Table I
Values of QD(K) Computed Using Eq. (19) Between K = 0.5–5.0 for the Eight Apodization Functions Dg(x) Shown in Fig. 1. QD(K)
K | BOXCAR | TRAPEZOIDAL | TRIANGULAR | TRIANGULAR2 | BESSEL | COS | SINC2 | GAUSSIAN |
---|
0.5 | .896 | .948 | .981 | 1.010 | .977 | .981 | .989 | 1.000 |
0.6 | .855 | .914 | .945 | .977 | .943 | .948 | .956 | .967 |
0.7 | .810 | .874 | .900 | .932 | .901 | .906 | .914 | .925 |
0.8 | .762 | .829 | .848 | .876 | .852 | .857 | .865 | .873 |
0.9 | .711 | .781 | .789 | .811 | .798 | .802 | .809 | .814 |
1.0 | .660 | .729 | .727 | .741 | .740 | .743 | .749 | .750 |
1.1 | .609 | .677 | .663 | .667 | .680 | .682 | .685 | .682 |
1.2 | .559 | .624 | .598 | .593 | .618 | .619 | .621 | .612 |
1.3 | .511 | .571 | .534 | .519 | .558 | .557 | .557 | .542 |
1.4 | .464 | .519 | .473 | .449 | .499 | .497 | .494 | .474 |
1.5 | .420 | .469 | .416 | .384 | .443 | .440 | .435 | .410 |
1.6 | .379 | .422 | .363 | .325 | .390 | .386 | .379 | .351 |
1.7 | .340 | .377 | .314 | .272 | .342 | .336 | .328 | .297 |
1.8 | .304 | .336 | .270 | .225 | .297 | .291 | .281 | .249 |
1.9 | .271 | .297 | .231 | .185 | .257 | .250 | .239 | .207 |
2.0 | .241 | .262 | .197 | .150 | .220 | .213 | .202 | .170 |
2.1 | .214 | .230 | .166 | .122 | .188 | .181 | .170 | .139 |
2.2 | .189 | .201 | .140 | .0978 | .160 | .153 | .142 | .113 |
2.3 | .167 | .175 | .118 | .0781 | .135 | .128 | .117 | .0910 |
2.4 | .147 | .152 | .0984 | .0620 | .114 | .107 | .0969 | .0730 |
2.5 | .129 | .131 | .0819 | .0489 | .0957 | .0891 | .0794 | .0582 |
2.6 | .113 | .113 | .0680 | .0384 | .0799 | .0739 | .0648 | .0461 |
2.7 | .0986 | .0974 | .0562 | .0301 | .0665 | .0609 | .0527 | .0364 |
2.8 | .0861 | .0835 | .0464 | .0234 | .0552 | .0501 | .0426 | .0286 |
2.9 | .0750 | .0714 | .0381 | .0182 | .0456 | .0410 | .0344 | .0224 |
3.0 | .0653 | .0608 | .0313 | .0140 | .0376 | .0334 | .0276 | .0175 |
3.1 | .0567 | .0517 | .0256 | .0108 | .0309 | .0272 | .0220 | .0136 |
3.2 | .0491 | .0438 | .0209 | .00829 | .0253 | .0221 | .0176 | .0106 |
3.3 | .0426 | .0371 | .0170 | .00634 | .0207 | .0179 | .0139 | .00816 |
3.4 | .0368 | .0313 | .0138 | .00483 | .0169 | .0144 | .0111 | .00630 |
3.5 | .0318 | .0264 | .0112 | .00368 | .0137 | .0116 | .00872 | .00485 |
3.6 | .0275 | .0222 | .00907 | .00279 | .0111 | .00929 | .00686 | .00372 |
3.7 | .0237 | .0186 | .00734 | .00211 | .00900 | .00744 | .00539 | .00285 |
3.8 | .0204 | .0156 | .00592 | .00159 | .00727 | .00594 | .00422 | .00218 |
3.9 | .0175 | .0131 | .00477 | .00120 | .00586 | .00473 | .00329 | .00167 |
4.0 | .0151 | .0109 | .00384 | .000903 | .00471 | .00376 | .00257 | .00127 |
4.1 | .0129 | .00910 | .00308 | .000677 | .00378 | .00299 | .00199 | .000970 |
4.2 | .0111 | .00757 | .00247 | .000507 | .00303 | .00237 | .00155 | .000737 |
4.3 | .00950 | .00630 | .00198 | .000379 | .00243 | .00187 | .00120 | .000560 |
4.4 | .00813 | .00523 | .00159 | .000283 | .00194 | .00148 | .000925 | .000424 |
4.5 | .00696 | .00434 | .00127 | .000211 | .00155 | .00116 | .000714 | .000321 |
4.6 | .00595 | .00360 | .00101 | .000157 | .00123 | .000918 | .000549 | .000243 |
4.7 | .00508 | .00298 | .000806 | .000116 | .000981 | .000721 | .000422 | .000184 |
4.8 | .00434 | .00246 | .000643 | .0000863 | .000779 | .000566 | .000324 | .000139 |
4.9 | .00370 | .00203 | .000511 | .0000639 | .000618 | .000443 | .000248 | .000105 |
5.0 | .00316 | .00168 | .000406 | .0000472 | .000490 | .000347 | .000190 | .0000789 |
Table II
Values of Q0(K,5) Computed Using Eq. (22) Between K = 0.5–5.0 for the Eight Apodizatlon Functions Dg(x) Shown in Fig. 1. Qo(K,5)
K | BOXCAR | TRAPEZOIDAL | TRIANGULAR | TRIANGULAR2 | BESSEL | COS | SINC2 | GAUSSIAN |
---|
0.5 | 1.74 | 1.92 | 2.04 | 2.11 | 2.02 | 2.04 | 2.05 | 2.08 |
0.6 | 1.68 | 1.88 | 2.01 | 2.08 | 1.99 | 2.00 | 2.02 | 2.05 |
0.7 | 1.59 | 1.80 | 1.93 | 2.01 | 1.91 | 1.93 | 1.95 | 1.98 |
0.8 | 1.49 | 1.70 | 1.82 | 1.90 | 1.81 | 1.82 | 1.85 | 1.87 |
0.9 | 1.37 | 1.59 | 1.69 | 1.76 | 1.68 | 1.70 | 1.72 | 1.74 |
1.0 | 1.26 | 1.46 | 1.54 | 1.60 | 1.55 | 1.56 | 1.58 | 1.59 |
1.1 | 1.14 | 1.33 | 1.39 | 1.43 | 1.40 | 1.41 | 1.43 | 1.43 |
1.2 | 1.02 | 1.21 | 1.24 | 1.26 | 1.26 | 1.27 | 1.28 | 1.27 |
1.3 | .917 | 1.09 | 1.10 | 1.09 | 1.12 | 1.13 | 1.13 | 1.11 |
1.4 | .816 | .968 | .957 | .935 | .986 | .989 | .990 | .962 |
1.5 | .723 | .859 | .830 | .790 | .862 | .861 | .858 | .820 |
1.6 | .638 | .757 | .713 | .661 | .747 | .744 | .737 | .692 |
1.7 | .560 | .663 | .609 | .546 | .643 | .637 | .627 | .578 |
1.8 | .491 | .578 | .516 | .447 | .549 | .542 | .529 | .477 |
1.9 | .428 | .502 | .435 | .363 | .467 | .458 | .443 | .390 |
2.0 | .373 | .434 | .365 | .292 | .394 | .385 | .369 | .317 |
2.1 | .324 | .373 | .305 | .233 | .331 | .322 | .305 | .255 |
2.2 | .281 | .320 | .253 | .185 | .277 | .267 | .250 | .204 |
2.3 | .243 | .274 | .209 | .146 | .231 | .221 | .204 | .162 |
2.4 | .210 | .233 | .173 | .114 | .191 | .182 | .166 | .128 |
2.5 | .181 | .198 | .142 | .0893 | .158 | .149 | .134 | .100 |
2.0 | .155 | .168 | .116 | .0694 | .130 | .122 | .108 | .0786 |
2.7 | .133 | .142 | .0947 | .0536 | .107 | .0988 | .0866 | .0612 |
2.8 | .115 | .120 | .0772 | .0413 | .0872 | .0801 | .0691 | .0475 |
2.9 | .0981 | .101 | .0626 | .0317 | .0711 | .0646 | .0549 | .0367 |
3.0 | .0840 | .0843 | .0508 | .0242 | .0578 | .0520 | .0435 | .0283 |
3.1 | .0718 | .0706 | .0410 | .0184 | .0468 | .0418 | .0343 | .0217 |
3.2 | .0613 | .0590 | .0331 | .0140 | .0379 | .0334 | .0270 | .0166 |
3.3 | .0523 | .0492 | .0267 | .0106 | .0306 | .0267 | .0212 | .0127 |
3.4 | .0446 | .0409 | .0214 | .00800 | .0246 | .0213 | .0166 | .00969 |
3.5 | .0380 | .0340 | .0172 | .00603 | .0198 | .0169 | .0129 | .00737 |
3.0 | .0323 | .0282 | .0138 | .00453 | .0158 | .0134 | .0100 | .00560 |
3.7 | .0275 | .0234 | .0110 | .00340 | .0127 | .0106 | .00779 | .00424 |
3.8 | .0233 | .0194 | .00878 | .00254 | .0101 | .00836 | .00603 | .00321 |
3.9 | .0198 | .0160 | .00701 | .00190 | .00805 | .00659 | .00465 | .00242 |
4.0 | .0168 | .0132 | .00558 | .00141 | .00640 | .00518 | .00359 | .00183 |
4.1 | .0143 | .0109 | .00444 | .00105 | .00508 | .00407 | .00276 | .00138 |
4.2 | .0121 | .00894 | .00352 | .000779 | .00403 | .00319 | .00212 | .00104 |
4.3 | .0102 | .00735 | .00280 | .000577 | .00319 | .00250 | .00162 | .000780 |
4.4 | .00866 | .00604 | .00222 | .000427 | .00252 | .00195 | .00124 | .000585 |
4.5 | .00734 | .00496 | .00176 | .000315 | .00199 | .00152 | .000947 | .000439 |
4.6 | .00620 | .00406 | .00139 | .000232 | .00157 | .00119 | .000721 | .000329 |
4.7 | .00524 | .00333 | .00110 | .000171 | .00124 | .000923 | .000549 | .000246 |
4.8 | .00443 | .00272 | .000867 | .000126 | .000974 | .000717 | .000418 | .000184 |
4.9 | .00374 | .00222 | .000684 | .0000924 | .000766 | .000556 | .000317 | .000138 |
5.0 | .00316 | .00182 | .000539 | .0000677 | .000601 | .000431 | .000240 | .000103 |
Table III
Observed and Calculated Values of Q0(K,20) with K = 1, 2, 3, 4, and 5 for All Eight Apodlzatlon Functions Dg(x) Shown In Fig. 1. A, Boxcar; B, Trapezoidal; C, Triangular; D, Triangular2; E, Bessel; F, Cos; G, sinc2; and H, Gaussian. Qo(K,20)
K | | A | B | C | D | E | F | G | H |
---|
1 | calc. | 2.52 | 2.92 | 3.08 | 3.20 | 3.10 | 3.12 | 3.16 | 3.18 |
1 | obs. | 2.41 | 2.77 | 3.04 | 3.09 | 2.94 | 3.02 | 3.10 | 3.18 |
2 | calc. | 0.746 | 0.868 | 0.730 | 0.584 | 0.788 | 0.770 | 0.738 | 0.634 |
2 | obs. | 0.705 | 0.813 | 0.800 | 0.537 | 0.745 | 0.757 | 0.695 | 0.690 |
3 | calc. | 0.168 | 0.169 | 0.102 | 0.0484 | 0.116 | 0.104 | 0.0870 | 0.0566 |
3 | obs. | 0.167 | 0.170 | 0.107 | 0.0485 | 0.119 | 0.107 | 0.0896 | 0.0619 |
4 | calc. | 0.0336 | 0.0264 | 0.0112 | 0.00282 | 0.0128 | 0.0104 | 0.00718 | 0.00366 |
4 | obs. | 0.0356 | 0.0293 | 0.0109 | 0.00258 | 0.0126 | 0.0108 | 0.00771 | 0.00406 |
5 | calc. | 0.00632 | 0.00364 | 0.00108 | 0.000135 | 0.00120 | 0.000862 | 0.000480 | 0.000206 |
5 | obs. | 0.00688 | 0.00386 | 0.00104 | 0.000143 | 0.00127 | 0.000859 | 0.000495 | 0.000210 |