Analytic expressions are developed for describing the relationship between the maximum instrument error in the spectrophotometric measurement of colored samples and the corresponding maximum displacement of the CIE chromaticity coordinates. Accepting some empirical evidence concerning the sensitivity of the eye to small color differences, as recorded on the CIE color triangle, it becomes possible to estimate the chromatic significance of this error. To illustrate this procedure, we examined two cases: constant errors and errors independent of wavelength. The effect of these errors on the chromaticity specifications of some representative blue filters was discussed. The relation of error to luminosity is also noted.
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Some representative blue filters which lie in the critical region of the chromaticity plane.
Wratten filter
Series number
Chromaticity coordinates
Luminous transmittance % Y
x
y
CC-50B
0.2516
0.2197
35.66
CC-40B
0.2623
0.2387
42.68
CC-30B
I
0.2761
0.2585
51.87
CC-20B
0.2879
0.2787
62.21
CC-10B
0.2993
0.2987
75.48
CC-05B
0.3056
0.3086
82.76
38A
0.1610
0.1794
17.26
39
0.1624
0.0173
0.92
45A
0.1198
0.1371
2.97
46
II
0.1324
0.0753
2.49
47
0.1479
0.0475
2.78
48
0.1411
0.0580
1.94
48A
0.1533
0.0303
0.84
49B
0.1516
0.0258
0.37
32
0.3079
0.1161
12.09
34A
III
0.2077
0.0392
2.61
35
0.1754
0.0015
0.04
75
IV
0.0763
0.2371
1.68
Table II
The accuracy in the specification of the chromaticity coordinates of some blue filters as a function of a constant instrument error of 1% parallel displacement.
The corresponding values for −∊ differ by only one unit in the fourth place from the +∊ values in the table, all the others are identical.
Table III
The accuracy in the specification of the chromaticity coordinates of some blue filters as a function of a constant instrument error of 0.1% parallel displacement.
The corresponding values for −∊ are the same as these given here for +∊.
Table IV
The maximum tolerable instrument error, ∊min, in percent of full scale, for the adequate specification of the chromaticity coordinates of some blue filters as a function of the sensitivity of the human eye to small color differences.a
These figures differ slightly from those given in Table I of MacDonald and Bentley.4 All values in this table were computed from the raw data given in their Table II.
Tables (6)
Table I
Some representative blue filters which lie in the critical region of the chromaticity plane.
Wratten filter
Series number
Chromaticity coordinates
Luminous transmittance % Y
x
y
CC-50B
0.2516
0.2197
35.66
CC-40B
0.2623
0.2387
42.68
CC-30B
I
0.2761
0.2585
51.87
CC-20B
0.2879
0.2787
62.21
CC-10B
0.2993
0.2987
75.48
CC-05B
0.3056
0.3086
82.76
38A
0.1610
0.1794
17.26
39
0.1624
0.0173
0.92
45A
0.1198
0.1371
2.97
46
II
0.1324
0.0753
2.49
47
0.1479
0.0475
2.78
48
0.1411
0.0580
1.94
48A
0.1533
0.0303
0.84
49B
0.1516
0.0258
0.37
32
0.3079
0.1161
12.09
34A
III
0.2077
0.0392
2.61
35
0.1754
0.0015
0.04
75
IV
0.0763
0.2371
1.68
Table II
The accuracy in the specification of the chromaticity coordinates of some blue filters as a function of a constant instrument error of 1% parallel displacement.
The corresponding values for −∊ differ by only one unit in the fourth place from the +∊ values in the table, all the others are identical.
Table III
The accuracy in the specification of the chromaticity coordinates of some blue filters as a function of a constant instrument error of 0.1% parallel displacement.
The corresponding values for −∊ are the same as these given here for +∊.
Table IV
The maximum tolerable instrument error, ∊min, in percent of full scale, for the adequate specification of the chromaticity coordinates of some blue filters as a function of the sensitivity of the human eye to small color differences.a
These figures differ slightly from those given in Table I of MacDonald and Bentley.4 All values in this table were computed from the raw data given in their Table II.