Appendix
A physiologically based system for color measurements
As a supplement to the existing XYZ system for color measurements, committee TC 1-36 of the CIE has for some time been engaged in the development of a physiological based system for colorimetry. The committee has already adopted as cone fundamentals (fundamental color matching functions) the spectral sensitivities L , M , and S for a 2 field of Stockman and Sharpe (2000). In Table A1 these cone sensitivities (here called specific tristimulus values) are tabulated from 390 to 830 nm in 5 nm intervals.
Figure A1 shows the chromaticity diagram derived from the Stockman–Sharpe2000 fundamentals of Table A1, where the integrated values are normalized to equal values of 20.0000 for CIE Illuminant E (the equal energy spectrum) such that (lE; mEÞ ¼ ð1=3; 1=3Þ. The chromaticity coordinates ðl; mÞ for the spectrum locus are:
l ¼ L =ðL þ M þ S Þ; m ¼ M =ðL þ M þ S Þ; s ¼ S =ðL þ M þ S Þ:
Light Vision Color. Arne Valberg
# 2005 John Wiley & Sons Ltd
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Stockman−Sharpe2000 fundamentals |
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0.6 |
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E (1/3, 1/3) |
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550 |
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500 |
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0.4 |
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m |
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600 |
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0.2 |
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470 |
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650 |
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700 |
400 |
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0 |
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0.2 |
0.4 |
0.6 |
0.8 |
1.0 |
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l |
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Figure A1 A chromaticity diagram (1, m) derived from the Stockman–Sharpe2000 fundamentals L, M, and S of Table A1 (courtesy of J. H. Wold).
A PHYSIOLOGICALLY BASED SYSTEM FOR COLOR MEASUREMENTS |
417 |
Table A1 Specific tristimulus values and spectral chromaticity coordinates based on the
Stockman–Sharpe2000 cone fundamentals for 2 fields (energy units) at wavelengths from 390 to 830 nm and 5-nm intervalsa,b
Wavelength (nm) |
Specific Tristimulus Values (1/nm) |
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Chromaticity Coordinates |
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L |
M |
S |
l |
m |
390 |
3.57825E-04 |
3.88464E-04 |
395 |
9.06989E-04 |
1.01101E-03 |
400 |
2.07654E-03 |
2.39386E-03 |
405 |
4.16746E-03 |
4.95676E-03 |
410 |
7.51968E-03 |
9.27389E-03 |
415 |
1.15397E-02 |
1.53210E-02 |
420 |
1.59063E-02 |
2.28480E-02 |
425 |
1.97722E-02 |
3.11862E-02 |
430 |
2.43041E-02 |
4.16112E-02 |
435 |
2.94064E-02 |
5.46497E-02 |
440 |
3.47099E-02 |
6.83156E-02 |
445 |
3.87466E-02 |
8.00249E-02 |
450 |
4.29938E-02 |
9.18061E-02 |
455 |
4.77169E-02 |
1.03555E-01 |
460 |
5.57999E-02 |
1.22621E-01 |
465 |
6.95722E-02 |
1.52434E-01 |
470 |
8.57700E-02 |
1.85498E-01 |
475 |
1.02434E-01 |
2.16614E-01 |
480 |
1.20836E-01 |
2.48628E-01 |
485 |
1.41363E-01 |
2.82701E-01 |
490 |
1.65164E-01 |
3.20210E-01 |
495 |
2.00834E-01 |
3.76559E-01 |
500 |
2.49147E-01 |
4.51123E-01 |
505 |
3.10155E-01 |
5.43742E-01 |
510 |
3.82553E-01 |
6.49132E-01 |
515 |
4.62577E-01 |
7.58425E-01 |
520 |
5.41959E-01 |
8.61203E-01 |
525 |
6.07625E-01 |
9.33908E-01 |
530 |
6.64455E-01 |
9.86782E-01 |
535 |
7.11947E-01 |
1.02176E00 |
540 |
7.59627E-01 |
1.04956E00 |
545 |
7.92440E-01 |
1.05165E00 |
550 |
8.10660E-01 |
1.03056E00 |
555 |
8.32677E-01 |
1.00882E00 |
560 |
8.46224E-01 |
9.67866E-01 |
565 |
8.57468E-01 |
9.20888E-01 |
570 |
8.62216E-01 |
8.57933E-01 |
575 |
8.55592E-01 |
7.80716E-01 |
580 |
8.35863E-01 |
6.88948E-01 |
585 |
8.23942E-01 |
6.03865E-01 |
590 |
7.99861E-01 |
5.19499E-01 |
595 |
7.63902E-01 |
4.33703E-01 |
600 |
7.19078E-01 |
3.52691E-01 |
605 |
6.68311E-01 |
2.79336E-01 |
610 |
6.08482E-01 |
2.16482E-01 |
615 |
5.43867E-01 |
1.64775E-01 |
620 |
4.77864E-01 |
1.23010E-01 |
625 |
4.13816E-01 |
9.02609E-02 |
630 |
3.45502E-01 |
6.55038E-02 |
1.63368E-02 |
0.02095 |
0.02274 |
4.07681E-02 |
0.02125 |
0.02368 |
9.69362E-02 |
0.02048 |
0.02361 |
2.09532E-01 |
0.01906 |
0.02267 |
3.98711E-01 |
0.01810 |
0.02232 |
6.52569E-01 |
0.01698 |
0.02255 |
9.30211E-01 |
0.01642 |
0.02358 |
1.15413E00 |
0.01641 |
0.02588 |
1.37329E00 |
0.01689 |
0.02891 |
1.54615E00 |
0.01804 |
0.03352 |
1.69578E00 |
0.01930 |
0.03798 |
1.69663E00 |
0.02134 |
0.04408 |
1.63482E00 |
0.02430 |
0.05188 |
1.47200E00 |
0.02940 |
0.06379 |
1.34617E00 |
0.03660 |
0.08043 |
1.26329E00 |
0.04684 |
0.10263 |
1.10602E00 |
0.06227 |
0.13468 |
8.83656E-01 |
0.08517 |
0.18011 |
6.67918E-01 |
0.11648 |
0.23967 |
4.96784E-01 |
0.15351 |
0.30700 |
3.62536E-01 |
0.19479 |
0.37765 |
2.74684E-01 |
0.23570 |
0.44193 |
2.10196E-01 |
0.27365 |
0.49549 |
1.52115E-01 |
0.30830 |
0.54049 |
1.04074E-01 |
0.33683 |
0.57154 |
7.32582E-02 |
0.35741 |
0.58599 |
4.99712E-02 |
0.37296 |
0.59265 |
3.31812E-02 |
0.38586 |
0.59307 |
2.15627E-02 |
0.39721 |
0.58990 |
1.38509E-02 |
0.40740 |
0.58468 |
8.70803E-03 |
0.41786 |
0.57735 |
5.42251E-03 |
0.42846 |
0.56861 |
3.35207E-03 |
0.43948 |
0.55870 |
2.05812E-03 |
0.45167 |
0.54721 |
1.26655E-03 |
0.46615 |
0.53315 |
7.80248E-04 |
0.48196 |
0.51760 |
4.82202E-04 |
0.50110 |
0.49862 |
2.99518E-04 |
0.52278 |
0.47703 |
1.87292E-04 |
0.54811 |
0.45177 |
1.18068E-04 |
0.57702 |
0.42290 |
7.51235E-05 |
0.60621 |
0.39373 |
4.82934E-05 |
0.63783 |
0.36213 |
3.13926E-05 |
0.67091 |
0.32906 |
2.06479E-05 |
0.70522 |
0.29476 |
1.37489E-05 |
0.73757 |
0.26241 |
9.27174E-06 |
0.76747 |
0.23252 |
0.00000c |
0.79528 |
0.20472 |
0.00000c |
0.82094 |
0.17906 |
0.00000c |
0.84063 |
0.15937 |
(continued)
418 |
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APPENDIX |
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Wavelength (nm) |
Specific Tristimulus Values (1/nm) |
Chromaticity Coordinates |
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L |
M |
S |
l |
m |
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635 |
2.82692E-01 |
4.69173E-02 |
0.00000c |
0.85766 |
0.14234 |
640 |
2.29165E-01 |
3.31444E-02 |
0.00000c |
0.87364 |
0.12636 |
645 |
1.83898E-01 |
2.29943E-02 |
0.00000c |
0.88886 |
0.11114 |
650 |
1.42388E-01 |
1.62916E-02 |
0.00000c |
0.89733 |
0.10267 |
655 |
1.07561E-01 |
1.12970E-02 |
0.00000c |
0.90495 |
0.09505 |
660 |
8.01940E-02 |
7.70132E-03 |
0.00000c |
0.91238 |
0.08762 |
665 |
5.90709E-02 |
5.24329E-03 |
0.00000c |
0.91847 |
0.08153 |
670 |
4.29957E-02 |
3.62434E-03 |
0.00000c |
0.92226 |
0.07774 |
675 |
3.08877E-02 |
2.50593E-03 |
0.00000c |
0.92496 |
0.07504 |
680 |
2.18823E-02 |
1.72675E-03 |
0.00000c |
0.92686 |
0.07314 |
685 |
1.52787E-02 |
1.18251E-03 |
0.00000c |
0.92816 |
0.07184 |
690 |
1.04933E-02 |
8.02610E-04 |
0.00000c |
0.92895 |
0.07105 |
695 |
7.30449E-03 |
5.54151E-04 |
0.00000c |
0.92949 |
0.07051 |
700 |
5.08495E-03 |
3.85266E-04 |
0.00000c |
0.92957 |
0.07043 |
705 |
3.52760E-03 |
2.67255E-04 |
0.00000c |
0.92957 |
0.07043 |
710 |
2.41808E-03 |
1.83926E-04 |
0.00000c |
0.92931 |
0.07069 |
715 |
1.65597E-03 |
1.27194E-04 |
0.00000c |
0.92867 |
0.07133 |
720 |
1.14406E-03 |
8.87680E-05 |
0.00000c |
0.92800 |
0.07200 |
725 |
7.91328E-04 |
6.21532E-05 |
0.00000c |
0.92718 |
0.07282 |
730 |
5.51282E-04 |
4.38768E-05 |
0.00000c |
0.92628 |
0.07372 |
735 |
3.84581E-04 |
3.10428E-05 |
0.00000c |
0.92531 |
0.07469 |
740 |
2.68038E-04 |
2.20265E-05 |
0.00000c |
0.92406 |
0.07594 |
745 |
1.89110E-04 |
1.58674E-05 |
0.00000c |
0.92259 |
0.07741 |
750 |
1.33256E-04 |
1.14109E-05 |
0.00000c |
0.92112 |
0.07888 |
755 |
9.44203E-05 |
8.24989E-06 |
0.00000c |
0.91965 |
0.08035 |
760 |
6.72458E-05 |
6.00170E-06 |
0.00000c |
0.91806 |
0.08194 |
765 |
4.79623E-05 |
4.36605E-06 |
0.00000c |
0.91656 |
0.08344 |
770 |
3.44281E-05 |
3.19212E-06 |
0.00000c |
0.91515 |
0.08485 |
775 |
2.46736E-05 |
2.33174E-06 |
0.00000c |
0.91366 |
0.08634 |
780 |
1.78757E-05 |
1.72358E-06 |
0.00000c |
0.91206 |
0.08794 |
785 |
1.29706E-05 |
1.27664E-06 |
0.00000c |
0.91039 |
0.08961 |
790 |
9.43668E-06 |
9.48271E-07 |
0.00000c |
0.90869 |
0.09131 |
795 |
6.87838E-06 |
7.06159E-07 |
0.00000c |
0.90689 |
0.09311 |
800 |
5.04449E-06 |
5.30665E-07 |
0.00000c |
0.90482 |
0.09518 |
805 |
3.71706E-06 |
4.00799E-07 |
0.00000c |
0.90267 |
0.09733 |
810 |
2.73332E-06 |
3.01965E-07 |
0.00000c |
0.90052 |
0.09948 |
815 |
2.02164E-06 |
2.28721E-07 |
0.00000c |
0.89836 |
0.10164 |
820 |
1.50601E-06 |
1.74177E-07 |
0.00000c |
0.89633 |
0.10367 |
825 |
1.12297E-06 |
1.32362E-07 |
0.00000c |
0.89456 |
0.10544 |
830 |
8.40069E-07 |
1.00547E-07 |
0.00000c |
0.89311 |
0.10689 |
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Totals |
2.00000E01 |
2.00000E01 |
2.00000E01 |
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a Denoting the wavelengths 390, 395; . . . ; 830 by 1; 2; . . . ; 89, the specific tristimulus values are normalized
so that |
89 |
L |
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89 |
M |
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P |
89 S |
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100, where |
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5 nm. |
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b |
The |
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i ¼ |
P |
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i |
¼ |
i¼1 i ¼ |
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¼ |
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i¼1 |
i¼1 |
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89 |
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ð Þ |
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89 |
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chromaticity coordinates l and m of a stimulus with relative spectral energy distribution P |
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are defined |
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by |
the |
equations |
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L |
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M |
þ |
S |
and m |
¼ |
M |
L |
þ |
M |
S , |
where L |
¼ i¼1 |
P |
L |
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M |
¼ i¼1 |
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l ¼ L=ð89 þ |
ð |
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=ð |
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þ Þ |
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ð iÞ |
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i |
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mðE |
Þ |
0:33333.i |
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¼ Pi¼1 |
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Þ |
i |
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this |
gives |
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¼ |
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and |
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P i M |
and |
S |
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P i S . For |
the |
equal-energy |
stimulus, E,P |
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lE |
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0:33333P |
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c |
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¼ |
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The zero-values of S from 620 to 830 nm do not have a physiological meaning, but only signify that the values |
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are so small, that these values can be neglected. Without introducing the zero-values here, the chromaticity coordinates l and m would be undetermined for wavelengths beyond 615 nm.