Table I
List of Triplet Lens Parameters Designed by Using the Caustic Merit Function Optimization Technique for Design Angles αD and Based on Hopkins Lenses
Lens no. | Radius (cm) | Thickness (cm) | Refractive index |
---|
1 | 3.7185592 | 0.6000 | 1.6200 |
αD = 10° | −80.6451568 | 1.1560 | 1.0000 |
| −4.9522238 | 0.2500 | 1.6203 |
| 4.4008317 | 2.1318 | 1.0000 |
| 14.2797097 | 0.6000 | 1.6200 |
| −4.6503774 | 8.6119 (BFL) | 1.0000 |
2 | 4.4021511 | 0.6000 | 1.6200 |
αD = 20° | −67.1140940 | 1.3190 | 1.0000 |
| −4.1603018 | 0.2500 | 1.6203 |
| 3.5202327 | 1.53302 | 1.0000 |
| 11.8415876 | 0.6000 | 1.6200 |
| −3.8890625 | 9.3039 (BFL) | 1.0000 |
3 | 4.3712078 | 0.6000 | 1.6200 |
αD = 10° | −65.7894737 | 1.4500 | 1.0000 |
| −4.2255058 | 0.2500 | 1.6203 |
| 2.9235227 | 1.95515 | 1.0000 |
| 10.0158003 | 0.6000 | 1.6200 |
| −4.0267046 | 9.3039 (BFL) | 1.0000 |
4 | 4.9904411 | 0.6000 | 1.6200 |
αD = 20° | −56.1797753 | 1.6520 | 1.0000 |
| −3.2445115 | 0.2500 | 1.6203 |
| 2.9934387 | 1.05481 | 1.0000 |
| 8.5463550 | 0.6000 | 1.6200 |
| −3.0514446 | 9.5442 (BFL) | 1.0000 |
5 | 4.3081006 | 0.6000 | 1.6200 |
αD = 20° | −95.2380952 | 1.2100 | 1.0000 |
| −4.5055485 | 0.2500 | 1.6235 |
| 4.0037773 | 1.06721 | 1.0000 |
| 14.5205727 | 0.6000 | 1.6200 |
| −3.8273295 | 8.5335 (BFL) | 1.0000 |
6 | 4.5401636 | 0.6000 | 1.6200 |
αD = 20° | −78.1250000 | 1.3810 | 1.0000 |
| −4.0561937 | 0.2500 | 1.6235 |
| 3.7819860 | 1.05409 | 1.0000 |
| 12.4586980 | 0.6000 | 1.6200 |
| −3.5443282 | 8.7272 (BFL) | 1.0000 |
7 | 4.6419179 | 0.6000 | 1.6200 |
αD = 20° | −69.9300699 | 1.5080 | 1.0000 |
| −3.7606435 | 0.2500 | 1.6235 |
| 3.5304386 | 1.04364 | 1.0000 |
| 11.1395273 | 0.6000 | 1.6200 |
| −3.3381864 | 8.7687 (BFL) | 1.0000 |
10 | 3.8074762 | 0.6000 | 1.6200 |
αD = 10° | −78.1250000 | 1.1390 | 1.0000 |
| −5.4951822 | 0.2500 | 1.62572 |
| 3.5671582 | 1.41681 | 1.0000 |
| 15.0259603 | 0.6000 | 1.6200 |
| −4.4813327 | 7.9781 (BFL) | 1.0000 |
11 | 4.2058967 | 0.6000 | 1.6200 |
αD = 20° | −75.7575757 | 1.3850 | 1.0000 |
| −4.5935646 | 0.2500 | 1.6257 |
| 3.5671582 | 1.31437 | 1.0000 |
| 13.1534785 | 0.6000 | 1.6200 |
| −3.8804637 | 8.3522 (BFL) | 1.0000 |
12 | 4.4702726 | 0.6000 | 1.6200 |
αD = 20° | −71.4285714 | 1.5240 | 1.0000 |
| −4.0518638 | 0.2500 | 1.62572 |
| 3.5323207 | 1.0492 | 1.0000 |
| 12.0192307 | 0.6000 | 1.6200 |
| −3.4435261 | 8.3473 (BFL) | 1.0000 |
13 | 4.1718433 | 0.6000 | 1.6200 |
αD = 10° | −64.1025641 | 1.7090 | 1.7090 |
| −4.0963015 | 0.2500 | 1.62572 |
| 2.5338315 | 2.09763 | 1.0000 |
| 10.4326666 | 0.6000 | 1.6200 |
| −3.7203677 | 9.5331 (BFL) | 1.0000 |
14 | 3.5824435 | 0.6000 | 1.6200 |
αD = 10° | −59.8802395 | 1.3780 | 1.0000 |
| −5.0114498 | 0.2500 | 1.63963 |
| 2.9333628 | 1.93164 | 1.0000 |
| 13.0101184 | 0.6000 | 1.6200 |
| −4.2328767 | 7.7902 (BFL) | 1.0000 |
15 | 4.4134229 | 0.6000 | 1.6900 |
αD = 20° | −158.7301587 | 1.4166 | 1.0000 |
| −4.7001206 | 0.2500 | 1.5500 |
| 3.4023303 | 2.19726 | 1.0000 |
| 14.2259218 | 0.6000 | 1.6200 |
| −4.5072000 | 9.0405 (BFL) | 1.0000 |
16 | 3.6139257 | 0.6000 | 1.6900 |
αD = 10° | −196.0784314 | 1.3460 | 1.0000 |
| −6.2517266 | 0.2500 | 1.6203 |
| 3.1397689 | 4.28623 | 1.0000 |
| 20.6185567 | 0.6000 | 1.6900 |
| −5.808818 | 7.6838 (BFL) | 1.0000 |
Table II
List of Triplet Lens Parameters Designed by Kingslake (Lens No. 1) and by Using the Caustic Merit Function Optimization Technique for Design Angles αD = 0°,10°,20° (Lens Nos. 2, 3, and 4, Respectively)
Lens no. | Radius (cm) | Thickness (cm) | Refractive index |
---|
1 | 4.2987899 | 0.40000 | 1.62031 |
| 24.8077400 | 1.05102 | 1.00000 |
| −3.8210349 | 0.25000 | 1.61644 |
| 4.3958942 | 0.986946 | 1.00000 |
| 65.6663492 | 0.45000 | 1.62031 |
| −3.3507539 | 8.64907 (BFL) | 1.00000 |
2 | 4.2297258 | 0.40000 | 1.62031 |
| −24.8077400 | 1.05102 | 1.00000 |
| −3.8978961 | 0.25000 | 1.61644 |
| 4.3958942 | 1.01462 | 1.00000 |
| 65.6618502 | 0.45000 | 1.62031 |
| −3.4382533 | 8.55375 (BFL) | 1.00000 |
3 | 4.0423412 | 0.40000 | 1.62031 |
| −24.8077400 | 1.05102 | 1.00000 |
| −4.1085224 | 0.25000 | 1.61644 |
| 4.1451298 | 1.45899 | 1.00000 |
| 65.6495892 | 0.45000 | 1.62031 |
| −3.6784207 | 8.60193 (BFL) | 1.00000 |
4 | 4.1933105 | 0.40000 | 1.62031 |
| −24.8257812 | 1.05102 | 1.00000 |
| −3.9364079 | 0.25000 | 1.61644 |
| 4.2928027 | 1.16916 | 1.00000 |
| 65.6595307 | 0.45000 | 1.62031 |
| −3.4817226 | 8.64273 (BFL) | 1.00000 |
Table III
List of Triplet Lens Parameters for the Chang and Stavroudis Initial Lens (No. 1), Chang and Stavroudis Off-Axis Design (No. 2), Kassim Off-Axis Design (No. 3), and Caustic Merit Function Optimization Technique for Design Angle αD = 10° (No. 4)
Lens no. | Radius (mm) | Thickness (mm) | Refractive index |
---|
1 | 37.0999971 | 7.40000 | 1.59015 |
| ∞ | 9.90000 | 1.00000 |
| −55.0000551 | 2.60000 | 1.62377 |
| 36.7000086 | 8.70000 | 1.00000 |
| 126.9999959 | 6.40000 | 1.62176 |
| −43.1999900 | 81.50742 (BFL) | 1.00000 |
2 | 37.10010720 | 7.8611843 | 1.59015 |
| ∞ | 9.6099740 | 1.00000 |
| −55.14989740 | 2.5951660 | 1.62377 |
| 36.63178100 | 8.7028980 | 1.00000 |
| 113.73200190 | 6.6488800 | 1.62176 |
| −44.87995950 | 81.345571 (BFL) | 1.00000 |
3 | 37.39846130 | 7.400000 | 1.59015 |
| ∞ | 8.758728 | 1.00000 |
| −54.87733571 | 2.600000 | 1.62377 |
| 36.66113279 | 9.841272 | 1.00000 |
| 127.0278568 | 6.400000 | 1.62176 |
| −43.1999704 | 85.529954 (BFL) | 1.00000 |
4 | 35.3187794 | 7.40000 | 1.59015 |
| ∞ | 9.90000 | 1.00000 |
| −56.2015660 | 2.60000 | 1.62377 |
| 34.8993776 | 10.03545 | 1.00000 |
| 126.4729693 | 6.40000 | 1.62176 |
| −44.7296933 | 75.85710 (BFL) | 1.00000 |
Table IV
List of Four-Element Lens Parameters of the Initial System (Lens No. 1) and Optimized System for Design Angle αD = 0°, 10°, and 20° (Lens Nos. 2, 3, and 4, Respectively)
Lens no. | Radius (mm) | Thickness (mm) | Refractive index |
---|
1 | 25.01 | 9.71000 | 1.611 |
| 35.00 | 1.95000 | 1.000 |
| 19.90 | 1.05000 | 1.720 |
| 16.53 | 25.28000 | 1.000 |
| −16.53 | 0.99000 | 1.720 |
| −20.00 | 3.20000 | 1.000 |
| −40.07 | 11.00000 | 1.611 |
| −27.30 | 121.33187 (BFL) | 1.000 |
2 | 24.44338 | 9.71000 | 1.611 |
| 35.00000 | 1.95000 | 1.000 |
| 19.18409 | 1.05000 | 1.720 |
| 15.66244 | 24.71954 | 1.000 |
| −17.36309 | 0.99000 | 1.720 |
| −20.69278 | 7.12800 | 1.000 |
| −40.41931 | 9.65906 | 1.611 |
| −27.30000 | 114.67815 (BFL) | 1.000 |
3 | 24.67972 | 9.71000 | 1.611 |
| 34.76399 | 1.95000 | 1.000 |
| 19.48490 | 1.05000 | 1.720 |
| 16.03028 | 25.28000 | 1.000 |
| −17.02972 | 0.99000 | 1.720 |
| −20.41302 | 3.87703 | 1.000 |
| −40.27615 | 11.00000 | 1.611 |
| −27.60258 | 120.67039 (BFL) | 1.000 |
4 | 24.76146 | 9.7100 | 1.611 |
| 34.82269 | 1.9500 | 1.000 |
| 19.58704 | 1.0500 | 1.720 |
| 16.15233 | 25.2800 | 1.000 |
| −16.90200 | 0.9900 | 1.720 |
| −20.30818 | 3.6882 | 1.000 |
| −40.22441 | 11.0000 | 1.611 |
| −27.52631 | 120.8478(BFL) | 1.000 |