Table I
Sampled values of point spread function t(υ) for slit aperture having W2 = 0.5λ.
±n | t(±nπ/2) |
---|
0 | 0.394741 |
1 | 0.270989 |
2 | 0.239151 |
3 | 0.139601 |
4 | 0.049520 |
5 | 0.043538 |
6 | 0.009624 |
7 | 0.015731 |
8 | 0.002511 |
9 | 0.007532 |
10 | 0.000888 |
11 | 0.004408 |
12 | 0.000391 |
13 | 0.002916 |
14 | 0.000199 |
15 | 0.002084 |
16 | 0.000112 |
Table II
Comparison of transfer function of slit aperture having W2 = 0.5λ as computed by exact integration and by sampling method using 33, 27, and 21 sampling points.
ω | Exact | 33 points | 27 points | 21 points |
---|
0 | 1.0 | 0.9866 | 0.9842 | 0.9765 |
0.2 | 0.7200 | 0.7174 | 0.7174 | 0.7236 |
0.4 | 0.3600 | 0.3593 | 0.3617 | 0.3589 |
0.6 | 0.1278 | 0.1285 | 0.1284 | 0.1281 |
0.8 | 0.0249 | 0.0258 | 0.0237 | 0.0250 |
1.0 | 0.0000 | 0.0004 | 0.0001 | 0.0003 |
1.2 | 0.0166 | 0.0158 | 0.0178 | 0.0171 |
1.4 | 0.0548 | 0.0540 | 0.0540 | 0.0540 |
1.6 | 0.0900 | 0.0906 | 0.0888 | 0.0913 |
1.8 | 0.0800 | 0.0824 | 0.0825 | 0.0769 |
2.0 | 0.0000 | 0.0130 | 0.0147 | 0.0217 |
Table III
Comparison of transfer function of perfect circular aperture as computed by exact integration and by sampling method using 10 sampling points.
ω | Sampling | Exact |
---|
0 | 0.9618 | 1.0000 |
0.1 | 0.9368 | 0.9364 |
0.2 | 0.8765 | 0.8729 |
0.3 | 0.8083 | 0.8097 |
0.4 | 0.7459 | 0.7471 |
0.5 | 0.6861 | 0.6850 |
0.6 | 0.6242 | 0.6238 |
0.7 | 0.5628 | 0.5636 |
0.8 | 0.5045 | 0.5046 |
0.9 | 0.4476 | 0.4470 |
1.0 | 0.3909 | 0.3910 |
1.1 | 0.3363 | 0.3368 |
1.2 | 0.2850 | 0.2848 |
1.3 | 0.2355 | 0.2351 |
1.4 | 0.1878 | 0.1881 |
1.5 | 0.1428 | 0.1443 |
1.6 | 0.1046 | 0.1041 |
1.7 | 0.0682 | 0.0681 |
1.8 | 0.0366 | 0.0374 |
1.9 | 0.0140 | 0.0133 |
2.0 | 0.0000 | 0.0000 |
Table IV
Selected values of F(αn,υ0).
υ0 αn | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|
0.5 | 0.20772 | −0.05520 | 0.02778 | −0.01741 | 0.01220 | −0.00916 | 0.00720 | −0.00585 |
1.0 | 0.37023 | −0.07502 | 0.03696 | −0.02300 | 0.01607 | −0.01204 | 0.00945 | −0.00768 |
1.5 | 0.45906 | −0.04178 | 0.02135 | −0.013401 | 0.00940 | −0.00705 | 0.00554 | −0.00451 |
2.0 | 0.47132 | 0.03725 | −0.00822 | 0.00385 | −0.00235 | 0.00164 | −0.00123 | 0.00097 |
2.5 | 0.42704 | 0.13455 | −0.03012 | 0.01574 | −0.01023 | 0.00739 | −0.00568 | 0.00455 |
3.0 | 0.35743 | 0.21712 | −0.02482 | 0.01317 | −0.00860 | 0.00622 | −0.00479 | 0.00384 |
3.5 | 0.29068 | 0.26221 | 0.01358 | −0.02020 | 0.00061 | −0.00023 | 0.00010 | −0.00004 |
4.0 | 0.24235 | 0.26577 | 0.07413 | −0.01754 | 0.00935 | −0.00619 | 0.00454 | −0.00354 |
4.5 | 0.21384 | 0.24035 | 0.13548 | −0.01819 | 0.00972 | −0.00645 | 0.00473 | −0.00369 |
5.0 | 0.19762 | 0.20538 | 0.17757 | 0.00447 | 0.00040 | −0.00067 | 0.00062 | −0.00053 |
5.5 | 0.18486 | 0.17642 | 0.19131 | 0.04664 | −0.01148 | 0.00617 | −0.00411 | 0.00304 |
6.0 | 0.17073 | 0.15930 | 0.18104 | 0.09438 | −0.01442 | 0.00773 | −0.00516 | 0.00382 |
6.5 | 0.15538 | 0.15103 | 0.15946 | 0.13153 | −0.00008 | 0.00162 | −0.00133 | 0.00106 |
7.0 | 0.14146 | 0.14518 | 0.13932 | 0.14827 | 0.03107 | −0.00785 | 0.00422 | −0.00282 |
7.5 | 0.13102 | 0.13724 | 0.12711 | 0.14514 | 0.06960 | −0.01184 | 0.00636 | −0.00427 |
8.0 | 0.12390 | 0.12687 | 0.12200 | 0.13074 | 0.10244 | −0.00260 | −0.00231 | −0.00170 |
8.5 | 0.11832 | 0.11657 | 0.11918 | 0.11550 | 0.12006 | 0.02118 | −0.00988 | 0.00289 |
9.0 | 0.11256 | 0.10876 | 0.11454 | 0.10585 | 0.12098 | 0.05304 | −0.00404 | 0.00532 |
Table V
Comparison of tolal illuminance L(υ0) of perfect circular aperture as computed by exact integration and by sampling method using eight sampling points.
υ0 | Exact | Sampling |
---|
0.5 | 0.0606 | 0.0606 |
1.0 | 0.2208 | 0.2209 |
2.0 | 0.6173 | 0.6172 |
3.0 | 0.8174 | 0.8173 |
4.0 | 0.8379 | 0.8380 |
5.0 | 0.8612 | 0.8612 |
6.0 | 0.9008 | 0.9006 |
7.0 | 0.9099 | 0.9106 |
8.0 | 0.9155 | 0.9155 |
9.0 | 0.9317 | 0.9316 |
Table VI
Selected values of $1(αn,υ0).
υ0 αn | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|
0 | 0.61140 | 0.12117 | 0.14655 | 0.06523 | 0.08075 | 0.04498 | 0.05529 | 0.03443 |
0.5 | 0.55814 | 0.15225 | 0.13297 | 0.07457 | 0.07455 | 0.04984 | 0.05159 | 0.03752 |
1.0 | 0.41869 | 0.22651 | 0.10442 | 0.09469 | 0.06164 | 0.06010 | 0.04390 | 0.04400 |
1.5 | 0.24389 | 0.29835 | 0.08833 | 0.10845 | 0.05414 | 0.06667 | 0.03938 | 0.04805 |
2.0 | 0.09039 | 0.32251 | 0.10662 | 0.10406 | 0.06003 | 0.06376 | 0.04254 | 0.04605 |
3.0 | 0.03539 | 0.18603 | 0.21697 | 0.07301 | 0.08900 | 0.04744 | 0.05769 | 0.03558 |
4.0 | 0.00038 | 0.00247 | 0.22832 | 0.12378 | 0.07564 | 0.06396 | 0.04933 | 0.04467 |
5.0 | 0.01161 | −0.02370 | 0.07809 | 0.20691 | 0.07059 | 0.07855 | 0.04485 | 0.05163 |
6.0 | −0.00711 | 0.01279 | −0.02459 | 0.14955 | 0.14632 | 0.05797 | 0.06748 | 0.03970 |
7.0 | 0.00135 | 0.00244 | −0.00460 | 0.01445 | 0.17956 | 0.08643 | 0.06397 | 0.04917 |
8.0 | 0.00483 | −0.00806 | 0.01254 | −0.02245 | 0.07921 | 0.15908 | 0.05444 | 0.06541 |
Table VII
Comparison of line spread function τ(υ) of perfect circular aperture as computed by exact solution (7.13) and by sampling method (7.5) using eight sampling points.
υ | Exact | Sampling |
---|
0.0 | 0.8488 | 0.8472 |
0.5 | 0.7938 | 0.7921 |
1.0 | 0.6467 | 0.6450 |
2.0 | 0.2674 | 0.2656 |
4.0 | 0.0305 | 0.0287 |
5.0 | 0.0357 | 0.0338 |
6.0 | 0.0162 | 0.0145 |
Table VIII
Selected values of $2(αn,υ0).
υ0 αn | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|
0.5 | 0.5934 | 0.1318 | 0.1419 | 0.0684 | 0.0786 | 0.0467 | 0.0540 | 0.0355 |
1.0 | 1.0872 | 0.3192 | 0.2608 | 0.1529 | 0.1468 | 0.1015 | 0.1018 | 0.0762 |
1.5 | 1.4189 | 0.5840 | 0.3549 | 0.2556 | 0.2037 | 0.1656 | 0.1429 | 0.1227 |
2.0 | 1.5823 | 0.8997 | 0.4492 | 0.3635 | 0.2597 | 0.2316 | 0.1832 | 0.1702 |
2.5 | 1.6196 | 1.2063 | 0.5796 | 0.4590 | 0.3272 | 0.2908 | 0.2298 | 0.2133 |
3.0 | 1.5949 | 1.4420 | 0.7680 | 0.5372 | 0.4104 | 0.3410 | 0.2847 | 0.2507 |
4.0 | 1.5518 | 1.6125 | 1.2466 | 0.7154 | 0.5833 | 0.4463 | 0.3959 | 0.3275 |
5.0 | 1.5743 | 1.5658 | 1.5654 | 1.0579 | 0.7175 | 0.5957 | 0.4846 | 0.4278 |
6.0 | 1.5771 | 1.5591 | 1.5951 | 1.4421 | 0.9258 | 0.7330 | 0.5962 | 0.5193 |
7.0 | 1.5648 | 1.5809 | 1.5546 | 1.6011 | 1.2736 | 0.8629 | 0.7348 | 0.6028 |
8.0 | 1.5713 | 1.5701 | 1.5714 | 1.5719 | 1.5479 | 1.1126 | 0.8460 | 0.7215 |
9.0 | 1.5741 | 1.5654 | 1.5787 | 1.5583 | 1.5956 | 1.4302 | 1.0006 | 0.8405 |
10.0 | 1.5682 | 1.5750 | 1.5650 | 1.5789 | 1.5587 | 1.5912 | 1.2786 | 0.9452 |