83.60
625	147.23	100.36	88.06	92.30	85.50	81.15
630	150.83	100.00	88.00	90.40	83.30	78.70
635	154.42	101.56	87.86	91.35	83.50	78.55
640	157.98	102.20	87.80	91.30	83.70	78.40
645	161.51	103.05	87.99	90.60	81.85	76.60
650	165.03	103.90	88.30	88.90	80.00	74.80
655	168.51	104.59	88.20	89.60	80.10	74.55
660	171.96	105.00	87.90	90.30	80.20	74.30
665	175.38	105.08	87.22	92.10	81.25	74.85
670	178.77	104.90	86.30	93.90	82.80	75.40
675	182.12	104.55	85.30	91.95	80.30	73.50
680	184.43	103.90	84.00	90.00	78.30	71.60
685	188.70	102.84	82.21	84.85	74.00	69.75
690	191.93	101.60	80.20	79.70	69.70	63.00
695	195.12	100.38	78.24	81.25	70.65	64.50
700	198.26	99.10	76.30	82.80	71.60	65.10
705	201.36	97.70	74.36	83.80	72.95	66.60
710	204.41	96.20	72.40	84.80	74.30	68.10
715	207.41	94.60	70.40	77.50	67.95	62.25
720	210.36	92.90	68.30	70.20	61.60	56.40
725	213.26	91.10	66.30	74.75	65.75	60.30
730	216.12	89.40	64.40	79.30	69.90	64.20
735	218.92	88.00	62.80	82.15	72.50	66.70
740	221.66	86.90	61.50	85.00	75.10	69.20
745	224.36	85.90	60.20	78.45	69.35	63.90
750	227.00	85.20	59.20	71.90	63.60	58.60
755	229.58	84.80	58.50	62.35	55.00	50.60
760	232.11	84.70	58.10	52.80	46.40	42.60
765	234.59	84.90	58.00	64.35	56.60	52.00
770	237.01	85.40	58.20	75.90	66.80	61.40
775	239.37	86.10	58.50	73.85	65.10	59.85
780	241.67	87.00	59.10	71.80	63.40	58.30

Table 4a. Computation form

CIE coordinates (2°) Source A (2854 "K.)

Sample	Source of Trans. Data
Submitted by

 

λ (nm)	$E{\overline {ax}}_{2}$	$E{\overline {ay}}_{2}$	$E{\overline {az}}_{2}$	$\tau$	$\tau E{\overline {ax}}_{2}$	$\tau E{\overline {ay}}_{2}$	$\tau E{\overline {az}}_{2}$
380	1		6	0.
90	5		23	.
400	19	1	93	.
10	71	2	340	.
20	262	8	1256	.
30	649	27	3167	.
40	926	61	4647	.
450	1031	117	5435	.
60	1019	210	5851	.
70	776	362	5116	.
80	428	622	3636	.
90	160	1039	2324	.
500	27	1792	1509	.
10	57	3080	969	.
20	425	4771	525	.
30	1214	6322	309	.
40	2313	7600	162	.
550	3732	8568	75	.
60	5510	9222	36	.
70	7571	9457	21	.
80	9719	9228	18	.
90	11579	8540	12	.
600	12704	7547	10	.
10	12669	6356	4	.
20	11373	5071	8	.
30	8980	3704		.
40	6558	2562		.
650	4336	1637		.
60	2628	972		.
70	1448	530		.
80	804	292		.
90	404	146		.
700	209	75		.
10	110	40		.
20	57	19		.
30	28	10		.
40	14	6		.
750	6	2		.
60	4	2		.
70	2			.
Sums	109828	100000	35547	Sums	$X=$	$Y=$	$Z=$
$x_{w},y_{w},z_{w}$	0.4476	0.4075	0.1449	$S=X+Y+Z$
$x$, $y$, and $z$ $(x=X/S,y=Y/S,z=Z/S)$

Computed by   Checked by  

Planck 2854 °K., C2 = 14,380
Planck 2848 °K., C2 = 14,350

Table 4b. Computation form

CIE Coordinates Source C (Davis Gibson, 2854 °K. to 6800°K)

Sample	Source of Trans. Data
Submitted by

 

λ (nm)	$E{\overline {ax}}_{2}$	$E{\overline {ay}}_{2}$	$E{\overline {az}}_{2}$	$\tau$	$\tau E{\overline {ax}}_{2}$	$\tau E{\overline {ay}}_{2}$	$\tau E{\overline {az}}_{2}$
380	4		20	0.
90	19		89	.
400	85	2	404	.
10	329	9	1570	.
20	1238	37	5949	.
30	2997	122	14628	.
40	3975	262	19938	.
450	3915	443	20638	.
60	3362	694	19299	.
70	2272	1058	14972	.
80	1112	1618	9461	.
90	363	2358	5274	.
500	52	3401	2864	.
10	89	4833	1520	.
20	876	6462	712	.
30	1523	7934	388	.
40	2785	9149	195	.
560	4282	9832	86	.
60	5880	9841	89	.
70	7322	9147	20	.
80	8417	7992	16	.
90	8984	6627	10	.
600	8949	5316	7	.
10	8325	4176	2	.
20	7070	3153	2	.
30	5309	2190		.
40	3693	1443		.
650	2349	886		.
60	1361	504		.
7O	708	259		.
80	369	134		.
90	171	62		.
700	82	29		.
10	39	14		.
20	19	6		.
30	8	3		.
40	4	2		.
750	2	1		.
60	1	1		.
70	1			.
Sums	98041	100000	118103	Sums	$X=$	$Y=$	$Z=$
$x_{w},y_{w},z_{w}$	0.3101	0.3163	0.3736	$S=X+Y+Z$
$x$, $y$, and $z$ $(X=X/S,y-Y/S,z=Z/S)$

Planck 2854 "K., $C_{1}$ = 14,380
Planck 2848 °K., $C_{2}$ = 14.350

Computed by   Checked by  

Table 4c. 10° Distribution coefficients for sources S_A and S_C

	For SA			For SC
λ (nm)	$Ea{\overline {x}}_{10}$	$Ea{\overline {y}}_{10}$	$Ea{\overline {z}}_{10}$	$Ec{\overline {x}}_{10}$	$Ec{\overline {y}}_{10}$	$Ec{\overline {z}}_{10}$
380			1	1		2
90	3		11	9	1	43
400	25	3	111	103	11	463
10	132	14	605	581	60	2672
20	377	40	1795	1708	179	8122
30	682	83	3368	3011	370	14865
40	968	156	4962	3969	343	20349
450	1078	260	5802	3914	945	21058
60	1005	426	5802	3168	1343	18292
70	737	698	4965	2062	1952	13887
80	341	1076	3274	840	2675	8144
90	76	1607	1968	167	3484	4268
500	20	2424	1150	37	4398	2085
10	218	3523	650	327	5284	976
20	750	4854	387	971	6285	501
30	1644	6086	212	1973	7302	255
40	2847	7267	104	3275	8362	119
550	4326	8099	33	4744	8882	36
60	8198	8766		6322	8941
70	8277	9002		7653	9322
80	10201	8740		8444	7235
90	11967	8317		8874	6168
600	12748	7466		8583	5027
10	12349	6327		7756	3974
20	10809	5026		6422	2986
30	8583	3758		4851	2124
40	5992	2496		3226	1344
650	3892	1561		2014	808
60	2306	911		1142	451
70	1277	499		598	233
80	666	259		293	114
90	336	130		136	53
700	167	64		62	24
10	83	33		28	11
20	40	15		13	4
30	19	8		5	3
40	10	4		3	1
750	6	2		2	1
60	2			1
70	2			1
	111,159	100,000	32,200	97,298	100,000	116,137

2.3. Spectrophotometric Colorimetry

The fundamental nature of the tristimulus specification of color permits it to be used as a common denominator by means of which colorimeters involving color standards of glass, plastic, or solutions, or systems of material color standards, transparent and opaque, may be inter-compared. In order to demonstrate how the CIE standard observer and coordinate system may be used for this purpose, four printing inks, red purple, greenish yellow, greenish blue, and blue, have been evaluated, and the steps are reproduced here in detail. Figure 4 shows spectral reflectances of these four printing inks obtained on a recording spectrophotometer. Table 5a gives the spectral reflectances read from the originals of the curves of figure 4. These reflectances apply to the specimens measured except for small wave-length-scale and photometric-scale corrections which have not been applied. Table 5b gives for the greenish yellow specimen the products indicated on the form for computation of luminous reflectance, $Y$, and chromaticity coordinates, $x$,$y$,$z$, under standard source C; see table 4b. The sums of these products are the tristimulus values, $X$,$Y$,$Z$. The luminous reflectance is found as $Y/100,000$; and the chromaticity coordinates, $x$,$y$,$z$, are found by dividing $X$,$Y$, and $Z$, respectively, by the corresponding sum, $X+Y+Z$. Table 5c lists these results for all four printing-ink specimens. Figure 5 is the ($x$,$y$)-chromaticity diagram on which have been plotted large dots to represent these chromaticity coordinates, $x$,$y$.

Comparison of figure 5 with figure 3 shows that the chromaticity points of the four printing-ink specimens correspond to the hue designations red purple, greenish yellow, and blue. This accords well with the color designations found by visual inspection of the specimens. Furthermore, it will be noted that one of the blues is greener than the other. The position of the chromaticity point for the greener-ink color is in accord with the greener hue of this ink. Note also that the greenish yellow is much lighter than the red purple or either of the blues; this accords with the luminous reflectance determinations (compare 0.74 with 0.221, 0.242, and 0.246 in table 5c).

2.4. Short-Cuts and Automatic Computation

The labor of computing $X$,$Y$,$Z$, or $Y$,$x$,$y$, corresponding to pairs of spectrophotometric curves to see how the colors of the corresponding specimens compare is considerably great. Often the degree of metamerism exhibited by the pair is sufficiently small that the comparison can be made directly from the curves themselves, and much product-control work can be handled in this way. There is still frequent need, in the establishment of color standards and tests for conformity to those standards, to compute the tristimulus values, $X$,$Y$,$Z$, by a short-cut method, the selected ordinate method, to reduce spectrophotometric data.

In this method the ordinates of the spectrophotometric curve are read at a series of selected wavelengths different for each source. Instead of multiplying by the tristimulus values of the spectrum of the source, $(E{\overline {x}})_{\lambda }$, $(E{\overline {y}})_{\lambda }$, $(E{\overline {z}})_{\lambda }$, the selected ordinates are spaced proportionately closer in the wavelength regions where the tristimulus values are higher, and the corresponding readings of spectral reflectance are simply added. Tables 6 gives [21, 49] selected ordinates for source A (incandescent lamp light) and source C (average daylight). Table 7 gives the spectral reflectances of the greenish yellow printing-ink specimen read from figure 4b for the selected ordinates for source C together with the sums of these spectral reflectances, both for ten ordinates and for thirty. It will be noted that, after applying the multiplying factors listed in table 6, the tristimulus values, for the greenish yellow printing-ink specimen are found again to a close approximation (compare 0.630, 0.704, and 0.145 from table 7 with 0.631, 0.704, and 0.145, respectively, from table 5c.

Fig. 4.Spectral reflectance of printing-ink specimens: (a) red-purple; (h) greenish yellow; (c) greenish blue; (d) blue.

Ten selected ordinates sometimes give significant information (see table 7); thirty selected ordinates are often sufficient (as above); and one hundred selected ordinates are sufficient for all but a few very irregular spectral distributions (such as produced by gaseous discharge tubes). These wavelengths are available for many sources in other publications [13, 21, 49]. Nickerson [114] and De Kerf [27] have published studies of the reliability of the selected-ordinate method of computation.

Analog and digital techniques have been developed for use with automatic computing devices to abbreviate the labor of computation required by spectrophotometric colorimetry. In the application of the analog technique [25] data are sent directly from the spectrophotometer to the computer without wavelength-scale and photometric-scale corrections. In one application of the digital technique [12, 95] spectral data are punched directly on cards and fed into the computer, while in another [75] the spectral data are corrected and then punched on cards and fed into the computer.

2.5. Visual Tristimulus Colorimeters

Tristimulus values, may be obtained by direct comparison of the unknown light with an optical mixture of three primary lights in a divided photometric field. Since the primaries of the CIE standard colorimetric coordinate system are imaginery, such a tristimulus colorimeter cannot be made to read directly. It must be calibrated by measurements of four known stimuli, and then may yield tristimulus values, $X$,$Y$,$Z$, by a transformation the reverse of that indicated in eq. (3). Since the color matches set up in a tristimulus colorimeter designed to cover any substantial part of all possible colors with a single set of primaries exhibit serious metamerism, the field has to be relatively small, subtrending about 2 deg at the observer's eye. This restriction to a small angular size of field severely limits the precision of setting compared to what is possible by direct comparison of large specimens in daylight. Furthermore, the metamerism also prevents one normal observer from getting the same reading as another except by accident. If a reasonable approximation to the standard values of $X,Y,$ and $Z$ is to be assured, either the readings of a group of five or ten observers must be averaged, or a color standard yielding a spectral composition similar to that of the unknown specimen must be used. Because of industrial interest in large-field color matching Stiles and Burch [146] and Speranskaya [144] determined the color-matching functions for 10°-field viewing. In this determination either the observers were instructed to ignore the Maxwell spot [73, 98, 103, 104, 156] or it was masked. The color-matching functions thus found are significantly different from the 2°-field functions of the 1931 CIE Standard Observer. The difference is chiefly that expected from the removal of an intervening yellow filter, the macular pigment, from the field of view.

Table 5a. Spectral reflectances of four printing-ink specimens

Wave­length, nm	Spectral reflectance relative to magnesium oxide
	Red purple	Greenish yellow	Greenish blue	Blue
380	0.375[2]	0.091	0.150	0.230[2]
390	.375[2]	.089[2]	.187	.293[2]
400	.376	.085	.228	.354
410	.379	.079	.269	.415
420	.381	.077	.306	.458
430	.373	.076	.353	.505
440	.345	.077	.407	.563
450	.295	.086	.467	.616
460	.235	.095	.520	.639
470	.174	.108	.552	.645
480	.120	.145	.560	.635
490	.083	.250	.548	.608
500	.066	.445	.523	.568
510	.061	.635	.483	.508
520	.057	.708	.432	.438
530	.054	.725	.363	.353
540	.055	.733	.292	.272
550	.062	.743	.220	.198
560	.071	.752	.162	.145
570	.095	.768	.128	.117
580	.220	.782	.113	.106
590	.440	.787	.102	.102
600	.597	.790	.093	.098
610	.676	.793	.088	.097
620	.715	.798	.088	.103
630	.739	.803	.098	.122
640	.756	.809	.110	.147
650	.768	.814	.124	.172
660	.776	.818	.136	.187
670	.780	.822	.145	.186
680	.782	.824	.147	.172
690	.783	.827	.149	.162
700	.788	.829	.160	.169
710	.794	.832	.177	.192
720	.799	.883	.196	.221
730	.805	.885	.218	.256
740	.809	.836	.258	.304
750	.812	.837	.298	.362
760	.815[2]	.838[2]	.338[2]	.422[2]
770	.817[2]	.839[2]	.375[2]	.484[2]

Table 5b. Computation of tristimulus values, X, Y, Z, and chroniaticity coordinates, x, y, for the greenish-yellow printing-ink specimen under source C

(The computation form given as table 4b has been used.)

Wave­length, nm	Reflect­ance ($\rho$)	$\rho E_{c}{\overline {x}}$	$\rho E_{c}{\overline {y}}$	$\rho E_{c}{\overline {z}}$
380	0.091	0		2
390	.089	2		8
400	.085	7	0	34
410	.079	26	1	124
420	.077	95	3	458
430	.076	228	9	1112
440	.077	306	20	1535
450	.086	337	38	1775
460	.095	319	66	1833
470	.108	245	114	1617
480	.145	161	235	1372
490	.250	91	590	1319
500	.445	23	1513	1274
510	.635	57	3069	965
520	.708	408	4575	504
530	.725	1104	5752	281
540	.733	2041	6706	143
550	.743	3182	7305	64
560	.752	4422	7400	29
570	.768	5623	7025	15
580	.782	6582	6250	13
590	.787	7070	5215	8
600	.790	7070	4200	6
610	.793	6602	3312	2
620	.798	5642	2516	2
630	.803	4263	1759	0
640	.809	2988	1167
650	.814	1912	721
660	.818	1113	412
670	.822	582	213
680	.824	304	110
690	.827	141	51
700	.829	639
710	.832	68
720	.833	32
730	.835	16
740	.836
750	.837
760	.838
770	.839
Tristimulus values	$X,Y,Z$	63,076	70,395	14,495
Chromaticity coordinates	$x,y,z$	0.4263	0.4758	0.0980

Table 5c. Tristimulus values, $X$, $Y$, $Z$, under source C, luminous reflectance relative to magnesium oxide, $Y/Y_{0}$, and chromaticity coordinates, x, y, computed from the spectral reflectance of four printing-ink specimens as in table 5b

Hue designa­tion of specimen	Tristimulus values, arbitrary units			Lumi­nous reflect­ance, $Y/Y_{0}$	Chromaticity coordinates
	$X$	$Y$	$Z$		$x$	$y$
Red purple	39788	22124	30570	0.221	0.430	0.239
Greenish yellow	63076	70395	14495	.704	.426	.476
Greenish blue	19003	24245	54529	.242	.194	.248
Blue	21948	24633	69010	.246	.190	.213

It will be seen that tristimulus colorimeters give only poor information regarding the unknown specimen. Their application to product-control problems is negligible, but because of the ease of calibration and simplicity of the theory they are very useful research tools. Tristimulus colorimeters Fig. 5.Points representing the colors of four printing ink specimens whose spectral reflectances are shown in figure 9.4.The colors of the ideal closed-cavity radiator are also shown, the temperatures of the radiators being indicated in degrees Kelvin. The smooth curve connecting these points is often called the Planckian locus. have been built and described by Allen [3], Donaldson [28], Guild [43], McAdam [96], Newhall [110], Stiles [145], Verbeek [154], and Wright [157]. The Wright instrument has spectrum primaries; the other four have primaries formed by combining a light source with glass filters. To the Guild and Wright instruments we owe our accurate information regarding the properties of the normal visual system which have been expressed in terms of the standard observer.

The foregoing instruments make up the comparison-field mixture by optical combination of light beams from different sources so that a sum of the separate effects is obtained. A similar optical effect is obtained if the beams are caused to fall upon the same portion of the retina in such rapid succession that a nonflickering spot of color is seen. The effect is that of a time-weighted average of the separate beams. A very simple and widely used tristimulus colorimeter is obtained by taking four disks that have been cut along a radius, interlocking them so as to expose a sector of each, and causing them to rotate on the spindle of a motor so rapidly that neither the separate sectors nor even flicker is perceived. Such an arrangement for combining colors by rotary mixture is called a Maxwell disk. The four disks provide the necessary three degrees of freedom in the adjustment for a match, and if the tristimulus values of the component disks be known ($X_{1},Y_{1},Z_{1};X_{2},Y_{2},Z_{2};X_{3},Y_{3},Z_{3};X_{4},Y_{4},Z_{4})$, the tristimulus values of the mixture can be computed from the fractions of the total area occupied by the respective sectors, $f_{1},f_{2},f_{3},f_{4}$:

${\begin{alignedat}{7}X&=f_{1}X_{1}&+&f_{2}X_{2}&+&f_{3}X_{3}&+&f_{4}X_{4}\\Y&=f_{1}Y_{1}&+&f_{2}Y_{2}&+&f_{3}Y_{3}&+&f_{4}Y_{4}\\Z&=f_{1}Z_{1}&+&f_{2}Z_{2}&+&f_{3}Z_{3}&+&f_{4}Z_{4}.\end{alignedat}}$

(4)

If the disks are chosen anew for each kind of unknown color to be measured so as to be all fairly similar in color to the unknown, the spectral composition of the mixture color is usually sufficiently nonmetameric that no restriction to the central 2 deg of the retina is required. Furthermore any two normal observers with some experience at making the adjustment can check each other closely. The chief drawback of this simple arrangement for product-control work in color is the time lost in adjustment of the sector disk areas. The motor must be turned off, brought to a stop, the disks loosened and readjusted, the motor turned on and allowed to resume speed several times to obtain a final setting of reasonably good, precision.

Nickerson has described a disk colorimeter [105] that avoids the difficulties of the elementary Maxwell disk. Light reflected from the unknown specimen fills one-half of a photometric field, and that from a stationary sector disk fills the other. By having the observer look at the sector disk through a rapidly rotating glass wedge, each sector is presented to view in sufficiently quick succession that no flicker is produced; and at the same time the sectors, since they are stationary, may be continuously adjusted until a color match is obtained. A further advantage is obtained by extending the rotary scanning to the unknown specimen. In this way the average color of a notably nonuniform specimen such as that made up of coarse salt crystals may be obtained. The disk, colorimeter has been extensively used by the United States Department of Agriculture for the color-grading of food products and is well adapted to product-control colorimetry of many kinds.

2.6. Dominant Wavelength and Purity

Another way to identify a combination of lights to specify a color, alternate to the tristimulus method, is to determine the luminance (photometric brightness) of one spot of light of fixed spectral composition (such as average daylight) and the luminance of a spot of light of continuously variable spectral composition separately identified (as by wavelength in the spectrum). In this way the requisite three degrees of freedom in adjustment to a color match are supplied. This form of identification leads naturally into a specification in which the luminance [20] of the unknown is given and the chromaticity is specified by two variables in polar coordinates. One of these variables is an angle, the other a radius, and both can be computed from the chromaticity coordinates of the fixed spot of light, the variable spot of light, and the unknown, these coordinates serving to locate the respective positions in a chromaticity diagram. If the fixed light is nearly achromatic, the angle often correlates well with the hue of the color perception, and the radius fairly well with its saturation. The most fundamental way to specify the direction on a chromaticity diagram from the point representing the fixed light to the point representing the unknown light is by wavelength of the part of the spectrum required to make the match. If the unknown color can be matched by adding some part of the spectrum to the fixed light, it is said to have a spectral color, and the required wavelength is called dominant wavelength. But if a color match is produced for the fixed light by adding some part of the spectrum to the unknown color, the unknown is said to be nonspectral, and the required wavelength is called the complementary wavelength. Either dominant wavelength or complementary wavelength may be obtained for the standard observer by drawing on a chromaticity diagram a straight line through the point representing the fixed light and that representing the unknown color, and then by reading the wavelength corresponding to the point at which this line extended intersects the locus of spectrum colors. If the unknown color is plotted between the fixed light and the spectrum, the intersection gives the dominant wavelength; but if the fixed light is represented by a point intermediate to the unknown and the intersection of the straight line with the spectrum locus, the intersection indicates the complementary wave-length.

Table 6. Selected Ordinates (In Nanometers) for Computing Tristimuliis Values, X, Y, Z, for Specimens Under Standard Sources A and C [20]

Number	Source A			Source C
	X	Y	Z	X	Y	Z
1	444.0	487.8	416.4	424.4	465.9	414.1
2[3]	516.9[3]	507.7[3]	424.9[3]	435.5[3]	489.4[3]	422.2[3]
3	544.0	517.3	429.4	443.9	500.4	426.3
4	554.2	524.1	432.9	452.1	508.7	429.4
5[3]	561.4[3]	529.8[3]	436.0[3]	461.2[3]	515.1[3]	432.0[3]
6	567.1	534.8	438.7	474.0	520.6	434.3
7	572.0	539.4	441.3	531.2	525.4	436.5
8[3]	576.3[3]	543.7[3]	443.7[3]	544.3[3]	529.8[3]	438.6[3]
9	580.2	547.8	446.0	552.4	533.9	440.6
10	583.9	551.7	448.3	558.7	537.7	442.5
11[3]	587.2[3]	555.4[3]	450.5[3]	564.1[3]	541.4[3]	444.4[3]
12	590.5	559.1	452.6	568.9	544.9	446.3
13	593.5	562.7	454.7	573.2	548.4	448.2
14[3]	596.5[3]	566.3[3]	456.8[3]	577.3[3]	551.8[3]	450.1[3]
15	599.4	569.8	458.8	581.3	555.1	452.1
16	602.3	573.3	460.8	585.0	558.5	454.0
17[3]	605.2[3]	576.9[3]	462.9[3]	588.7[3]	561.9[3]	455.9[3]
18	608.0	580.5	464.9	592.4	565.3	457.9
19	610.9	584.1	467.0	596.0	568.9	459.9
20[3]	613 8[3]	587.9[3]	469.2[3]	599.6[3]	572.5[3]	462.0[3]
21	616.9	591.8	471.6	603.3	576.4	464.1
22	620.0	595.9	474.1	607.0	580.5	466.3
23[3]	623.3[3]	600.1[3]	476.8[3]	610.9[3]	584.8[3]	468.7[3]
24	626.9	604.7	479.9	615.0	589.6	471.4
25	630.8	609.7	483.4	619.4	594.8	474.3
26[3]	635.3[3]	615.2[3]	487.5[3]	624.2[3]	600.8[3]	477.7[3]
27	640.5	621.5	492.7	629.8	607.7	481.8
28	646.9	629.2	499.3	636.6	616.1	487.2
29[3]	655.9[3]	639.7[3]	508.4[3]	645.9[3]	627.3[3]	495.2[3]
30	673.5	659.0	526.7	663.0	647.4	511.2
Multiplying factors
30 ordinates	0.03661	0.03333	0.01185	0.03268	0.03333	0.03938
10 ordinates	.10984	.10000	.03555	.09804	.10000	.11812

The degree of approach of the unknown color to the spectrum color is commonly indicated by the ratio of the amount of the spectrum color to the total amount of the two-part combination; this ratio is called purity, and if the amounts are specified in luminance units, the ratio is called luminance (formerly colorimetric) purity. By far the most common convention, however, is to express the amounts in units of the excitation sum $X+Y+Z$; the resulting ratio is called excitation purity and corresponds simply to distance ratios on the chromaticity diagram of a colorimetric coordinate system [49, 64, 133]. Formulas have been derived by Hardy [49] and MacAdam [91] to convert from luminance purity to excitation purity, and the reverse.

Table 7. Spectral Reflectances of Greenish Yellow Printing-ink Specimen (see fig. 4b) Read for the Selected Ordinates for Source G (see table 6)

Number	X		Y		Z
1	0 076		0 102		0.078
2*	.076	0.076	.240	0.240	.076	0.076
3	.079		.460		.076
4	.088		.615		.075
5*	.096	.096	.683	.683	.075	.075
6	.117		.711		.076
7	.727		.720		.076
8*	.739	.739	.725	.725	.077	.077
9	.745		.728		.077
10	.750		.731		.078
11*	.758	.758	.735	.735	.080	.080
12	.765		.738		.082
13	.772		.742		.084
14*	.779	.779	.745	.745	.086	.086
15	.783		.747		.088
16	.785		.750		.089
17*	.787	.787	.755	.755	.091	.091
18	.788		.760		.093
19	.789		.765		.095
20*	.790	.790	.772	.772	.097	.097
21	.791		.778		.100
22	.792		.782		.103
23*	.793	.793	.785	.785	.106	.106
24	.795		.787		.110
25	.797		.788		.119
26*	.800	.800	.790	.790	.133	.133
27	.803		.792		.155
28	.807		.796		.210
29*	.812	.812	.802	.802	.342	.342
30	.819		.812		.650
Totals	19.298	6.430	21.136	7.032	3.677	1.163
Times factor	0.630	0.630	0.704	0.703	0.145	0.137

*r1Values for calculation with 10 selected ordinates.

Fig. 6.Dominant wavelenth and purity evaluated from the (x,y)-chromaticity diagram.

The four points indicated by circles represent the colors of the four printing-ink specimens shown in figures 9.4 and 9.5.

Table 8. Dominant wavelengths and excitation purities of four printing-ink specimens (see fig. 4)

Hue designation of specimen	Chromaticity coordinates (from table 5c)		Dominant wave­length, nm	Excita­tion purity, percent
	x	y
Red purple	0.430	0.239	498. 9C[4]	53.7
Greenish yellow	.426	.476	573.2	74.0
Greenish blue	.194	.248	483.6	49.6
Blue	.190	.213	479.7	55.1

Figure 6 indicates how dominant wavelength and excitation purity of the four printing-ink specimens would be found from their chromaticity coordinates $x,y$, relative to source C taken as the fixed light. Table 8 gives the dominant and complementary (C) wavelengths found as in figure 10 by the intersections of the straight lines with the spectrum locus. Table 8 also gives the excitation purities found by dividing the distance from the fixed point (source C) to the specimen point by the total distance from the fixed point to the boundary (spectrum locus plus straight line connecting its extremes). Large-scale charts for reading dominant wavelength and purity relative to source C are provided in the Hardy Handbook of Colorimetry [49].

Apparatus for the direct measurement of dominant wavelength and luminance purity has been designated by Nutting [125] and by Priest [132]. The degree of metamerism ordinarily obtained with such apparatus leaves it open to the same objections as have prevented tristimulus colorimeters with single sets of primaries from being useful for production control. There is a further disadvantage in the direct measurement of luminance purity in that the luminance of the spectrum component has to be determined relative to the luminance of the mixture by separate photometry. Since there is usually a large chromatic difference between these two fields, simple equality-of-brightness settings are not reliable, and an auxiliary flicker photometers, as in Priest's apparatus [132], must be used. This method has been found to exaggerate individual-observer differences; often-times observers will differ only slightly in the mixtures of spectrum light and fixed light that they find to be equivalent to an unknown color, but they will disagree importantly in their photomerty of the components.

1. This was formerly called ICI for the initial letters of the English name of this commission.
2. Extrapolated.
3. Values for calculation with 10 selected ordinates.
4. C denotes complementary wavelength.