Roof angle error effect on modulation transfer function and spread function

Leo Levi; Abraham Reichert

doi:10.1364/AO.27.000915

Applied Optics
Vol. 27,
Issue 5,
pp. 915-921
(1988)
•https://doi.org/10.1364/AO.27.000915

Roof angle error effect on modulation transfer function and spread function

Leo Levi and Abraham Reichert

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Leo Levi and Abraham Reichert, "Roof angle error effect on modulation transfer function and spread function," Appl. Opt. 27, 915-921 (1988)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

Prisms including roof sections are frequent components in optical systems, usually serving to rectify images for direct viewing. Often the image forming rays pass the roof section in both directions. In such applications, the tolerances on the roof angle must be kept very tight to assure an acceptable resolving power. If, for example, the blurring due to this discrepancy is to be kept to a modest 0.1 mrad and the prism is made of crown glass, the tolerance on the roof angle will be ~15 μrad, i.e., ~3 sec of arc. This extremely tight tolerance illustrates the fact that the roof angle error can be an important factor in determining system performance. Here we develop the physical optics (OTF) and point spread functions associated with the roof angle error, assuming the rest of the optical system to be aberrationless.

Full Article | PDF Article

More Like This

Roof-angle error effect on modulation transfer function. II

Leo Levi and Abraham Reichert
Appl. Opt. 30(28) 4016-4016 (1991)

Effects of misalignment errors on the optical transfer functions of synthetic aperture telescopes

Jorge L. Flores, Marija Strojnik, Gonzalo Páez, and Guillermo García-Torales
Appl. Opt. 43(32) 5926-5932 (2004)

Transfer function characterization of grazing incidence optical systems

James E. Harvey, Edward C. Moran, and William P. Zmek
Appl. Opt. 27(8) 1527-1533 (1988)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (4)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (1)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (27)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

	ϕ= 0
	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	1.0000	0.9873	0.9745	0.9618	0.9491	0.9364	0.9237	0.9109	0.8982	0.8856
0.1	0.8729	0.8602	0.8476	0.8349	0.8223	0.8097	0.7972	0.7846	0.7721	0.7595
0.2	0.7471	0.7346	0.7222	0.7098	0.6974	0.6850	0.6727	0.6604	0.6482	0.6360
0.3	0.6238	0.6117	0.5996	0.5876	0.5756	0.5636	0.5517	0.5399	0.5281	0.5163
0.4	0.5046	0.4930	0.4814	0.4699	0.4584	0.4470	0.4357	0.4244	0.4132	0.4021
0.5	0.3910	0.3800	0.3691	0.3583	0.3475	0.3368	0.3262	0.3157	0.3053	0.2950
0.6	0.2848	0.2746	0.2646	0.2546	0.2448	0.2351	0.2255	0.2159	0.2066	0.1973
0.7	0.1881	0.1791	0.1702	0.1614	0.1528	0.1443	0.1359	0.1277	0.1197	0.1118
0.8	0.1041	0.0965	0.0892	0.0820	0.0750	0.0681	0.0615	0.0552	0.0490	0.0431
0.9	0.0374	0.0320	0.0268	0.0220	0.0175	0.0133	0.0095	0.0062	0.0034	0.0012
	ϕ= 1
	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.8801	0.8713	0.8624	0.8534	0.8444	0.8352	0.8260	0.8167	0.8074	0.7979
0.1	0.7884	0.7789	0.7692	0.7595	0.7498	0.7400	0.7301	0.7202	0.7102	0.7002
0.2	0.6902	0.6801	0.6699	0.6597	0.6495	0.6393	0.6290	0.6187	0.6083	0.5980
0.3	0.5876	0.5772	0.5668	0.5564	0.5459	0.5355	0.5250	0.5146	0.5041	0.4936
0.4	0.4832	0.4727	0.4623	0.4519	0.4415	0.4311	0.4207	0.4104	0.4001	0.3898
0.5	0.3795	0.3693	0.3591	0.3490	0.3389	0.3288	0.3188	0.3089	0.2990	0.2892
0.6	0.2794	0.2697	0.2601	0.2506	0.2411	0.2317	0.2224	0.2132	0.2041	0.1951
0.7	0.1862	0.1773	0.1686	0.1601	0.1516	0.1432	0.1350	0.1270	0.1190	0.1112
0.8	0.1036	0.0961	0.0888	0.0817	0.0747	0.0680	0.0614	0.0550	0.0489	0.0430
0.9	0.0373	0.0319	0.0268	0.0220	0.0175	0.0133	0.0095	0.0062	0.0034	0.0012
	ϕ= 2
	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.5767	0.5768	0.5767	0.5763	0.5757	0.5749	0.5738	0.5726	0.5711	0.5694
0.1	0.5675	0.5653	0.5630	0.5604	0.5576	0.5547	0.5515	0.5481	0.5446	0.5408
0.2	0.5368	0.5327	0.5284	0.5239	0.5192	0.5143	0.5093	0.5040	0.4987	0.4931
0.3	0.4874	0.4816	0.4756	0.4694	0.4631	0.4567	0.4501	0.4434	0.4366	0.4296
0.4	0.4226	0.4154	0.4081	0.4007	0.3932	0.3856	0.3780	0.3702	0.3624	0.3544
0.5	0.3464	0.3384	0.3303	0.3221	0.3139	0.3056	0.2973	0.2890	0.2806	0.2723
0.6	0.2639	0.2554	0.2470	0.2386	0.2302	0.2218	0.2135	0.2051	0.1968	0.1885
0.7	0.1803	0.1722	0.1640	0.1560	0.1480	0.1401	0.1323	0.1246	0.1170	0.1095
0.8	0.1022	0.0949	0.0878	0.0809	0.0741	0.0674	0.0610	0.0547	0.0487	0.0428
0.9	0.0372	0.0319	0.0268	0.0219	0.0175	0.0133	0.0095	0.0062	0.0034
	ϕ= 3
	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.2260	0.2336	0.2410	0.2481	0.2550	0.2617	0.2682	0.2744	0.2804	0.2862
0.1	0.2917	0.2970	0.3020	0.3067	0.3112	0.3155	0.3194	0.3231	0.3265	0.3297
0.2	0.3326	0.3352	0.3375	0.3396	0.3414	0.3429	0.3442	0.3451	0.3458	0.3462
0.3	0.3464	0.3462	0.3458	0.3452	0.3442	0.3430	0.3416	0.3398	0.3379	0.3356
0.4	0.3332	0.3304	0.3275	0.3243	0.3209	0.3172	0.3133	0.3093	0.3050	0.3005
0.5	0.2957	0.2909	0.2858	0.2805	0.2751	0.2695	0.2637	0.2578	0.2517	0.2456
0.6	0.2392	0.2328	0.2263	0.2196	0.2129	0.2060	0.1991	0.1921	0.1851	0.1780
0.7	0.1709	0.1638	0.1566	0.1494	0.1422	0.1351	0.1279	0.1208	0.1138	0.1067
0.8	0.0998	0.0929	0.0862	0.0795	0.0730	0.0666	0.0603	0.0542	0.0483	0.0425
0.9	0.0370	0.0317	0.0267	0.0219	0.0174	0.0133	0.0095	0.0062	0.0034	0.0012
	ϕ= 4
	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	−0.0330	−0.0243	−0.0156	−0.0069	0.0019	0.0107	0.0194	0.0282	0.0369	0.0455
0.1	0.0541	0.0626	0.0711	0.0794	0.0876	0.0957	0.1037	0.1115	0.1192	0.1267
0.2	0.1340	0.1411	0.1481	0.1548	0.1613	0.1676	0.1736	0.1794	0.1850	0.1903
0.3	0.1953	0.2000	0.2045	0.2087	0.2126	0.2162	0.2195	0.2225	0.2252	0.2276
0.4	0.2297	0.2315	0.2329	0.2341	0.2349	0.2354	0.2356	0.2355	0.2351	0.2344
0.5	0.2334	0.2320	0.2304	0.2285	0.2263	0.2238	0.2211	0.2180	0.2148	0.2112
0.6	0.2075	0.2034	0.1992	0.1947	0.1901	0.1852	0.1801	0.1749	0.1695	0.1640
0.7	0.1583	0.1525	0.1465	0.1405	0.1344	0.1282	0.1219	0.1156	0.1093	0.1029
0.8	0.0966	0.0902	0.0839	0.0777	0.0715	0.0654	0.0593	0.0535	0.0477	0.0421
0.9	0.0367	0.0315	0.0265	0.0218	0.0174	0.0133	0.0095	0.0062	0.0034	0.0012
	ϕ= 5
	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	−0.1310	−0.1274	−0.1235	−0.1193	−0.1148	−0.1100	−0.1049	−0.0995	−0.0939	−0.0880
0.1	−0.0820	−0.0756	−0.0691	−0.0624	−0.0555	−0.0485	−0.0413	−0.0340	−0.0266	−0.0191
0.2	−0.0116	−0.0039	0.0037	0.0114	0.0191	0.0268	0.0344	0.0420	0.0495	0.0569
0.3	0.0642	0.0714	0.0785	0.0854	0.0921	0.0987	0.1051	0.1112	0.1171	0.1228
0.4	0.1282	0.1334	0.1383	0.1429	0.1472	0.1511	0.1548	0.1582	0.1612	0.1639
0.5	0.1663	0.1683	0.1700	0..1713	0.1723	0.1729	0.1732	0.1731	0.1727	0.1719
0.6	0.1709	0.1694	0.1677	0.1656	0.1632	0.1606	0.1576	0.1543	0.1508	0.1470
0.7	0.1430	0.1388	0.1343	0.1296	0.1247	0.1197	0.1145	0.1091	0.1037	0.0981
0.8	0.0925	0.0868	0.0811	0.0753	0.0696	0.0638	0.0581	0.0525	0.0470	0.0416
0.9	0.0363	0.0312	0.0263	0.0217	0.0173	0.0132	0.0095	0.0062	0.0034	0.0012
	ϕ= 10
	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.0087	0.0137	0.0187	0.0234	0.0279	0.0321	0.0360	0.0396	0.0428	0.0455
0.1	0.0479	0.0497	0.0511	0.0519	0.0523	0.0522	0.0515	0.0504	0.0488	0.0467
0.2	0.0442	0.0413	0.0379	0.0343	0.0303	0.0260	0.0215	0.0169	0.0121	0.0072
0.3	0.0023	−0.0026	−0.0074	−0.0121	−0.0167	−0.0210	−0.0251	−0.0289	−0.0323	−0.0354
0.4	0.0380	−0.0402	−0.0420	−0.0433	−0.0441	−0.0443	−0.0441	0.0434	−0.0422	−0.0404
0.5	−0.0383	−0.0356	−0.0325	−0.0290	−0.0252	−0.0210	−0.0165	−0.0118	−0.0068	−0.0017
0.6	0.0035	0.0087	0.0140	0.0193	0.0244	0.0294	0.0342	0.0388	0.0432	0.0472
0.7	0.0508	0.0541	0.0570	0.0594	0.0614	0.0629	0.0639	0.0644	0.0644	0.0640
0.8	0.0631	0.0617	0.0598	0.0576	0.0550	0.0520	0.0487	0.0451	0.0413	0.0374
0.9	0.0333	0.0291	0.0249	0.0208	0.0168	0.0129	0.0094	0.0061	0.0034	0.0012
	ϕ= 20
	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	0.0067	0.0033	−0.0002	−0.0037	−0.0071	−0.0102	−0.0128	−0.0150	−0.0165	−0.0174
0.1	−0.0175	−0.0170	−0.0157	−0.0138	−0.0114	−0.0085	−0.0052	−0.0017	0.0019	0.0055
0.2	0.0088	0.0118	0.0144	0.0164	0.0179	0.0186	0.0186	0.0179	0.0166	0.0146
0.3	0.0120	0.0091	0.0058	0.0023	−0.0012	−0.0047	−0.0079	−0.0107	−0.0130	−0.0148
0.4	−0.0160	−0.0164	−0.0162	−0.0152	−0.0136	−0.0113	−0.0086	−0.0054	−0.0020	0.0016
0.5	0.0052	0.0087	0.0119	0.0147	0.0170	0.0186	0.0197	0.0200	0.0196	0.0186
0.6	0.0169	0.0146	0.0118	0.0087	0.0053	0.0018	−0.0017	−0.0049	−0.0079	−0.0104
0.7	−0.0124	−0.0138	−0.0145	−0.0145	0.0138	−0.0123	−0.0103	−0.0077	−0.0046	−0.0012
0.8	0.0024	0.0061	0.0098	0.0132	0.0163	0.0189	0.0210	0.0224	0.0232	0.0233
0.9	0.0227	0.0215	0.0197	0.0174	0.0148	0.0119	0.0089	0.0060	0.0033	0.0012
	ϕ= 50
	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	−0.0039	−0.0045	−0.0040	−0.0025	−0.0004	0.0018	0.0036	0.0045	0.0043	0.0031
0.1	0.0011	−0.0011	−0.0030	−0.0042	−0.0044	−0.0034	−0.0016	0.0006	0.0027	0.0042
0.2	0.0046	0.0040	0.0024	0.0002	−0.0019	−0.0036	−0.0044	−0.0040	−0.0026	−0.0006
0.3	0.0016	0.0035	0.0046	0.0045	0.0034	0.0016	−0.0007	−0.0027	−0.0040	−0.0043
0.4	−0.0034	−0.0017	0.0005	0.0026	0.0042	0.0048	0.0043	0.0028	0.0007	−0.0015
0.5	−0.0033	−0.0042	−0.0039	−0.0027	−0.0007	0.0015	0.0035	0.0047	0.0048	0.0038
0.6	0.0020	−0.0002	−0.0022	−0.0037	−0.0041	−0.0034	−0.0018	0.0004	0.0026	0.0042
0.7	0.0050	0.0046	0.0033	0.0012	−0.0010	−0.0028	−0.0038	−0.0037	−0.0026	−0.0007
0.8	0.0016	0.0036	0.0049	0.0052	0.0044	0.0027	0.0006	−0.0015	−0.0030	−0.0035
0.9	−0.0030	−0.0014	0.0008	0.0031	0.0049	0.0059	0.0058	0.0047	0.0030	0.0012
	ϕ= 100
	0.00	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08	0.09
0.0	−0.0015	−0.0012	0.0003	0.0015	0.0013	0.0000	−0.0014	−0.0014	−0.0002	0.0012
0.1	0.0015	0.0004	−0.0011	−0.0016	−0.0006	0.0009	0.0016	0.0008	−0.0007	−0.0016
0.2	−0.0010	0.0005	0.0016	0.0012	−0.0003	−0.0014	−0.0013	0.0001	0.0014	0.0015
0.3	0.0002	−0.0012	−0.0015	−0.0003	0.0011	0.0016	0.0007	−0.0009	−0.0015	−0.0008
0.4	0.0008	0.0016	0.0010	−0.0005	−0.0015	−0.0011	0.0004	0.0015	0.0014	0.0000
0.5	−0.0013	−0.0013	−0.0001	0.0013	0.0016	0.0005	−0.0010	−0.0015	−0.0005	0.0010
0.6	0.0017	0.0009	−0.0006	−0.0015	−0.0009	0.0006	0.0017	0.0013	−0.0002	−0.0014
0.7	−0.0012	0.0002	0.0015	0.0015	0.0003	−0.0011	−0.0014	−0.0002	0.0013	6.0017
0.8	0.0007	−0.0008	−0.0014	−0.0006	0.0009	0.0018	0.0012	−0.0003	−0.0013	−0.0009
0.9	0.0006	0.0018	0.0016	0.0002	−0.0011	−0.0010	0.0003	0.0018	0.0021	0.0011

Abstract

Cited By

Figures (4)

Tables (1)

Equations (27)

Applied Optics