The 1931 I. C. I. Standard Observer and Coordinate System for Colorimetrya,b

Deane B. Judd

doi:10.1364/JOSA.23.000359

Journal of the Optical Society of America
Vol. 23,
Issue 10,
pp. 359-374
(1933)
•https://doi.org/10.1364/JOSA.23.000359

The 1931 I. C. I. Standard Observer and Coordinate System for Colorimetry

Deane B. Judd

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Deane B. Judd, "The 1931 I. C. I. Standard Observer and Coordinate System for Colorimetrya,b," J. Opt. Soc. Am. 23, 359-374 (1933)

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Abstract

This report makes available in convenient form the properties of the standard observer recently recommended for colorimetric purposes by the International Commission on Illumination. These data supersede the values published in the 1922 report of the committee on colorimetry known as the O.S.A. excitation data. Forms are given for computing trilinear coordinates (trichromatic coefficients), dominant wave-length, colorimetric purity, and luminous transmission (or reflectance) from spectrophotometric data. Tables of the data needed are included for the 1931 I.C.I. standard illuminants A, B and C.

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Wave-length (mμ)	E_A	E_B	E_C
380	9.79	22.40	33.00
385	10.90	26.85	39.92
390	12.09	31.30	47.40
395	13.36	36.18	55.17
400	14.71	41.30	63.30
405	16.15	46.62	71.81
410	17.68	52.10	80.60
415	19.29	57.70	89.53
420	21.00	63.20	98.10
425	22.79	68.37	105.80
430	24.67	73.10	112.40
435	26.64	77.31	117.75
440	28.70	80.80	121.50
445	30.85	83.44	123.45
450	33.09	85.40	124.00
455	35.41	86.88	123.60
460	37.82	88.30	123.10
465	40.30	90.08	123.30
470	42.87	92.00	123.80
475	45.52	93.75	124.09
480	48.25	95.20	123.90
485	51.04	96.23	122.92
490	53.91	96.50	120.70
495	56.85	95.71	116.90
500	59.86	94.20	112.10
505	62.93	92.37	106.98
510	66.06	90.70	102.30
515	69.25	89.65	98.81
520	72.50	89.50	96.90
525	75.79	90.43	96.78
530	79.13	92.20	98.00
535	82.52	94.46	99.94
540	85.95	96.90	102.10
545	89.41	99.16	103.95
550	92.91	101.00	105.20
555	96.44	102.20	105.67
560	100.00	102.80	105.30
565	103.58	102.92	104.11
570	107.18	102.60	102.30
575	110.80	101.90	100.15
580	114.44	101.00	97.80
580	114.44	101.00	97.80
585	118.08	100.07	95.43
590	121.73	99.20	93.20
595	125.39	98.44	91.22
600	129.04	98.00	89.70
605	132.70	98.08	88.83
610	136.34	98.50	88.40
615	139.99	99.06	88.19
620	143.62	99.70	88.10
625	147.23	100.36	88.06
630	150.83	101.00	88.00
635	154.42	101.56	87.86
640	157.98	102.20	87.80
645	161.51	103.05	87.99
650	165.03	103.90	88.20
655	168.51	104.59	88.20
660	171.96	105.00	87.90
665	175.38	105.08	87.22
670	178.77	104.90	86.30
675	182.12	104.55	85.30
680	185.43	103.90	84.00
685	188.70	102.84	82.21
690	191.93	101.60	80.20
695	195.12	100.38	78.24
700	198.26	99.10	76.30
705	201.36	97.70	74.36
710	204.41	96.20	72.40
715	207.41	94.60	70.40
720	210.36	92.90	68.30
725	213.26	91.10	66.30
730	216.12	89.40	64.40
735	218.92	88.00	62.80
740	221.66	86.90	61.50
745	224.36	85.90	60.20
750	227.00	85.20	59.20
755	229.58	84.80	58.50
760	232.11	84.70	58.10
765	234.59	84.90	58.00
770	237.01	85.40	58.20
775	239.37	86.10	58.50
780	241.67	87.00	59.10

Trichromatic coefficients			Wave-length (mμ)	Distribution coefficients for equal energy stimulus

x	y	z		$\bar{x}$	$\bar{y}$	$\bar{z}$
0.1741	0.0050	0.8209	380	0.0014	0.0000	0.0065
0.1740	0.0050	0.8210	385	0.0022	0.0001	0.0105
0.1738	0.0049	0.8213	390	0.0042	0.0001	0.0201
0.1736	0.0049	0.8215	395	0.0076	0.0002	0.0362
0.1733	0.0048	0.8219	400	0.0143	0.0004	0.0679
0.1730	0.0048	0.8222	405	0.0232	0.0006	0.1102
0.1726	0.0048	0.8226	410	0.0435	0.0012	0.2074
0.1721	0.0048	0.8231	415	0.0776	0.0022	0.3713
0.1714	0.0051	0.8235	420	0.1344	0.0040	0.6456
0.1703	0.0058	0.8239	425	0.2148	0.0073	1.0391
0.1689	0.0069	0.8242	430	0.2839	0.0116	1.3856
0.1669	0.0086	0.8245	435	0.3285	0.0168	1.6230
0.1644	0.0109	0.8247	440	0.3483	0.0230	1.7471
0.1611	0.0138	0.8251	445	0.3481	0.0298	1.7826
0.1566	0.0177	0.8257	450	0.3362	0.0380	1.7721
0.1510	0.0227	0.8263	455	0.3187	0.0480	1.7441
0.1440	0.0297	0.8263	460	0.2908	0.0600	1.6692
0.1355	0.0399	0.8246	465	0.2511	0.0739	1.5281
0.1241	0.0578	0.8181	470	0.1954	0.0910	1.2876
0.1096	0.0868	0.8036	475	0.1421	0.1126	1.0419
0.0913	0.1327	0.7760	480	0.0956	0.1390	0.8130
0.0687	0.2007	0.7306	485	0.0580	0.1693	0.6162
0.0454	0.2950	0.6596	490	0.0320	0.2080	0.4652
0.0235	0.4127	0.5638	495	0.0147	0.2586	0.3533
0.0082	0.5384	0.4534	500	0.0049	0.3230	0.2720
0.0039	0.6548	0.3413	505	0.0024	0.4073	0.2123
0.0139	0.7502	0.2359	510	0.0093	0.5030	0.1582
0.0389	0.8120	0.1491	515	0.0291	0.6082	0.1117
0.0743	0.8338	0.0919	520	0.0633	0.7100	0.0782
0.1142	0.8262	0.0596	525	0.1096	0.7932	0.0573
0.1547	0.8059	0.0394	530	0.1655	0.8620	0.0422
0.1929	0.7816	0.0255	535	0.2257	0.9149	0.0298
0.2296	0.7543	0.0161	540	0.2904	0.9540	0.0203
0.2658	0.7243	0.0099	545	0.3597	0.9803	0.0134
0.3016	0.6923	0.0061	550	0.4334	0.9950	0.0087
0.3373	0.6589	0.0038	555	0.5121	1.0002	0.0057
0.3731	0.6245	0.0024	560	0.5945	0.9950	0.0039
0.4087	0.5896	0.0017	565	0.6784	0.9786	0.0027
0.4441	0.5547	0.0012	570	0.7621	0.9520	0.0021
0.4788	0.5202	0.0010	575	0.8425	0.9154	0.0018
0.5125	0.4866	0.0009	580	0.9163	0.8700	0.0017
0.5125	0.4866	0.0009	580	0.9163	0.8700	0.0017
0.5448	0.4544	0.0008	585	0.9786	0.8163	0.0014
0.5752	0.4242	0.0006	590	1.0263	0.7570	0.0011
0.6029	0.3965	0.0006	595	1.0567	0.6949	0.0010
0.6270	0.3725	0.0005	600	1.0622	0.6310	0.0008
0.6482	0.3514	0.0004	605	1.0456	0.5668	0.0006
0.6658	0.3340	0.0002	610	1.0026	0.5030	0.0003
0.6801	0.3197	0.0002	615	0.9384	0.4412	0.0002
0.6915	0.3083	0.0002	620	0.8544	0.3810	0.0002
0.7006	0.2993	0.0001	625	0.7514	0.3210	0.0001
0.7079	0.2920	0.0001	630	0.6424	0.2650	0.0000
0.7140	0.2859	0.0001	635	0.5419	0.2170	0.0000
0.7190	0.2809	0.0001	640	0.4479	0.1750	0.0000
0.7230	0.2770	0.0000	645	0.3608	0.1382	0.0000
0.7260	0.2740	0.0000	650	0.2835	0.1070	0.0000
0.7283	0.2717	0.0000	655	0.2187	0.0816	0.0000
0.7300	0.2700	0.0000	660	0.1649	0.0610	0.0000
0.7311	0.2689	0.0000	665	0.1212	0.0446	0.0000
0.7320	0.2680	0.0000	670	0.0874	0.0320	0.0000
0.7327	0.2673	0.0000	675	0.0636	0.0232	0.0000
0.7334	0.2666	0.0000	680	0.0468	0.0170	0.0000
0.7340	0.2660	0.0000	685	0.0329	0.0119	0.0000
0.7344	0.2656	0.0000	690	0.0227	0.0082	0.0000
0.7346	0.2654	0.0000	695	0.0158	0.0057	0.0000
0.7347	0.2653	0.0000	700	0.0114	0.0041	0.0000
0.7347	0.2653	0.0000	705	0.0081	0.0029	0.0000
0.7347	0.2653	0.0000	710	0.0058	0.0021	0.0000
0.7347	0.2653	0.0000	715	0.0041	0.0015	0.0000
0.7347	0.2653	0.0000	720	0.0029	0.0010	0.0000
0.7347	0.2653	0.0000	725	0.0020	0.0007	0.0000
0.7347	0.2653	0.0000	730	0.0014	0.0005	0.0000
0.7347	0.2653	0.0000	735	0.0010	0.0004	0.0000
0.7347	0.2653	0.0000	740	0.0007	0.0003	0.0000
0.7347	0.2653	0.0000	745	0.0005	0.0002	0.0000
0.7347	0.2653	0.0000	750	0.0003	0.0001	0.0000
0.7347	0.2653	0.0000	755	0.0002	0.0001	0.0000
0.7347	0.2653	0.0000	760	0.0002	0.0001	0.0000
0.7347	0.2653	0.0000	765	0.0001	0.0000	0.0000
0.7347	0.2653	0.0000	770	0.0001	0.0000	0.0000
0.7347	0.2653	0.0000	775	0.0000	0.0000	0.0000
0.7347	0.2653	0.0000	780	0.0000	0.0000	0.0000

			Totals	21.3713	21.3714	21.3715

Observer: 1931 C.I.E. Basic stimulus: Equal energy Illuminant: Planck 2848°K (C₂=14,350) (1931 C.I.E. Standard A)					Sample: Davis–Gibson 2848-to-4800°K filter Source of trans. data: B. S. Jour. Research 7, 796 (1931)

λ	$\bar{x}$ E	$\bar{y}$ E	zE	T	$\bar{x}$ ET	$\bar{y}$ ET	$\bar{z}$ ET
380	1		6	0.588	1		4
90	5		23	.666	3		15
400	19	1	93	.721	14	1	67
10	71	2	340	.757	54	2	257
20	262	8	1256	.774	203	6	972
30	649	27	3167	.761	494	21	2410
40	926	61	4647	.723	669	44	3360
450	1031	117	5435	.663	684	78	3603
60	1019	210	5851	.601	612	126	3516
70	776	362	5116	.551	428	199	2819
80	428	622	3636	.507	217	315	1843
90	160	1039	2324	.460	74	478	1069
500	27	1792	1509	.404	11	724	610
10	57	3080	969	.353	20	1087	342
20	425	4771	525	.317	135	1512	166
30	1214	6322	309	.300	364	1897	93
40	2313	7600	162	.290	671	2204	47
550	3732	8568	75	.279	1041	2390	21
60	5510	9222	36	.264	1455	2435	10
70	7571	9457	21	.246	1862	2326	5
80	9719	9228	18	.227	2206	2095	4
90	11579	8540	12	.209	2420	1785	3
600	12704	7547	10	.195	2477	1472	2
10	12669	6356	4	.186	2356	1182	1
20	11373	5071	3	.178	2024	903	1
30	8980	3704		.172	1545	637
40	6558	2562		.166	1089	425
650	4336	1637		.162	702	265
60	2628	972		.157	413	153
70	1448	530		.151	219	80
80	804	292		.1440	116	42
90	404	146		.1360	55	20
700	209	75		.1284	27	10
10	110	40		.1210	13	5
20	57	19		.1134	6	2
30	28	10		.1063	3	1
40	14	6		.1007	1	1
750	6	2		.0964	1	0
60	4	2		.0938	0
70	2			.0926

Sums	109828	100000	35547		24685	24923	21240
x_w, y_w, z_w	0.44759	0.40754	0.14487	x, y, z	0.34842	0.35178	0.29980

Illuminant B			Wave-length in mμ	Illuminant C

$\bar{x}$ E	$\bar{y}$ E	$\bar{z}$ E		$\bar{x}$ E	$\bar{y}$ E	$\bar{z}$ E
3		14	380	4		20
13		60	90	19		89
56	2	268	400	85	2	404
217	6	1033	10	329	9	1570
812	24	3899	20	1238	37	5949
1983	81	9678	30	2997	122	14628
2689	178	13489	40	3975	262	19938
2744	310	14462	450	3915	443	20638
2454	506	14085	60	3362	694	19299
1718	800	11319	70	2272	1058	14972
870	1265	7396	80	1112	1618	9461
295	1918	4290	90	363	2358	5274
44	2908	2449	500	52	3401	2864
81	4360	1371	10	89	4833	1520
541	6072	669	20	576	6462	712
1458	7594	372	30	1523	7934	388
2689	8834	188	40	2785	9149	195
4183	9603	84	550	4282	9832	86
5840	9774	38	60	5880	9841	39
7472	9334	21	70	7322	9147	20
8843	8396	16	80	8417	7992	16
9728	7176	10	90	8984	6627	10
9948	5909	7	600	8949	5316	7
9436	4734	3	10	8325	4176	2
8140	3630	2	20	7070	3153	2
6200	2558		30	5309	2190
4374	1709		40	3693	1443
2815	1062		650	2349	886
1655	612		60	1361	504
876	321		70	708	259
465	169		80	369	134
220	80		90	171	62
108	39		700	82	29
53	19		10	39	14
26	9		20	19	6
12	4		30	8	3
6	2		40	4	2
2	1		750	2	1
2	1		60	1	1
1			70	1

99072	100000	85223	Sums	98041	100000	118103
0.34848	0.35175	0.29977	x_w, y_w, z_w	0.31012	0.31631	0.37357

Color temperature (C₂=14,350) θ°K	Trilinear coordinates according to the 1931 I.C.I. coordinate system

	x	y	z
100 (or less)	0.7347	0.2653	0.0000
300	.7341	.2659	.0000
600	.7090	.2909	.0001
1,000	.6524	.3448	.0028
1,500	.5852	.3934	.0214
1,900	.5372	.4114	.0514
2,360	.4893	.4150	.0957
2,848	.4476	.4075	.1449
3,500	.4049	.3906	.2046
4,800	.3506	.3560	.2933
6,500	.3133	.3235	.3632
10,000	.2806	.2883	.4311
24,000	.2532	.2532	.4936
∞	.2399	.2342	.5259

Illuminant A		Illuminant B		Wave-length (mμ)	Illuminant C		Equal energy		Wave-length (mμ)	x	y
x_w=0.4476,	y_w=0.4075	x_w=0.3485,	y_w=0.3517		x_w=0.3101,	y_w=0.3163	x_w=0.3334,	y_w=0.3334
$\frac{(x - x_{w})}{(y - y_{w})}$	$\frac{(y - y_{w})}{(x - x_{w})}$	$\frac{(x - x_{w})}{(y - y_{w})}$	$\frac{(y - y_{w})}{(x - x_{w})}$		$\frac{(x - x_{w})}{(y - y_{w})}$	$\frac{(y - y_{w})}{(x - x_{w})}$	$\frac{(x - x_{w})}{(y - y_{w})}$	$\frac{(y - y_{w})}{(x - x_{w})}$

+0.67950		+0.50303		380	+0.43688		+0.48508		380	0.17410	0.00500
.67954		.50307		381	.43693		.48513		381	.17408	.00499
.67957		.50311		382	.43698		.48517		382	.17406	.00498
.67963		.50319		383	.43706		.48525		383	.17403	.00497
.67968		.50326		384	.43714		.48532		384	.17400	.00496
+ .67972		+ .50330		385	+ .43719		+ .48537		385	.17398	.00495
.67980		.50340		386	.43731		.48548		386	.17394	.00494
.67986		.50347		387	.43739		.48555		387	.17391	.00493
.67991		.50355		388	.43747		.48563		388	.17388	.00492
.68000		.50365		389	.43759		.48574		389	.17384	.00491
+ .68008		+ .50375		390	+ .43770		+ .48584		390	.17380	.00490
.68016		.50385		391	.43782		.48595		391	.17376	.00489
.68024		.50395		392	.43793		.48606		392	.17372	.00488
.68035		.50408		393	.43808		.48620		393	.17367	.00487
.68046		.50421		394	.43822		.48633		394	.17362	.00486
+ .68052		+ .50430		395	+ .43832		+ .48643		395	.17358	.00484
.68066		.50445		396	.43850		.48659		396	.17352	.00483
.68076		.50458		397	.43865		.48673		397	.17347	.00482
.68087		.50471		398	.43879		.48687		398	.17342	.00481
.68102		.50489		399	.43899		.48705		399	.17336	.00481
+ .68115		+ .50504		400	+ .43917		+ .48722		400	.17330	.00480
.68130		.50522		401	.43936		.48740		401	.17324	.00480
.68143		.50538		402	.43954		.48757		402	.17318	.00479
.68157		.50553		403	.43971		.48774		403	.17312	.00478
.68171		.50571		404	.43991		.48792		404	.17306	.00478
+ .68189		+ .50591		405	+ .44013		+ .48813		405	.17299	.00478
.68202		.50607		406	.44031		.48830		406	.17293	.00477
.68222		.50630		407	.44057		.48854		407	.17285	.00477
.68241		.50651		408	.44081		.48877		408	.17278	.00478
.68265		.50679		409	.44111		.48906		409	.17269	.00479
+ .6829		+ .5071		410	+ .4414		+ .4893		410	.1726	.0048
.6831		.5074		411	.4417		.4897		411	.1725	.0048
.6834		.5076		412	.4421		.4900		412	.1724	.0048
.6836		.5079		413	.4424		.4903		413	.1723	.0048
.6839		.5082		414	.4427		.4906		414	.1722	.0048
+ .6841		+ .5085		415	+ .4430		+ .4909		415	.1721	.0048
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	.9143	.7298		513	.5947		.6677		513	.0274	.7917
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− .8757		− .5688		520	− .4557		− .5178		520	.0743	.8338
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− .7963		− .4938		525	− .3842		− .4448		525	.1142	.8262
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− .7352		− .4267		530	− .3174		− .3782		530	.1547	.8059
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− .6808		− .3619		535	− .2519		− .3135		535	.1929	.7816
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− .6286		− .2953		540	− .1838		− .2466		540	.2296	.7543
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− .5739		− .2220		545	− .1086		− .1729		545	.2658	.7243
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− .5126		− .1377		550	− .0226		− .0886		550	.3016	.6923
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− .4387		− .0365		555	+ .0794		+ .0120		555	.3373	.6589
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+ .8205			+ .8226	580		+ .8414		+ .8554	580	.5125	.4866
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	− .4067		− .1265	620		− .0210		− .0701	620	.6915	.3083
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	− .4437		− .1661	630		− .0611		− .1105	630	.7079	.2920
	.4465		.1691	631		.0641		.1136	631	.7092	.2907
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	.4542		.1776	634		.0727		.1223	634	.7129	.2870
	− .4565		− .1800	635		− .0753		− .1248	635	.7140	.2859
	.4587		.1825	636		.0778		.1273	636	.7151	.2848
	.4607		.1847	637		.0800		.1296	637	.7161	.2838
	.4627		.1869	638		.0823		.1319	638	.7171	.2828
	.4647		.1891	639		.0846		.1341	639	.7181	.2818
	− .4665		− .1911	640		− .0866		− .1362	640	.7190	.2809
	.4682		.1931	641		.0886		.1382	641	.7199	.2800
	.4696		.1947	642		.0903		.1399	642	.7208	.2792
	.4712		.1965	643		.0921		.1417	643	.7216	.2784
	.4725		.1980	644		.0936		.1432	644	.7223	.2777
	− .4739		− .1995	645		− .0952		− .1448	645	.7230	.2770
	.4752		.2010	646		.0967		.1463	646	.7237	.2763
	.4763		.2022	647		.0980		.1476	647	.7243	.2757
	.4775		.2035	648		.0993		.1489	648	.7249	.2751
	.4786		.2048	649		.1006		.1502	649	.7255	.2745
	− .4795		− .2058	650		− .1017		− .1513	650	.7260	.2740
	.4805		.2069	651		.1028		.1524	651	.7265	.2735
	.4814		.2079	652		.1039		.1535	652	.7270	.2730
	.4821		.2088	653		.1047		.1543	653	.7274	.2726
	.4831		.2098	654		.1058		.1554	654	.7279	.2721
	− .4838		− .2106	655		− .1066		− .1562	655	.7283	.2717
	.4845		.2115	656		.1075		.1571	656	.7287	.2713
	.4851		.2121	657		.1081		.1577	657	.7290	.2710
	.4858		.2129	658		.1090		.1586	658	.7294	.2706
	.4864		.2135	659		.1096		.1592	659	.7297	.2703
	− .4869		− .2142	660		− .1103		− .1599	660	.7300	.2700
	.4873		.2146	661		.1107		.1603	661	.7302	.2698
	.4878		.2152	662		.1113		.1609	662	.7305	.2695
	.4882		.2156	663		.1117		.1613	663	.7307	.2693
	.4885		.2160	664		.1122		.1618	664	.7309	.2691
	− .4889		− .2164	665		− .1126		− .1622	665	.7311	.2689
	.4892		.2168	666		.1130		.1626	666	.7313	.2687
	.4896		.2172	667		.1134		.1630	667	.7315	.2685
	.4900		.2176	668		.1139		.1634	668	.7317	.2683
	.4901		.2178	669		.1141		.1637	669	.7318	.2682
	− .4905		− .2183	670		− .1145		− .1641	670	.7320	.2680
	.4907		.2185	671		.1147		.1643	671	.7321	.2679
	.4910		.2189	672		.1151		.1647	672	.7323	.2677
	.4912		.2191	673		.1153		.1649	673	.7324	.2676
	.4916		.2195	674		.1157		.1653	674	.7326	.2674
	− .4918		− .2197	675		− .1159		− .1655	675	.7327	.2673
	.4921		.2201	676		.1164		.1660	676	.7329	.2671
	.4923		.2203	677		.1166		.1662	677	.7330	.2670
	.4925		.2205	678		.1168		.1664	678	.7331	.2669
	.4928		.2209	679		.1172		.1668	679	.7333	.2667
	− .49300		− .22110	680		− .11741		− .16700	680	.73340	.26660
	.49321		.22134	681		.11766		.16725	681	.73352	.26648
	.49343		.22158	682		.11791		.16750	682	.73364	.26636
	.49362		.22180	683		.11814		.16773	683	.73375	.26625
	.49382		.22203	684		.11837		.16796	684	.73386	.26614
	− .49401		− .22225	685		− .11860		− .16819	685	.73397	.26603
	.49419		.22245	686		.11881		.16839	686	.73407	.26593
	.49435		.22263	687		.11899		.16858	687	.73416	.26584
	.49451		.22281	688		.11918		.16877	688	.73425	.26575
	.49465		.22297	689		.11935		.16893	689	.73433	.26567
	− .49477		− .22311	690		− .11949		− .16908	690	.73440	.26560
	.49488		.22324	691		.11962		.16920	691	.73446	.26554
	.49496		.22334	692		.11972		.16931	692	.73451	.26549
	.49503		.22342	693		.11980		.16939	693	.73455	.26545
	.49510		.22350	694		.11987		.16947	694	.73459	.26541
	− .49514		− .22354	695		− .11993		− .16951	695	.73461	.26539
	.49519		.22360	696		.11999		.16957	696	.73464	.26536
	.49521		.22362	697		.12001		.16960	697	.73465	.26535
	.49523		.22364	698		.12003		.16962	698	.73466	.26534
	− .49525		− .22366	699		− .12005		− .16964	699	.73467	.26533

Abstract

Cited By

Figures (2)

Tables (6)

Equations (17)

Journal of the Optical Society of America