A new method for automatic lens design is described. Instead of finding the approximate solution to the system of simultaneous nonlinear equations, the solution is found to the system of simultaneous nonlinear inequalities. Thus, the aberrations are driven into the domains which have been set up around target values. The bandwidth of the domain is the allowable tolerance associated with each aberration. A relaxation method is used to solve the system of linearized inequalities and iterative cycles are used to find the solution to the system of nonlinear ones. This method allows a high degree of control of individual performance functions. Mechanical conditions can be treated in the same way as aberrations. The program was written for the IBM 7090 computer and satisfactory designs were obtained in general within a few minutes for gauss-type photographic lenses.
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Object plane is counted as the first surface.
No. 7 is the stop surface.
Table II
Configuration data for f/1.7 gauss-type photographic lens at the first solution.
Surface No.
Curvature
Thickness
Ng
Nd
2
0.042060
4.0
1.77685
1.75700
3
0.013253
0.5
1.0
1.0
4
0.081091
4.0
1.68801
1.67003
5
0.017606
0.8424
1.74916
1.71736
6
0.112010
4.0
1.0
1.0
7
0.0
3.0601
1.0
1.0
8
−0.096174
1.0
1.61453
1.59270
9
0.008567
3.5695
1.75180
1.73400
10
−0.070100
0.5913
1.0
1.0
11
0.008629
3.0
1.83131
1.80610
12
−0.022078
Table III
Configuration data for f/1.7 gauss-type photographic lens at the second solution.
Surface No.
Curvature
Thickness
Ng
Nd
2
0.042310
4.0
1.77685
1.75700
3
0.013425
0.5
1.0
1.0
4
0.081127
4.0
1.68801
1.67003
5
0.017836
0.8332
1.74916
1.71736
6
0.112352
4.0
1.0
1.0
7
0.0
3.0324
1.0
1.0
8
−0.096190
1.0
1.61453
1.59270
9
0.008622
3.5300
1.75180
1.73400
10
−0.070003
0.6071
1.0
1.0
11
0.008599
3.0
1.83131
1.80610
12
−0.022340
Table IV
Lower and upper boundary conditions and image errors at the initial, the first, and the second stages. No. 1, 2, ⋯, 26, 27, represent the boundaries and the image errors at the 1st stage and No. 1, 2, ⋯, 26, 27′ represent the boundaries and the image errors at the 2nd stage. The tolerances of 5% of bandwidths themselves were allowed at both sides of the respective boundaries.
Performance functions
Lower boundaries
Image errors
Upper boundaries
Initial design
First solution
Second solution (final)
No. 1
Bf
19.3
17.35022
19.29257
19.31548
23.0
2
f
32.0
31.12359
32.34293
32.34477
32.5
3
f/
1.7
1.66263
1.75015
1.75031
1.75
4
S(0.7)
−0.11
−0.58235
−0.09135
−0.07985
−0.08
5
S(1.0)
−0.02
−1.50369
0.00279
0.03586
0.046
6
MA(20°)
−0.16
−2.10270
−0.14678
−0.15586
−0.13
7
SA(20°)
−0.13
−0.73220
−0.13016
−0.13195
−0.08
8
MA(25°)
−0.13
−5.07097
−0.12817
−0.13326
−0.02
9
SA(25°)
0.0
−1.19172
0.06601
0.06601
0.065
10
Dis(25°)
−2.0
8.01146
0.00733
−0.05602
2.0
11
Coma M(20°, 0.63)
−0.02
−0.13525
−0.00827
−0.00270
0.02
12
Coma S(20°, 0.63)
−0.01
−0.09060
−0.00998
−0.00758
0.01
13
Ey(20°, 0.63)
−0.2
0.72864
−0.07994
−0.08010
0.2
14
Ez(20°, 0.63)
−0.1
−0.16859
0.01045
0.01194
0.1
15
Coma M(25°, 0.50)
−0.02
0.03200
0.01541
0.01916
0.02
16
Coma S(25°, 0.50)
−0.01
−0.06086
−0.00368
−0.00179
0.01
17
Ey(25°, 0.50)
−0.05
1.31666
−0.03325
−0.03304
0.05
18
Ez(25°, 0.50)
−0.1
−0.16908
0.04077
0.04169
0.1
19
CBf(G−D)
−0.015
0.03340
−0.00998
−0.00987
0.015
20
CY(20°, G−D)
−0.015
−0.00049
0.01512
0.01511
0.015
21
L(6, 0, 1.0)
0.8
1.75017
1.54546
1.53969
3.0
22
L(7, 0, 1.0)
0.8
1.19745
1.34375
1.31320
3.0
23
T(5)
0.8
1.00000
0.84249
0.83324
2.2
24
T(7)
2.8
3.00000
3.06018
3.03248
5.8
25
T(9)
3.5
4.00000
3.56957
3.53005
6.0
26
T(10)
0.4
0.50000
0.59134
0.60717
2.0
27
SINC(0.7)
−0.125
−0.89589
−0.12500
⋯
−0.1
No. 27′
SINC(0.7)
−0.105
⋯
⋯
−0.10546
−0.08
Tables (4)
Table I
Initial configuration data for f/1.7 gauss-type photographic lens.
Object plane is counted as the first surface.
No. 7 is the stop surface.
Table II
Configuration data for f/1.7 gauss-type photographic lens at the first solution.
Surface No.
Curvature
Thickness
Ng
Nd
2
0.042060
4.0
1.77685
1.75700
3
0.013253
0.5
1.0
1.0
4
0.081091
4.0
1.68801
1.67003
5
0.017606
0.8424
1.74916
1.71736
6
0.112010
4.0
1.0
1.0
7
0.0
3.0601
1.0
1.0
8
−0.096174
1.0
1.61453
1.59270
9
0.008567
3.5695
1.75180
1.73400
10
−0.070100
0.5913
1.0
1.0
11
0.008629
3.0
1.83131
1.80610
12
−0.022078
Table III
Configuration data for f/1.7 gauss-type photographic lens at the second solution.
Surface No.
Curvature
Thickness
Ng
Nd
2
0.042310
4.0
1.77685
1.75700
3
0.013425
0.5
1.0
1.0
4
0.081127
4.0
1.68801
1.67003
5
0.017836
0.8332
1.74916
1.71736
6
0.112352
4.0
1.0
1.0
7
0.0
3.0324
1.0
1.0
8
−0.096190
1.0
1.61453
1.59270
9
0.008622
3.5300
1.75180
1.73400
10
−0.070003
0.6071
1.0
1.0
11
0.008599
3.0
1.83131
1.80610
12
−0.022340
Table IV
Lower and upper boundary conditions and image errors at the initial, the first, and the second stages. No. 1, 2, ⋯, 26, 27, represent the boundaries and the image errors at the 1st stage and No. 1, 2, ⋯, 26, 27′ represent the boundaries and the image errors at the 2nd stage. The tolerances of 5% of bandwidths themselves were allowed at both sides of the respective boundaries.
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