Table 1
To evaluate the sums of the squares and the cross-products indicated by the
Least Square Analysis. Columns 2, 3, and 4 (Headed R,
G, and B, respectively) are the
ordinates of the color excitation curves for the specified wave-length of
column one as given by Troland (Lot. cit), and column 5 (Headed
L) evaluates the I.E.S. Visibility Function. The
remaining columns are filled in with the squares and cross-products as
indicated.
Wave Length
mμ | R | G | B | L | RR | RG | RB | RL | GG | GB | GL | BB | BL |
---|
|
---|
400 | 0 | 0 | 25 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 625 | 0 |
10 | 0 | 0 | 43 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1849 | 0 |
20 | 0 | 0 | 61 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 3721 | 0 |
30 | 0 | 0 | 92 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 8464 | 92 |
40 | 0 | 1 | 102 | 2 | 0 | 0 | 0 | 0 | 1 | 102 | 2 | 10404 | 204 |
|
450 | 0 | 2 | 95 | 4 | 0 | 0 | 0 | 0 | 4 | 190 | 8 | 9025 | 380 |
60 | 0 | 4 | 84 | 6 | 0 | 0 | 0 | 0 | 16 | 336 | 24 | 7056 | 504 |
70 | 0 | 8 | 70 | 9 | 0 | 0 | 0 | 0 | 64 | 560 | 72 | 4900 | 630 |
80 | 1 | 12 | 47 | 14 | 1 | 12 | 47 | 14 | 144 | 564 | 168 | 2209 | 658 |
90 | 4 | 17 | 22 | 21 | 16 | 68 | 88 | 84 | 289 | 374 | 357 | 484 | 462 |
|
500 | 8 | 26 | 12 | 32 | 64 | 208 | 96 | 256 | 676 | 312 | 832 | 144 | 384 |
10 | 15 | 39 | 9 | 48 | 225 | 585 | 135 | 720 | 1521 | 351 | 1872 | 81 | 432 |
20 | 23 | 51 | 6 | 67 | 529 | 1173 | 138 | 1541 | 2601 | 306 | 3417 | 36 | 402 |
30 | 31 | 57 | 4 | 84 | 961 | 1767 | 124 | 2604 | 3249 | 228 | 4788 | 16 | 336 |
40 | 37 | 60 | 3 | 94 | 1360 | 2220 | 111 | 3478 | 3600 | 180 | 5640 | 9 | 282 |
|
550 | 42 | 61 | 2 | 99 | 1764 | 2562 | 84 | 4158 | 3721 | 122 | 6039 | 4 | 198 |
60 | 47 | 58 | 1 | 100 | 2209 | 2726 | 47 | 4700 | 3364 | 58 | 5800 | 1 | 100 |
70 | 51 | 52 | 1 | 95 | 2601 | 2652 | 51 | 4845 | 2704 | 52 | 4940 | 1 | 95 |
80 | 52 | 42 | 0 | 87 | 2704 | 2184 | 0 | 4524 | 1764 | 0 | 3654 | 0 | 0 |
90 | 54 | 30 | 0 | 76 | 2916 | 1620 | 0 | 4104 | 900 | 0 | 2280 | 0 | 0 |
|
600 | 51 | 20 | 0 | 63 | 2601 | 1020 | 0 | 3213 | 400 | 0 | 1260 | 0 | 0 |
10 | 46 | 11 | 0 | 50 | 2116 | 506 | 0 | 2300 | 121 | 0 | 550 | 0 | 0 |
20 | 38 | 6 | 0 | 38 | 1444 | 228 | 0 | 1444 | 36 | 0 | 228 | 0 | 0 |
30 | 29 | 3 | 0 | 26 | 841 | 87 | 0 | 754 | 9 | 0 | 78 | 0 | 0 |
40 | 20 | 1 | 0 | 17 | 400 | 20 | 0 | 340 | 1 | 0 | 17 | 0 | 0 |
|
650 | 12 | 0 | 0 | 10 | 144 | 0 | 0 | 120 | 0 | 0 | 0 | 0 | 0 |
60 | 7 | 0 | 0 | 6 | 49 | 0 | 0 | 42 | 0 | 0 | 0 | 0 | 0 |
70 | 4 | 0 | 0 | 3 | 16 | 0 | 0 | 12 | 0 | 0 | 0 | 0 | 0 |
80 | 2 | 0 | 0 | 2 | 4 | 0 | 0 | 4 | 0 | 0 | 0 | 0 | 0 |
90 | 3 | 0 | 0 | 1 | 9 | 0 | 0 | 3 | 0 | 0 | 0 | 0 | 0 |
|
Totals | 22983 | 19638 | 921 | 39260 | 25185 | 3735 | 42026 | 49029 | 5159 |
From these totals are built up the equations (See text) whose solution
yields the values of the chromatic visibility coefficients.
Table 2
Comparison of the visibilities as calculated from the color excitation curves
weighted by the Least Square Coefficients with the accepted I.E.S.
Visibility Function.
Wave Length
mμ | Excitations | Products by the
Coefficients | Some of the Products
(Calculated visibility) | I.E.S. Visibility | Diff.
(υ) | Square of Diff.
(υ2) |
---|
|
|
---|
Red | Green | Blue | .848 | 1.006 | .0129 |
---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|
|
---|
400 | 0 | 0 | 25.3 | 0 | 0 | 0.3 | 0.3 | 0.04 | +0.3 | .09 |
10 | 0 | 0 | 43.3 | 0 | 0 | 0.6 | 0.6 | 0.12 | +0.5 | .25 |
20 | 0 | 0 | 61.4 | 0 | 0 | 0.8 | 0.8 | 0.40 | +0.4 | .16 |
30 | 0 | 0 | 91.5 | 0 | 0 | 1.2 | 1.2 | 1.16 | 0.0 | .00 |
40 | 0 | 0.7 | 101.9 | 0 | 0.7 | 1.3 | 2.0 | 2.3 | −0.3 | .09 |
|
450 | 0 | 1.6 | 95.0 | 0 | 1.6 | 1.2 | 2.8 | 3.8 | −1.0 | 1.00 |
60 | 0 | 3.8 | 84.2 | 0 | 3.8 | 1.1 | 4.9 | 6.0 | −1.1 | 1.21 |
70 | 0 | 8.1 | 69.7 | 0 | 8.1 | 0.9 | 9.0 | 9.1 | −0.1 | .01 |
80 | 1.4 | 12.2 | 47.3 | 1.2 | 12.3 | 0.6 | 14.1 | 13.9 | +0.2 | .04 |
90 | 4.1 | 16.9 | 22.0 | 3.5 | 17.0 | 0.3 | 20.8 | 20.8 | 0.0 | .00 |
|
500 | 8.3 | 26.0 | 12.3 | 7.0 | 26.2 | 0.2 | 33.4 | 32.3 | + 1.1 | 1.21 |
10 | 15.1 | 39.1 | .8.7 | 12.8 | 39.3 | 0.1 | 52.2 | 48.4 | +3.8 | 14.44 |
20 | 23.3 | 51.0 | 6.1 | 19.8 | 51.3 | 0.1 | 71.2 | 67.0 | +4.2 | 17.64 |
30 | 30.7 | 57.2 | 4.3 | 26.0 | 57.5 | 0.1 | 83.6 | 83.6 | 0.0 | .00 |
40 | 37.3 | 60.3 | 2.9 | 31.6 | 60.7 | 0 | 92.3 | 94.2 | −1.9 | .3.61 |
|
550 | 42.4 | 61.2 | 1.8 | 36.0 | 61.6 | 0 | 97.6 | 99.3 | −1.7 | 2.89 |
60 | 46.6 | 57.8 | 1.1 | 39.5 | 58.2 | 0 | 97.7 | 99.6 | −1.9 | 3.61 |
70 | 50.5 | 51.7 | 0.7 | 42.8 | 52.0 | 0 | 94.8 | 95.2 | −0.4 | .16 |
80 | 52.0 | 41.5 | 0.4 | 44.1 | 41.7 | 0 | 85.8 | 87.0 | −1.2 | 1.44 |
90 | 53.5 | 29.6 | 0 | 45.4 | 29.8 | 0 | 75.2 | 75.7 | −0.5 | .25 |
|
600 | 51.0 | 19.6 | 0 | 43.2 | 19.7 | 0 | 62.9 | 63.1 | −0.2 | .04 |
10 | 46.2 | 11.3 | 0 | 39.2 | 11.4 | 0 | 50.6 | 50.3 | +0.3 | .09 |
20 | 37.5 | 5.9 | 0 | 31.8 | 5.9 | 0 | 37.7 | 38.0 | −0.3 | .09 |
30 | 28.5 | 2.9 | 0 | 24.2 | 2.9 | 0 | 27.1 | 26.2 | +0.9 | .81 |
40 | 19.5 | 1.0 | 0 | 16.5 | 1.0 | 0 | 17.5 | 17.0 | +0.5 | .25 |
|
650 | 11.8 | 0.3 | 0 | 10.0 | 0.3 | 0 | 10.3 | 10.3 | 0.0 | .00 |
60 | 6.8 | 0 | 0 | 5.8 | 0 | 0 | 5.8 | 5.9 | −0.1 | .01 |
70 | 4.0 | 0 | 0 | 3.4 | 0 | 0 | 3.4 | 3.0 | +0.4 | .16 |
80 | 2.2 | 0 | 0 | 1.9 | 0 | 0 | 1.9 | 1.6 | +0.3 | .09 |
90 | 1.1 | 0 | 0 | 0.9 | 0 | 0 | 0.9 | 0.8 | +0.1 | .01 |
|
| | | | | | | | | Total | 49.65 |
Probable Error of any single calculated visibility
Table 3
Use of the chromatic visibility coefficients in brightness calculations. With
equal energy spectrum as. the white reference point, the following two sets
of coefficients were used: | Troland’s
Experimental Coefficients | Least Square
Coefficients |
---|
Red | .366 | .449 |
Green | .624 | .545 |
Blue | .010 | .0058 |
Color Name | Brightness
Planimeter | Troland’s
Coefficients | Least Square
Coefficients |
---|
|
|
---|
Brightness | Error | Brightness | Error | Diff. |
---|
1 | 2 | 3 | 4 | 5 | 6 | 7 |
---|
|
---|
Red | 13.5 | 12.1 | −1.4 | 13.0 | −0.5 | +0.9 |
Red | 20.0 | 18.6 | −1.4 | 20.2 | +0.2 | + 1.6 |
Red Orange | 29.5 | 27.1 | −2.4 | 29.1 | −0.4 | +2.0 |
Orange | 43.8 | 42.5 | −1.3 | 45.1 | + 1.3 | +2.6 |
Yellow | 70.6 | 69.9 | −0.7 | 71.9 | + 1.3 | +2.0 |
|
Yellow | 83.0 | 83.5 | +0.5 | 85.7 | +2.7 | +2.2 |
Yellow | 89.2 | 86.6 | −2.6 | 88.5 | −0.7 | +1.9 |
Yellow Green | 69.6 | 71.0 | + 1.4 | 71.0 | + 1.4 | 0.0 |
Green | 40.2 | 41.7 | + 1.5 | 41.0 | +0.8 | −0.7 |
Blue Green | 42.9 | 43.3 | +0.4 | 42.7 | −0.2 | −0.6 |
|
Green Blue | 24.9 | 26.8 | + 1.9 | 25.6 | +0.7 | −1.2 |
Blue | 15.5 | 14.4 | −1.1 | 13.1 | −2.4 | −1.3 |
Blue Violet | 11.5 | 11.9 | +0.4 | 11.0 | −0.5 | −0.9 |
Violet | 14.8 | 15.1 | +0.3 | 14.7 | −0.1 | −0.4 |
Violet Red | 20.8 | 21.1 | +0.3 | 21.6 | +0.8 | +0.5 |
|
Black | 4.9 | 4.8 | −0.1 | 5.0 | +0.1 | +0.2 |
White | 100.0 | 100.0 | 0.0 | 100.0 | 0.0 | 0.0 |
|
| | 1 Average. 07 | Average 0.88 1.2 |
Table 4
Comparison of the visibilities as calculated from the color excitation curves
weighted by the least square coefficients and the average weighted results
of Gibson and Tyndall.
Wave Length
mμ | Excitations | Products by the
Coefficients | Sum of the products
(Calculated visibility) | Gibson and Tyndall
visibility | Diff.
(υ) | Square of diff.
(υ2) |
---|
|
|
---|
Red | Green | Blue | .835 | 1.044 | .0287 |
---|
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
---|
|
---|
400 | 0 | 0 | 25.3 | 0 | 0 | 0.7 | 0.7 | 0.5 | +0.2 | .04 |
10 | 0 | 0 | 43.3 | 0 | 0 | 1.2 | 1.2 | 1.2 | 0.0 | .00 |
20 | 0 | 0 | 61.4 | 0 | 0 | 1.8 | 1.8 | 2.2 | −0.4 | .16 |
30 | 0 | 0 | 91.5 | 0 | 0 | 2.6 | 2.6 | 3.3 | −0.7 | .49 |
40 | 0 | 0.7 | 101.9 | 0 | 0.7 | 2.9 | 3.6 | 4.3 | −0.7 | .49 |
|
450 | 0 | 1.6 | 95.0 | 0 | 1.7 | 2.7 | 4.4 | 5.1 | −0.7 | .49 |
60 | 0 | 3.8 | 84.2 | 0 | 4.0 | 2.4 | 6.4 | 6.9 | −0.5 | .25 |
70 | 0 | 8.1 | 69.7 | 0 | 8.5 | 2.0 | 10.5 | 10.3 | +0.2 | .04 |
80 | 1.4 | 12.2 | 47.3 | 1.2 | 12.7 | 1.4 | 15.3 | 14.3 | +1.0 | 1.00 |
90 | 4.1 | 16.9 | 22.0 | 3.4 | 17.6 | 0.6 | 21.6 | 19.6 | +2.0 | 4.00 |
|
500 | 8.3 | 26.0 | 12.3 | 6.9 | 27.2 | 0.4 | 34.5 | 31.8 | +2.7 | 7.29 |
10 | 15.1 | 39.1 | 8.7 | 12.6 | 40.8 | 0.2 | 53.6 | 52.3 | +1.3 | 1.69 |
20 | 23.3 | 51.0 | 6.1 | 19.4 | 53.2 | 0.2 | 72.8 | 73.2 | −0.4 | .16 |
30 | 30.7 | 57.2 | 4.3 | 25.6 | 59.7 | 0.1 | 85.4 | 87.8 | −2.4 | 5.76 |
40 | 37.3 | 60.3 | 2.9 | 31.2 | 63.0 | 0.1 | 94.3 | 96.4 | −2.1 | 4.41 |
|
550 | 42.4 | 61.2 | 1.8 | 35.4 | 64.0 | 0.1 | 99.5 | 99.8 | −0.3 | .09 |
60 | 46.6 | 57.8 | 1.1 | 38.9 | 60.4 | 0 | 99.3 | 99.1 | +0.2 | .04 |
70 | 50.5 | 51.7 | 0.7 | 42.1 | 54.0 | 0 | 96.1 | 94.7 | +1.4 | 1.96 |
80 | 52.0 | 41.5 | 0.4 | 43.4 | 43.4 | 0 | 86.8 | 86.3 | +0.5 | .25 |
90 | 53.5 | 29.6 | 0 | 44.6 | 30.9 | 0 | 75.5 | 75.4 | +0.1 | .01 |
|
600 | 51.0 | 19.6 | 0 | 42.5 | 20.5 | 0 | 63.0 | 63.4 | −0.4 | .16 |
10 | 46.2 | 11.3 | 0 | 38.6 | 11.8 | 0 | 50.4 | 51.1 | −0.7 | .49 |
20 | 37.5 | 5.9 | 0 | 31.3 | 6.2 | 0 | 37.5 | 38.9 | −1.4 | 1.96 |
30 | 28.5 | 2.9 | 0 | 23.8 | 3.0 | 0 | 26.8 | 27.9 | −1.1 | 1.21 |
40 | 19.5 | 1.0 | 0 | 16.3 | 1.0 | 0 | 17.3 | 18.4 | −1.1 | 1.21 |
|
650 | 11.8 | 0.3 | 0 | 9.9 | 0.3 | 0 | 10.2 | 11.3 | −1.1 | 1.21 |
60 | 6.8 | 0 | 0 | 5.7 | 0 | 0 | 5.7 | 6.4 | −0.7 | .49 |
70 | 4.0 | 0 | 0 | 3.3 | 0 | 0 | 3.3 | 3.5 | −0.2 | .04 |
80 | 2.2 | 0 | 0 | 1.8 | 0 | 0 | 1.8 | 1.8 | 0.0 | .00 |
90 | 1.1 | 0 | 0 | 0.9 | 0 | 0 | 0.9 | 0.9 | 0.0 | .00 |
|
| | | | | | | | Total | 35.39 |
Probable Error of any single calculated visibility