2In the prosecution of the researches described in this paper we wish to acknowledge the help we have received from various sources, particularly from Mr. Prentice Reeves, who planned a large part of the “J.N.D.” work, and from Miss G. K. Walker, who was of great assistance in compiling the experimental data. Acknowledgment should also be made to Mr. I. G. Priest (now deceased) of the Bureau of Standards, whose keen interest in visual psychophysics and whose help and advice were an invaluable aid, and to Dr. D. B. Judd, of the same Bureau, who read the manuscript and gave very valuable criticisms.
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Showing the smallest change in reflectance obtainable with pairs of rotating disks.
———Reflectance of———
Smallest significant change in reflectance that can be obtained with each combination of disks (percent)
Standard field (percent)
Lighter disk (percent)
Darker disk (percent)
72.9
82.2
58.5
0.034
35.7
40.2
28.5
0.103
17.9
20.7
10.4
0.12
4.2
7.23
2.4
0.24
Table II
Just noticeable differences at five levels of reflectance.(Data given in both reflectance and brightness units. A reflectance of 100 percent corresponds to a brightness of 24.5 ml.)
Showing series of reflectances dividing area under curve into ten equal parts. Observer L.L.S.
Area (Number of just-noticeable-difference units)
Reflectance (percent)
0.
210.6
0.
29.2
35.1
245.7
1.25
40.7
70.2
280.8
3.1
55.7
105.3
315.9
6.5
74.2
140.4
351.0
12.1
100.
175.5
19.6
Table VI
Data used in plotting curve shown in Fig. 9.Observer L.L.S.
ΔR
R
1/ΔR
Experimentally determined data
0.1446
0.009685
0.0209
103.2525
1.769
0.08429
3.13
118.64
4.278
0.250
18.3
4.00
5.992
0.2715
35.9
3.6832
8.741
0.615
76.4
1.626
Data obtained by interpolation on ΔR,
curve (Fig. 9)
0.5
0.0225
0.25
44.444
1.0
0.045
1.0
22.222
1.5
0.070
2.25
14.286
2.0
0.102
4.0
9.8039
3.0
0.185
9.0
5.4054
4.0
0.2415
16.0
4.1408
5.0
0.263
25.0
3.8023
6.0
0.274
36.0
3.6496
7.0
0.350
49.0
2.8571
8.0
0.483
64.0
2.0704
9.0
0.667
81.0
1.4993
10.0
1.0
100.
1.0
Table VII
Total number of just-noticeable-difference units between 0 and 24.5 ml. (0 and 100 percent reflectance.)
No. of J.N.D.’s
Observer
185
A.E.O.M.
223
W.L.V.
157
C.E.B.
351
L.L.S.
185
G.K.W.
185
P.R.
214
Average
Table VIII
Six individual value scales. Showing series of reflectances corresponding to equal value intervals between 0 and 100 percent reflectance. Natural pupil, light adaptations, light surrounding field (19.1 percent), intensity of illumination 22.8 f.c.
Value
1/
2/
3/
4/
5/
6/
7/
8/
9/
10/
Observer
Percent reflectance
L.L.S.
1.25
3.1
6.5
12.1
19.6
29.2
40.7
55.7
74.2
100
G.K.W.
1.3
2.5
4.6
9.2
15.7
24.0
35.0
49.5
69.1
100
A.E.O.M.
1.0
2.9
6.4
12.3
20.2
31.0
43.3
57.7
75.5
100
W.L.V.
1.2
3.1
6.4
11.4
17.5
25.7
36.5
50.5
70.5
100
C.E.B.
1.2
3.9
8.0
13.3
20.0
29.0
40.0
55.0
75.0
100
P.R.
0.75
1.9
3.8
8.0
15.0
25.0
37.9
53.4
72.6
100
Average
1.12
2.90
5.95
11.05
18.0
27.3
38.9
53.6
72.8
100
Table IX
Showing series of reflectances selected by each of sixteen observers to form evenly graded scales of values.
Observer
No. of observations
A1
A2
A3
A4
A5
A6
A7
A8
A9
———Percent reflectance———
H. T.
1
2.9
6.4
13.0
18.5
25.3
34.1
46.3
61.6
88.3
M. T.
1
2.9
6.2
9.7
16.6
27.3
35.6
50.8
65.5
88.3
W. C.
1
2.9
6.4
9.7
14.6
22.3
32.3
46.3
61.6
88.3
L. T. L.
1
2.9
5.1
8.8
13.2
25.3
34.1
48.3
65.5
88.3
E. B. T.
1
2.9
4.8
8.8
14.6
22.3
35.6
53.6
70.0
88.3
F. A. C.
1
2.9
6.2
11.7
18.5
25.3
35.0
48.3
64.6
88.3
G. B.
1
2.9
6.2
10.7
17.4
26.4
35.6
50.4
64.6
88.3
C. F.
1
2.9
6.4
10.7
18.5
25.3
34.1
50.4
70.0
88.3
C. K.
1
2.9
5.6
11.7
17.4
25.3
34.1
48.3
64.6
88.3
D. B. J.
1
2.9
6.2
13.2
22.3
32.2
43.5
56.0
74.2
88.3
G. W.
1
2.9
6.7
13.0
17.9
25.3
35.4
52.7
74.4
88.3
L. S.
1
2.9
6.2
10.7
17.4
26.4
35.0
50.8
74.2
88.3
C. E. B.
2
2.9
7.8
15.6
22.3
31.8
43.7
58.5
74.2
88.3
I. H. G.
2
2.9
5.0
10.2
17.9
26.9
38.7
52.4
74.4
88.3
Average of first set (1926)
% 2.90
6.10
11.26
17.66
26.2
36.2
50.9
68.5
88.3%
Value
2.00
2.95
3.91
4.86
5.82
6.77
7.73
8.68
9.63
E. L.
4
3.65
7.7
12.0
16.9
24.0
32.0
47.0
64.6
82.7
B. R.
4
3.65
7.4
12.2
16.6
24.9
32.7
44.5
60.7
82.7
I. H. G.
2
3.65
7.6
12.9
17.5
27.8
37.8
49.3
63.8
82.7
Average of second set (1929–30)
% 3.65
7.57
12.28
16.92
25.1
33.4
46.5
62.9
82.7%
Value
2.30
3.19
4.08
4.97
5.86
6.75
7.64
8.53
9.42
Average of two sets (weighted 3:2) %
3.20
6.69
11.67
17.36
25.8
35.1
49.2
66.3
86.1%
Value
2.12
3.05
3.98
4.90
5.83
6.76
7.69
8.62
9.55
Table X
Showing the mean variations of individual value scales from the average value scales.
Except, two observers, 2 determinations.
Except, one observer, 2 determinations.
Tables (10)
Table I
Showing the smallest change in reflectance obtainable with pairs of rotating disks.
———Reflectance of———
Smallest significant change in reflectance that can be obtained with each combination of disks (percent)
Standard field (percent)
Lighter disk (percent)
Darker disk (percent)
72.9
82.2
58.5
0.034
35.7
40.2
28.5
0.103
17.9
20.7
10.4
0.12
4.2
7.23
2.4
0.24
Table II
Just noticeable differences at five levels of reflectance.(Data given in both reflectance and brightness units. A reflectance of 100 percent corresponds to a brightness of 24.5 ml.)
Showing series of reflectances dividing area under curve into ten equal parts. Observer L.L.S.
Area (Number of just-noticeable-difference units)
Reflectance (percent)
0.
210.6
0.
29.2
35.1
245.7
1.25
40.7
70.2
280.8
3.1
55.7
105.3
315.9
6.5
74.2
140.4
351.0
12.1
100.
175.5
19.6
Table VI
Data used in plotting curve shown in Fig. 9.Observer L.L.S.
ΔR
R
1/ΔR
Experimentally determined data
0.1446
0.009685
0.0209
103.2525
1.769
0.08429
3.13
118.64
4.278
0.250
18.3
4.00
5.992
0.2715
35.9
3.6832
8.741
0.615
76.4
1.626
Data obtained by interpolation on ΔR,
curve (Fig. 9)
0.5
0.0225
0.25
44.444
1.0
0.045
1.0
22.222
1.5
0.070
2.25
14.286
2.0
0.102
4.0
9.8039
3.0
0.185
9.0
5.4054
4.0
0.2415
16.0
4.1408
5.0
0.263
25.0
3.8023
6.0
0.274
36.0
3.6496
7.0
0.350
49.0
2.8571
8.0
0.483
64.0
2.0704
9.0
0.667
81.0
1.4993
10.0
1.0
100.
1.0
Table VII
Total number of just-noticeable-difference units between 0 and 24.5 ml. (0 and 100 percent reflectance.)
No. of J.N.D.’s
Observer
185
A.E.O.M.
223
W.L.V.
157
C.E.B.
351
L.L.S.
185
G.K.W.
185
P.R.
214
Average
Table VIII
Six individual value scales. Showing series of reflectances corresponding to equal value intervals between 0 and 100 percent reflectance. Natural pupil, light adaptations, light surrounding field (19.1 percent), intensity of illumination 22.8 f.c.
Value
1/
2/
3/
4/
5/
6/
7/
8/
9/
10/
Observer
Percent reflectance
L.L.S.
1.25
3.1
6.5
12.1
19.6
29.2
40.7
55.7
74.2
100
G.K.W.
1.3
2.5
4.6
9.2
15.7
24.0
35.0
49.5
69.1
100
A.E.O.M.
1.0
2.9
6.4
12.3
20.2
31.0
43.3
57.7
75.5
100
W.L.V.
1.2
3.1
6.4
11.4
17.5
25.7
36.5
50.5
70.5
100
C.E.B.
1.2
3.9
8.0
13.3
20.0
29.0
40.0
55.0
75.0
100
P.R.
0.75
1.9
3.8
8.0
15.0
25.0
37.9
53.4
72.6
100
Average
1.12
2.90
5.95
11.05
18.0
27.3
38.9
53.6
72.8
100
Table IX
Showing series of reflectances selected by each of sixteen observers to form evenly graded scales of values.
Observer
No. of observations
A1
A2
A3
A4
A5
A6
A7
A8
A9
———Percent reflectance———
H. T.
1
2.9
6.4
13.0
18.5
25.3
34.1
46.3
61.6
88.3
M. T.
1
2.9
6.2
9.7
16.6
27.3
35.6
50.8
65.5
88.3
W. C.
1
2.9
6.4
9.7
14.6
22.3
32.3
46.3
61.6
88.3
L. T. L.
1
2.9
5.1
8.8
13.2
25.3
34.1
48.3
65.5
88.3
E. B. T.
1
2.9
4.8
8.8
14.6
22.3
35.6
53.6
70.0
88.3
F. A. C.
1
2.9
6.2
11.7
18.5
25.3
35.0
48.3
64.6
88.3
G. B.
1
2.9
6.2
10.7
17.4
26.4
35.6
50.4
64.6
88.3
C. F.
1
2.9
6.4
10.7
18.5
25.3
34.1
50.4
70.0
88.3
C. K.
1
2.9
5.6
11.7
17.4
25.3
34.1
48.3
64.6
88.3
D. B. J.
1
2.9
6.2
13.2
22.3
32.2
43.5
56.0
74.2
88.3
G. W.
1
2.9
6.7
13.0
17.9
25.3
35.4
52.7
74.4
88.3
L. S.
1
2.9
6.2
10.7
17.4
26.4
35.0
50.8
74.2
88.3
C. E. B.
2
2.9
7.8
15.6
22.3
31.8
43.7
58.5
74.2
88.3
I. H. G.
2
2.9
5.0
10.2
17.9
26.9
38.7
52.4
74.4
88.3
Average of first set (1926)
% 2.90
6.10
11.26
17.66
26.2
36.2
50.9
68.5
88.3%
Value
2.00
2.95
3.91
4.86
5.82
6.77
7.73
8.68
9.63
E. L.
4
3.65
7.7
12.0
16.9
24.0
32.0
47.0
64.6
82.7
B. R.
4
3.65
7.4
12.2
16.6
24.9
32.7
44.5
60.7
82.7
I. H. G.
2
3.65
7.6
12.9
17.5
27.8
37.8
49.3
63.8
82.7
Average of second set (1929–30)
% 3.65
7.57
12.28
16.92
25.1
33.4
46.5
62.9
82.7%
Value
2.30
3.19
4.08
4.97
5.86
6.75
7.64
8.53
9.42
Average of two sets (weighted 3:2) %
3.20
6.69
11.67
17.36
25.8
35.1
49.2
66.3
86.1%
Value
2.12
3.05
3.98
4.90
5.83
6.76
7.69
8.62
9.55
Table X
Showing the mean variations of individual value scales from the average value scales.