Page:Colorimetry104nime.djvu/19

server. 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 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 print-