A. P. H. Trivelli, "Investigations of the Exposure Scales of Characteristic Curves of Photographic Emulsion Layers*," J. Opt. Soc. Am. 42, 467-474 (1952)
The application of a quantum theory of photographic exposure to photographic films of extended exposure latitude is studied, and it is shown that the density-log exposure data of such materials are incapable of representation by equations based on the simple theory. The applicability of binary functions, as well as functions based on variable intrinsic sensitivity (ϵ) or quantic sensitivity (γ) of the emulsions, is examined for a number of exemplary films, including some experiments on the effects of supersensitizing-optical sensitizing combinations.
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Relations between the minimum number of quanta, r, required to make the grains of a simple emulsion developable and the corresponding exposure scales, l, of the characteristic curves in logE units for Dmax=0.50 and the theoretical γ/Dmax ratios. γ/Dmax is derived from Eq. (3), as in reference 1.
r=1
2
3
4
5
6
7
8
9
10
etc.
1=1.34
2.6
2.2
2.0
1.8
1.8
1.6
1.6
1.4
1.4
etc.
γ/Dmax=0.682
0.862
0.955
1.011
1.048
1.076
1.097
1.113
1.124
1.135
etc.
Table II
Quantic data from six characteristic curves with the shortest exposure scales.
Curve
Development
γ/Dmax obs
r
ϵ·104r
1 in logE units
1
FeOx
6 min
1.014
5
5.43
1.09
1.8
2
FeOx
9 min
1.033
5
10.6
2.12
1.8
3
DK-50
12 min
1.030
5
15.5
3.1
1.8
4
FeOx
18 min
1.101
7
8.61
1.23
1.6
5
FeOx
18 min
1.112
8
18.8
2.35
1.6
6
FeOx
18 min
1.163
14
18.8
1.34
<1.4
Table III
Quantic data for two “simple” curves with long exposure scales.
Curve
Development
γ/Dmax obs
r
ϵ·104
1 in logE units
7
DK-50
3 min
0.686
1
0.484
3
8
DK-50
8 min
0.681
1
0.684
3
Table IV
Quantic data for “complex”a curves with long exposure scales.
Curve
Dev. time in min
γ/Dmax
ā in μ2
α
β
r1
r2
ϵ1·104
ϵ2·104
m
9
5
0.516
0.77
0.70
1.43
2
2
53.0
3.67
14.4
10
5
0.526
0.77
0.43
0.88
2
2
5.95
0.312
19.1
11
8
0.532
0.81
1.00
0.41
2
3
62.95
11.19
5.6
12
8
0.533
0.77
0.44
1.06
2
2
8.03
0.431
18.6
13
3
0.578
1.66
0.50
0.32
3
2
58.63
4.88
12.0
14
8
0.586
0.50
1.22
0.93
2
2
64.11
7.89
8.1
Curves which have two or more components.
Table V
Quantic data for characteristic curves with long exposure scales measured by Eqs. (7) and (8) for a constant r and variable ϵ’s.
Curve
Development
Equation
γ/Dmax
ā in μ2
r
=cā
15
DK-50
2 min
(9)
0.578
1.656
2
11.3×10−4
16
DK-50
3 min
(9)
0.598
1.656
2
14.3×10−4
17
FeOx
2 min
(10)
0.569
0.480
2
2.7×10−4
Table VI
Quantic data for the characteristic curves in Table V measured with Eq. (6) and a constant r and a constant ϵ.
curve
α
β
r1
r2
ϵ1·104
ϵ2·104
m
15
0.40
0.24
3
2
49.9
4.45
11.21
16
0.50
0.32
3
2
58.7
4.88
12.02
17
0.95
0.50
2
2
11.0
1.03
10.70
Table VII
Quantic data of the four components of the most complicated characteristic curve observed to date.
Component
r
ϵ·104
1
2
9.94
2
3
20.8
3
2
15.81
4
2
1.02
Table VIII
Quantic data of the emulsion layer without dyes.
t
r1
r2
α
β
α/β
ϵ1×104
ϵ2×104
m
3′
2
2
1.12
1.12
1.0
20.83
3.01
6.92
5′
2
2
1.14
1.14
1.0
28.75
3.38
8.51
8′
2
2
1.16
1.16
1.0
33.01
3.46
9.54
Table IX
Quantic data of the emulsion layer with dyes.
t
r1
r2
α
β
α/β
ϵ1×104
ϵ2×104
m
3′
2
2
0.64
1.75
0.37
28.75
3.54
8.12
5′
2
2
0.67
1.74
0.39
37.90
3.88
6.77
8′
2
2
0.66
1.77
0.39
40.61
4.35
9.34
Tables (9)
Table I
Relations between the minimum number of quanta, r, required to make the grains of a simple emulsion developable and the corresponding exposure scales, l, of the characteristic curves in logE units for Dmax=0.50 and the theoretical γ/Dmax ratios. γ/Dmax is derived from Eq. (3), as in reference 1.
r=1
2
3
4
5
6
7
8
9
10
etc.
1=1.34
2.6
2.2
2.0
1.8
1.8
1.6
1.6
1.4
1.4
etc.
γ/Dmax=0.682
0.862
0.955
1.011
1.048
1.076
1.097
1.113
1.124
1.135
etc.
Table II
Quantic data from six characteristic curves with the shortest exposure scales.
Curve
Development
γ/Dmax obs
r
ϵ·104r
1 in logE units
1
FeOx
6 min
1.014
5
5.43
1.09
1.8
2
FeOx
9 min
1.033
5
10.6
2.12
1.8
3
DK-50
12 min
1.030
5
15.5
3.1
1.8
4
FeOx
18 min
1.101
7
8.61
1.23
1.6
5
FeOx
18 min
1.112
8
18.8
2.35
1.6
6
FeOx
18 min
1.163
14
18.8
1.34
<1.4
Table III
Quantic data for two “simple” curves with long exposure scales.
Curve
Development
γ/Dmax obs
r
ϵ·104
1 in logE units
7
DK-50
3 min
0.686
1
0.484
3
8
DK-50
8 min
0.681
1
0.684
3
Table IV
Quantic data for “complex”a curves with long exposure scales.
Curve
Dev. time in min
γ/Dmax
ā in μ2
α
β
r1
r2
ϵ1·104
ϵ2·104
m
9
5
0.516
0.77
0.70
1.43
2
2
53.0
3.67
14.4
10
5
0.526
0.77
0.43
0.88
2
2
5.95
0.312
19.1
11
8
0.532
0.81
1.00
0.41
2
3
62.95
11.19
5.6
12
8
0.533
0.77
0.44
1.06
2
2
8.03
0.431
18.6
13
3
0.578
1.66
0.50
0.32
3
2
58.63
4.88
12.0
14
8
0.586
0.50
1.22
0.93
2
2
64.11
7.89
8.1
Curves which have two or more components.
Table V
Quantic data for characteristic curves with long exposure scales measured by Eqs. (7) and (8) for a constant r and variable ϵ’s.
Curve
Development
Equation
γ/Dmax
ā in μ2
r
=cā
15
DK-50
2 min
(9)
0.578
1.656
2
11.3×10−4
16
DK-50
3 min
(9)
0.598
1.656
2
14.3×10−4
17
FeOx
2 min
(10)
0.569
0.480
2
2.7×10−4
Table VI
Quantic data for the characteristic curves in Table V measured with Eq. (6) and a constant r and a constant ϵ.
curve
α
β
r1
r2
ϵ1·104
ϵ2·104
m
15
0.40
0.24
3
2
49.9
4.45
11.21
16
0.50
0.32
3
2
58.7
4.88
12.02
17
0.95
0.50
2
2
11.0
1.03
10.70
Table VII
Quantic data of the four components of the most complicated characteristic curve observed to date.
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