Diffraction Effects in Long Path Interferometers

W. J. Tango; R. Q. Twiss

doi:10.1364/AO.13.001814

Applied Optics
Vol. 13,
Issue 8,
pp. 1814-1819
(1974)
•https://doi.org/10.1364/AO.13.001814

Diffraction Effects in Long Path Interferometers

W. J. Tango and R. Q. Twiss

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W. J. Tango and R. Q. Twiss, "Diffraction Effects in Long Path Interferometers," Appl. Opt. 13, 1814-1819 (1974)

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Abstract

Diffraction caused by finite apertures in long baseline interferometers leads to a significant loss of signal, decreased fringe visibility, and a phase shift in the interference pattern. Formulas are developed for the general case of an interferometer with unequal path lengths for monochromatic plane wave illumination. Numerical results are given for a range of path lengths. The consequences of diffraction on the performance of long path instruments, particularly with reference to a long baseline Michelson stellar interferometer, are discussed.

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$p_{1} / p_{2}$	1.00	1.41	2.00	2.83	4.00	5.66	8.00	11.31	16.00	22.63	32.00	45.26	64.00	90.51	∞
1.00	1.00
1.41	0.98	1.00
2.00	0.92	0.96	1.00
2.83	0.90	0.91	0.95	1.00
4.00	0.89	0.90	0.92	0.95	1.00
5.66	0.89	0.89	0.90	0.93	0.96	1.00
8.00	0.89	0.89	0.89	0.92	0.94	0.96	1.00
11.31	0.89	0.89	0.88	0.91	0.93	0.95	0.97	1.00
16.00	0.89	0.89	0.88	0.91	0.92	0.94	0.95	0.97	1.00
22.63	0.90	0.89	0.88	0.91	0.92	0.93	0.95	0.96	0.98	1.00
32.00	0.89	0.89	0.88	0.91	0.92	0.93	0.94	0.96	0.97	0.98	1.00
45.26	0.90	0.89	0.88	0.91	0.91	0.92	0.94	0.95	0.96	0.97	0.98	1.00
64.00	0.90	0.89	0.87	0.91	0.91	0.93	0.94	0.95	0.96	0.97	0.98	0.99	1.00
90.51	0.90	0.89	0.87	0.90	0.91	0.93	0.94	0.95	0.96	0.96	0.97	0.98	0.99	1.00
∞	0.92	0.90	0.87	0.91	0.91	0.93	0.94	0.94	0.95	0.96	0.97	0.97	0.98	0.98	1.00

$p_{1} / p_{2}$	1.00	1.41	2.00	2.83	4.00	5.66	8.00	11.31	16.00	22.63	32.00	45.26	64.00	90.51	∞
1.00	0.57
1.41	0.62	0.69
2.00	0.58	0.66	0.69
2.83	0.60	0.67	0.69	0.77
4.00	0.61	0.67	0.68	0.74	0.79
5.66	0.62	0.68	0.69	0.74	0.78	0.83
8.00	0.64	0.69	0.69	0.75	0.76	0.81	0.86
11.31	0.64	0.70	0.69	0.75	0.78	0.81	0.84	0.88
16.00	0.66	0.71	0.70	0.76	0.78	0.81	0.84	0.86	0.90
22.63	0.66	0.71	0.71	0.76	0.78	0.81	0.84	0.86	0.89	0.92
32.00	0.67	0.72	0.71	0.77	0.79	0.82	0.84	0.86	0.88	0.90	0.93
45.26	0.68	0.73	0.71	0.77	0.79	0.82	0.85	0.87	0.89	0.90	0.92	0.94
64.00	0.69	0.73	0.72	0.78	0.80	0.83	0.85	0.87	0.89	0.90	0.92	0.93	0.95
90.51	0.69	0.73	0.72	0.78	0.80	0.83	0.85	0.87	0.89	0.90	0.92	0.93	0.94	0.96
∞	0.72	0.76	0.74	0.81	0.82	0.85	0.87	0.89	0.90	0.92	0.93	0.94	0.95	0.96	1.00

$p_{1} / p_{2}$	1.00	1.41	2.00	2.83	4.00	5.66	8.00	11.31	16.00	22.63	32.00	45.26	64.00	90.51	∞
1.00	0.00
1.41	0.27	0.00
2.00	0.42	0.18	0.00
2.83	0.44	0.24	0.12	0.00
4.00	0.50	0.29	0.18	0.11	0.00
5.66	0.54	0.33	0.22	0.16	0.09	0.00
8.00	0.57	0.36	0.26	0.20	0.14	0.08	0.00
11.31	0.59	0.38	0.28	0.22	0.16	0.11	0.06	0.00
16.00	0.61	0.34	0.29	0.24	0.18	0.13	0.08	0.05	0.00
22.63	0.62	0.40	0.30	0.25	0.19	0.14	0.10	0.07	0.04	0.00
32.00	0.63	0.41	0.31	0.26	0.21	0.16	0.11	0.08	0.06	0.03	0.00
45.26	0.63	0.41	0.32	0.27	0.21	0.16	0.12	0.09	0.07	0.05	0.03	0.00
64.00	0.64	0.42	0.33	0.28	0.22	0.17	0.13	0.10	0.08	0.06	0.04	0.02	0.00
90.51	0.64	0.42	0.33	0.28	0.27	0.18	0.13	0.10	0.08	0.06	0.05	0.03	0.02	0.00
∞	0.66	0.43	0.36	0.30	0.25	0.20	0.16	0.13	0.11	0.09	0.08	0.06	0.05	0.04	0.00

$p_{1} / p_{2}$	1.00	1.41	2.00	2.83	4.00	5.66	8.00	11.31	16.00	22.63	32.00	45.26	64.00	90.51	∞
1.00	1.00
1.41	0.98	1.00
2.00	0.92	0.96	1.00
2.83	0.90	0.91	0.95	1.00
4.00	0.89	0.90	0.92	0.95	1.00
5.66	0.89	0.89	0.90	0.93	0.96	1.00
8.00	0.89	0.89	0.89	0.92	0.94	0.96	1.00
11.31	0.89	0.89	0.88	0.91	0.93	0.95	0.97	1.00
16.00	0.89	0.89	0.88	0.91	0.92	0.94	0.95	0.97	1.00
22.63	0.90	0.89	0.88	0.91	0.92	0.93	0.95	0.96	0.98	1.00
32.00	0.89	0.89	0.88	0.91	0.92	0.93	0.94	0.96	0.97	0.98	1.00
45.26	0.90	0.89	0.88	0.91	0.91	0.92	0.94	0.95	0.96	0.97	0.98	1.00
64.00	0.90	0.89	0.87	0.91	0.91	0.93	0.94	0.95	0.96	0.97	0.98	0.99	1.00
90.51	0.90	0.89	0.87	0.90	0.91	0.93	0.94	0.95	0.96	0.96	0.97	0.98	0.99	1.00
∞	0.92	0.90	0.87	0.91	0.91	0.93	0.94	0.94	0.95	0.96	0.97	0.97	0.98	0.98	1.00

$p_{1} / p_{2}$	1.00	1.41	2.00	2.83	4.00	5.66	8.00	11.31	16.00	22.63	32.00	45.26	64.00	90.51	∞
1.00	0.57
1.41	0.62	0.69
2.00	0.58	0.66	0.69
2.83	0.60	0.67	0.69	0.77
4.00	0.61	0.67	0.68	0.74	0.79
5.66	0.62	0.68	0.69	0.74	0.78	0.83
8.00	0.64	0.69	0.69	0.75	0.76	0.81	0.86
11.31	0.64	0.70	0.69	0.75	0.78	0.81	0.84	0.88
16.00	0.66	0.71	0.70	0.76	0.78	0.81	0.84	0.86	0.90
22.63	0.66	0.71	0.71	0.76	0.78	0.81	0.84	0.86	0.89	0.92
32.00	0.67	0.72	0.71	0.77	0.79	0.82	0.84	0.86	0.88	0.90	0.93
45.26	0.68	0.73	0.71	0.77	0.79	0.82	0.85	0.87	0.89	0.90	0.92	0.94
64.00	0.69	0.73	0.72	0.78	0.80	0.83	0.85	0.87	0.89	0.90	0.92	0.93	0.95
90.51	0.69	0.73	0.72	0.78	0.80	0.83	0.85	0.87	0.89	0.90	0.92	0.93	0.94	0.96
∞	0.72	0.76	0.74	0.81	0.82	0.85	0.87	0.89	0.90	0.92	0.93	0.94	0.95	0.96	1.00

Abstract

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Figures (4)

Tables (3)

Equations (22)

Applied Optics