Table I
Telescope First-Order Properties
M | R | S | T | J |
---|
1.5 | 0.440 | −1.800 | 0.560 | 0.405 |
2.0 | 0.533 | −0.934 | 0.467 | −0.071 |
2.5 | 0.600 | −0.667 | 0.400 | −0.500 |
3.0 | 0.650 | −0.525 | 0.350 | −0.905 |
3.5 | 0.689 | −0.436 | 0.311 | −1.296 |
4.0 | 0.720 | −0.373 | 0.280 | −0.679 |
4.5 | 0.746 | −0.327 | 0.255 | −2.056 |
5.0 | 0.767 | −0.292 | 0.233 | −2.429 |
6.0 | 0.800 | −0.240 | 0.200 | −3.167 |
7.0 | 0.825 | −0.204 | 0.175 | −3.898 |
8.0 | 0.844 | −0.178 | 0.156 | −4.623 |
−1.5 | 3.800 | 1.680 | −2.800 | 1.595 |
−2.0 | 2.400 | 0.933 | −1.400 | 2.071 |
−2.5 | 1.933 | 0.667 | −0.933 | 2.500 |
−3.0 | 1.700 | 0.525 | −0.700 | 2.905 |
−3.5 | 1.560 | 0.436 | −0.560 | 3.296 |
−4.0 | 1.467 | 0.373 | −0.467 | 3.678 |
−4.5 | 1.400 | 0.327 | −0.400 | 4.056 |
−5.0 | 1.350 | 0.292 | −0.350 | 4.429 |
−6.0 | 1.280 | 0.240 | −0.280 | 5.167 |
−7.0 | 1.233 | 0.204 | −0.233 | 5.899 |
−8.0 | 1.200 | 0.178 | −0.200 | 6.625 |
Back vertex ratio fixed at
E = 0.4.
Table II
Third-Order Aberration Summations for an f/10 Two-Lens Cassegrainian Telescope Design with all Spherical Surfaces
Aberration | Summation thin lens: [Eqs. (4), (5), and (6)] | Exact summations |
---|
| 0.0033 | 0.0083 |
| −0.0958 | −0.0938 |
8fpΣC | 0.2460 | 0.2323 |
ΣJ | −1.0289 | −1.0288 |
This design has an rms geometric spot diameter of 6 μm with C, D, and F light (6563 Å, 5893 Å, and 4861 Å) on axis and 32 μm at ϕ at = ½°. The growth in spot size is dominated by third-order coma. The first-order properties are slightly different from those predicted by Sec. II due to the correctors having thickness and a very slight total power. The exact aberration contribution is taken to be the values obtained |
Configuration data: | y1 = 15.88 cm | t1 = 1.91 cm | T = 0.332 | Q1 = Q2 = 0.2728 |
| fo = 319.80 cm | t1−2 = 0.32 cm (air) | E = 0.359 | L1 = 2.2689 |
| fp = 103.11 cm | t2 = 1.02 cm | D = 0.688 | |
| N = 1.517 (BK-7) | R = 0.6655 | M = 3.094 | |
| | S = −0.4929 | | |
Table III
Aplanatic and Anastigmatic Two-Lens Designs with Matching Curvatures on the Correctors
Aplanats (R/D = 0.95) | Anastigmats |
---|
M | L1 | Q1 | 8fpΣC | D | L1 | Q1 | D* | L1* | Q1* |
---|
1.5 | 4.458 | 1.662 | 1.848 | 3.654 | −1.923 | −0.133 | 1.731 | 1.922 | 0.133 |
2.0 | 3.509 | 0.799 | 1.372 | 2.752 | −0.872 | −0.012 | 1.880 | 0.872 | 0.012 |
2.5 | 2.610 | 0.367 | 0.897 | 2.029 | −0.185 | −0.000 | 1.844 | 0.185 | 0.000 |
3.0 | 2.024 | 0.189 | 0.469 | 2.168 | −0.944 | −0.019 | 1.224 | 0.944 | 0.019 |
3.5 | 1.637 | 0.108 | 0.066 | 2.296 | −1.505 | −0.084 | 0.791 | 1.505 | 0.084 |
4.0 | 1.368 | 0.067 | −0.324 | 2.416 | −1.949 | −0.194 | 0.467 | 1.949 | 0.194 |
4.5 | 1.171 | 0.044 | −0.704 | 2.528 | −2.316 | −0.341 | | | |
5.0 | 1.021 | 0.030 | −1.078 | 2.634 | −2.634 | −0.520 | | | |
6.0 | 0.807 | 0.016 | −1.814 | 2.830 | −3.168 | −0.958 | | | |
7.0 | 0.662 | 0.009 | −2.542 | 3.008 | −3.617 | −1.482 | | | |
8.0 | 0.557 | 0.006 | −3.266 | 3.173 | −4.002 | −2.081 | | | |
−1.5 | −5.902 | −12.162 | 15.875 | | | | | | |
−2.0 | −3.217 | −1.977 | 7.344 | | | | | | |
−2.5 | −2.310 | −1.055 | 5.880 | | | | | | |
−3.0 | −1.841 | −0.344 | 5.561 | | | | | | |
−3.5 | −1.549 | −0.198 | 5.591 | | | | | | |
−4.0 | −1.346 | −0.126 | 5.765 | | | | | | |
−4.5 | −1.197 | −0.087 | 6.008 | | | | | | |
−5.0 | −1.082 | −0.064 | 5.259 | | | | | | |
−6.0 | −0.914 | −0.036 | 7.690 | | | | | | |
−7.0 | −0.796 | −0.024 | 7.575 | | | | | | |
−8.0 | −0.710 | −0.016 | 8.257 | | | | | | |
Common configuration data:
E = 0.4,
Q1 =
Q2,
N = 1.517.
Table IV
Aplanatic Two-Lens Design with Q1= 1 and a Common Curvature on the Second Corrector Element and the Secondary Mirror
M | L1 | Q2 | D | 8fp ΣC | R = D |
---|
|
---|
| 8fpΣC |
---|
1.5 | 6.202 | 0.854 | 1.338 | 0.438 | 0.432 | 2.378 |
2.0 | 9.771 | 6.412 | 1.267 | 0.433 | 0.348 | 1.791 |
2.5 | 13.416 | 11.404 | 1.101 | 0.365 | 0.266 | 1.260 |
3.0 | 17.432 | 18.166 | 1.004 | 0.150 | 0.207 | 0.780 |
3.5 | 22.006 | 22.671 | 0.954 | −0.139 | 0.168 | 0.335 |
4.0 | 27.108 | 38.543 | 0.928 | −0.460 | 0.140 | −0.087 |
4.5 | 32.843 | 52.894 | 0.915 | −0.799 | 0.119 | −0.493 |
5.0 | 39.179 | 70.464 | 0.909 | −1.146 | 0.104 | −0.887 |
6.0 | 53.642 | 116.554 | 0.905 | −1.851 | 0.082 | −1.655 |
7.0 | 70.500 | 179.494 | 0.910 | −2.563 | 0.068 | −2.406 |
8.0 | 89.788 | 262.082 | 0.915 | −3.277 | 0.058 | −3.146 |
−4.0 | 9.396 | −12.012 | 1.474 | 5.646 | 0.009 | 5.661 |
−4.5 | 14.223 | −21.466 | 1.376 | 5.869 | −0.031 | 5.815 |
−5.0 | 19.365 | −33.322 | 1.316 | 6.177 | −0.043 | 6.083 |
−6.0 | 31.125 | −66.048 | 1.242 | 6.808 | −0.046 | 6.395 |
−7.0 | 45.085 | −113.148 | 1.196 | 7.490 | −0.044 | 7.409 |
−8.0 | 61.343 | −177.372 | 1.165 | 8.187 | −0.041 | 8.111 |
Common configuration data:
E = 0.4;
N = 1.517;
Q1 = 1;
Q2 = 1 − {[
L1(
N − 1)]/
S}.
Table V
Third-Order Aberration Summations for an f/8 Maksutov Cassegrainian Telescope Design with all Spherical Surfaces
Aberration | Corrector contribution Eqs. (9), (10), and (11) | Exact corrector contribution | Mirror contribution Eqs. (1), (2), and (3) | Exact mirror contribution | Summation thick lens | Exact summations |
---|
| −0.556 | −0.554 | 0.569 | 0.601 | 0.013 | 0.047 |
| −1.027 | −0.994 | 1.101 | 1.103 | 0.074 | 0.108 |
8fpΣC | −1.830 | −1.721 | 2.126 | 2.017 | 0.296 | 0.297 |
ΣJ | — | 0.029 | −0.549 | −0.549 | −0.549 | −0.520 |
This design is essentially diffraction limited (with C, D, and F light) over a semifield of 1°. The residual third-order spherical aberration summation is balanced by the fifth-order term. To a degree, this is also true for the residual third-order coma. As the corrector has some power, the first order parameters depart slightly from values predicted by the equations of Sec. II. |
Configuration data: | fo = 222.84 cm | y1 = 13.97 cm | fp = 91.63 cm | N = 1.517 (BK-7) | t = 2.88 cm |
| H = 31.8402 | R = 0.6304 | S = −0.6457 | D = 1.0574 | |
| T = 0.370 | E = 0.339 | M = 2.3386 | Q = 51.7027 | |
Table VI
Aplanatic Maksutov Designs
M | Q | D | 8fpΣC | Q′ | D′ | (8fpΣC′) |
---|
1.5 | 57.5 | 1.889 | −0.383 | −57.0 | 3.526. | −0.384 |
2.0 | 57.6 | 1.501 | −0.023 | −57.2 | 3.161 | −0.022 |
2.5 | 56.2 | 1.154 | 0.059 | −55.7 | 2.749 | 0.058 |
3.0 | 54.8 | 0.934 | −0.064 | −54.3 | 2.491 | −0.063 |
3.5 | 53.7 | 0.795 | −0.289 | −53.2 | 2.303 | −0.305 |
4.0 | 52.9 | 0.703 | −0.565 | −52.4 | 2.212 | −0.565 |
4.5 | 52.3 | 0.642 | −0.836 | −51.8 | 2.132 | −0.869 |
5.0 | 51.6 | 0.586 | −1.185 | −51.2 | 2.076 | −1.186 |
6.0 | 51.1 | 0.536 | −1.865 | −50.7 | 1.986 | −1.865 |
7.0 | 50.6 | 0.495 | −2.551 | −50.2 | 1.934 | −2.553 |
8.0 | 50.3 | 0.472 | −3.253 | −49.8 | 1.898 | −3.250 |
−1.5 | | | | −42.7 | 1.679 | 2.758 |
−2.0 | | | | −42.7 | 1.546 | 3.508 |
−2.5 | | | | −43.1 | 1.513 | 4.026 |
−3.0 | | | | −43.5 | 1.510 | 4.466 |
−3.5 | | | | −43.9 | 1.514 | 4.874 |
−4.0 | | | | −44.2 | 1.521 | 5.065 |
−4.5 | | | | −44.5 | 1.529 | 5.642 |
−5.0 | | | | −44.7 | 1.538 | 6.017 |
−6.0 | | | | −45.1 | 1.555 | 6.755 |
−7.0 | | | | −45.4 | 1.566 | 7.479 |
−8.0 | | | | −45.6 | 1.579 | 8.204 |
Common configuration data:
E = 0.4,
N = 1.517,
H = 35.
Table VII
Maksutov Designs with an Aluminized Spot Secondary Mirror
E | M | R | T |
| 8fpΣC |
---|
0.6 | 7.791 | 0.818 | 0.182 | −0.275 | −3.299 |
0.4 | 6.851 | 0.822 | 0.178 | −0.254 | −3.118 |
0.2 | 5.916 | 0.827 | 0.174 | −0.226 | −2.883 |
0 | 4.989 | 0.833 | 0.167 | −0.187 | −2.569 |
−0.2 | 4.076 | 0.842 | 0.158 | −0.129 | −2.134 |
0.6 | −8.995 | 1.200 | −0.200 | −1.121 | 4.858 |
0.4 | −7.900 | 1.203 | −0.203 | −1.137 | 5.013 |
0.2 | −6.810 | 1.207 | −0.207 | −1.157 | 5.222 |
0 | −5.727 | 1.212 | −0.212 | −1.182 | 5.521 |
−0.2 | −4.657 | 1.219 | −0.219 | −1.216 | 5.976 |
Common configuration data: | H = 35 | R = D | N = 1.517 |
For Cassegrainians: | Q = 50.700 | S = −0.209 | J = −3.789 |
For Gregorians: | Q = −45.900 | S = 0.180 | J = 6.552 |