The coefficients of the spectral reflectances β1, β2, and β3 (at 430, 560, and 660 mμ, respectively) in the formula W = aβ1 + bβ2 + cβ3 were determined by least squares to fit visual judgments of the whitenesses of two groups of white cement samples. Somewhat different results were obtained for the two groups, for one of which β2 > β3, for the other set β2 < β3. The results were combined in the formula W = 1.68β1 − 0.34(β2 + β3) − q(β2 − β3), where q = 2.28 when β2 > β3, or q = −0.02 when β2 < β3. This formula was tested by application to the original two sets and to two other sets of white cements which differed even more widely in dominant wavelength. The correlations between the results and the subjective judgments of whiteness were in all cases higher than for any of 15 other whiteness formulas tried.
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These have been placed in decreasing order of whiteness. V is visual whiteness. ∊ is the maximum error to be expected (at the 0.01 level).
Table III
Influence of “observer” factor on the results of visual comparisons of whiteness.
Cements second series
Comparison by 23 different observers
Comparison by the same observer
Standard visual whiteness VT
Exp. variance σT2
Standard visual whiteness Vi
Exp. variance σi′2
Standard classification of cements by decreasing visual whiteness order
To 23 observers
To a single observer
T 39
25.1
3.5
26.7
0.6
5.8
1
1
23
24.9
2.8
23.2
0.1
28.0
2
3
13
20.2
18.1
24.5
2.6
7.0
3
2
9
19.7
4.1
18.0
1.7
2.4
4
5
36
18.3
17.9
16.5
2.3
7.8
5
6
28
15.9
10.3
16.3
3.2
3.2
6
7
3
15.8
14.9
11.5
0.6
24.6
7
9
41
15.8
9.6
18.3
3.9
2.5
8
4
25
15.2
2.3
15.3
2.2
1
9
8
30
9.0
0
9.0
0
10
10
Table IV
Correlation in studied field between the dominant wavelength and the difference (β2 − β3).
Cements
λd (mμ)
β2 − β3 (%)
T 2
575.5
−2.0
T 33
575.5
−2.0
T 39
574.5
−0.9
T 3
574
−1.0
T 42
574
−0.9
T 5
573.5
−0.7
T 12
573.5
−1.6
T 38
573
−0.6
T 6
573
−0.3
T 46
573
−0.6
T 11
573
−0.1
T 45
572.5
−0.4
T 7
572.5
−0.2
T 4
572.5
−0.4
T 21
572.0
0.1
T 9
572.0
−0.3
T 19
572.0
0
T 14
572.0
−0.1
T 41
572.0
−0.2
T 44
572.0
−0.1
T 16
571.5
0.5
T 25
571.5
0.5
T 37
571.5
−0.7
T 40
571.5
−0.3
T 20
571
−0.4
T 29
571
0.4
T 47
570.5
0.8
T 10
570.5
1.1
T 43
570
0.8
T 28
570
0.5
T 23
569.5
0.5
T 1
569.5
0.1
T 22
569
1.8
T 36
569
0.9
T 35
567.5
1.9
T 24
567.5
1.1
T 31
567.5
2.1
T 8
566.5
1.3
T 18
566.5
2.0
T 15
566
1.3
T 17
563.5
2.5
T 13
556.5
1.6
T 30
526
4.0
Table V
Correlation between the visual whiteness and the whiteness calculated from Eq. (5)W = 1.68β1 − 0.34(β2 + β3) − q(β2 − β3) where q = 2.28 if β2 > β3, q = −0.02 if β2 < β3.
These have been placed in decreasing order of whiteness. V is visual whiteness. ∊ is the maximum error to be expected (at the 0.01 level).
Table III
Influence of “observer” factor on the results of visual comparisons of whiteness.
Cements second series
Comparison by 23 different observers
Comparison by the same observer
Standard visual whiteness VT
Exp. variance σT2
Standard visual whiteness Vi
Exp. variance σi′2
Standard classification of cements by decreasing visual whiteness order
To 23 observers
To a single observer
T 39
25.1
3.5
26.7
0.6
5.8
1
1
23
24.9
2.8
23.2
0.1
28.0
2
3
13
20.2
18.1
24.5
2.6
7.0
3
2
9
19.7
4.1
18.0
1.7
2.4
4
5
36
18.3
17.9
16.5
2.3
7.8
5
6
28
15.9
10.3
16.3
3.2
3.2
6
7
3
15.8
14.9
11.5
0.6
24.6
7
9
41
15.8
9.6
18.3
3.9
2.5
8
4
25
15.2
2.3
15.3
2.2
1
9
8
30
9.0
0
9.0
0
10
10
Table IV
Correlation in studied field between the dominant wavelength and the difference (β2 − β3).
Cements
λd (mμ)
β2 − β3 (%)
T 2
575.5
−2.0
T 33
575.5
−2.0
T 39
574.5
−0.9
T 3
574
−1.0
T 42
574
−0.9
T 5
573.5
−0.7
T 12
573.5
−1.6
T 38
573
−0.6
T 6
573
−0.3
T 46
573
−0.6
T 11
573
−0.1
T 45
572.5
−0.4
T 7
572.5
−0.2
T 4
572.5
−0.4
T 21
572.0
0.1
T 9
572.0
−0.3
T 19
572.0
0
T 14
572.0
−0.1
T 41
572.0
−0.2
T 44
572.0
−0.1
T 16
571.5
0.5
T 25
571.5
0.5
T 37
571.5
−0.7
T 40
571.5
−0.3
T 20
571
−0.4
T 29
571
0.4
T 47
570.5
0.8
T 10
570.5
1.1
T 43
570
0.8
T 28
570
0.5
T 23
569.5
0.5
T 1
569.5
0.1
T 22
569
1.8
T 36
569
0.9
T 35
567.5
1.9
T 24
567.5
1.1
T 31
567.5
2.1
T 8
566.5
1.3
T 18
566.5
2.0
T 15
566
1.3
T 17
563.5
2.5
T 13
556.5
1.6
T 30
526
4.0
Table V
Correlation between the visual whiteness and the whiteness calculated from Eq. (5)W = 1.68β1 − 0.34(β2 + β3) − q(β2 − β3) where q = 2.28 if β2 > β3, q = −0.02 if β2 < β3.