The following questions motivated this study, which summarizes and
illustrates the answers. How can the number of gray levels visible on a
display be maximized? How can a designer maximize the discriminability of a
set of gray symbols that use only a part of the luminance range available from
the display technology? Can we calculate whether particular shades of gray
will be discriminable from each other? How big should successive gray-scale
steps be (in luminance, reflectance, or optical density) to make them appear
equal? How many discriminable shades of gray can be seen with a particular
display technology in a particular light environment? What is the probability
that two specified shades of gray will be mistaken for each other at a glance?
How does the luminance of the screen background affect the visibility of gray
symbols? Is there a single principle that describes the appearances of areas
more luminous than the background (positive contrasts) and less luminous areas
(negative contrasts)? Limitations on the answers are discussed, issues for
further research are suggested, and applications are
described.
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Data for positive contrast from
Ref. 9; data for negative contrast from
Ref. 10.
The 3-mm pupil expected for
Lb > 100 cd/m2, and the 7-mm pupil for
Lb < 3 cd/m2 (an approximation based on data reported by
Wyszecki and Stiles,40 pp.
213–214).
Table 2
Effect on Test-Field Apparent Brightness of a Second
Field in the Neighborhood of the Test Field: ADI Document 4548, Subject
ECPa
La1
Lb1
La2
Lb2
B1
B2
19.95
33.88
7.08
11.22
-4.88
-4.45
11.22
19.95
7.08
11.22
-5.11
-4.45
4.47
5.5
7.08
11.22
-.58
-4.45
1.12
1.29
7.08
11.22
-1.82
-4.45
3.55
3.55
7.08
11.22
0.00
-4.45
3.55
35.48
2
11.22
-10.33
-9.07
2.51
16.22
2
11.22
-9.43
-9.07
1.12
7.76
2
11.22
-9.48
-9.07
0.63
3.09
2
11.22
-8.48
-9.07
0.35
1.07
2
11.22
-6.74
-9.07
2
56.23
0.63
11.22
-11.63
-11.01
1.12
25.12
0.63
11.22
-11.37
-11.01
0.63
14.45
0.63
11.22
-11.32
-11.01
0.355
5.5
0.63
11.22
-10.66
-11.01
Data from
Heinemann (Ref. 22,
Table 3). La1 and
La2 are judged to match.
La1 is surrounded by
Lb1, and
La2 by
Lb2.
Values of L are given in millilamberts (1 mL = 3.183 cd/m2). B is calculated
with Whittle’s equations (Ref. 3). Only data for La1, La2 > 0.349 mL (∼3
Ldk) are
shown to emphasize suprathreshold effects.
Table 3
Effect on Test-Field
(La) Apparent Brightness of a Second Field
Lb in the
Neighborhood of the Test Field: ADI Document 4548, Subject
EGHa
La1
Lb1
La2
Lb2
B1
B2
19.95
42.66
7.08
11.22
-6.02
-4.45
11.22
21.38
7.08
11.22
-5.47
-4.45
3.55
5.12
7.08
11.22
-3.81
-4.45
1.12
1.38
7.08
11.22
-2.47
-4.45
0.355
0.398
7.08
11.22
-1.32
-4.45
4.47
31.62
2
11.22
-9.67
-9.07
2.51
10.72
2
11.22
-8.37
-9.07
1.12
3.63
2
11.22
-7.39
-9.07
0.63
1.74
2
11.22
-6.65
-9.07
0.35
1.05
2
11.22
-6.67
-9.07
0.63
33.88
0.35
11.22
-12.01
-11.54
0.35
12.88
0.35
11.22
-11.66
-11.54
Data from Heinemann
(Ref. 22, Table 3). See footnote to Table 2 for details.
Table 4
Calculated Effects of Variation of the Symbol Size,
Lmax, or
Lmin on Sopt and the JND’s of the Gray Scale
Symbol Size 2°
Symbol Size 15″
Lmin (kp
= 0.05)
Sopt
Lmax (kn = 0.01)
Lmin (kp
= 0.71)
Sopt
Lmax (kn
= 0.069)
Candelas/square meter
3
20
110
3
15
110
JND’s
16
22
16
15
21
12
Candelas/square meter
10
31
110
10
29
110
JND’s
13
18
13
13
17
11
Candelas/square meter
3
14
60
3
12
60
JND’s
16
20
14
14
19
12
Table 5
Verification of the Optimum Number of JND’s for
Targets Subtending 15 arcmina
Lb (cd/m2)
Theoretical
Total JND’s
SD of Total
Naïve Observer
3
14.7
13.5
0.38
29
6
19.2
15.6
0.26
9
20.4
18
0.4
43
15
20.82
19
0.58
16.6
20.83
20.75
0.56
41
18
20.82
19.875
0.52
23
20.7
18.625
0.6
63
18.1
18.25
0.45
35
92
15.4
16.25
0.37
111
12.7
13.75
0.45
25
Lmax
= 111 cd/m2 and Lmin = 3 cd/m2.
Theoretical numbers of JND’s were calculated from Whittle’s
equations
(kp = 0.071; kn = 0.069). JND totals (including positive
and negative contrast) are averages from eight series of JND’s that I
set. One series was set by a naïve observer. SD, standard
deviation.
Table 6
Empirical Effects of Variation of the Symbol
Size, Lmax, or
Lmin on Sopt and the JND’s fo a Gray
Scalea
Symbol Size 2°
Symbol Size 15″
Lmin (kp
= 0.05)
Sopt
Lmax (kn
= 0.01)
Lmin (kp
= 0.071)
Sopt
Lmax (kn
= 0.069)
Candelas/square meter
3
10
20
110
3
16
110
JND’s
15
21
26
16
14
21
14
Candelas/square meter
10
30
110
10
30
110
JND’s
17
25
16
14
20
14
Candelas/square meter
3
14
60
3
12
60
JND’s
19
27
18
17
24
18
Values are the average of eight series of
JND’s.
Tables (6)
Table 1
Proportion of Positive-Contrast
(kp)
and Negative-Contrast (kn) Light Increment ΔL Lost to Ocular Scattering for Disk Contrasts of
Various Subtensesa
Data for positive contrast from
Ref. 9; data for negative contrast from
Ref. 10.
The 3-mm pupil expected for
Lb > 100 cd/m2, and the 7-mm pupil for
Lb < 3 cd/m2 (an approximation based on data reported by
Wyszecki and Stiles,40 pp.
213–214).
Table 2
Effect on Test-Field Apparent Brightness of a Second
Field in the Neighborhood of the Test Field: ADI Document 4548, Subject
ECPa
La1
Lb1
La2
Lb2
B1
B2
19.95
33.88
7.08
11.22
-4.88
-4.45
11.22
19.95
7.08
11.22
-5.11
-4.45
4.47
5.5
7.08
11.22
-.58
-4.45
1.12
1.29
7.08
11.22
-1.82
-4.45
3.55
3.55
7.08
11.22
0.00
-4.45
3.55
35.48
2
11.22
-10.33
-9.07
2.51
16.22
2
11.22
-9.43
-9.07
1.12
7.76
2
11.22
-9.48
-9.07
0.63
3.09
2
11.22
-8.48
-9.07
0.35
1.07
2
11.22
-6.74
-9.07
2
56.23
0.63
11.22
-11.63
-11.01
1.12
25.12
0.63
11.22
-11.37
-11.01
0.63
14.45
0.63
11.22
-11.32
-11.01
0.355
5.5
0.63
11.22
-10.66
-11.01
Data from
Heinemann (Ref. 22,
Table 3). La1 and
La2 are judged to match.
La1 is surrounded by
Lb1, and
La2 by
Lb2.
Values of L are given in millilamberts (1 mL = 3.183 cd/m2). B is calculated
with Whittle’s equations (Ref. 3). Only data for La1, La2 > 0.349 mL (∼3
Ldk) are
shown to emphasize suprathreshold effects.
Table 3
Effect on Test-Field
(La) Apparent Brightness of a Second Field
Lb in the
Neighborhood of the Test Field: ADI Document 4548, Subject
EGHa
La1
Lb1
La2
Lb2
B1
B2
19.95
42.66
7.08
11.22
-6.02
-4.45
11.22
21.38
7.08
11.22
-5.47
-4.45
3.55
5.12
7.08
11.22
-3.81
-4.45
1.12
1.38
7.08
11.22
-2.47
-4.45
0.355
0.398
7.08
11.22
-1.32
-4.45
4.47
31.62
2
11.22
-9.67
-9.07
2.51
10.72
2
11.22
-8.37
-9.07
1.12
3.63
2
11.22
-7.39
-9.07
0.63
1.74
2
11.22
-6.65
-9.07
0.35
1.05
2
11.22
-6.67
-9.07
0.63
33.88
0.35
11.22
-12.01
-11.54
0.35
12.88
0.35
11.22
-11.66
-11.54
Data from Heinemann
(Ref. 22, Table 3). See footnote to Table 2 for details.
Table 4
Calculated Effects of Variation of the Symbol Size,
Lmax, or
Lmin on Sopt and the JND’s of the Gray Scale
Symbol Size 2°
Symbol Size 15″
Lmin (kp
= 0.05)
Sopt
Lmax (kn = 0.01)
Lmin (kp
= 0.71)
Sopt
Lmax (kn
= 0.069)
Candelas/square meter
3
20
110
3
15
110
JND’s
16
22
16
15
21
12
Candelas/square meter
10
31
110
10
29
110
JND’s
13
18
13
13
17
11
Candelas/square meter
3
14
60
3
12
60
JND’s
16
20
14
14
19
12
Table 5
Verification of the Optimum Number of JND’s for
Targets Subtending 15 arcmina
Lb (cd/m2)
Theoretical
Total JND’s
SD of Total
Naïve Observer
3
14.7
13.5
0.38
29
6
19.2
15.6
0.26
9
20.4
18
0.4
43
15
20.82
19
0.58
16.6
20.83
20.75
0.56
41
18
20.82
19.875
0.52
23
20.7
18.625
0.6
63
18.1
18.25
0.45
35
92
15.4
16.25
0.37
111
12.7
13.75
0.45
25
Lmax
= 111 cd/m2 and Lmin = 3 cd/m2.
Theoretical numbers of JND’s were calculated from Whittle’s
equations
(kp = 0.071; kn = 0.069). JND totals (including positive
and negative contrast) are averages from eight series of JND’s that I
set. One series was set by a naïve observer. SD, standard
deviation.
Table 6
Empirical Effects of Variation of the Symbol
Size, Lmax, or
Lmin on Sopt and the JND’s fo a Gray
Scalea
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