A method is described that permits the calculation of a cemented doublet with a given spherical aberration and coma at the edge of the lens. In particular the aberrations can be set to zero. Given one glass, the equations reported in this paper permit the determination of a second matching glass that minimizes the spherochromatism and coma of the lens. This result is obtained by the introduction, into the third-order thin-lens formulas, the third-order values of the aberration coefficients, as derived from the equation developed by Mossotti which yields zero finite aberrations for the same lens with added thickness. After a brief historical introduction, the third-order equations are developed and tables for the color-correcting glasses and SI and SII (the Seidel third-order coefficients) are given for objects at infinity and at a magnification of −1, both for flint- and crown-leading cases. The paper closes with a table of corrected doublets.
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Rayleigh Tolerances for Various Aberrations with Different Focal Numbersa
Aberration (units)
Rayleigh Tolerance
F/3
F/4
F/5
RAN (μm)
2λ(F/D)2
10.4
18.6
29.0
PSP (μm)
16λ(F/D)2
83
149
232
ZSP (μm)
24λ(F/D)2
125
223
350
PCR (μm)
4λ(F/D)2
20.8
37.2
58.0
SCR (μm)
5λ(F/D)2
26.0
46.5
75.5
SCR (λ)
dw′
0.62
0.62
0.62
CVS (λ)
Δdw′
2.0
2.0
2.0
OSC′ (10−4)
6.3
8.4
10.0
See text for variable definitions.
Table 2
Computations of Aberrations for Three Values of F/D for a Thin Doublet with PCR = 0 and F = 100 mma
Aberration
F/D
Units
F/3
F/4
F/5
0.975
0.265
0.102
Millimeters
0.205
0.061
0.024
Millimeters
PCR
0.000
0.000
0.000
Millimeters
SCR
−4.84
−1.40
−0.51
λd
CVS
−4.87
−1.40
−0.55
λd
OSC′
−21.2
−5.65
−2.15
×10−4
For glass 517642, the following values were used: R = 60.65 and T = 0.00; for glass 648332, the following values were used: R = −42.48 and T = 0.00. R = −141.85 and T = 100.00 represent the distance, in air, from the lens to the image (BFL).
Table 3
Computations of Aberrations for Three Values of F/D for a Thick Doublet with Zero Spherical Aberration and Zero Coma at the 1.1 Aperture and with F = 100 mm
Variable
F/D
Units
F/3
F/4
F/5
0.000
0.000
0.000
Millimeters
−0.18
−0.06
−0.02
Millimeters
PCR
−0.15
−0.08
−0.05
Millimeters
SCR
−0.12
−0.11
−0.07
λd
CVS
−3.60
−1.18
−0.49
λd
OSC′
3.74
1.05
0.42
×10−4
Table 4
Values of R and T Used in the Calculations for the Thick Doublet from Table 3
F/D
Glass
R
T
F/3
517642
62.40
8.00
648331
−43.25
3.00
−132.77
94.65
F/4
517642
61.79
6.00
648331
−42.49
3.00
−134.20
95.71
F/5
517642
61.68
4.00
648331
−42.37
3.00
−134.93
96.82
Table 5
Computations for Achromatization Values of (ν + Δν2) for Flint Leading at m = 0, −1 and for Crown Leading at m = 0 and Satisfying Zero-Longitudinal Secondary Chromatic Aberration for the 0.71 Zonea
Flint Leading
Crown Leading
Flint Leading m = −1
m = 0
m = 0
n1, ν1
n2
ν2
Δν2
n1
ν1
n2, ν2
Δν1
n1, ν1
n2
ν2
Δν2
F/3
F/4
F/5
F/3
F/4
F/5
F/3
F/4
F/5
1.88, 22.70
1.48
47.32
1.93
1.96
2.17
1.48
50.49
1.88, 22.70
0.20
0.32
0.46
1.88, 22.70
1.48
48.58
0.91
0.97
1.14
1.56
44.94
1.21
1.16
1.34
1.56
47.90
−0.01
0.08
0.17
1.56
46.02
0.49
0.52
0.62
1.64
42.41
0.74
0.73
0.81
1.64
44.87
−0.03
0.06
0.12
1.64
43.21
0.26
0.27
0.34
1.72
39.45
0.44
0.43
0.49
1.72
41.34
−0.03
0.03
0.08
1.72
39.95
0.12
0.13
0.18
1.80
35.54
0.26
0.25
0.31
1.80
36.68
0.00
0.05
0.09
1.80
35.72
0.04
0.05
0.09
1.80, 25.40
1.48
52.58
1.72
1.76
1.99
1.48
55.60
1.80, 25.40
0.12
0.24
0.39
1.80, 25.40
1.48
53.72
0.78
0.84
1.02
1.54
50.20
1.16
1.17
1.32
1.54
52.94
0.00
0.10
0.21
1.54
51.16
0.46
0.50
0.62
1.60
47.61
0.77
0.77
0.89
1.60
49.96
−0.03
0.04
0.12
1.60
48.34
0.26
0.29
0.38
1.66
44.63
0.50
0.50
0.60
1.66
46.48
−0.04
0.04
0.10
1.66
45.10
0.15
0.17
0.24
1.72
40.88
0.29
0.29
0.37
1.72
42.11
−0.02
0.03
0.09
1.72
41.08
0.06
0.08
0.14
1.72, 29.50
1.48
59.99
1.51
1.54
1.81
1.48
62.84
1.72, 29.50
0.02
0.15
0.31
1.72, 29.50
1.48
61.00
0.62
0.68
0.90
1.54
56.48
0.95
0.96
1.15
1.54
58.84
0.00
0.09
0.21
1.54
57.22
0.33
0.38
0.52
1.60
52.36
0.58
0.59
0.73
1.60
54.20
−0.05
0.02
0.11
1.60
52.82
0.16
0.19
0.30
1.66
46.94
0.30
0.32
0.46
1.66
48.04
−0.03
0.03
0.12
1.66
47.08
0.07
0.09
0.20
1.64, 35.00
1.48
68.53
1.21
1.25
1.58
1.48
71.00
1.64, 35.00
−0.06
0.07
0.26
1.64, 35.00
1.48
69.30
0.43
0.51
0.76
1.52
64.75
1.03
1.17
1.20
1.52
66.80
−0.08
0.03
0.18
1.52
65.30
0.26
0.32
0.52
1.56
60.27
0.54
0.57
0.81
1.56
61.81
−0.07
0.02
0.15
1.56
60.58
0.14
0.19
0.37
1.60
54.29
0.31
0.36
0.61
1.60
55.20
0.06
0.15
0.19
1.60
54.34
0.08
0.13
0.32
1.56, 44.00
1.48
79.07
0.83
0.93
1.39
1.48
80.87
1.56, 44.00
−0.10
0.05
0.31
1.56, 44.00
1.48
79.47
0.25
0.35
0.71
1.50
75.25
0.63
0.72
1.29
1.50
76.69
−0.07
0.06
0.31
1.50
75.50
0.17
0.26
0.62
1.52
70.63
0.50
0.62
1.06
1.52
71.70
−0.05
0.07
0.35
1.52
70.73
0.13
0.23
0.60
1.54
64.38
0.32
0.56
1.10
1.54
65.03
−0.01
0.13
0.50
1.54
64.36
0.11
0.24
0.74
Blank entries indicate that the initial entries in that column section are the same for the succeeding rows in that section. The values to be used for the achromatization are given by (ν + Δν2) for different values of F/D.
Table 6
Flint-Leading Values, at m = 0, of SI and SII for Different Values of F/D that Yield Zero Spherical Aberration at the Edge of the Lens and Zero Coma at Aperture 1.1a
Flint Leading
n2
SI
SII
F/3
F/4
F/5
F/3
F/4
F/5
n1 = 1.88
1.48
−0.76
−1.19
− 1.42
−12.71
−19.80
−22.60
1.56
−0.33
−0.59
−0.74
−5.14
−9.43
−11.20
1.64
−0.12
−0.31
− 0.40
−1.02
−4.09
−5.21
1.72
0.00
−0.14
−0.21
1.47
−0.93
−1.79
1.80
0.11
−0.02
−0.08
3.37
1.21
0.42
n1 = 1.80
1.48
−0.40
−0.81
−1.03
−4.18
−11.20
−13.80
1.54
−0.16
−0.45
−0.60
−0.61
−5.51
−7.35
1.60
−0.03
−0.24
−0.36
1.67
−2.07
− 3.44
1.66
0.07
−0.11
−0.20
3.24
0.18
−0.94
1.72
0.16
0.00
−0.09
4.64
1.85
0.83
n1 = 1.72
1.48
−0.08
−0.47
−0.68
3.17
−3.83
− 6.45
1.54
0.07
−0.22
−0.36
4.67
−0.39
−2.27
1.60
0.16
−0.06
−0.18
5.80
1.75
0.26
1.66
0.27
0.07
−0.04
7.17
3.43
2.05
n1 = 1.64
1.48
0.23
−0.16
−0.36
9.57
2.32
−0.36
1.52
0.29
−0.03
−0.20
9.54
3.40
1.20
1.56
0.35
0.07
−0.08
9.88
4.56
2.61
1.60
0.47
0.20
0.05
11.24
5.80
3.83
n1 = 1.56
1.48
0.57
0.16
−0.05
15.89
7.63
4.65
1.50
0.60
0.23
0.02
15.80
7.98
5.15
1.52
0.70
0.31
0.11
16.74
9.00
5.75
1.54
0.89
0.47
0.25
20.37
10.50
9.04
Multiply the table values by 10−6.
Table 7
Crown-Leading Values, at m = 0, of SI and SII for Different Values of F/D that Yield Zero Spherical Aberration at the Edge of the Lens and Zero Coma at Aperture 1.1a
Crown-Leading Glass Refractive Index
n1
SI
SII
F/3
F/4
F/5
F/3
F/4
F/5
n2 = 1.88
1.48
0.14
0.01
0.00
−12.30
− 8.45
−7.95
1.56
0.06
−0.02
−0.01
−7.17
−4.71
−4.59
1.64
0.02
−0.02
−0.01
− 4.42
−2.70
−2.75
1.72
0.02
−0.02
−0.01
−2.91
−1.59
−1.78
1.80
0.03
−0.01
0.00
−2.30
−1.08
−1.11
n2 = 1.80
1.48
0.17
0.03
0.02
−12.30
−8.20
−7.62
1.54
0.10
0.01
0.01
−8.17
−5.25
−4.98
1.60
0.06
0.00
0.00
−5.68
−3.45
−3.34
1.66
0.05
0.00
0.00
−4.17
−2.34
−2.29
1.72
0.07
0.01
0.01
−3.77
−1.74
−1.65
n2 = 1.72
1.48
0.21
0.06
0.04
−12.30
−7.92
−7.20
1.54
0.14
0.03
0.02
−8.29
−5.09
−4.68
1.60
0.11
0.02
0.02
−6.02
−3.43
−3.14
1.66
0.14
0.05
0.03
−5.10
−2.64
−2.30
n2 = 1.64
1.48
0.26
0.10
0.06
−12.40
−7.64
−6.73
1.52
0.22
0.08
0.05
−9.77
−5.75
−5.03
1.56
0.22
0.08
0.06
−8.16
−4.55
−3.89
1.60
0.28
0.13
0.08
−7.86
−4.11
−3.30
n2 = 1.56
1.48
0.39
0.18
0.12
−13.40
−7.66
−6.33
1.50
0.40
0.19
0.12
−12.40
−6.91
−5.59
1.52
0.45
0.22
0.14
−12.20
−6.94
−5.12
1.54
0.60
0.33
0.22
−13.80
−7.03
−5.19
Multiply the table values by 10−6.
Table 8
Flint-Leading Values, at m = −1, of SI and SII for Different Values of F/D that Yield Zero Spherical Aberration at the Edge of the Lens and Zero Coma at Aperture 1.1; F = 100 mma
Flint-Leading Glass Refractive Index
n2
SI
SII
F/3
F/4
F/5
F/3
F/4
F/5
n1 = 1.88
1.48
0.07
−0.21
−0.35
7.05
0.93
−1.72
1.56
0.14
−0.05
−0.13
7.72
3.55
1.73
1.64
0.15
0.02
−0.04
7.58
4.43
3.04
1.72
0.16
0.06
0.01
7.24
4.65
3.50
1.80
0.19
0.09
0.05
7.15
4.77
3.69
n1 = 1.80
1.48
0.22
−0.07
−0.20
11.00
4.85
2.19
1.54
0.23
0.02
−0.07
10.40
5.69
3.67
1.60
0.22
0.06
−0.01
9.64
5.88
4.24
1.66
0.22
0.09
0.03
9.03
5.83
4.41
1.72
0.25
0.12
0.06
8.75
5.79
4.47
n1 = 1.72
1.48
0.35
0.07
−0.07
14.50
8.15
5.43
1.54
0.32
0.11
0.01
12.80
7.86
5.74
1.60
0.31
0.14
0.06
11.50
7.45
5.66
1.66
0.35
0.18
0.10
11.10
7.26
5.57
n1 = 1.64
1.48
0.49
0.19
0.06
17.60
10.90
8.00
1.52
0.46
0.21
0.09
15.80
10.10
7.61
1.56
0.46
0.23
0.12
14.70
9.51
7.26
1.60
0.53
0.29
0.17
14.60
9.42
7.16
n1 = 1.56
1.48
0.69
0.35
0.19
18.70
11.80
9.30
1.50
0.69
0.37
0.21
18.00
11.40
8.97
1.52
0.74
0.41
0.25
17.90
11.20
8.80
1.54
0.90
0.53
0.34
19.90
11.90
9.10
Multiply the table values by 10−6.
Table 9
Aplanatic Doubletsa Computed for Various Glasses for F/D = 4
All doublets have F = 100 mm and F/D = 4. The thickness of the flint is 3 mm and that of the crown is 6 mm.
Best defocusing value is ∼−0.03 mm.
Best defocusing value is ∼−0.045 mm.
Best defocusing value is ∼−0.14 mm.
Tables (9)
Table 1
Rayleigh Tolerances for Various Aberrations with Different Focal Numbersa
Aberration (units)
Rayleigh Tolerance
F/3
F/4
F/5
RAN (μm)
2λ(F/D)2
10.4
18.6
29.0
PSP (μm)
16λ(F/D)2
83
149
232
ZSP (μm)
24λ(F/D)2
125
223
350
PCR (μm)
4λ(F/D)2
20.8
37.2
58.0
SCR (μm)
5λ(F/D)2
26.0
46.5
75.5
SCR (λ)
dw′
0.62
0.62
0.62
CVS (λ)
Δdw′
2.0
2.0
2.0
OSC′ (10−4)
6.3
8.4
10.0
See text for variable definitions.
Table 2
Computations of Aberrations for Three Values of F/D for a Thin Doublet with PCR = 0 and F = 100 mma
Aberration
F/D
Units
F/3
F/4
F/5
0.975
0.265
0.102
Millimeters
0.205
0.061
0.024
Millimeters
PCR
0.000
0.000
0.000
Millimeters
SCR
−4.84
−1.40
−0.51
λd
CVS
−4.87
−1.40
−0.55
λd
OSC′
−21.2
−5.65
−2.15
×10−4
For glass 517642, the following values were used: R = 60.65 and T = 0.00; for glass 648332, the following values were used: R = −42.48 and T = 0.00. R = −141.85 and T = 100.00 represent the distance, in air, from the lens to the image (BFL).
Table 3
Computations of Aberrations for Three Values of F/D for a Thick Doublet with Zero Spherical Aberration and Zero Coma at the 1.1 Aperture and with F = 100 mm
Variable
F/D
Units
F/3
F/4
F/5
0.000
0.000
0.000
Millimeters
−0.18
−0.06
−0.02
Millimeters
PCR
−0.15
−0.08
−0.05
Millimeters
SCR
−0.12
−0.11
−0.07
λd
CVS
−3.60
−1.18
−0.49
λd
OSC′
3.74
1.05
0.42
×10−4
Table 4
Values of R and T Used in the Calculations for the Thick Doublet from Table 3
F/D
Glass
R
T
F/3
517642
62.40
8.00
648331
−43.25
3.00
−132.77
94.65
F/4
517642
61.79
6.00
648331
−42.49
3.00
−134.20
95.71
F/5
517642
61.68
4.00
648331
−42.37
3.00
−134.93
96.82
Table 5
Computations for Achromatization Values of (ν + Δν2) for Flint Leading at m = 0, −1 and for Crown Leading at m = 0 and Satisfying Zero-Longitudinal Secondary Chromatic Aberration for the 0.71 Zonea
Flint Leading
Crown Leading
Flint Leading m = −1
m = 0
m = 0
n1, ν1
n2
ν2
Δν2
n1
ν1
n2, ν2
Δν1
n1, ν1
n2
ν2
Δν2
F/3
F/4
F/5
F/3
F/4
F/5
F/3
F/4
F/5
1.88, 22.70
1.48
47.32
1.93
1.96
2.17
1.48
50.49
1.88, 22.70
0.20
0.32
0.46
1.88, 22.70
1.48
48.58
0.91
0.97
1.14
1.56
44.94
1.21
1.16
1.34
1.56
47.90
−0.01
0.08
0.17
1.56
46.02
0.49
0.52
0.62
1.64
42.41
0.74
0.73
0.81
1.64
44.87
−0.03
0.06
0.12
1.64
43.21
0.26
0.27
0.34
1.72
39.45
0.44
0.43
0.49
1.72
41.34
−0.03
0.03
0.08
1.72
39.95
0.12
0.13
0.18
1.80
35.54
0.26
0.25
0.31
1.80
36.68
0.00
0.05
0.09
1.80
35.72
0.04
0.05
0.09
1.80, 25.40
1.48
52.58
1.72
1.76
1.99
1.48
55.60
1.80, 25.40
0.12
0.24
0.39
1.80, 25.40
1.48
53.72
0.78
0.84
1.02
1.54
50.20
1.16
1.17
1.32
1.54
52.94
0.00
0.10
0.21
1.54
51.16
0.46
0.50
0.62
1.60
47.61
0.77
0.77
0.89
1.60
49.96
−0.03
0.04
0.12
1.60
48.34
0.26
0.29
0.38
1.66
44.63
0.50
0.50
0.60
1.66
46.48
−0.04
0.04
0.10
1.66
45.10
0.15
0.17
0.24
1.72
40.88
0.29
0.29
0.37
1.72
42.11
−0.02
0.03
0.09
1.72
41.08
0.06
0.08
0.14
1.72, 29.50
1.48
59.99
1.51
1.54
1.81
1.48
62.84
1.72, 29.50
0.02
0.15
0.31
1.72, 29.50
1.48
61.00
0.62
0.68
0.90
1.54
56.48
0.95
0.96
1.15
1.54
58.84
0.00
0.09
0.21
1.54
57.22
0.33
0.38
0.52
1.60
52.36
0.58
0.59
0.73
1.60
54.20
−0.05
0.02
0.11
1.60
52.82
0.16
0.19
0.30
1.66
46.94
0.30
0.32
0.46
1.66
48.04
−0.03
0.03
0.12
1.66
47.08
0.07
0.09
0.20
1.64, 35.00
1.48
68.53
1.21
1.25
1.58
1.48
71.00
1.64, 35.00
−0.06
0.07
0.26
1.64, 35.00
1.48
69.30
0.43
0.51
0.76
1.52
64.75
1.03
1.17
1.20
1.52
66.80
−0.08
0.03
0.18
1.52
65.30
0.26
0.32
0.52
1.56
60.27
0.54
0.57
0.81
1.56
61.81
−0.07
0.02
0.15
1.56
60.58
0.14
0.19
0.37
1.60
54.29
0.31
0.36
0.61
1.60
55.20
0.06
0.15
0.19
1.60
54.34
0.08
0.13
0.32
1.56, 44.00
1.48
79.07
0.83
0.93
1.39
1.48
80.87
1.56, 44.00
−0.10
0.05
0.31
1.56, 44.00
1.48
79.47
0.25
0.35
0.71
1.50
75.25
0.63
0.72
1.29
1.50
76.69
−0.07
0.06
0.31
1.50
75.50
0.17
0.26
0.62
1.52
70.63
0.50
0.62
1.06
1.52
71.70
−0.05
0.07
0.35
1.52
70.73
0.13
0.23
0.60
1.54
64.38
0.32
0.56
1.10
1.54
65.03
−0.01
0.13
0.50
1.54
64.36
0.11
0.24
0.74
Blank entries indicate that the initial entries in that column section are the same for the succeeding rows in that section. The values to be used for the achromatization are given by (ν + Δν2) for different values of F/D.
Table 6
Flint-Leading Values, at m = 0, of SI and SII for Different Values of F/D that Yield Zero Spherical Aberration at the Edge of the Lens and Zero Coma at Aperture 1.1a
Flint Leading
n2
SI
SII
F/3
F/4
F/5
F/3
F/4
F/5
n1 = 1.88
1.48
−0.76
−1.19
− 1.42
−12.71
−19.80
−22.60
1.56
−0.33
−0.59
−0.74
−5.14
−9.43
−11.20
1.64
−0.12
−0.31
− 0.40
−1.02
−4.09
−5.21
1.72
0.00
−0.14
−0.21
1.47
−0.93
−1.79
1.80
0.11
−0.02
−0.08
3.37
1.21
0.42
n1 = 1.80
1.48
−0.40
−0.81
−1.03
−4.18
−11.20
−13.80
1.54
−0.16
−0.45
−0.60
−0.61
−5.51
−7.35
1.60
−0.03
−0.24
−0.36
1.67
−2.07
− 3.44
1.66
0.07
−0.11
−0.20
3.24
0.18
−0.94
1.72
0.16
0.00
−0.09
4.64
1.85
0.83
n1 = 1.72
1.48
−0.08
−0.47
−0.68
3.17
−3.83
− 6.45
1.54
0.07
−0.22
−0.36
4.67
−0.39
−2.27
1.60
0.16
−0.06
−0.18
5.80
1.75
0.26
1.66
0.27
0.07
−0.04
7.17
3.43
2.05
n1 = 1.64
1.48
0.23
−0.16
−0.36
9.57
2.32
−0.36
1.52
0.29
−0.03
−0.20
9.54
3.40
1.20
1.56
0.35
0.07
−0.08
9.88
4.56
2.61
1.60
0.47
0.20
0.05
11.24
5.80
3.83
n1 = 1.56
1.48
0.57
0.16
−0.05
15.89
7.63
4.65
1.50
0.60
0.23
0.02
15.80
7.98
5.15
1.52
0.70
0.31
0.11
16.74
9.00
5.75
1.54
0.89
0.47
0.25
20.37
10.50
9.04
Multiply the table values by 10−6.
Table 7
Crown-Leading Values, at m = 0, of SI and SII for Different Values of F/D that Yield Zero Spherical Aberration at the Edge of the Lens and Zero Coma at Aperture 1.1a
Crown-Leading Glass Refractive Index
n1
SI
SII
F/3
F/4
F/5
F/3
F/4
F/5
n2 = 1.88
1.48
0.14
0.01
0.00
−12.30
− 8.45
−7.95
1.56
0.06
−0.02
−0.01
−7.17
−4.71
−4.59
1.64
0.02
−0.02
−0.01
− 4.42
−2.70
−2.75
1.72
0.02
−0.02
−0.01
−2.91
−1.59
−1.78
1.80
0.03
−0.01
0.00
−2.30
−1.08
−1.11
n2 = 1.80
1.48
0.17
0.03
0.02
−12.30
−8.20
−7.62
1.54
0.10
0.01
0.01
−8.17
−5.25
−4.98
1.60
0.06
0.00
0.00
−5.68
−3.45
−3.34
1.66
0.05
0.00
0.00
−4.17
−2.34
−2.29
1.72
0.07
0.01
0.01
−3.77
−1.74
−1.65
n2 = 1.72
1.48
0.21
0.06
0.04
−12.30
−7.92
−7.20
1.54
0.14
0.03
0.02
−8.29
−5.09
−4.68
1.60
0.11
0.02
0.02
−6.02
−3.43
−3.14
1.66
0.14
0.05
0.03
−5.10
−2.64
−2.30
n2 = 1.64
1.48
0.26
0.10
0.06
−12.40
−7.64
−6.73
1.52
0.22
0.08
0.05
−9.77
−5.75
−5.03
1.56
0.22
0.08
0.06
−8.16
−4.55
−3.89
1.60
0.28
0.13
0.08
−7.86
−4.11
−3.30
n2 = 1.56
1.48
0.39
0.18
0.12
−13.40
−7.66
−6.33
1.50
0.40
0.19
0.12
−12.40
−6.91
−5.59
1.52
0.45
0.22
0.14
−12.20
−6.94
−5.12
1.54
0.60
0.33
0.22
−13.80
−7.03
−5.19
Multiply the table values by 10−6.
Table 8
Flint-Leading Values, at m = −1, of SI and SII for Different Values of F/D that Yield Zero Spherical Aberration at the Edge of the Lens and Zero Coma at Aperture 1.1; F = 100 mma
Flint-Leading Glass Refractive Index
n2
SI
SII
F/3
F/4
F/5
F/3
F/4
F/5
n1 = 1.88
1.48
0.07
−0.21
−0.35
7.05
0.93
−1.72
1.56
0.14
−0.05
−0.13
7.72
3.55
1.73
1.64
0.15
0.02
−0.04
7.58
4.43
3.04
1.72
0.16
0.06
0.01
7.24
4.65
3.50
1.80
0.19
0.09
0.05
7.15
4.77
3.69
n1 = 1.80
1.48
0.22
−0.07
−0.20
11.00
4.85
2.19
1.54
0.23
0.02
−0.07
10.40
5.69
3.67
1.60
0.22
0.06
−0.01
9.64
5.88
4.24
1.66
0.22
0.09
0.03
9.03
5.83
4.41
1.72
0.25
0.12
0.06
8.75
5.79
4.47
n1 = 1.72
1.48
0.35
0.07
−0.07
14.50
8.15
5.43
1.54
0.32
0.11
0.01
12.80
7.86
5.74
1.60
0.31
0.14
0.06
11.50
7.45
5.66
1.66
0.35
0.18
0.10
11.10
7.26
5.57
n1 = 1.64
1.48
0.49
0.19
0.06
17.60
10.90
8.00
1.52
0.46
0.21
0.09
15.80
10.10
7.61
1.56
0.46
0.23
0.12
14.70
9.51
7.26
1.60
0.53
0.29
0.17
14.60
9.42
7.16
n1 = 1.56
1.48
0.69
0.35
0.19
18.70
11.80
9.30
1.50
0.69
0.37
0.21
18.00
11.40
8.97
1.52
0.74
0.41
0.25
17.90
11.20
8.80
1.54
0.90
0.53
0.34
19.90
11.90
9.10
Multiply the table values by 10−6.
Table 9
Aplanatic Doubletsa Computed for Various Glasses for F/D = 4
All doublets have F = 100 mm and F/D = 4. The thickness of the flint is 3 mm and that of the crown is 6 mm.
Best defocusing value is ∼−0.03 mm.
Best defocusing value is ∼−0.045 mm.
Best defocusing value is ∼−0.14 mm.