The one-radius triplet is an optical system that consists of three lenses. Either the radii of curvature of the lenses have the same absolute value or one radius of curvature has an infinitely large value. The advantage of such optical systems is that their production cost is less than that of systems with ordinary triplets. Here a theory of one-radius triplets is described and tables of parameters for their modification are provided. Residual aberrations are given for several selected triplets. One-radius triplets are suitable for use in laser technology and metrology.
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c, f-number; n1–n3, refractive indices of triplet lenses for λ = 632.8 nm (Ohara optical glass); r, radius of curvature (in millimeters); d1–d4, vertex separations (in millimeters).
S-BAM 12.
S-NPH 2.
S-BAL 41 for N = 1, S-BAL 14 for N = 2, and S-BAL 35 for N = 3.
Table 7
Residual Spherical Aberration δs′ and Sine Condition δf′ of the ORT for Apertures H and 0.63H
N
r
H
δs′
δf′
H
0.63H
H
0.63H
1
90.197
12.5
-0.0038
-0.0051
-0.0012
-0.0021
2
90.926
17.0
-0.0003
-0.0115
0.0040
-0.0035
3
92.900
25.0
-0.0023
-0.0590
0.0360
-0.0104
Note: N, serial number of ORT; r, radius of curvature (in millimeters).
c, f-number; n1, n3, refractive indices of the triplet lenses; r, radius of curvature (in millimeters); d1–d4, vertex separations (in millimeters); δs′, spherical aberration for apertures H and 0.63H. Lens n2 has a refractive index of 1.75606 and is made from SF14 glass in both cases.
c, f-number; n1–n3, refractive indices of the triplet lenses; r, radius of curvature (in millimeters); d1–d4, vertex separations (in millimeters); W, wave aberration (λ).
Tables (9)
Table 1
Refractive Indices of Lenses of an ORT with Parameters 0, 1, 1, 1, -1, and 1 for SI = SII = 0
Triplet Lens
Radius of Curvature (r)
n1
n2
n3
1.60
1.87
1.55
0.88
1.60
1.88
1.57
0.89
1.61
1.84
1.47
0.85
1.61
1.89
1.57
0.90
1.61
1.92
1.62
0.92
1.62
1.90
1.56
0.90
1.62
1.92
1.60
0.92
1.62
1.94
1.63
0.93
1.62
1.96
1.66
0.94
1.63
1.87
1.48
0.87
1.63
1.89
1.52
0.89
1.63
1.92
1.58
0.92
1.63
1.95
1.63
0.94
1.64
1.88
1.48
0.88
1.64
1.90
1.52
0.90
1.64
1.93
1.57
0.92
1.64
1.97
1.64
0.95
1.65
1.89
1.47
0.88
1.65
1.92
1.53
0.91
1.65
1.99
1.65
0.96
1.66
1.92
1.51
0.91
1.66
1.97
1.60
0.95
1.66
2.00
1.65
0.97
1.67
1.92
1.48
0.90
1.68
2.12
1.84
1.04
1.69
2.19
1.86
1.05
Table 2
Refractive Indices of Lenses of an ORT with Parameters 0, 1, 1, 1, -1, and 1 for SI = 0
Triplet Lens
Radius of Curvature (r)
n1
n2
n3
1.50
1.73
1.50
0.77
1.50
1.74
1.52
0.78
1.50
1.75
1.54
0.79
1.50
1.78
1.59
0.81
1.50
1.80
1.62
0.82
1.51
1.74
1.50
0.78
1.51
1.75
1.52
0.79
1.51
1.76
1.54
0.80
1.52
1.75
1.50
0.79
1.52
1.76
1.52
0.80
1.52
1.80
1.59
0.83
1.54
1.80
1.55
0.83
1.56
1.80
1.51
0.83
Table 3
Refractive Indices of Lenses of an ORT with Parameters 0, 0, 1, 1, -1, and 1 for SI = SII = 0
Triplet Lens
Radius of Curvature (r)
n1
n2
n3
1.84
2.03
2.17
0.79
1.89
2.07
2.15
0.79
1.91
2.08
2.12
0.78
1.96
2.11
2.06
0.76
Table 4
Refractive Indices of Lenses of an ORT with Parameters 1, 0, 0, 1, 1, and -1 for SI = SII = 0
Triplet Lens
Radius of Curvature (r)
n1
n2
n3
1.77
2.13
2.19
0.65
1.82
1.60
1.67
0.68
1.82
1.64
1.71
0.68
1.82
1.68
1.75
0.68
1.83
1.63
1.70
0.69
1.83
1.70
1.77
0.69
1.89
1.45
1.53
0.73
Table 5
Refractive Indices of Lenses of an ORT with Parameters 0, 0, 0, 1, -1, and 1 for SI = SII = 0
c, f-number; n1–n3, refractive indices of triplet lenses for λ = 632.8 nm (Ohara optical glass); r, radius of curvature (in millimeters); d1–d4, vertex separations (in millimeters).
S-BAM 12.
S-NPH 2.
S-BAL 41 for N = 1, S-BAL 14 for N = 2, and S-BAL 35 for N = 3.
Table 7
Residual Spherical Aberration δs′ and Sine Condition δf′ of the ORT for Apertures H and 0.63H
N
r
H
δs′
δf′
H
0.63H
H
0.63H
1
90.197
12.5
-0.0038
-0.0051
-0.0012
-0.0021
2
90.926
17.0
-0.0003
-0.0115
0.0040
-0.0035
3
92.900
25.0
-0.0023
-0.0590
0.0360
-0.0104
Note: N, serial number of ORT; r, radius of curvature (in millimeters).
c, f-number; n1, n3, refractive indices of the triplet lenses; r, radius of curvature (in millimeters); d1–d4, vertex separations (in millimeters); δs′, spherical aberration for apertures H and 0.63H. Lens n2 has a refractive index of 1.75606 and is made from SF14 glass in both cases.
c, f-number; n1–n3, refractive indices of the triplet lenses; r, radius of curvature (in millimeters); d1–d4, vertex separations (in millimeters); W, wave aberration (λ).
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