Table I
Focal lengths, transverse third-order aberrations and merit functions of three optical systems. (1) A Cooke triplet. British patent No. 155640. (2) A perturbed triplet system obtained from the original by arbitrarily changing all radii and separations. (3) A corrected triplet obtained from the perturbed system by means of the least squares method. The computer was required to reach the original aberrations by variations of the changed parameters.
System No. | Focal length | Transverse spherical | Coma | Transverse astigmatism | Transverse Petzval displacement | % Distortion | Transverse axial color | Lateral color | Merit function |
---|
1 | 9.96246 | −0.0376492 | 0.0015320 | −0.0289303 | −0.0478263 | −0.0007001 | −0.0043449 | −0.0010254 | 0 |
2 | 9.52328 | −0.1655320 | 0.0368417 | 0.0332925 | −0.0457180 | 0.0121248 | −0.0108165 | 0.0114128 | 1.83×10−2 |
3 | 9.96249 | −0.0376492 | 0.0015322 | −0.0289299 | −0.0478265 | −0.0007010 | −0.0043442 | −0.0010257 | 1.69×10−12 |
Table II
Lens parameters of the three optical systems listed in Table I (c—curvature, t—separation, nd—refractive index, Δn—dispersion nF—nC).
Original system 1. | Perturbed system 2. | Corrected system 3. |
---|
c | t | nd | Δn | c | t | nd | Δn | c | t | nd | Δn |
---|
0.249400 | | | | 0.310000 | | | | 0.249403 | | | |
| 0.600 | 1.6130 | 0.01048 | | 0.750 | 1.6130 | 0.01048 | | 0.599881 | 1.6130 | 0.01048 |
−0.018620 | | | | 0.041980 | | | | −0.018617 | | | |
| 1.000 | | | | 1.300 | | | | 0.999996 | | |
−0.212800 | | | | −0.180000 | | | | −0.212802 | | | |
| 0.100 | 1.6210 | 0.01715 | | 0.100 | 1.6210 | 0.01715 | | 0.100000 | 1.6210 | 0.01715 |
0.250000 | | | | 0.282800 | | | | 0.249997 | | | |
| 1.080 | | | | 0.800 | | | | 1.080000 | | |
−0.042730 | | | | 0.000000 | | | | −0.042725 | | | |
| 0.600 | 1.6130 | 0.01048 | | 0.750 | 1.6130 | 0.01048 | | 0.599881 | 1.6130 | 0.01048 |
−0.263800 | | | | −0.306530 | | | | −0.263804 | | | |
Table III
Focal lengths, transverse third-order aberrations and merit functions of two Tessar systems. (1) Initial system, lens parameters chosen arbitrarily. (2) Corrected system, obtained from the initial system by using the least squares method. The computer was required to reach a focal length of 10 and zero third-order aberrations by changing all curvatures, refractive indices, and dispersions (see also, Table IV).
System No. | Focal length | Transverse spherical | Coma | Transverse astigmatism | Transverse Petzval displacement | % Distortion | Transverse axial color | Lateral color | Merit function |
---|
1 | 19.6038 | 0.049550 | 0.135635 | 0.046501 | 0.044371 | 0.028293 | −0.060560 | −0.000645 | 0.115562 |
2 | 9.9973 | −0.000215 | 0.000004 | 0.000132 | −0.005840 | 0.000416 | −0.024200 | 0.000011 | 0.000620 |
Table IV
Lens parameters of three Tessar systems. (1) Initial system, parameters chosen arbitrarily. (2) Partially corrected system, obtained from 1 by minimization of third-order aberrations. (3) Final system, obtained from 2 by correction of residual aberrations (see also, Figs. 1 and 2).
1. | 2. | 3. |
---|
c | t | nd | Δn | c | t | nd | Δn | c | t | nd | Δn |
---|
0.350000 | | | | 0.237457 | | | | 0.212310 | | | |
| 0.400 | 1.6185 | 0.01021 | | 0.400 | 1.6130 | 0.01029 | | 0.400 | 1.6316 | 0.01138 |
0.000000 | | | | −0.075772 | | | | −0.048186 | | | |
| 0.850 | | | | 0.850 | | | | 0.840 | | |
−0.101500 | | | | −0.367362 | | | | −0.229449 | | | |
| 0.150 | 1.5647 | 0.01011 | | 0.150 | 1.5565 | 0.00826 | | 0.150 | 1.5746 | 0.01405 |
0.582000 | | | | 0.332777 | | | | 0.237035 | | | |
| 0.800 | | | | 0.800 | | | | 1.239 | | |
−0.153300 | | | | −0.073088 | | | | 0.016667 | | | |
| 0.150 | 1.4967 | 0.00743 | | 0.150 | 1.4917 | 0.00746 | | 0.150 | 1.5425 | 0.00882 |
0.260000 | | | | 0.300462 | | | | 0.090256 | | | |
| 0.320 | 1.6031 | 0.01587 | | 0.320 | 1.5973 | 0.00987 | | 0.320 | 1.6091 | 0.01032 |
−0.320000 | | | | −0.401930 | | | | −0.260565 | | | |
Stop position 0.300 after c4f=19.6038 | Stop position 0.239 after c4f=9.9973 | Stop position 0.389 after c4f=10.0130 |