ASTM E308-99

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Designation: E 308 – 99
Standard Practice for
Computing the Colors of Objects by Using the CIE System
This standard is issued under the fixed designation E 308; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (e) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the Department of Defense.
INTRODUCTION
Standard tables (Tables 1-4) of color matching functions and illuminant spectral power distributions
have since 1931 been defined by the CIE, but the CIE has eschewed the role of preparing tables of
tristimulus weighting factors for the convenient calculation of tristimulus values. There have
subsequently appeared numerous compilations of tristimulus weighting factors in the literature with
disparity of data resulting from, for example, different selections of wavelength intervals and methods
of truncating abbreviated wavelength ranges. In 1970, Foster et al. (1) proposed conventions to
standardize these two features, and Stearns (2) published a more complete set of tables. Stearns’ work
and later publications such as the 1985 revision of E 308 have greatly reduced the substantial
variations in methods for tristimulus computation that existed several decades ago.
The disparities among earlier tables were largely caused by the introduction of computations based
on 20-nm wavelength intervals. With the increasing precision of modern instruments, there is a
likelihood of a need for tables for narrower wavelength intervals. Stearns’ tables, based on a 10-nm
interval, did not allow the derivation of consistent tables with wavelength intervals less than 10 nm.
The 1-nm table must be designated the basic table if others with greater wavelength intervals are to
have the same white point, and this was the reason for the 1985 revision of E308, resulting in tables
that are included in the present revision as Tables 5.
The 1994 revision was made in order to introduce to the user a method of reducing the dependence
of the computed tristimulus values on the bandpass of the measuring instrument, using methods that
are detailed in this practice. These changes, however, lead to tables (Tables 6 in this practice) that are
substantially different from the Tables 5 that have been in use since 1985. There is accordingly a
danger, if the new tables are introduced but not universally adopted, that there may again be, perhaps
for several decades, a significant disparity among the tables of tristimulus weighting factors commonly
used. It is highly desirable that this should be avoided.
1. Scope six CIE standard illuminants and three CIE recommended
fluorescent illuminants.
1.1 This practice provides the values and practical compu-
1.4 Procedures are included for cases in which data are
tation procedures needed to obtain CIE tristimulus values from
available only in more limited wavelength ranges than those
spectral reflectance, transmittance, or radiance data for object-
recommended, or for a measurement interval wider than that
color specimens.
recommended by the CIE. This practice is applicable to
1.2 Procedures and tables of standard values are given for
spectral data obtained according to Practice E 1164 with 1-, 5-,
computing from spectral measurements the CIE tristimulus
10-, or 20-nm measurement interval.
values X, Y, Z, and chromaticity coordinates x, y for the CIE
1.5 Procedures are included for cases in which the spectral
1931 standard observer and X ,Y ,Z and x .y for the
10 10 10 10 10
data are, and those in which they are not, corrected for
CIE 1964 supplementary standard observer.
bandpass dependence. For the uncorrected cases, it is assumed
1.3 Standard values are included for the spectral power of
that the spectral bandpass of the instrument used to obtain the
data was approximately equal to the measurement interval and
This practice is under the jurisdiction of ASTM Committee E-12 on Color and
was triangular in shape. These choices are believed to corre-
Appearanceand is the direct responsibility of Subcommittee E12.04 on Color and
spond to the most widely used industrial practice.
Appearance Analysis.
Current edition approved June 10, 1999. Published October 1999. Originally 1.6 This practice includes procedures for conversion of
published as E 308 – 66. Last previous edition E 308 – 96.
results to color spaces that are part of the CIE system, such as
The boldface numbers in parentheses refer to the list of references at the end of
CIELAB and CIELUV (3). Equations for calculating color
this practice.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
E 308
differences in these and other systems are given in Test Method
TABLE 1 Continued
D 2244.
l(nm) x¯(l) y¯(l) z¯(l)
665 0.1212 0.0446 0.0000
TABLE 1 Spectral Tristimulus Values (Color-Matching
670 0.0874 0.0320 0.0000
Functions) x¯, y¯, z¯ of the CIE 1931 Standard (2°) Observer, at 5 nm
Intervals from 380 to 780 nm (See Note 2 and Ref (3))
675 0.0636 0.0232 0.0000
680 0.0468 0.0170 0.0000
685 0.0329 0.0119 0.0000
l(nm) x¯(l) y¯(l) z¯(l)
690 0.0227 0.0082 0.0000
380 0.0014 0.0000 0.0065
695 0.0158 0.0057 0.0000
385 0.0022 0.0001 0.0105
390 0.0042 0.0001 0.0201
700 0.0114 0.0041 0.0000
395 0.0076 0.0002 0.0362
705 0.0081 0.0029 0.0000
710 0.0058 0.0021 0.0000
400 0.0143 0.0004 0.0679
715 0.0041 0.0015 0.0000
405 0.0232 0.0006 0.1102
720 0.0029 0.0010 0.0000
410 0.0435 0.0012 0.2074
415 0.0776 0.0022 0.3713
725 0.0020 0.0007 0.0000
420 0.1344 0.0040 0.6456
730 0.0014 0.0005 0.0000
735 0.0010 0.0004 0.0000
425 0.2148 0.0073 1.0391
740 0.0007 0.0002 0.0000
430 0.2839 0.0116 1.3856
745 0.0005 0.0002 0.0000
435 0.3285 0.0168 1.6230
440 0.3483 0.0230 1.7471
750 0.0003 0.0001 0.0000
445 0.3481 0.0298 1.7826
755 0.0002 0.0001 0.0000
760 0.0002 0.0001 0.0000
450 0.3362 0.0380 1.7721
765 0.0001 0.0000 0.0000
455 0.3187 0.0480 1.7441
770 0.0001 0.0000 0.0000
460 0.2908 0.0600 1.6692
465 0.2511 0.0739 1.5281
775 0.0001 0.0000 0.0000
470 0.1954 0.0910 1.2876
780 0.0000 0.0000 0.0000
Summation at 5 nm intervals:
475 0.1421 0.1126 1.0419
480 0.0956 0.1390 0.8130
(x¯ (l) = 21.3714
485 0.0580 0.1693 0.6162
(y¯ (l) = 21.3711
490 0.0320 0.2080 0.4652
(z¯ (l) = 21.3715
495 0.0147 0.2586 0.3533
TABLE 2 Spectral Tristimulus Values (Color-Matching
500 0.0049 0.3230 0.2720
Functions) x¯ , y¯ , z¯ of the CIE 1964 Supplementary Standard
505 0.0024 0.4073 0.2123
10 10 10
510 0.0093 0.5030 0.1582 (10°) Observer, At 5 nm Intervals from 380 to 780 nm (See Note 2
515 0.0291 0.6082 0.1117
and Ref 3)
520 0.0633 0.7100 0.0782
l(nm) x¯ (l) y¯ (l) z¯ (l)
10 10 10
525 0.1096 0.7932 0.0573
530 0.1655 0.8620 0.0422 380 0.0002 0.0000 0.0007
535 0.2257 0.9149 0.0298 385 0.0007 0.0001 0.0029
390 0.0024 0.0003 0.0105
540 0.2904 0.9540 0.0203
545 0.3597 0.9803 0.0134 395 0.0072 0.0008 0.0323
550 0.4334 0.9950 0.0087 400 0.0191 0.0020 0.0860
555 0.5121 1.0000 0.0057 405 0.0434 0.0045 0.1971
560 0.5945 0.9950 0.0039 410 0.0847 0.0088 0.3894
565 0.6784 0.9786 0.0027 415 0.1406 0.0145 0.6568
570 0.7621 0.9520 0.0021 420 0.2045 0.0214 0.9725
575 0.8425 0.9154 0.0018 425 0.2647 0.0295 1.2825
580 0.9163 0.8700 0.0017 430 0.3147 0.0387 1.5535
585 0.9786 0.8163 0.0014 435 0.3577 0.0496 1.7985
590 1.0263 0.7570 0.0011 440 0.3837 0.0621 1.9673
595 1.0567 0.6949 0.0010 445 0.3867 0.0747 2.0273
600 1.0622 0.6310 0.0008 450 0.3707 0.0895 1.9948
605 1.0456 0.5668 0.0006 455 0.3430 0.1063 1.9007
610 1.0026 0.5030 0.0003 460 0.3023 0.1282 1.7454
615 0.9384 0.4412 0.0002 465 0.2541 0.1528 1.5549
620 0.8544 0.3810 0.0002 470 0.1956 0.1852 1.3176
625 0.7514 0.3210 0.0001 475 0.1323 0.2199 1.0302
630 0.6424 0.2650 0.0000 480 0.0805 0.2536 0.7721
635 0.5419 0.2170 0.0000 485 0.0411 0.2977 0.5701
640 0.4479 0.1750 0.0000 490 0.0162 0.3391 0.4153
645 0.3608 0.1382 0.0000 495 0.0051 0.3954 0.3024
650 0.2835 0.1070 0.0000 500 0.0038 0.4608 0.2185
655 0.2187 0.0816 0.0000 505 0.0154 0.5314 0.1592
660 0.1649 0.0610 0.0000 510 0.0375 0.6067 0.1120
E 308
TABLE 2 Continued TABLE 2 Continued
l(nm) x¯ (l) y¯ (l) z¯ (l) l(nm) x¯ (l) y¯ (l) z¯ (l)
10 10 10 10 10 10
515 0.0714 0.6857 0.0822 665 0.1122 0.0441 0.0000
520 0.1177 0.7618 0.0607 670 0.0813 0.0318 0.0000
525 0.1730 0.8233 0.0431 675 0.0579 0.0226 0.0000
530 0.2365 0.8752 0.0305 680 0.0409 0.0159 0.0000
535 0.3042 0.9238 0.0206 685 0.0286 0.0111 0.0000
540 0.3768 0.9620 0.0137 690 0.0199 0.0077 0.0000
545 0.4516 0.9822 0.0079 695 0.0138 0.0054 0.0000
550 0.5298 0.9918 0.0040 700 0.0096 0.0037 0.0000
555 0.6161 0.9991 0.0011 705 0.0066 0.0026 0.0000
560 0.7052 0.9973 0.0000 710 0.0046 0.0018 0.0000
565 0.7938 0.9824 0.0000 715 0.0031 0.0012 0.0000
570 0.8787 0.9556 0.0000 720 0.0022 0.0008 0.0000
575 0.9512 0.9152 0.0000 725 0.0015 0.0006 0.0000
580 1.0142 0.8689 0.0000 730 0.0010 0.0004 0.0000
585 1.0743 0.8256 0.0000 735 0.0007 0.0003 0.0000
590 1.1185 0.7774 0.0000 740 0.0005 0.0002 0.0000
595 1.1343 0.7204 0.0000 745 0.0004 0.0001 0.0000
600 1.1240 0.6583 0.0000 750 0.0003 0.0001 0.0000
605 1.0891 0.5939 0.0000 755 0.0002 0.0001 0.0000
610 1.0305 0.5280 0.0000 760 0.0001 0.0000 0.0000
615 0.9507 0.4618 0.0000 765 0.0001 0.0000 0.0000
620 0.8563 0.3981 0.0000 770 0.0001 0.0000 0.0000
625 0.7549 0.3396 0.0000 775 0.0000 0.0000 0.0000
630 0.6475 0.2835 0.0000 780 0.0000 0.0000 0.0000
635 0.5351 0.2283 0.0000
Summation at 5 nm intervals:
640 0.4316 0.1798 0.0000
645 0.3437 0.1402 0.0000 (x¯ (l) = 23.3294
(y¯ (l) = 23.3324
650 0.2683 0.1076 0.0000 (z¯ (l) = 23.3343
655 0.2043 0.0812 0.0000
660 0.1526 0.0603 0.0000
TABLE 3 Relative Spectral Power Distributions S(l) of CIE Standard Illuminants A, C, D , D , D , and D at 5-nm Intervals from 380
50 55 65 75
to 780 nm (See Note 2 and Ref 3)
l A C D D D D
50 55 65 75
(nm) S(l) S(l) S(l) S(l) S(l) S(l)
380 9.80 33.00 24.49 32.58 49.98 66.70
385 10.90 39.92 27.18 35.34 52.31 68.33
390 12.09 47.40 29.87 38.09 54.65 69.96
395 13.35 55.17 39.59 49.52 68.70 85.95
400 14.71 63.30 49.31 60.95 82.75 101.93
405 16.15 71.81 52.91 64.75 87.12 106.91
410 17.68 80.60 56.51 68.55 91.49 111.89
415 19.29 89.53 58.27 70.07 92.46 112.35
420 20.99 98.10 60.03 71.58 93.43 112.80
425 22.79 105.80 58.93 69.75 90.06 107.94
430 24.67 112.40 57.82 67.91 86.68 103.09
435 26.64 117.75 66.32 76.76 95.77 112.14
440 28.70 121.50 74.82 85.61 104.86 121.20
445 30.85 123.45 81.04 91.80 110.94 127.10
450 33.09 124.00 87.25 97.99 117.01 133.01
455 35.41 123.60 88.93 99.23 117.41 132.68
460 37.81 123.10 90.61 100.46 117.81 132.36
465 40.30 123.30 90.99 100.19 116.34 129.84
470 42.87 123.80 91.37 99.91 114.86 127.32
475 45.52 124.09 93.24 101.33 115.39 127.06
480 48.24 123.90 95.11 102.74 115.92 126.80
485 51.04 122.92 93.54 100.41 112.37 122.29
490 53.91 120.70 91.96 98.08 108.81 117.78
495 56.85 116.90 93.84 99.38 109.08 117.19
500 59.86 112.10 95.72 100.68 109.35 116.59
505 62.93 106.98 96.17 100.69 108.58 115.15
510 66.06 102.30 96.61 100.70 107.80 113.70
515 69.25 98.81 96.87 100.34 106.30 111.18
520 72.50 96.90 97.13 99.99 104.79 108.56
525 75.79 96.78 99.61 102.10 106.24 109.55
E 308
TABLE 3 Continued
l A C D D D D
50 55 65 75
(nm) S(l) S(l) S(l) S(l) S(l) S(l)
530 79.13 98.00 102.10 104.21 107.69 110.44
535 82.52 99.94 101.43 103.16 106.05 108.37
540 85.95 102.10 100.75 102.10 104.41 106.29
545 89.41 103.95 101.54 102.53 104.23 105.60
550 92.91 105.20 102.32 102.97 104.05 104.90
555 96.44 105.67 101.16 101.48 102.02 102.45
560 100.00 105.30 100.00 100.00 100.00 100.00
565 103.58 104.11 98.87 98.61 98.17 97.81
570 107.18 102.30 97.74 97.22 96.33 95.62
575 110.80 100.15 98.33 97.48 96.06 94.91
580 114.44 97.80 98.92 97.75 95.79 94.21
585 118.08 95.43 96.21 94.59 92.24 90.60
590 121.73 93.20 93.50 91.43 88.69 87.00
595 125.39 91.22 95.59 92.93 89.35 87.11
600 129.04 89.70 97.69 94.42 90.01 87.23
605 132.70 88.83 98.48 94.78 89.80 86.68
610 136.35 88.40 99.27 95.14 89.60 86.14
615 139.99 88.19 99.16 94.68 88.65 84.86
620 143.62 88.10 99.04 94.22 87.70 83.58
625 147.24 88.06 97.38 92.33 85.49 81.16
630 150.84 88.00 95.72 90.45 83.29 78.75
635 154.42 87.86 97.29 91.39 83.49 78.59
640 157.98 87.80 98.86 92.33 83.70 78.43
645 161.52 87.99 97.26 90.59 81.86 76.61
650 165.03 88.20 95.67 88.85 80.03 74.80
655 168.51 88.20 96.93 89.59 80.12 74.56
660 171.96 87.90 98.19 90.32 80.21 74.32
665 175.38 87.22 100.60 92.13 81.25 74.87
670 178.77 86.30 103.00 93.95 82.28 75.42
675 182.12 85.30 101.07 91.95 80.28 73.50
680 185.43 84.00 99.13 89.96 78.28 71.58
685 188.70 82.21 93.26 84.82 74.00 67.71
690 191.93 80.20 87.38 79.68 69.72 63.85
695 195.12 78.24 89.49 81.26 70.67 64.46
700 198.26 76.30 91.60 82.84 71.61 65.08
705 201.36 74.36 92.25 83.84 72.98 66.57
710 204.41 72.40 92.89 84.84 74.35 68.07
715 207.41 70.40 84.87 77.54 67.98 62.26
720 210.36 68.30 76.85 70.24 61.60 56.44
725 213.27 66.30 81.68 74.77 65.74 60.34
730 216.12 64.40 86.51 79.30 69.89 64.24
735 218.92 62.80 89.55 82.15 72.49 66.70
740 221.67 61.50 92.58 84.99 75.09 69.15
745 224.36 60.20 85.40 78.44 69.34 63.89
750 227.00 59.20 78.23 71.88 63.59 58.63
755 229.59 58.50 67.96 62.34 55.01 50.62
760 232.12 58.10 57.69 52.79 46.42 42.62
765 234.59 58.00 70.31 64.36 56.61 51.98
770 237.01 58.20 82.92 75.93 66.81 61.35
775 239.37 58.50 80.60 73.87 65.09 59.84
780 241.68 59.10 78.27 71.82 63.38 58.32
TABLE 4 Relative Spectral Power Distributions S(l)ofCIE
TABLE 4 Continued
Fluorescent Illuminants F2, F7, and F11 at 5-nm Intervals from
l(nm) F2 F7 F11
380 to 780 nm (See Note 2 and Ref 3)
440 11.81 17.52 12.13
445 6.27 11.35 6.95
l(nm) F2 F7 F11
450 6.63 12.00 7.19
380 1.18 2.56 0.91
385 1.48 3.18 0.63
455 6.93 12.58 7.12
390 1.84 3.84 0.46
460 7.19 13.08 6.72
395 2.15 4.53 0.37
465 7.40 13.45 6.13
400 3.44 6.15 1.29
470 7.54 13.71 5.46
475 7.62 13.88 4.79
405 15.69 19.37 12.68
410 3.85 7.37 1.59
480 7.65 13.95 5.66
415 3.74 7.05 1.79
485 7.62 13.93 14.29
420 4.19 7.71 2.46
490 7.62 13.82 14.96
425 4.62 8.41 3.38
495 7.45 13.64 8.97
500 7.28 13.43 4.72
430 5.06 9.15 4.49
435 34.98 44.14 33.94
505 7.15 13.25 2.33
E 308
2. Referenced Documents
TABLE 4 Continued
2.1 ASTM Standards:
l(nm) F2 F7 F11
D 2244 Test Method for Calculation of Color Differences
510 7.05 13.08 1.47
515 7.04 12.93 1.10 from Instrumentally Measured Color Coordinates
520 7.16 12.78 0.89
E 284 Terminology of Appearance
525 7.47 12.60 0.83
E 313 Practice for Calculating Yellowness and Whiteness
530 8.04 12.44 1.18
Indices from Instrumentally Measured Color Coordinates
...