CIE1931_RGB

TABLE 1. Wright's original spectral chromaticity co-ordinates (Wright's (Wright's initial units). units). Wavelength (nm)

r1

g1

b1

400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700

0.037 0.037 0.035 0.032 0.026 0.015 0.000 -0.021 -0.062 -0.106 -0.135 -0.117 -0.064 0.000 0.076 0.151 0.244 0.352 0.473 0.603 0.717 0.813 0.885 0.943 0.979 1.000 1.010 1.015 1.019 1.022 1.026

-0.058 -0.057 -0.056 -0.052 -0.044 -0.029 0.000 0.066 0.203 0.440 0.754 0.952 1.013 1.000 0.945 0.876 0.786 0.672 0.547 0.409 0.292 0.193 0.121 0.061 0.023 0.000 -0.010 -0.015 -0.019 -0.022 -0.026

1.021 1.020 1.021 1.020 1.019 1.014 1.000 0.955 0.859 0.665 0.381 0.165 0.051 0.000 -0 - 0.021 -0 - 0.027 -0 - 0.030 -0 - 0.024 -0 - 0.020 -0 - 0.012 -0 - 0.009 -0 - 0.007 -0 - 0.005 -0 - 0.004 -0 - 0.003 0.000 0.000 0.000 0.000 0.000 0.000

TABLE 2. Wright's spectral chromaticity chromaticity co-ordinates (based on equal amounts of the primaries matching the NPL standard white). Wavelength (nm)

r2

g2

b2

400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700

0.052 0.051 0.049 0.045 0.036 0.021 0.000 -0.031 -0.094 -0.170 -0.233 -0.207 -0.111 0.000 0.123 0.232 0.354 0.480 0.604 0.720 0.811 0.881 0.929 0.966 0.988 1.000 1.006 1.009 1.011 1.013 1.015

-0.048 -0.047 -0.046 -0.043 -0.037 -0.024 0.000 0.057 0.182 0.420 0.772 1.002 1.049 1.000 0.901 0.797 0.676 0.543 0.414 0.290 0.196 0.124 0.075 0.037 0.014 0.000 -0.006 -0.009 -0.011 -0.013 -0.015

0.996 0.996 0.997 0.998 1.001 1.003 1.000 0.974 0.912 0.750 0.461 0.205 0.062 0.000 -0 - 0.024 -0 - 0.029 -0 - 0.030 -0 - 0.023 -0 - 0.018 -0 - 0.010 -0 - 0.007 -0 - 0.005 -0 - 0.004 -0 - 0.003 -0 - 0.002 0.000 0.000 0.000 0.000 0.000 0.000

Values of r2, g2 and b2 were calculated from TABLE 1 using equation 6 in the text. They are identical to the values published on p. 211 in W. D. Wright. A re-determination of the mixture curves of the spectrum, Trans. Opt. Soc. London , 31, 201-218 (1929-30).

TABLE 2. Wright's spectral chromaticity chromaticity co-ordinates (based on equal amounts of the primaries matching the NPL standard white). Wavelength (nm)

r2

g2

b2

400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700

0.052 0.051 0.049 0.045 0.036 0.021 0.000 -0.031 -0.094 -0.170 -0.233 -0.207 -0.111 0.000 0.123 0.232 0.354 0.480 0.604 0.720 0.811 0.881 0.929 0.966 0.988 1.000 1.006 1.009 1.011 1.013 1.015

-0.048 -0.047 -0.046 -0.043 -0.037 -0.024 0.000 0.057 0.182 0.420 0.772 1.002 1.049 1.000 0.901 0.797 0.676 0.543 0.414 0.290 0.196 0.124 0.075 0.037 0.014 0.000 -0.006 -0.009 -0.011 -0.013 -0.015

0.996 0.996 0.997 0.998 1.001 1.003 1.000 0.974 0.912 0.750 0.461 0.205 0.062 0.000 -0 - 0.024 -0 - 0.029 -0 - 0.030 -0 - 0.023 -0 - 0.018 -0 - 0.010 -0 - 0.007 -0 - 0.005 -0 - 0.004 -0 - 0.003 -0 - 0.002 0.000 0.000 0.000 0.000 0.000 0.000

Values of r2, g2 and b2 were calculated from TABLE 1 using equation 6 in the text. They are identical to the values published on p. 211 in W. D. Wright. A re-determination of the mixture curves of the spectrum, Trans. Opt. Soc. London , 31, 201-218 (1929-30).

Figure 1. Wright's chromaticity co-ordinates r2, g2 and b2 as a function of  wavelength (primaries with units such that equal amounts match the NPL wh ite).

1.200

1.000

0.800

0.600    2    b   r   o    2   g  ,    2   r

0.400

0.200

0.000

400

450

500

550

600

-0.200

-0.400 Wavelength (nm)

650

700

The chromaticity coefficients of the three NPL primaries are given by the following matrix. R'(650) R(700) = 1.0150 G(546) = 0.1938 B(436) = 0.0407

G'(530) -0.0150 0.8337 -0.0412

B'(460) 0.0000 -0.0275 1.0005

The inversion of the above 3 x 3 matrix gives the coefficients for expressing Wright's primaries in terms of the NPL primaries. R(700) R'(650) = 0.9818 G'(530) = -0.2299 B'(460) = -0.0494 0.7026 Sums

G(546) 0.0177 1.1970 0.0486 1.2632

B(436) 0.0005 0.0329 1.0008 1.0342

The normalised set of coefficients, for matching white with equal amounts, are therefore R(700) R'(650) = 1.3975 G'(530) = -0.3272 B'(460) = -0.0703 1.000 Sums

G(546) 0.0140 0.9475 0.0384 1.000

B(436) 0.0005 0.0318 0.9677 1.000

Sums 1.4120 0.6522 0.9358

This ensures that the R'(650) + G'(530) + B'(460) = R(700) + G(546) + B(436).

TABLE 3. Wright's spectral chromaticity co-ordinates caluclated from TABLE 2 (based on the NPL primaries). Wavelength (nm)

r3

g3

b3

400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700

0.019 0.017 0.014 0.007 -0.008 -0.035 -0.075 -0.144 -0.304 -0.581 -1.008 -1.142 -0.859 -0.502 -0.164 0.080 0.302 0.490 0.642 0.762 0.845 0.902 0.939 0.966 0.981 0.990 0.994 0.996 0.997 0.999 1.000

-0.007 -0.006 -0.005 -0.002 0.004 0.017 0.041 0.101 0.246 0.577 1.231 1.726 1.699 1.453 1.157 0.923 0.706 0.515 0.362 0.238 0.155 0.098 0.062 0.035 0.019 0.010 0.006 0.004 0.003 0.001 0.000

0.988 0.989 0.991 0.995 1.004 1.018 1.034 1.044 1.058 1.004 0.777 0.416 0.159 0.049 0.007 -0.003 -0.008 -0.005 -0.004 0.000 0.000 0.000 -0.001 -0.001 -0.001 0.000 0.000 0.000 0.000 0.000 0.000

Values of r3, g3 and b3 calculated using equation 14 in the text. Only the calculated values shown in bold in TABLE 3 differ from those published by Wright by more than 0.002. See W. D. Wright. A re-determination of the mixture curves of the spectrum. Trans. Opt. Soc. London , 31, 201-218 (1929-30), p. 217 given below.

TABLE 4. Wright's tabulated spectral chromaticity co-ordinates (NPL primaries). from Trans. Opt. Soc. London , 31, 201-218 (1929-30), p. 217 Absolute differences Wavelength (nm) r3 g3 b3 from TABLE 3.

400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700

0.018 0.016 0.013 0.007 -0.008 -0.035 -0.075 -0.144 -0.304 -0.580 -1.004 -1.142 -0.859 -0.502 -0.162 0.079 0.302 0.489 0.642 0.763 0.846 0.902 0.939 0.966 0.982 0.990 0.994 0.996 0.997 0.999 1.000

-0.006 -0.006 -0.005 -0.002 0.004 0.016 0.041 0.101 0.246 0.576 1.229 1.725 1.700 1.453 1.154 0.923 0.706 0.516 0.362 0.238 0.155 0.098 0.062 0.035 0.019 0.010 0.006 0.004 0.003 0.001 0.000

0.988 0.990 0.992 0.995 1.004 1.019 1.034 1.043 1.058 1.004 0.775 0.417 0.159 0.049 0.008 -0.002 -0.008 -0.005 -0.004 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 0.000 0.000 0.000 0.000 0.000 0.000

0.0008 0.0011 0.0008 0.0000 0.0003 0.0000 0.0001 0.0002 0.0002 0.0013 0.0038 0.0001 0.0003 0.0003 0.0021 0.0009 0.0000 0.0007 0.0001 0.0007 0.0013 0.0002 0.0001 0.0001 0.0005 0.0003 0.0001 0.0001 0.0003 0.0004 0.0000

0.0006 0.0003 0.0003 0.0002 0.0001 0.0009 0.0001 0.0004 0.0004 0.0009 0.0021 0.0007 0.0007 0.0001 0.0026 0.0003 0.0000 0.0010 0.0003 0.0002 0.0004 0.0002 0.0002 0.0000 0.0003 0.0001 0.0001 0.0001 0.0004 0.0003 0.0000

0.0002 0.0014 0.0011 0.0002 0.0002 0.0009 0.0001 0.0006 0.0002 0.0005 0.0016 0.0008 0.0004 0.0002 0.0006 0.0012 0.0001 0.0003 0.0004 0.0009 0.0009 0.0006 0.0002 0.0001 0.0003 0.0003 0.0002 0.0001 0.0001 0.0000 0.0000

TABLE 5. Chromaticity co-ordinates in terms of the initial primaries based on coloured filters used by Guild. Units based on NPL white. Wavelength (nm)

r4

g4

b4

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535 540 545 550 555

0.0683 0.0683 0.0683 0.0683 0.0683 0.0670 0.0655 0.0638 0.0613 0.0590 0.0554 0.0502 0.0443 0.0365 0.0262 0.0130 -0.0030 -0.0255 -0.0554 -0.0980 -0.1531 -0.2290 -0.3178 -0.4120 -0.5010 -0.5550 -0.5660 -0.5250 -0.4440 -0.3430 -0.2390 -0.1417 -0.0500 0.0404 0.1279 0.2143

-0.0819 -0.0819 -0.0819 -0.0819 -0.0819 -0.0808 -0.0795 -0.0780 -0.0754 -0.0725 -0.0688 -0.0646 -0.0596 -0.0528 -0.0448 -0.0327 -0.0175 0.0056 0.0420 0.1010 0.1843 0.3125 0.4839 0.6964 0.9247 1.1290 1.2870 1.3670 1.3620 1.3020 1.2230 1.1410 1.0590 0.9740 0.8890 0.8030

1.0136 1.0136 1.0136 1.0136 1.0136 1.0138 1.0140 1.0142 1.0141 1.0135 1.0134 1.0144 1.0153 1.0163 1.0186 1.0197 1.0205 1.0199 1.0134 0.9970 0.9688 0.9165 0.8339 0.7156 0.5763 0.4260 0.2790 0.1580 0.0820 0.0410 0.0160 0.0007 -0.0090 -0.0144 -0.0169 -0.0173

560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700

0.2977 0.3796 0.4600 0.5380 0.6120 0.6815 0.7427 0.7980 0.8465 0.8876 0.9238 0.9523 0.9748 0.9925 1.0068 1.0188 1.0290 1.0370 1.0430 1.0480 1.0509 1.0532 1.0550 1.0565 1.0580 1.0590 1.0599 1.0603 1.0604

0.7190 0.6360 0.5540 0.4740 0.3980 0.3270 0.2640 0.2070 0.1570 0.1150 0.0780 0.0490 0.0260 0.0078 -0.0068 -0.0188 -0.0290 -0.0370 -0.0430 -0.0480 -0.0509 -0.0532 -0.0550 -0.0565 -0.0580 -0.0590 -0.0599 -0.0603 -0.0604

-0.0167 -0.0156 -0.0140 -0.0120 -0.0100 -0.0085 -0.0067 -0.0050 -0.0035 -0.0026 -0.0018 -0.0013 -0.0008 -0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Data from J. Guild. The colorimetric properties of the spectrum. Philos. Trans. Roy. Soc. London, Ser. A , 230, 149-187 (1931). The values shown in bold in TABLE 5 are experimental measurements. The remaining values were obtained by interpolation.

Matrix giving the chromaticity co-ordinates of the NPL primaries in terms of Guild's filter primaries.

R(700) G(546) B(436)

RF 1.0604 0.0600 0.0493

GF -0.0604 0.9552 -0.0639

BF 0.0000 -0.0152 1.0146

The inversion of the above 3 x 3 matrix gives the coefficients for expressing the old primaries in terms of the new ones.

RF

R(700) 0.9396

G(546) 0.0595

B(436) 0.0009

GF

-0.0598

1.0442

0.0156

BF Sums

-0.0494 0.8305

0.0628 1.1665

0.9866 1.0031

The normalised set of coefficients, for matching white with equal amounts, so that RF + GF + BF = R(700) + G(546) + B(436) are therefore

RF

R(700) 1.1315

G(546) 0.0510

B(436) 0.0009

1.1833

GF

-0.0720

0.8952

0.0156

0.8387

BF Sums

-0.0595 1.0000

0.0539 1.0000

0.9835 1.0000

0.9779

The spectral chromaticity co-ordinates in terms of the NPL primaries are therefore

TABLE 6. Guild's spectral chromaticity co-ordinates in terms of the NPL primaries calculated from TABLE 5.

TABLE 4. Wright's spectral chromaticity co-ordinates (NPL primaries).

Wavelength (nm)

r5

g5

b5

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535

0.0228 0.0228 0.0228 0.0228 0.0228 0.0213 0.0195 0.0175 0.0145 0.0117 0.0074 0.0011 -0.0060 -0.0154 -0.0280 -0.0442 -0.0641 -0.0925 -0.1311 -0.1880 -0.2651 -0.3788 -0.5253 -0.7018 -0.8947 -1.0394 -1.0984 -1.0325 -0.8683 -0.6669 -0.4738 -0.3070

-0.0152 -0.0152 -0.0152 -0.0152 -0.0152 -0.0143 -0.0132 -0.0119 -0.0097 -0.0073 -0.0042 -0.0006 0.0036 0.0094 0.0163 0.0267 0.0400 0.0603 0.0930 0.1474 0.2274 0.3577 0.5464 0.8048 1.1165 1.4224 1.6677 1.7732 1.7227 1.5838 1.4282 1.2838

0.9924 0.9924 0.9924 0.9924 0.9924 0.9930 0.9937 0.9945 0.9953 0.9956 0.9968 0.9995 1.0024 1.0060 1.0117 1.0175 1.0242 1.0322 1.0381 1.0406 1.0377 1.0211 0.9789 0.8970 0.7782 0.6170 0.4307 0.2593 0.1456 0.0831 0.0456 0.0232

r3

g3

b3

0.018

-0.006

0.988

0.016

-0.006

0.990

0.013

-0.005

0.992

0.007

-0.002

0.995

-0.008

0.004

1.004

-0.035

0.016

1.019

-0.075

0.041

1.034

-0.144

0.101

1.043

-0.304

0.246

1.058

-0.580

0.576

1.004

-1.004

1.229

0.775

-1.142

1.725

0.417

-0.859

1.700

0.159

-0.502

1.453

0.049

540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700

-0.1613 -0.0277 0.0928 0.2040 0.3046 0.3976 0.4837 0.5627 0.6338 0.6975 0.7513 0.7981 0.8378 0.8706 0.8988 0.9206 0.9375 0.9506 0.9612 0.9700 0.9774 0.9832 0.9875 0.9911 0.9932 0.9949 0.9961 0.9972 0.9983 0.9990 0.9996 0.9999 1.0000

1.1520 1.0265 0.9102 0.8007 0.7006 0.6077 0.5211 0.4412 0.3691 0.3049 0.2504 0.2028 0.1624 0.1294 0.1010 0.0792 0.0621 0.0488 0.0382 0.0295 0.0222 0.0165 0.0123 0.0087 0.0067 0.0051 0.0038 0.0027 0.0017 0.0010 0.0004 0.0001 0.0000

0.0093 0.0012 -0.0030 -0.0047 -0.0053 -0.0053 -0.0047 -0.0038 -0.0029 -0.0025 -0.0017 -0.0009 -0.0002 0.0000 0.0002 0.0003 0.0004 0.0006 0.0007 0.0005 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

-0.162

1.154

0.008

0.079

0.923

-0.002

0.302

0.706

-0.008

0.489

0.516

-0.005

0.642

0.362

-0.004

0.763

0.238

-0.001

0.846

0.155

-0.001

0.902

0.098

-0.001

0.939

0.062

-0.001

0.966

0.035

-0.001

0.982

0.019

-0.001

0.990

0.010

0.000

0.994

0.006

0.000

0.996

0.004

0.000

0.997

0.003

0.000

0.999

0.001

0.000

1.000

0.000

0.000

Values in bold do not agree exactly with Guild's Table III. Guild's values of b 5 are all zero above 605 nm. Philos. Trans. Roy. Soc. London, Ser. A , 230, 149-187 (1931).

FIGURE 2. Comparison of Wright's and Guild's spectral chromaticity co-ordinates in terms of the NPL primaries. Guild's values are shown as lines (data at 5nm intervals) and Wright's values as points (every 10 nm).

1.80

1.30

0.80

   b   r   o   g  ,   r

0.30

380

430

480

530

580

-0.20

-0.70

-1.20 Wavelength (nm)

630

680

TABLE 5. Chromaticity co-ordinates in terms of the initial primaries based on colored filters used by Guild. Primary units based on matching the NPL white. Wavelength (nm)

r4

g4

b4

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535 540 545

0.0683 0.0683 0.0683 0.0683 0.0683 0.0670 0.0655 0.0638 0.0613 0.0590 0.0554 0.0502 0.0443 0.0365 0.0262 0.0130 -0.0030 -0.0255 -0.0554 -0.0980 -0.1531 -0.2290 -0.3178 -0.4120 -0.5010 -0.5550 -0.5660 -0.5250 -0.4440 -0.3430 -0.2390 -0.1417 -0.0500 0.0404

-0.0819 -0.0819 -0.0819 -0.0819 -0.0819 -0.0808 -0.0795 -0.0780 -0.0754 -0.0725 -0.0688 -0.0646 -0.0596 -0.0528 -0.0448 -0.0327 -0.0175 0.0056 0.0420 0.1010 0.1843 0.3125 0.4839 0.6964 0.9247 1.1290 1.2870 1.3670 1.3620 1.3020 1.2230 1.1410 1.0590 0.9740

1.0136 1.0136 1.0136 1.0136 1.0136 1.0138 1.0140 1.0142 1.0141 1.0135 1.0134 1.0144 1.0153 1.0163 1.0186 1.0197 1.0205 1.0199 1.0134 0.9970 0.9688 0.9165 0.8339 0.7156 0.5763 0.4260 0.2790 0.1580 0.0820 0.0410 0.0160 0.0007 -0.0090 -0.0144

550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740 745 750 755

0.1279 0.2143 0.2977 0.3796 0.4600 0.5380 0.6120 0.6815 0.7427 0.7980 0.8465 0.8876 0.9238 0.9523 0.9748 0.9925 1.0068 1.0188 1.0290 1.0370 1.0430 1.0480 1.0509 1.0532 1.0550 1.0565 1.0580 1.0590 1.0599 1.0603 1.0604 1.0604 1.0604 1.0604 1.0604 1.0604 1.0604 1.0604 1.0604 1.0604 1.0604 1.0604

0.8890 0.8030 0.7190 0.6360 0.5540 0.4740 0.3980 0.3270 0.2640 0.2070 0.1570 0.1150 0.0780 0.0490 0.0260 0.0078 -0.0068 -0.0188 -0.0290 -0.0370 -0.0430 -0.0480 -0.0509 -0.0532 -0.0550 -0.0565 -0.0580 -0.0590 -0.0599 -0.0603 -0.0604 -0.0604 -0.0604 -0.0604 -0.0604 -0.0604 -0.0604 -0.0604 -0.0604 -0.0604 -0.0604 -0.0604

-0.0169 -0.0173 -0.0167 -0.0156 -0.0140 -0.0120 -0.0100 -0.0085 -0.0067 -0.0050 -0.0035 -0.0026 -0.0018 -0.0013 -0.0008 -0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

760 765 770 775 780

1.0604 1.0604 1.0604 1.0604 1.0604

-0.0604 -0.0604 -0.0604 -0.0604 -0.0604

0.0000 0.0000 0.0000 0.0000 0.0000

Data from J. Guild. The colorimetric properties of the spectrum. Philos. Trans. Roy. Soc. London, Ser. A , 230, 149-187 (1931).

Guild established the relative luminances of one trichromatic unit of his filter primaries. LRF 1.000

LGF 2.858

LBF 0.169

TABLE 7. Calculation of the color matching functions nr, ng and nb so that (nr x LR) + (ng x LG) + (nb x LB) = E x V x 100 NPL white (Guild) Wavelength (nm) E x V x 100

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515

0.0000 0.0020 0.0049 0.0103 0.0170 0.0360 0.0620 0.1200 0.2410 0.4730 0.7810 1.1610 1.6700 2.2750 2.8850 3.7250 4.6900 5.8700 7.2900 9.1300 11.2900 13.9100 16.9800 20.9600 26.1200 32.4000 39.7700 48.1500

n r4

n g4

n b4

r

g

b

0.0000 0.0261 0.0641 0.1347 0.2223 0.3396 0.4343 0.6395 0.8749 1.2255 1.4553 1.5880 1.6351 1.4556 1.0798 0.5288 -0.1181 -0.9208 -1.7142 -2.4933 -3.2184 -3.8906 -4.4750 -5.0826 -5.8446 -6.5543 -7.1249 -7.4163

0.0000 -0.0314 -0.0768 -0.1615 -0.2665 -0.4096 -0.5271 -0.7819 -1.0762 -1.5059 -1.8073 -2.0435 -2.1999 -2.1056 -1.8464 -1.3303 -0.6889 0.2022 1.2996 2.5697 3.8743 5.3092 6.8139 8.5911 10.7874 13.3330 16.2010 19.3106

0.0000 0.3880 0.9507 1.9984 3.2984 5.1392 6.7233 10.1661 14.4739 21.0511 26.6216 32.0883 37.4755 40.5291 41.9812 41.4821 40.1713 36.8279 31.3574 25.3659 20.3658 15.5709 11.7423 8.8279 6.7230 5.0309 3.5121 2.2320

520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725

57.5700 66.4700 74.7700 81.7400 88.0900 93.1500 96.6200 98.8100 99.5000 98.3900 95.3000 90.3100 85.1500 79.2900 71.6600 64.8000 58.1500 51.2600 45.0000 39.2800 33.5700 28.0900 23.1600 18.9500 15.3400 12.2000 9.4100 7.2400 5.3600 3.8500 2.8000 2.0300 1.4800 1.0400 0.7100 0.5030 0.3510 0.2510 0.1780 0.1210 0.0870 0.0625

-7.3824 -6.7353 -5.4832 -3.7131 -1.4805 1.3337 4.6356 8.4485 12.6059 17.0181 21.4790 25.6982 29.8157 33.4665 35.5742 37.2349 38.0221 37.4216 36.2616 34.2510 31.1963 27.4743 23.6159 20.0050 16.6838 13.5853 10.6668 8.3305 6.2212 4.4996 3.2902 2.3962 1.7550 1.2370 0.8468 0.6006 0.4192 0.2998 0.2126 0.1445 0.1039 0.0747

22.6460 25.5666 28.0585 29.8985 31.3560 32.1541 32.2210 31.6573 30.4456 28.5129 25.8682 22.6412 19.3900 16.0580 12.6452 9.6587 7.0519 4.8485 3.0617 1.7624 0.8321 0.2159 -0.1595 -0.3692 -0.4702 -0.4847 -0.4398 -0.3815 -0.3013 -0.2273 -0.1715 -0.1281 -0.0962 -0.0689 -0.0479 -0.0342 -0.0239 -0.0171 -0.0121 -0.0082 -0.0059 -0.0043

1.3634 0.8051 0.3671 0.0183 -0.2665 -0.4754 -0.6125 -0.6820 -0.7071 -0.6994 -0.6537 -0.5732 -0.4872 -0.4174 -0.3209 -0.2333 -0.1572 -0.1096 -0.0707 -0.0468 -0.0256 -0.0083 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

730 735 740 745 750 755 760 765 770 775 780

0.0425 0.0290 0.0200 0.0130 0.0090 0.0065 0.0045 0.0000 0.0000 0.0000 0.0000 Sums Normalized

0.0508 0.0346 0.0239 0.0155 0.0107 0.0078 0.0054 0.0000 0.0000 0.0000 0.0000

-0.0029 -0.0020 -0.0014 -0.0009 -0.0006 -0.0004 -0.0003 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

485.13 0.3328

484.52 0.3328

488.10 0.3348

These are the equal chromaticity co-ordinates of the NPL standard white based on matching with Guild's filter primaries.

The following matrix corresponds to the three equations giving one trichromatic unit of each of  RF, GF and BF in terms of the NPL primaries, each set of primaries being in their own units.

RF

R(700) 1.1315

G(546) 0.0510

B(436) 0.0009

GF

-0.0720

0.8952

0.0156

BF Sums

-0.0595 1.0000

0.0539 1.0000

0.9835 1.0000

If these equations are added together RF + GF + BF = R(700) + G(546) + B(436) Relative luminous intensities of one trichromatic unit for each of the filter primaries LRF LGF LBF 1.000 2.858 0.169 The three equations in the above matrix can be written in terms of luminance, using L R, LG and LB for the relative luminances of one trichromatic unit of each of the NPL primaries. 1.1315

0.0510

0.0009

-0.0720

0.8952

0.0156

-0.0595

0.0539

0.9835

LR x

1.000

LG

=

LB

2.858 0.169

The solution of this is obtained using the inverse of the first matrix. LR

0.8806

-0 -0.0502

0.0000

0.0700

1.1142

-0.0177

LB

0.0494

-0 -0.0641

1.0177

LR

0.7373

when

LR

3.2514

normalized

LG

LG

LG LB

=

=

0.0384

1.000 x

0.169 1.0000 =

LB

4.4102 0.0521

Note that the sums of the relative luminances are equal for both sets of primaries since these sums correspond to the relative luminance of the NPL standard white light. 1.000 1.000 + 2.858 2.858 + 0.169 0.169 = 0.7373 0.7373 + 3.2514 3.2514 + 0.04944 0.04944 =

2.858

4.0270 4.0270

TABLE 8. Spectral chromaticity co-ordinates and color matching functions in terms of the NPL primaries calculated from TABLE 5. Wavelength (nm)

r5

g5

b5

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535

0.0228 0.0228 0.0228 0.0228 0.0228 0.0213 0.0195 0.0175 0.0145 0.0117 0.0074 0.0011 -0.0060 -0.0154 -0.0280 -0.0442 -0.0641 -0.0925 -0.1311 -0.1880 -0.2651 -0.3788 -0.5253 -0.7018 -0.8947 -1.0394 -1.0984 -1.0325 -0.8683 -0.6669 -0.4738 -0.3070

-0.0152 -0.0152 -0.0152 -0.0152 -0.0152 -0.0143 -0.0132 -0.0119 -0.0097 -0.0073 -0.0042 -0.0006 0.0036 0.0094 0.0163 0.0267 0.0400 0.0603 0.0930 0.1474 0.2274 0.3577 0.5464 0.8048 1.1165 1.4224 1.6677 1.7732 1.7227 1.5838 1.4282 1.2838

0.9924 0.9924 0.9924 0.9924 0.9924 0.9930 0.9937 0.9945 0.9953 0.9956 0.9968 0.9995 1.0024 1.0060 1.0117 1.0175 1.0242 1.0322 1.0381 1.0406 1.0377 1.0211 0.9789 0.8970 0.7782 0.6170 0.4307 0.2593 0.1456 0.0831 0.0456 0.0232

540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740 745

-0.1613 -0.0277 0.0928 0.2040 0.3046 0.3976 0.4837 0.5627 0.6338 0.6975 0.7513 0.7981 0.8378 0.8706 0.8988 0.9206 0.9375 0.9506 0.9612 0.9700 0.9774 0.9832 0.9875 0.9911 0.9932 0.9949 0.9961 0.9972 0.9983 0.9990 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.1520 1.0265 0.9102 0.8007 0.7006 0.6077 0.5211 0.4412 0.3691 0.3049 0.2504 0.2028 0.1624 0.1294 0.1010 0.0792 0.0621 0.0488 0.0382 0.0295 0.0222 0.0165 0.0123 0.0087 0.0067 0.0051 0.0038 0.0027 0.0017 0.0010 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0093 0.0012 -0.0030 -0.0047 -0.0053 -0.0053 -0.0047 -0.0038 -0.0029 -0.0025 -0.0017 -0.0009 -0.0002 0.0000 0.0002 0.0003 0.0004 0.0006 0.0007 0.0005 0.0004 0.0003 0.0002 0.0002 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

750 755 760 765 770 775 780

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Relative luminance values. LR LG LB 1.0000 4.4102 0.0521 Color matching functions NPL white Wavelength (nm) E x V x 100

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535

0.0000 0.0020 0.0049 0.0103 0.0170 0.0360 0.0620 0.1200 0.2410 0.4730 0.7810 1.1610 1.6700 2.2750 2.8850 3.7250 4.6900 5.8700 7.2900 9.1300 11.2900 13.9100 16.9800 20.9600 26.1200 32.4000 39.7700 48.1500 57.5700 66.4700 74.7700 81.7400

n r5

n g5

n b5

r

g

b

0.0000 0.0061 0.0149 0.0313 0.0517 0.0763 0.0923 0.1259 0.1496 0.1769 0.1415 0.0264 -0.1607 -0.4479 -0.8374 -1.3018 -1.8177 -2.3883 -2.8695 -3.3252 -3.7809 -4.2083 -4.6084 -5.0822 -5.7424 -6.3955 -6.9574 -7.3095 -7.4203 -7.0111 -6.0798 -4.6856

0.0000 -0.0040 -0.0099 -0.0208 -0.0344 -0.0511 -0.0624 -0.0859 -0.1007 -0.1103 -0.0801 -0.0146 0.0970 0.2728 0.4867 0.7863 1.1329 1.5580 2.0355 2.6070 3.2426 3.9744 4.7938 5.8283 7.1658 8.7520 10.5631 12.5537 14.7217 16.6514 18.3256 19.5926

0.0000 0.2645 0.6480 1.3621 2.2482 3.5583 4.7049 7.1672 10.2841 15.0320 19.0738 23.0393 26.9540 29.1965 30.2777 29.9558 29.0397 26.6514 22.7193 18.4040 14.8009 11.3447 8.5877 6.4956 4.9946 3.7966 2.7281 1.8355 1.2441 0.8733 0.5852 0.3546

540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740 745

88.0900 93.1500 96.6200 98.8100 99.5000 98.3900 95.3000 90.3100 85.1500 79.2900 71.6600 64.8000 58.1500 51.2600 45.0000 39.2800 33.5700 28.0900 23.1600 18.9500 15.3400 12.2000 9.4100 7.2400 5.3600 3.8500 2.8000 2.0300 1.4800 1.0400 0.7100 0.5030 0.3510 0.2510 0.1780 0.1210 0.0870 0.0625 0.0425 0.0290 0.0200 0.0130

-2.8881 -0.5739 2.1830 5.3966 8.9300 12.7129 16.5725 20.2599 23.8635 27.0828 29.0179 30.5580 31.3498 30.9638 30.0893 28.4801 25.9803 22.9075 19.7084 16.7075 13.9423 11.3584 8.9215 6.9694 5.2056 3.7656 2.7538 2.0057 1.4691 1.0355 0.7089 0.5028 0.3510 0.2510 0.1780 0.1210 0.0870 0.0625 0.0425 0.0290 0.0200 0.0130

20.6271 21.2514 21.4142 21.1828 20.5384 19.4291 17.8532 15.8854 13.8979 11.8390 9.6698 7.7647 6.0770 4.6021 3.3809 2.4488 1.7208 1.1749 0.7825 0.5084 0.3169 0.1908 0.1108 0.0613 0.0350 0.0191 0.0105 0.0055 0.0025 0.0010 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.1663 0.0259 -0.0707 -0.1250 -0.1545 -0.1681 -0.1625 -0.1385 -0.1108 -0.0961 -0.0640 -0.0337 -0.0080 0.0008 0.0077 0.0088 0.0114 0.0145 0.0136 0.0089 0.0055 0.0033 0.0019 0.0011 0.0006 0.0003 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

750 755 760 765 770 775 780

0.0090 0.0065 0.0045 0.0000 0.0000 0.0000 0.0000

0.0090 0.0065 0.0045 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Sums Normalized

357.58 0.3335

357.37 0.3335

357.36 0.3333

These are the three equal chromaticity co-ordinates of the NPL white light based on matching with the NPL primaries.

TABLE 9. Guild's and Wright's averaged spectral chromaticity co-ordinates in terms of the NPL primaries (see Tables 4 and 6). Wavelength (nm)

r5

g5

b5

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530

0.0204 0.0204 0.0204 0.0204 0.0204 0.0191 0.0177 0.0162 0.0137 0.0114 0.0072 0.0011 -0.0070 -0.0178 -0.0315 -0.0487 -0.0697 -0.0983 -0.1376 -0.1990 -0.2846 -0.4019 -0.5527 -0.7480 -0.9494 -1.0800 -1.1203 -1.0311 -0.8637 -0.6739 -0.4879

-0.0106 -0.0106 -0.0106 -0.0106 -0.0106 -0.0101 -0.0096 -0.0089 -0.0074 -0.0060 -0.0037 -0.0005 0.0039 0.0093 0.0161 0.0264 0.0405 0.0632 0.0970 0.1520 0.2367 0.3689 0.5613 0.8440 1.1727 1.4750 1.6964 1.7647 1.7114 1.5849 1.4406

0.9902 0.9902 0.9902 0.9902 0.9902 0.9910 0.9919 0.9927 0.9937 0.9946 0.9965 0.9994 1.0031 1.0085 1.0154 1.0223 1.0292 1.0351 1.0406 1.0470 1.0479 1.0330 0.9914 0.9040 0.7767 0.6050 0.4239 0.2664 0.1523 0.0890 0.0473

535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740

-0.3165 -0.1617 -0.0279 0.0859 0.1990 0.3032 0.3988 0.4864 0.5664 0.6376 0.7003 0.7572 0.8031 0.8406 0.8738 0.9010 0.9219 0.9385 0.9526 0.9639 0.9732 0.9799 0.9853 0.9889 0.9917 0.9937 0.9950 0.9961 0.9971 0.9976 0.9985 0.9993 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.2944 1.1530 1.0267 0.9166 0.8064 0.7029 0.6068 0.5185 0.4376 0.3655 0.3020 0.2442 0.1979 0.1600 0.1267 0.0995 0.0786 0.0620 0.0479 0.0366 0.0273 0.0206 0.0152 0.0111 0.0083 0.0063 0.0050 0.0039 0.0029 0.0024 0.0015 0.0007 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0221 0.0087 0.0012 -0.0025 -0.0054 -0.0061 -0.0056 -0.0049 -0.0040 -0.0031 -0.0023 -0.0014 -0.0010 -0.0006 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

745 750 755 760 765 770 775 780

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Data from J. Guild. The colorimetric properties of the spectrum. Philos. Trans. Roy. Soc. London, Ser. A , 230, 149-187 (1931). Table IV, p. 186

Relative luminance values revised by Guild. LR 1.000

Wavelength (nm)

LB 0.048

TABLE 10. Color matching functions based on revised luminance values (NPL white) NPL white E x V x 100 n r5 n g5 n b5

r 380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530

LG 4.390

0.0000 0.0020 0.0049 0.0103 0.0170 0.0360 0.0620 0.1200 0.2410 0.4730 0.7810 1.1610 1.6700 2.2750 2.8850 3.7250 4.6900 5.8700 7.2900 9.1300 11.2900 13.9100 16.9800 20.9600 26.1200 32.4000 39.7700 48.1500 57.5700 66.4700 74.7700

0.0000 0.0019 0.0047 0.0098 0.0162 0.0308 0.0474 0.0785 0.1142 0.1644 0.1450 0.0272 -0.2006 -0.5669 -1.0337 -1.5603 -2.0756 -2.5216 -2.9662 -3.5038 -3.9924 -4.4118 -4.7906 -5.2251 -5.8541 -6.4510 -7.0195 -7.3784 -7.4697 -7.1237 -6.2481

g

0.0000 -0.0010 -0.0024 -0.0051 -0.0084 -0.0163 -0.0257 -0.0431 -0.0617 -0.0865 -0.0745 -0.0124 0.1118 0.2962 0.5283 0.8458 1.2060 1.6212 2.0910 2.6763 3.3205 4.0495 4.8652 5.8957 7.2310 8.8104 10.6292 12.6280 14.8010 16.7536 18.4485

b 0.0000 0.0926 0.2268 0.4767 0.7868 1.5977 2.6545 4.8075 8.2832 14.3425 20.0641 24.7525 28.7486 32.1178 33.3199 32.7529 30.6480 26.5523 22.4318 18.4348 14.7001 11.3396 8.5932 6.3148 4.7892 3.6137 2.6560 1.9063 1.3172 0.9408 0.6057

535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740

81.7400 88.0900 93.1500 96.6200 98.8100 99.5000 98.3900 95.3000 90.3100 85.1500 79.2900 71.6600 64.8000 58.1500 51.2600 45.0000 39.2800 33.5700 28.0900 23.1600 18.9500 15.3400 12.2000 9.4100 7.2400 5.3600 3.8500 2.8000 2.0300 1.4800 1.0400 0.7100 0.5030 0.3510 0.2510 0.1780 0.1210 0.0870 0.0625 0.0425 0.0290 0.0200

-4.8204 -2.9067 -0.5802 2.0196 5.2592 8.9028 12.8129 16.7804 20.5653 24.2158 27.4075 29.6642 31.1280 31.6797 31.3226 30.3077 28.5827 26.0234 23.0110 19.8514 16.8726 14.0442 11.4264 8.9681 6.9834 5.2149 3.7669 2.7527 2.0044 1.4645 1.0332 0.7078 0.5023 0.3510 0.2510 0.1780 0.1210 0.0870 0.0625 0.0425 0.0290 0.0200

19.7139 20.7265 21.3506 21.5497 21.3115 20.6391 19.4956 17.8879 15.8888 13.8815 11.8193 9.5668 7.6706 6.0299 4.5417 3.3470 2.4369 1.7192 1.1571 0.7538 0.4733 0.2952 0.1763 0.1007 0.0584 0.0331 0.0189 0.0108 0.0058 0.0035 0.0016 0.0005 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.3366 0.1564 0.0250 -0.0588 -0.1427 -0.1791 -0.1799 -0.1690 -0.1452 -0.1177 -0.0900 -0.0548 -0.0388 -0.0226 -0.0179 -0.0168 -0.0155 -0.0139 -0.0121 -0.0103 -0.0087 -0.0072 -0.0058 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

745 750 755 760 765 770 775 780

0.0130 0.0090 0.0065 0.0045 0.0000 0.0000 0.0000 0.0000 Sums Normalized

0.0130 0.0090 0.0065 0.0045 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

358.39 0.3329

359.14 0.3336

359.08 0.3335

These are the equal chromaticity co-ordinates of the NPL standard white based on matching with the NPL primaries.

Revised relative luminance values. LR LG LB

1.000

Wavelength (nm)

0.048

TABLE 11. Color matching functions based on on revised luminance values Equal energy (equal energy white) white V x 100 n r5 n g5 n b5

r 380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530

4.390

0.0039 0.0064 0.0120 0.0217 0.0396 0.0640 0.1210 0.2180 0.4000 0.7300 1.1600 1.6840 2.3000 2.9800 3.8000 4.8000 6.0000 7.3900 9.0980 11.2600 13.9020 16.9300 20.8020 25.8600 32.3000 40.7300 50.3000 60.8200 71.0000 79.3200 86.2000

0.0037 0.0061 0.0114 0.0207 0.0378 0.0547 0.0924 0.1425 0.1895 0.2537 0.2153 0.0395 -0.2763 -0.7425 -1.3615 -2.0106 -2.6553 -3.1745 -3.7018 -4.3213 -4.9161 -5.3696 -5.8690 -6.4466 -7.2392 -8.1095 -8.8780 -9.3200 -9.2122 -8.5008 -7.2033

g

-0.0019 -0.0032 -0.0059 -0.0108 -0.0196 -0.0289 -0.0501 -0.0783 -0.1024 -0.1335 -0.1106 -0.0180 0.1539 0.3880 0.6959 1.0899 1.5429 2.0410 2.6096 3.3007 4.0887 4.9287 5.9603 7.2739 8.9419 11.0755 13.4435 15.9509 18.2538 19.9925 21.2687

b 0.1805 0.2962 0.5554 1.0043 1.8327 2.8404 5.1806 8.7337 13.7481 22.1354 29.8007 35.9029 39.5939 42.0708 43.8876 42.2051 39.2085 33.4279 27.9952 22.7356 18.1010 13.8015 10.5274 7.7910 5.9224 4.5428 3.3593 2.4080 1.6244 1.1227 0.6983

535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740

91.4850 95.4000 98.0300 99.4950 100.0000 99.5000 97.8600 95.2000 91.5400 87.0000 81.6300 75.7000 69.4900 63.1000 56.6800 50.3000 44.1200 38.1000 32.1000 26.5000 21.7000 17.5000 13.8200 10.7000 8.1600 6.1000 4.4580 3.2000 2.3200 1.7000 1.1920 0.8210 0.5723 0.4102 0.2929 0.2091 0.1484 0.1047 0.0740 0.0520 0.0361 0.0249

-5.3950 -3.1480 -0.6106 2.0796 5.3225 8.9028 12.7439 16.7628 20.8454 24.7419 28.2164 31.3366 33.3810 34.3764 34.6345 33.8772 32.1046 29.5351 26.2960 22.7143 19.3211 16.0218 12.9437 10.1975 7.8708 5.9348 4.3618 3.1459 2.2908 1.6822 1.1842 0.8185 0.5715 0.4102 0.2929 0.2091 0.1484 0.1047 0.0740 0.0520 0.0361 0.0249

22.0642 22.4464 22.4691 22.1909 21.5682 20.6391 19.3906 17.8691 16.1052 14.1831 12.1681 10.1062 8.2257 6.5432 5.0220 3.7412 2.7372 1.9512 1.3223 0.8625 0.5420 0.3368 0.1997 0.1145 0.0659 0.0376 0.0219 0.0123 0.0067 0.0040 0.0018 0.0006 0.0002 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.3767 0.1694 0.0263 -0.0605 -0.1444 -0.1791 -0.1790 -0.1689 -0.1472 -0.1203 -0.0927 -0.0579 -0.0416 -0.0245 -0.0198 -0.0188 -0.0174 -0.0157 -0.0138 -0.0118 -0.0099 -0.0082 -0.0066 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

745 750 755 760 765 770 775 780

0.0172 0.0120 0.0085 0.0060 0.0042 0.0030 0.0021 0.0015 Sums Normalized

0.0172 0.0120 0.0085 0.0060 0.0042 0.0030 0.0021 0.0015

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

378.23 0.3011

395.39 0.3148

482.47 0.3841

These are the chromaticity co-ordinates of the equal energy white light in terms of the NPL primaries. See J. Guild. The colorimetric properties of the spectrum. Philos. Trans. Roy. Soc. London, Ser. A , 230, 149-187 (1931). Table IV, p. 186

TABLE 9. Guild's and Wright's averaged spectral chromaticity co-ordinates in terms of the NPL primaries. Wavelength (nm)

r5

g5

b5

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530

0.0204 0.0204 0.0204 0.0204 0.0204 0.0191 0.0177 0.0162 0.0137 0.0114 0.0072 0.0011 -0.0070 -0.0178 -0.0315 -0.0487 -0.0697 -0.0983 -0.1376 -0.1990 -0.2846 -0.4019 -0.5527 -0.7480 -0.9494 -1.0800 -1.1203 -1.0311 -0.8637 -0.6739 -0.4879

-0.0106 -0.0106 -0.0106 -0.0106 -0.0106 -0.0101 -0.0096 -0.0089 -0.0074 -0.0060 -0.0037 -0.0005 0.0039 0.0093 0.0161 0.0264 0.0405 0.0632 0.0970 0.1520 0.2367 0.3689 0.5613 0.8440 1.1727 1.4750 1.6964 1.7647 1.7114 1.5849 1.4406

0.9902 0.9902 0.9902 0.9902 0.9902 0.9910 0.9919 0.9927 0.9937 0.9946 0.9965 0.9994 1.0031 1.0085 1.0154 1.0223 1.0292 1.0351 1.0406 1.0470 1.0479 1.0330 0.9914 0.9040 0.7767 0.6050 0.4239 0.2664 0.1523 0.0890 0.0473

535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 to 780 nm

-0.3165 -0.1617 -0.0279 0.0859 0.1990 0.3032 0.3988 0.4864 0.5664 0.6376 0.7003 0.7572 0.8031 0.8406 0.8738 0.9010 0.9219 0.9385 0.9526 0.9639 0.9732 0.9799 0.9853 0.9889 0.9917 0.9937 0.9950 0.9961 0.9971 0.9976 0.9985 0.9993 0.9997 1.0000 1.0000

1.2944 1.1530 1.0267 0.9166 0.8064 0.7029 0.6068 0.5185 0.4376 0.3655 0.3020 0.2442 0.1979 0.1600 0.1267 0.0995 0.0786 0.0620 0.0479 0.0366 0.0273 0.0206 0.0152 0.0111 0.0083 0.0063 0.0050 0.0039 0.0029 0.0024 0.0015 0.0007 0.0003 0.0000 0.0000

0.0221 0.0087 0.0012 -0.0025 -0.0054 -0.0061 -0.0056 -0.0049 -0.0040 -0.0031 -0.0023 -0.0014 -0.0010 -0.0006 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

EEW chromaticity co-ordinates rw 0.3011

gw 0.3148

bw 0.3841

TABLE 12. Calculated CIE values Wavelength (nm)

r

g

b

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530

0.0259 0.0259 0.0259 0.0259 0.0259 0.0243 0.0225 0.0206 0.0174 0.0145 0.0092 0.0014 -0.0089 -0.0228 -0.0404 -0.0626 -0.0898 -0.1271 -0.1785 -0.2594 -0.3728 -0.5283 -0.7259 -0.9739 -1.2152 -1.3412 -1.3420 -1.1908 -0.9674 -0.7389 -0.5262

-0.0129 -0.0129 -0.0129 -0.0129 -0.0129 -0.0123 -0.0117 -0.0108 -0.0090 -0.0073 -0.0045 -0.0006 0.0048 0.0114 0.0197 0.0325 0.0499 0.0781 0.1204 0.1895 0.2966 0.4638 0.7052 1.0512 1.4358 1.7522 1.9439 1.9496 1.8336 1.6624 1.4862

0.9870 0.9870 0.9870 0.9870 0.9870 0.9880 0.9892 0.9902 0.9916 0.9928 0.9953 0.9992 1.0042 1.0114 1.0206 1.0301 1.0399 1.0489 1.0581 1.0699 1.0762 1.0644 1.0207 0.9227 0.7793 0.5890 0.3981 0.2412 0.1337 0.0765 0.0400

535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 to 780 nm

-0.3370 -0.1706 -0.0292 0.0894 0.2060 0.3123 0.4091 0.4971 0.5769 0.6474 0.7092 0.7651 0.8099 0.8464 0.8785 0.9048 0.9250 0.9409 0.9545 0.9653 0.9742 0.9807 0.9858 0.9894 0.9921 0.9940 0.9952 0.9963 0.9972 0.9977 0.9986 0.9993 0.9997 1.0000 1.0000

1.3186 1.1634 1.0282 0.9126 0.7984 0.6926 0.5954 0.5069 0.4263 0.3550 0.2926 0.2360 0.1909 0.1541 0.1219 0.0956 0.0754 0.0595 0.0459 0.0351 0.0261 0.0197 0.0145 0.0106 0.0079 0.0060 0.0048 0.0037 0.0028 0.0023 0.0014 0.0007 0.0003 0.0000 0.0000

0.0184 0.0072 0.0010 -0.0020 -0.0044 -0.0049 -0.0045 -0.0039 -0.0032 -0.0025 -0.0018 -0.0011 -0.0008 -0.0005 -0.0004 -0.0004 -0.0004 -0.0004 -0.0004 -0.0004 -0.0004 -0.0004 -0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

CIE 1931 RGB

TABLE 13. Absolute differences from Table 12.

r

g

b

Wavelength (nm)

0.0272 0.0268 0.0263 0.0256 0.0247 0.0237 0.0225 0.0207 0.0181 0.0142 0.0088 0.0012 -0.0084 -0.0213 -0.0390 -0.0618 -0.0909 -0.1281 -0.1821 -0.2584 -0.3667 -0.5200 -0.7150 -0.9459 -1.1685 -1.3182 -1.3371 -1.2076 -0.9830 -0.7386 -0.5159

-0.0115 -0.0114 -0.0114 -0.0113 -0.0112 -0.0111 -0.0109 -0.0104 -0.0094 -0.0076 -0.0048 -0.0007 0.0048 0.0120 0.0218 0.0345 0.0517 0.0762 0.1175 0.1840 0.2906 0.4568 0.6996 1.0247 1.3905 1.7195 1.9318 1.9699 1.8534 1.6662 1.4761

0.9843 0.9846 0.9851 0.9857 0.9865 0.9874 0.9884 0.9897 0.9913 0.9934 0.9960 0.9995 1.0036 1.0093 1.0172 1.0273 1.0392 1.0519 1.0646 1.0744 1.0761 1.0632 1.0154 0.9212 0.7780 0.5987 0.4053 0.2377 0.1296 0.0724 0.0398

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530

0.001 0.001 0.000 0.000 0.001 0.001 0.000 0.000 0.001 0.000 0.000 0.000 0.001 0.001 0.001 0.001 0.001 0.001 0.004 0.001 0.006 0.008 0.011 0.028 0.047 0.023 0.005 0.017 0.016 0.000 0.010

0.001 0.001 0.001 0.002 0.002 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.002 0.002 0.002 0.002 0.003 0.006 0.006 0.007 0.006 0.026 0.045 0.033 0.012 0.020 0.020 0.004 0.010

0.003 0.002 0.002 0.001 0.000 0.001 0.001 0.001 0.000 0.001 0.001 0.000 0.001 0.002 0.003 0.003 0.001 0.003 0.006 0.005 0.000 0.001 0.005 0.001 0.001 0.010 0.007 0.003 0.004 0.004 0.000

-0.3304 -0.1707 -0.0293 0.0974 0.2121 0.3164 0.4112 0.4973 0.5751 0.6449 0.7071 0.7617 0.8087 0.8475 0.8800 0.9059 0.9265 0.9425 0.9550 0.9649 0.9730 0.9797 0.9850 0.9888 0.9918 0.9940 0.9954 0.9966 0.9975 0.9984 0.9991 0.9996 0.9999 1.0000 1.0000

1.3105 1.1628 1.0282 0.9051 0.7919 0.6881 0.5932 0.5067 0.4283 0.3579 0.2952 0.2402 0.1928 0.1537 0.1209 0.0949 0.0741 0.0580 0.0454 0.0353 0.0272 0.0205 0.0152 0.0113 0.0083 0.0061 0.0047 0.0035 0.0025 0.0016 0.0009 0.0004 0.0001 0.0000 0.0000

0.0199 0.0079 0.0011 -0.0025 -0.0040 -0.0045 -0.0044 -0.0040 -0.0034 -0.0028 -0.0023 -0.0019 -0.0015 -0.0012 -0.0009 -0.0008 -0.0006 -0.0005 -0.0004 -0.0003 -0.0002 -0.0002 -0.0002 -0.0001 -0.0001 -0.0001 -0.0001 -0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 to 780 nm

Data from CIE Publication No. 15.2. Colorimetry. 2 Vienna: Central Bureau of the CIE; 1986. p 66-67.

nd

ed.

0.007 0.000 0.000 0.008 0.006 0.004 0.002 0.000 0.002 0.003 0.002 0.003 0.001 0.001 0.001 0.001 0.002 0.002 0.001 0.000 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.000 0.000 0.000 0.000

0.008 0.001 0.000 0.008 0.007 0.005 0.002 0.000 0.002 0.003 0.003 0.004 0.002 0.000 0.001 0.001 0.001 0.001 0.001 0.000 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.000 0.000 0.000 0.000

0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

TABLE 14. "Smoothed" averaged spectral chromaticity co-ordinates in terms of the NPL primaries. Wavelength (nm)

r6

g6

b6

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510

0.0214 0.0210 0.0206 0.0201 0.0194 0.0186 0.0176 0.0162 0.0142 0.0111 0.0069 0.0009 -0.0066 -0.0166 -0.0304 -0.0480 -0.0704 -0.0988 -0.1399 -0.1977 -0.2795 -0.3952 -0.5447 -0.7274 -0.9157 -1.0629 -1.1186

-0.0094 -0.0093 -0.0093 -0.0092 -0.0092 -0.0091 -0.0089 -0.0085 -0.0077 -0.0062 -0.0039 -0.0006 0.0039 0.0098 0.0177 0.0279 0.0417 0.0613 0.0941 0.1468 0.2309 0.3620 0.5557 0.8216 1.1361 1.4457 1.6850

0.9881 0.9883 0.9887 0.9892 0.9898 0.9905 0.9913 0.9923 0.9935 0.9951 0.9970 0.9996 1.0027 1.0069 1.0127 1.0201 1.0286 1.0375 1.0458 1.0509 1.0485 1.0332 0.9890 0.9058 0.7795 0.6173 0.4335

515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720

-1.0498 -0.8815 -0.6768 -0.4803 -0.3113 -0.1623 -0.0281 0.0938 0.2054 0.3077 0.4015 0.4873 0.5653 0.6357 0.6987 0.7544 0.8024 0.8423 0.8757 0.9024 0.9237 0.9403 0.9533 0.9636 0.9719 0.9789 0.9844 0.9884 0.9915 0.9938 0.9952 0.9965 0.9974 0.9983 0.9991 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000

1.7856 1.7329 1.5920 1.4329 1.2873 1.1527 1.0267 0.9092 0.7996 0.6978 0.6040 0.5177 0.4390 0.3678 0.3042 0.2480 0.1995 0.1593 0.1254 0.0986 0.0770 0.0603 0.0473 0.0368 0.0283 0.0214 0.0158 0.0118 0.0087 0.0064 0.0049 0.0036 0.0026 0.0017 0.0009 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000

0.2642 0.1486 0.0848 0.0474 0.0240 0.0096 0.0013 -0.0031 -0.0050 -0.0056 -0.0055 -0.0050 -0.0043 -0.0035 -0.0029 -0.0024 -0.0019 -0.0015 -0.0011 -0.0010 -0.0008 -0.0006 -0.0005 -0.0004 -0.0003 -0.0003 -0.0003 -0.0001 -0.0001 -0.0001 -0.0001 -0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

725 730 735 740 745 750 755 760 765 770 775 780

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

TABLE 9. Guild's and Wright's averaged spectral chromaticity co-ordinates in terms of the NPL primaries (from Tables 4 and 6)..

Wavelength (nm)

r5

g5

b5

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510

0.0204 0.0204 0.0204 0.0204 0.0204 0.0191 0.0177 0.0162 0.0137 0.0114 0.0072 0.0011 -0.0070 -0.0178 -0.0315 -0.0487 -0.0697 -0.0983 -0.1376 -0.1990 -0.2846 -0.4019 -0.5527 -0.7480 -0.9494 -1.0800 -1.1203

-0.0106 -0.0106 -0.0106 -0.0106 -0.0106 -0.0101 -0.0096 -0.0089 -0.0074 -0.0060 -0.0037 -0.0005 0.0039 0.0093 0.0161 0.0264 0.0405 0.0632 0.0970 0.1520 0.2367 0.3689 0.5613 0.8440 1.1727 1.4750 1.6964

0.9902 0.9902 0.9902 0.9902 0.9902 0.9910 0.9919 0.9927 0.9937 0.9946 0.9965 0.9994 1.0031 1.0085 1.0154 1.0223 1.0292 1.0351 1.0406 1.0470 1.0479 1.0330 0.9914 0.9040 0.7767 0.6050 0.4239

Absolute differences between Tables 14 and 9.

0.001 0.001 0.000 0.000 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.001 0.001 0.002 0.001 0.005 0.007 0.008 0.021 0.034 0.017 0.002

0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.002 0.002 0.001 0.002 0.003 0.005 0.006 0.007 0.006 0.022 0.037 0.029 0.011

0.002 0.002 0.002 0.001 0.000 0.001 0.001 0.000 0.000 0.000 0.001 0.000 0.000 0.002 0.003 0.002 0.001 0.002 0.005 0.004 0.001 0.000 0.002 0.002 0.003 0.012 0.010

515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720

-1.0311 -0.8637 -0.6739 -0.4879 -0.3165 -0.1617 -0.0279 0.0859 0.1990 0.3032 0.3988 0.4864 0.5664 0.6376 0.7003 0.7572 0.8031 0.8406 0.8738 0.9010 0.9219 0.9385 0.9526 0.9639 0.9732 0.9799 0.9853 0.9889 0.9917 0.9937 0.9950 0.9961 0.9971 0.9976 0.9985 0.9993 0.9997 1.0000 1.0000 1.0000 1.0000 1.0000

1.7647 1.7114 1.5849 1.4406 1.2944 1.1530 1.0267 0.9166 0.8064 0.7029 0.6068 0.5185 0.4376 0.3655 0.3020 0.2442 0.1979 0.1600 0.1267 0.0995 0.0786 0.0620 0.0479 0.0366 0.0273 0.0206 0.0152 0.0111 0.0083 0.0063 0.0050 0.0039 0.0029 0.0024 0.0015 0.0007 0.0003 0.0000 0.0000 0.0000 0.0000 0.0000

0.2664 0.1523 0.0890 0.0473 0.0221 0.0087 0.0012 -0.0025 -0.0054 -0.0061 -0.0056 -0.0049 -0.0040 -0.0031 -0.0023 -0.0014 -0.0010 -0.0006 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 -0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.019 0.018 0.003 0.008 0.005 0.001 0.000 0.008 0.006 0.005 0.003 0.001 0.001 0.002 0.002 0.003 0.001 0.002 0.002 0.001 0.002 0.002 0.001 0.000 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.021 0.021 0.007 0.008 0.007 0.000 0.000 0.007 0.007 0.005 0.003 0.001 0.001 0.002 0.002 0.004 0.002 0.001 0.001 0.001 0.002 0.002 0.001 0.000 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.002 0.004 0.004 0.000 0.002 0.001 0.000 0.001 0.000 0.001 0.000 0.000 0.000 0.000 0.001 0.001 0.001 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

725 730 735 740 745 750 755 760 765 770 775 780

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Data from J. Guild. The colorimetric properties of the spectrum. Philos. Trans. Roy. Soc. London, Ser. A , 230, 149-187 (1931).

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

Calculate the color matching functions coefficients nr, ng and nb so that (nr x LR) + (ng x LG) + (nb x LB) = E x V x 100 for the NPL standard white light. The relative values of L R, LG and LB are modified to LR 1.0000

LG 4.4036

LB 0.0471

TABLE 15. Color matching functions based on revised luminance values (NPL white) Wavelength (nm)

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510

NPL white E x V x 100

n r6

n g6 g

0.0000 0.0000 0.0000 0.0000 0.0170 0.0360 0.0620 0.1200 0.2410 0.4730 0.7810 1.1610 1.6700 2.2750 2.8850 3.7250 4.6900 5.8700 7.2900 9.1300 11.2900 13.9100 16.9800 20.9600 26.1200 32.4000 39.7700

r 0.0000 0.0000 0.0000 0.0000 0.0129 0.0265 0.0437 0.0764 0.1260 0.1718 0.1471 0.0240 -0.1894 -0.5125 -0.9198 -1.4529 -2.0395 -2.6376 -3.1496 -3.6233 -4.0102 -4.4067 -4.7455 -5.1976 -5.7994 -6.4585 -7.0365

0.0000 0.0000 0.0000 0.0000 -0.0061 -0.0130 -0.0221 -0.0400 -0.0682 -0.0959 -0.0837 -0.0146 0.1129 0.3011 0.5361 0.8457 1.2095 1.6359 2.1190 2.6902 3.3136 4.0363 4.8415 5.8708 7.1957 8.7841 10.6000

n b6 b

0.0000 0.0000 0.0000 0.0000 0.6566 1.4129 2.4526 4.6693 8.8261 15.3654 21.2917 25.5160 28.9398 31.0508 30.6747 30.8807 29.8121 27.6928 23.5435 19.2628 15.0470 11.5203 8.6170 6.4721 4.9371 3.7506 2.7272

515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720

48.1500 57.5700 66.4700 74.7700 81.7400 88.0900 93.1500 96.6200 98.8100 99.5000 98.3900 95.3000 90.3100 85.1500 79.2900 71.6600 64.8000 58.1500 51.2600 45.0000 39.2800 33.5700 28.0900 23.1600 18.9500 15.3400 12.2000 9.4100 7.2400 5.3600 3.8500 2.8000 2.0300 1.4800 1.0400 0.7100 0.5030 0.3510 0.2510 0.1780 0.1210 0.0870

-7.4057 -7.5107 -7.0986 -6.1580 -4.7481 -2.9092 -0.5817 2.2127 5.4465 9.0581 12.9068 16.7846 20.4361 24.0001 27.1851 29.2756 30.9376 31.7305 31.4334 30.3860 28.7306 26.1750 23.0576 19.8295 16.7945 13.9955 11.3929 8.9409 6.9721 5.2131 3.7683 2.7556 2.0069 1.4692 1.0357 0.7087 0.5028 0.3510 0.2510 0.1780 0.1210 0.0870

12.5960 14.7654 16.6969 18.3712 19.6364 20.6629 21.2849 21.4394 21.2030 20.5399 19.4140 17.8316 15.8691 13.8877 11.8335 9.6259 7.6905 6.0001 4.5028 3.3190 2.3959 1.6795 1.1429 0.7564 0.4895 0.3054 0.1833 0.1065 0.0608 0.0334 0.0186 0.0101 0.0052 0.0025 0.0010 0.0003 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000

1.8638 1.2661 0.8897 0.6074 0.3657 0.1721 0.0279 -0.0726 -0.1313 -0.1647 -0.1766 -0.1726 -0.1545 -0.1332 -0.1131 -0.0934 -0.0734 -0.0574 -0.0411 -0.0343 -0.0238 -0.0178 -0.0123 -0.0079 -0.0044 -0.0037 -0.0030 -0.0012 -0.0009 -0.0007 -0.0005 -0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

725 730 735 740 745 750 755 760 765 770 775 780

0.0625 0.0425 0.0290 0.0200 0.0130 0.0090 0.0065 0.0045 0.0000 0.0000 0.0000 0.0000 Sums Normalized

0.0625 0.0425 0.0290 0.0200 0.0130 0.0090 0.0065 0.0045 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

358.35 0.3333

358.11 0.3330

358.82 0.3337

These are the equal chromaticity co-ordinates of the NPL standard white in terms of the NPL primaries.

LR 1.0000

LG 4.4036

LB 0.0471

TABLE 16. Color matching functions based on revised luminance values (equal energy white) Equal energy white Wavelength (nm) V x 100

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510

0.0039 0.0064 0.0120 0.0217 0.0396 0.0640 0.1210 0.2180 0.4000 0.7300 1.1600 1.6840 2.3000 2.9800 3.8000 4.8000 6.0000 7.3900 9.0980 11.2600 13.9020 16.9300 20.8020 25.8600 32.3000 40.7300 50.3000

n r6

n g6

n b6

0.0032 0.0051 0.0095 0.0168 0.0300 0.0472 0.0852 0.1388 0.2092 0.2651 0.2185 0.0348 -0.2609 -0.6713 -1.2115 -1.8722 -2.6091 -3.3205 -3.9307 -4.4686 -4.9380 -5.3635 -5.8137 -6.4127 -7.1715 -8.1189 -8.8996

-0.0014 -0.0023 -0.0043 -0.0077 -0.0142 -0.0230 -0.0430 -0.0727 -0.1133 -0.1479 -0.1243 -0.0211 0.1555 0.3943 0.7061 1.0898 1.5473 2.0595 2.6445 3.3178 4.0802 4.9126 5.9312 7.2433 8.8982 11.0425 13.4066

0.1459 0.2389 0.4545 0.8276 1.5296 2.5118 4.7866 8.4826 14.6492 23.7141 31.6241 37.0102 39.8572 40.6732 40.4034 39.7925 38.1392 34.8637 29.3825 23.7568 18.5282 14.0215 10.5565 7.9852 6.1052 4.7148 3.4492

515 520 525 530 535 540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720

60.8200 71.0000 79.3200 86.2000 91.4850 95.4000 98.0300 99.4950 100.0000 99.5000 97.8600 95.2000 91.5400 87.0000 81.6300 75.7000 69.4900 63.1000 56.6800 50.3000 44.1200 38.1000 32.1000 26.5000 21.7000 17.5000 13.8200 10.7000 8.1600 6.1000 4.4580 3.2000 2.3200 1.7000 1.1920 0.8210 0.5723 0.4102 0.2929 0.2091 0.1484 0.1047

-9.3544 -9.2628 -8.4709 -7.0993 -5.3141 -3.1506 -0.6122 2.2786 5.5121 9.0581 12.8373 16.7670 20.7145 24.5216 27.9874 30.9261 33.1767 34.4316 34.7570 33.9648 32.2707 29.7071 26.3492 22.6892 19.2317 15.9662 12.9057 10.1666 7.8581 5.9329 4.3634 3.1492 2.2936 1.6876 1.1871 0.8195 0.5720 0.4102 0.2929 0.2091 0.1484 0.1047

15.9105 18.2099 19.9248 21.1795 21.9774 22.3775 22.4000 22.0774 21.4584 20.5399 19.3094 17.8129 16.0852 14.1895 12.1828 10.1686 8.2471 6.5109 4.9789 3.7099 2.6911 1.9061 1.3061 0.8655 0.5606 0.3483 0.2077 0.1211 0.0686 0.0380 0.0215 0.0115 0.0060 0.0028 0.0011 0.0003 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000

2.3543 1.5615 1.0617 0.7003 0.4092 0.1864 0.0294 -0.0748 -0.1329 -0.1647 -0.1756 -0.1724 -0.1566 -0.1361 -0.1164 -0.0986 -0.0787 -0.0623 -0.0455 -0.0384 -0.0267 -0.0202 -0.0141 -0.0090 -0.0051 -0.0042 -0.0034 -0.0013 -0.0010 -0.0008 -0.0006 -0.0004 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

725 730 735 740 745 750 755 760 765 770 775 780

0.0740 0.0520 0.0361 0.0249 0.0172 0.0120 0.0085 0.0060 0.0042 0.0030 0.0021 0.0015 Sums Normalized

0.0740 0.0520 0.0361 0.0249 0.0172 0.0120 0.0085 0.0060 0.0042 0.0030 0.0021 0.0015

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

378.23 0.3013

394.26 0.3140

482.97 0.3847

These are the chromaticity co-ordinates of the equal energy white in terms of the NPL primaries.

These are the equal chromaticity co-ordinates of the equal energy white in terms of the NPL primaries. 0.3013

0.3140

0.3847

TABLE 14. Smoothed averaged spectral chromaticity co-ordinates in terms of the NPL primaries.

Wavelength (nm)

r6

g6

b6

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535

0.0214 0.0211 0.0207 0.0201 0.0194 0.0186 0.0177 0.0163 0.0142 0.0111 0.0069 0.0009 -0.0066 -0.0166 -0.0304 -0.0481 -0.0705 -0.0990 -0.1401 -0.1980 -0.2799 -0.3959 -0.5455 -0.7285 -0.9170 -1.0642 -1.1197 -1.0506 -0.8819 -0.6771 -0.4805 -0.3114

-0.0094 -0.0093 -0.0093 -0.0093 -0.0092 -0.0091 -0.0089 -0.0085 -0.0077 -0.0062 -0.0039 -0.0006 0.0039 0.0098 0.0177 0.0280 0.0418 0.0614 0.0943 0.1470 0.2313 0.3625 0.5565 0.8228 1.1375 1.4472 1.6864 1.7866 1.7335 1.5924 1.4332 1.2874

0.9880 0.9883 0.9887 0.9891 0.9898 0.9905 0.9913 0.9923 0.9935 0.9951 0.9970 0.9996 1.0027 1.0069 1.0127 1.0201 1.0287 1.0376 1.0459 1.0510 1.0487 1.0333 0.9891 0.9058 0.7794 0.6170 0.4333 0.2640 0.1484 0.0847 0.0473 0.0239

540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740 745

-0.1623 -0.0281 0.0939 0.2054 0.3078 0.4016 0.4873 0.5653 0.6357 0.6988 0.7544 0.8025 0.8423 0.8757 0.9025 0.9237 0.9403 0.9533 0.9636 0.9719 0.9789 0.9844 0.9884 0.9915 0.9938 0.9952 0.9965 0.9974 0.9983 0.9991 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.1527 1.0267 0.9092 0.7995 0.6978 0.6039 0.5177 0.4389 0.3678 0.3041 0.2480 0.1994 0.1592 0.1254 0.0986 0.0770 0.0603 0.0472 0.0368 0.0283 0.0214 0.0158 0.0118 0.0086 0.0064 0.0049 0.0036 0.0026 0.0017 0.0009 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0096 0.0013 -0.0031 -0.0049 -0.0056 -0.0055 -0.0050 -0.0043 -0.0035 -0.0029 -0.0024 -0.0019 -0.0015 -0.0011 -0.0010 -0.0008 -0.0006 -0.0005 -0.0004 -0.0003 -0.0003 -0.0003 -0.0001 -0.0001 -0.0001 -0.0001 -0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

750 755 760 765 770 775 780

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

TABLE 15. Calculated CIE values

Wavelength (nm)

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535

r

g

b

0.0272 0.0268 0.0263 0.0256 0.0247 0.0237 0.0225 0.0207 0.0181 0.0142 0.0088 0.0012 -0.0084 -0.0213 -0.0390 -0.0618 -0.0909 -0.1281 -0.1821 -0.2585 -0.3668 -0.5201 -0.7151 -0.9460 -1.1686 -1.3182 -1.3370 -1.2075 -0.9829 -0.7385 -0.5158 -0.3304

-0.0115 -0.0114 -0.0114 -0.0113 -0.0112 -0.0111 -0.0109 -0.0104 -0.0094 -0.0076 -0.0048 -0.0007 0.0048 0.0120 0.0218 0.0345 0.0517 0.0762 0.1175 0.1841 0.2907 0.4569 0.6998 1.0249 1.3907 1.7196 1.9318 1.9698 1.8533 1.6661 1.4761 1.3105

0.9843 0.9846 0.9851 0.9857 0.9865 0.9874 0.9884 0.9897 0.9913 0.9934 0.9960 0.9995 1.0036 1.0093 1.0172 1.0273 1.0392 1.0519 1.0646 1.0744 1.0761 1.0632 1.0153 0.9211 0.7779 0.5986 0.4052 0.2376 0.1296 0.0724 0.0398 0.0199

540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740 745

-0.1707 -0.0293 0.0974 0.2121 0.3164 0.4112 0.4973 0.5751 0.6449 0.7071 0.7617 0.8087 0.8475 0.8800 0.9059 0.9265 0.9425 0.9550 0.9650 0.9730 0.9797 0.9850 0.9888 0.9918 0.9940 0.9954 0.9966 0.9975 0.9984 0.9991 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.1628 1.0282 0.9051 0.7919 0.6881 0.5932 0.5067 0.4283 0.3579 0.2952 0.2402 0.1928 0.1537 0.1209 0.0949 0.0741 0.0580 0.0454 0.0353 0.0272 0.0205 0.0152 0.0113 0.0083 0.0061 0.0047 0.0035 0.0025 0.0016 0.0009 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0079 0.0011 -0.0025 -0.0040 -0.0045 -0.0044 -0.0040 -0.0034 -0.0028 -0.0023 -0.0019 -0.0015 -0.0012 -0.0009 -0.0008 -0.0006 -0.0005 -0.0004 -0.0003 -0.0002 -0.0002 -0.0002 -0.0001 -0.0001 -0.0001 -0.0001 -0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

750 755 760 765 770 775 780

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

TABLE 16. CIE Chromaticity co-ordinates

r

g

b

0.0272 0.0268 0.0263 0.0256 0.0247 0.0237 0.0225 0.0207 0.0181 0.0142 0.0088 0.0012 -0.0084 -0.0213 -0.0390 -0.0618 -0.0909 -0.1281 -0.1821 -0.2584 -0.3667 -0.5200 -0.7150 -0.9459 -1.1685 -1.3182 -1.3371 -1.2076 -0.9830 -0.7386 -0.5159 -0.3304

-0.0115 -0.0114 -0.0114 -0.0113 -0.0112 -0.0111 -0.0109 -0.0104 -0.0094 -0.0076 -0.0048 -0.0007 0.0048 0.0120 0.0218 0.0345 0.0517 0.0762 0.1175 0.1840 0.2906 0.4568 0.6996 1.0247 1.3905 1.7195 1.9318 1.9699 1.8534 1.6662 1.4761 1.3105

0.9843 0.9846 0.9851 0.9857 0.9865 0.9874 0.9884 0.9897 0.9913 0.9934 0.9960 0.9995 1.0036 1.0093 1.0172 1.0273 1.0392 1.0519 1.0646 1.0744 1.0761 1.0632 1.0154 0.9212 0.7780 0.5987 0.4053 0.2377 0.1296 0.0724 0.0398 0.0199

Absolute differences

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0002 0.0002 0.0002 0.0001 0.0000 0.0001 0.0001 0.0001 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001 0.0000 0.0000 0.0000 0.0000

-0.1707 -0.0293 0.0974 0.2121 0.3164 0.4112 0.4973 0.5751 0.6449 0.7071 0.7617 0.8087 0.8475 0.8800 0.9059 0.9265 0.9425 0.9550 0.9649 0.9730 0.9797 0.9850 0.9888 0.9918 0.9940 0.9954 0.9966 0.9975 0.9984 0.9991 0.9996 0.9999 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1.1628 1.0282 0.9051 0.7919 0.6881 0.5932 0.5067 0.4283 0.3579 0.2952 0.2402 0.1928 0.1537 0.1209 0.0949 0.0741 0.0580 0.0454 0.0353 0.0272 0.0205 0.0152 0.0113 0.0083 0.0061 0.0047 0.0035 0.0025 0.0016 0.0009 0.0004 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0079 0.0011 -0.0025 -0.0040 -0.0045 -0.0044 -0.0040 -0.0034 -0.0028 -0.0023 -0.0019 -0.0015 -0.0012 -0.0009 -0.0008 -0.0006 -0.0005 -0.0004 -0.0003 -0.0002 -0.0002 -0.0002 -0.0001 -0.0001 -0.0001 -0.0001 -0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.1132 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Calculation of the relative luminances of the NPL primaries based on units such that matching the equal energy white gives equal chromaticity co-ordinates. NPL white

LG 4.4036

LB 0.0471

EEW Chromaticity co-ordinates 0.3013 0.3140

0.3847

CIE

LR 1.0000

LR 0.9039 1.0000

LG 4.1491 4.5903

LB 0.0543 0.0601

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Table 17. Calculated CIE color matching functions

Equal energy white Wavelength (nm)

V x 100

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535

0.0039 0.0064 0.0120 0.0217 0.0396 0.0640 0.1210 0.2180 0.4000 0.7300 1.1600 1.6840 2.3000 2.9800 3.8000 4.8000 6.0000 7.3900 9.0980 11.2600 13.9020 16.9300 20.8020 25.8600 32.3000 40.7300 50.3000 60.8200 71.0000 79.3200 86.2000 91.4850

LR 1.0000

LG 4.5907

LB 0.0601

0.0032 0.0051 0.0095 0.0169 0.0300 0.0473 0.0855 0.1392 0.2098 0.2658 0.2190 0.0348 -0.2613 -0.6721 -1.2127 -1.8737 -2.6108 -3.3222 -3.9323 -4.4700 -4.9392 -5.3645 -5.8146 -6.4136 -7.1724 -8.1199 -8.9006 -9.3554 -9.2638 -8.4717 -7.1001 -5.3146

-0.0013 -0.0022 -0.0041 -0.0074 -0.0136 -0.0222 -0.0414 -0.0699 -0.1090 -0.1423 -0.1195 -0.0203 0.1493 0.3787 0.6779 1.0461 1.4850 1.9764 2.5375 3.1832 3.9145 4.7129 5.6899 6.9485 8.5358 10.5928 12.8605 15.2623 17.4680 19.1130 20.3165 21.0818

0.1144 0.1874 0.3565 0.6491 1.1997 1.9702 3.7546 6.6535 11.4883 18.5914 24.7829 28.9921 31.2112 31.8412 31.6227 31.1390 29.8407 27.2744 22.9836 18.5814 14.4909 10.9657 8.2556 6.2446 4.7744 3.6871 2.6973 1.8411 1.2211 0.8302 0.5476 0.3200

540 545 550 555 560 565 570 575 580 585 590 595 600 605 610 615 620 625 630 635 640 645 650 655 660 665 670 675 680 685 690 695 700 705 710 715 720 725 730 735 740 745

95.4000 98.0300 99.4950 100.0000 99.5000 97.8600 95.2000 91.5400 87.0000 81.6300 75.7000 69.4900 63.1000 56.6800 50.3000 44.1200 38.1000 32.1000 26.5000 21.7000 17.5000 13.8200 10.7000 8.1600 6.1000 4.4580 3.2000 2.3200 1.7000 1.1920 0.8210 0.5723 0.4102 0.2929 0.2091 0.1484 0.1047 0.0740 0.0520 0.0361 0.0249 0.0172

-3.1509 -0.6123 2.2788 5.5126 9.0588 12.8383 16.7683 20.7160 24.5232 27.9891 30.9278 33.1783 34.4331 34.7583 33.9659 32.2715 29.7077 26.3497 22.6895 19.2320 15.9663 12.9058 10.1666 7.8581 5.9329 4.3634 3.1492 2.2936 1.6876 1.1871 0.8195 0.5720 0.4102 0.2929 0.2091 0.1484 0.1047 0.0740 0.0520 0.0361 0.0249 0.0172

21.4656 21.4871 21.1775 20.5837 19.7026 18.5222 17.0867 15.4293 13.6108 11.6859 9.7538 7.9106 6.2452 4.7757 3.5585 2.5812 1.8283 1.2528 0.8301 0.5377 0.3341 0.1992 0.1162 0.0658 0.0364 0.0206 0.0111 0.0057 0.0027 0.0011 0.0003 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.1458 0.0230 -0.0585 -0.1039 -0.1288 -0.1373 -0.1348 -0.1224 -0.1064 -0.0910 -0.0771 -0.0615 -0.0487 -0.0355 -0.0300 -0.0209 -0.0158 -0.0110 -0.0071 -0.0040 -0.0033 -0.0026 -0.0010 -0.0008 -0.0006 -0.0004 -0.0003 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

750 755 760 765 770 775 780

0.0120 0.0085 0.0060 0.0042 0.0030 0.0021 0.0015

Equal energy white chromaticity co-ordinates

0.0120 0.0085 0.0060 0.0042 0.0030 0.0021 0.0015

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

378.225

378.196

378.075

0.3334

0.3334

0.3333

Table 18. CIE colour matching functions

380 385 390 395 400 405 410 415 420 425 430 435 440 445 450 455 460 465 470 475 480 485 490 495 500 505 510 515 520 525 530 535

Differences: Value in Table 17 divided by 100 less the value in Table 18.

r

g

b

0.00003 0.00005 0.00010 0.00017 0.00030 0.00047 0.00084 0.00139 0.00211 0.00266 0.00218 0.00036 -0.00261 -0.00673 -0.01213 -0.01874 -0.02608 -0.03324 -0.03933 -0.04471 -0.04939 -0.05364 -0.05814 -0.06414 -0.07137 -0.08120 -0.08901 -0.09356 -0.09264 -0.08473 -0.07101 -0.05316

-0.00001 -0.00002 -0.00004 -0.00007 -0.00014 -0.00022 -0.00041 -0.00070 -0.00110 -0.00143 -0.00119 -0.00021 0.00149 0.00379 0.00678 0.01046 0.01485 0.01977 0.02538 0.03183 0.03914 0.04713 0.05689 0.06948 0.08536 0.10593 0.12860 0.15262 0.17468 0.19113 0.20317 0.21083

0.00117 0.00189 0.00359 0.00647 0.01214 0.01969 0.03707 0.06637 0.11541 0.18575 0.24769 0.29012 0.31228 0.31860 0.31670 0.31166 0.29821 0.27295 0.22991 0.18592 0.14494 0.10968 0.08257 0.06246 0.04776 0.03688 0.02698 0.01842 0.01221 0.00830 0.00549 0.00320

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