Multiple annular circular aperture: maxima and minima of the diffraction pattern

Claudio Rivolta

doi:10.1364/AO.26.003119

Applied Optics
Vol. 26,
Issue 15,
pp. 3119-3122
(1987)
•https://doi.org/10.1364/AO.26.003119

Multiple annular circular aperture: maxima and minima of the diffraction pattern

Claudio Rivolta

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Claudio Rivolta, "Multiple annular circular aperture: maxima and minima of the diffraction pattern," Appl. Opt. 26, 3119-3122 (1987)

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Abstract

The radii of the first three minima (zeros) and secondary maxima of the diffraction pattern produced by a circular aperture divided into alternating opaque and transparent annular zones are calculated for some numbers of these zones. The intensities in the first five secondary maxima are also given.

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No. of annular zones	Z

	Zeros			Maxima

	First	Second	Third	First	Second	Third
2	3.1444	7.1832	10.9646	4.8226	8.6723	11.8724
4	3.4285	6.2852	9.1477	4.6647	7.7009	11.2876
8	3.6127	6.6150	9.5939	4.8597	7.9675	11.0049
10	3.6534	6.6894	9.7009	4.9082	8.0455	11.1089
20	3.7394	6.8465	9.9283	5.0149	8.2194	11.3468
40	3.7847	6.9295	10.0486	5.0734	8.3152	11.4790
80	3.8080	6.9721	10.1105	5.1040	8.3654	11.5483
100	3.8127	6.9808	10.1230	5.1103	8.3757	11.5625
200	3.8221	6.9981	10.1481	5.1228	8.3963	11.5910

No. of annular zones	Z

	Zeros			Maxima

	First	Second	Third	First	Second	Third
0	3.8317	7.0156	10.1734	5.1356	8.4172	11.6198
4	4.4296	8.1465	13.9034	6.1133	10.7842	16.0259
8	4.0965	7.5013	10.8804	5.5165	9.0466	12.5012
10	4.0390	7.3956	10.7254	5.4291	8.9000	12.2903
20	3.9312	7.1979	10.4378	5.2725	8.6417	11.9299
40	4.0169	7.4118	10.4710	5.2019	8.5258	11.7698
80	3.8559	7.0598	10.2376	5.1682	8.4707	11.6936
100	3.8510	7.0509	10.2247	5.1616	8.4599	11.6787
200	3.8413	7.0332	10.1990	5.1485	8.4384	11.6491

No. of annular zones	Z

	Zeros			Maxima

	First	Second	Third	First	Second	Third
2	2.8034	6.4334	10.0797	4.4227	8.0888	11.7034
4	3.1989	7.4390	9.7311	4.8064	8.3675	10.3999
8	3.4725	7.5302	9.0459	4.9783	8.2443	11.0632
10	3.5362	7.4393	9.1839	5.0102	8.2578	11.2125
20	3.6751	7.2274	9.6034	5.0727	8.3206	11.4570
40	3.7509	7.1199	9.8712	5.1039	8.3662	11.5453
80	3.7907	7.0672	10.0182	5.1197	8.3912	11.5834
100	3.7988	7.0568	10.0486	5.1228	8.3964	11.5908
200	3.8151	7.0361	10.1104	5.1292	8.4067	11.6053

No. of annular zones	Z

	Zeros			Maxima

	First	Second	Third	First	Second	Third
0	3.8317	7.0156	10.1734	5.1356	8.4172	11.6198
4	5.0570	6.3311	10.2762	5.6496	8.4665	12.5189
8	4.3311	6.5704	11.1880	5.3228	8.6033	12.3695
10	4.2160	6.6479	11.2455	5.2790	8.5898	12.1296
20	4.0102	6.8209	10.8440	5.2026	8.5194	11.7963
40	3.9179	6.9157	10.5045	5.1683	8.4699	11.6969
80	3.8741	6.9650	10.3361	5.1518	8.4436	11.6568
100	3.8655	6.9750	10.3030	5.1485	8.4384	11.6493
200	3.8485	6.9952	10.2377	5.1421	8.4278	11.6344

No. of annular zones	Intensities

	Axis	Secondary maxima

		First	Second	Third	Fourth	Fifth
2	563	54.189	6.989	0.209	0.483	1.226
4	391	9.757	4.862	14.657	3.351	0.083
8	316	6.078	1.703	0.846	0.600	0.586
10	303	5.624	1.485	0.670	0.408	0.309
20	276	4.899	1.196	0.479	0.245	0.147
40	263	4.614	1.104	0.429	0.212	0.121
80	256	4.489	1.068	0.412	0.201	0.113
100	255	4.465	1.062	0.409	0.200	0.112
200	252	4.419	1.050	0.404	0.197	0.110

No. of annular zones	Intensities

	Axis	Secondary maxima

		First	Second	Third	Fourth	Fifth
0	1000	17.498	4.158	1.601	0.779	0.437
4	141	4.634	7.537	1.420	0.035	0.067
8	191	3.779	1.114	0.605	0.502	0.675
10	203	3.817	1.033	0.485	0.313	0.261
20	226	4.017	0.983	0.395	0.204	0.123
40	238	4.176	0.999	0.389	0.192	0.109
80	244	4.270	1.016	0.392	0.192	0.108
100	245	4.290	1.021	0.393	0.192	0.108
200	247	4.331	1.029	0.396	0.193	0.108

No. of annular zones	Intensities

	Axis	Secondary maxima

		First	Second	Third	Fourth	Fifth
2	250	35.162	13.726	5.153	1.449	0.197
4	250	18.117	0.286	0.026	3.293	4.786
8	250	10.313	0.093	1.324	0.586	0.062
10	250	8.941	0.156	1.381	0.191	0.001
20	250	6.460	0.446	1.013	0.031	0.272
40	250	5.365	0.702	0.696	0.071	0.253
80	250	4.856	0.860	0.540	0.121	0.183
100	250	4.758	0.895	0.511	0.134	0.168
200	250	4.564	0.965	0.454	0.162	0.137

No. of annular zones	Intensities

	Axis	Secondary maxima

		First	Second	Third	Fourth	Fifth
0	1000	17.498	4.158	1.601	0.779	0.437
4	250	0.082	2.270	4.566	3.112	1.093
8	250	1.068	3.125	0.153	0.014	1.049
10	250	1.514	2.799	0.051	0.199	0.682
20	250	2.723	1.909	0.077	0.508	0.033
40	250	3.493	1.450	0.189	0.384	0.027
80	250	3.920	1.237	0.282	0.287	0.055
100	250	4.009	1.196	0.304	0.268	0.064
200	250	4.189	1.116	0.345	0.230	0.084

No. of annular zones	Intensities

	Axis	Secondary maxima

		First	Second	Third	Fourth	Fifth
0	1000	17.498	4.158	1.601	0.779	0.437
4	141	4.634	7.537	1.420	0.035	0.067
8	191	3.779	1.114	0.605	0.502	0.675
10	203	3.817	1.033	0.485	0.313	0.261
20	226	4.017	0.983	0.395	0.204	0.123
40	238	4.176	0.999	0.389	0.192	0.109
80	244	4.270	1.016	0.392	0.192	0.108
100	245	4.290	1.021	0.393	0.192	0.108
200	247	4.331	1.029	0.396	0.193	0.108

Abstract

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Figures (1)

Tables (8)

Equations (13)

Applied Optics