Considerations on Cemented Doublet Mangin Mirrors

N. v. d. W. Lessing

doi:10.1364/AO.8.000979

Considerations on Cemented Doublet Mangin Mirrors

N. v. d. W. Lessing

Applied Optics
Vol. 8,
Issue 5,
pp. 979-983
(1969)
•https://doi.org/10.1364/AO.8.000979

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N. v. d. W. Lessing, "Considerations on Cemented Doublet Mangin Mirrors," Appl. Opt. 8, 979-983 (1969)

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History
- Original Manuscript: September 16, 1968
- Published: May 1, 1969

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Abstract

Thin lens formulas are given for the focal length, longitudinal chromatic aberration, spherical aberration, and coma of a Mangin mirror, consisting of two lenses cemented together with the second surface of the second lens silvered. Application of these yields a rough solution for a spherically and chromatically corrected Mangin mirror. Methods of correction are discussed. Ten glass combinations, making coma correction possible, together with design details of thirty achromatic aplanatic cemented doublet Mangin mirrors using these combinations, are given.

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G1	ZK7	LLP2	KF8	BaF10	BaLF8	KzF4	KF7	KF4	BaLF7	KzF2
G2	KzFS4	SF16	F4	BaSFS3	BaSFS3	F13	F3	BaSFS3	BaSFS3	BaSFS3
N₁	1.50958	1.54287	1.51307	1.67270	1.55564	1.57264	1.52469	1.53552	1.59091	1.53136
dN₁	0.00832	0.01145	0.01004	0.01420	0.01078	0.01185	0.01021	0.01034	0.01151	0.01022
N₂	1.61603	1.64968	1.61976	1.71386	1.71386	1.62561	1.61605	1.71386	1.71386	1.71386
dN₂	0.01397	0.01901	0.01684	0.01946	0.01946	0.01725	0.01659	0.01946	0.01946	0.01946
c₁₁	−0.00498	−0.00531	−0.00501	−0.00573	−0.00611	−0.00506	−0.00498	−0.00622	−0.00595	−0.00623
c₁₂	−0.01136	−0.01125	−0.01134	−0.01287	−0.00990	−0.01269	−0.01175	−0.00951	−0.01077	−0.00948
$c_{12}^{'}$	−0.07067	−0.07848	−0.07221	+0.09929	−0.05118	+0.02375	−0.07521	−0.04020	−0.05907	−0.03571
f/1.5
r₁	−81.3299	−82.7222	−81.3664	−88.0518	−82.0158	−85.9910	−83.9153	−81.9608	−86.2189	−82.8727
r₂	+1132.12	+1472.95	+1148.40	+322.885	−2828.73	+397.830	+1000.02	−1551.40	−5873.32	−1248.25
r₃	−163.167	−161.879	−162.945	−154.519	−163.124	−159.110	−163.231	−165.517	−162.419	−166.700
LA_y	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
$\frac{1}{2} L_{CF}$	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
OSC_y	+0.00006	−0.00003	+0.00011	+0.00018	−0.00000	−0.00041	−0.00083	−0.00062	−0.00124	−0.00126
LAZ_y	−0.0081	−0.0067	−0.0079	+0.0177	−0.0144	+0.0088	−0.0058	−0.0187	−0.0091	−0.0195
LA_C	+0.0381	+0.0479	+0.0451	+0.0756	+0.0397	+0.0598	+0.0434	+0.0354	+0.0375	+0.0322
LA_d	+0.0156	+0.0197	+0.0186	+0.0302	+0.0159	+0.0245	+0.0177	+0.0144	+0.0152	+0.0132
LA_F	−0.0441	−0.0571	−0.0539	−0.0849	−0.0452	−0.0716	−0.0507	−0.0409	−0.0430	−0.0380
$\frac{1}{2} L_{Ce}$	−1.74	−2.27	−1.81	−1.69	−1.53	−2.19	−2.13	−1.80	−1.52	−2.05
$\frac{1}{2} L_{eg}$	+8.57	+11.13	+8.11	+10.69	+8.99	+11.57	+11.00	+9.22	+9.10	+10.36
$\frac{1}{2} L_{A^{'} d}$	−5.61	−6.43	−5.52	−4.82	−4.38	−7.63	−5.49	−4.68	−4.42	−6.36
$\frac{1}{2} L_{dg}$	+8.69	+11.05	+8.71	+10.15	+8.56	+11.71	+10.49	+8.96	+9.03	+10.15
f/1.75
r₁	−78.8485	−80.2770	−78.8638	−84.7697	−79.6732	−83.4141	−81.6920	−79.7993	−84.2269	−80.8721
r₂	+825.375	+1010.82	+833.432	+270.979	−8545.12	+337.587	+767.578	−2265.38	+23314.3	−1611.87
r₃	−161.059	−159.787	−160.806	−151.532	−161.138	−156.847	−161.348	−163.724	−160.738	−165.065
LA_y	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
$\frac{1}{2} L_{CF}$	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
OSC_y	+0.00090	+0.00082	+0.00095	+0.00136	+0.00078	+0.00059	+0.00010	+0.00021	−0.00031	−0.00035
LAZ_y	−0.0032	−0.0025	−0.0030	+0.0141	−0.0074	+0.0074	−0.0021	−0.0100	−0.0044	−0.0106
LA_C	−0.0428	+0.0394	+0.0372	+0.0651	+0.0325	+0.0496	+0.0352	+0.0286	+0.0301	+0.0258
LA_d	+0.0129	+0.0162	+0.0153	+0.0260	+0.0130	+0.0203	+0.0143	+0.0116	+0.0122	+0.0106
LA_F	−0.0362	−0.0469	−0.0444	−0.0731	−0.0368	−0.0592	−0.0411	−0.0330	−0.0344	−0.0304
$\frac{1}{2} L_{Ce}$	−1.32	−1.73	−1.38	−1.31	−1.17	−1.67	−1.61	−1.36	−1.15	−1.55
$\frac{1}{2} L_{eg}$	+6.54	+8.48	+6.19	+8.28	+6.83	+8.84	+8.34	+6.98	+6.87	+7.82
$\frac{1}{2} L_{A^{'} d}$	−4.28	−4.90	−4.21	−3.74	−3.33	−5.83	−4.16	−3.55	−3.34	−4.80
$\frac{1}{2} L_{dg}$	+6.62	+8.42	+6.65	+7.86	+6.51	+8.94	+7.95	+6.78	+6.82	+7.66
f/2
r₁	−76.9781	−78.4215	−76.9732	−81.3987	−77.9411	−81.3227	−80.0407	−78.2393	−82.7740	−79.4647
r₂	+679.908	+809.668	+684.778	+232.505	+15175.5	+299.676	+650.697	−3470.30	+4907.81	−2061.33
r₃	−159.421	−158.153	−159.141	−148.342	−159.628	−154.956	−159.914	−162.397	−159.485	−163.918
LA_y	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
$\frac{1}{2} L_{CF}$	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000	0.0000
OSC_y	+0.00122	+0.00115	+0.00127	+0.00214	+0.00107	+0.00105	+0.00050	+0.00055	+0.00012	+0.00007
LAZ_y	−0.0012	−0.0008	−0.0011	+0.0122	−0.0041	+0.0059	−0.0006	−0.0058	−0.0024	−0.0062
LA_C	+0.0264	+0.0330	+0.0313	+0.0593	+0.0270	+0.0421	+0.0292	+0.0236	+0.0246	+0.0211
LA_d	+0.0108	+0.0136	+0.0129	+0.0236	+0.0108	+0.0172	+0.0119	+0.0096	+0.0100	+0.0086
LA_F	−0.0304	−0.0392	−0.0372	−0.0664	−0.0306	−0.0502	−0.0339	−0.0271	−0.0281	−0.0248
$\frac{1}{2} L_{Ce}$	−1.05	−1.37	−1.09	−1.07	−0.92	−1.32	−1.27	−1.07	−0.90	−1.21
$\frac{1}{2} L_{eg}$	+5.16	+6.70	+4.89	+6.74	+5.38	+7.01	+6.56	+5.48	+5.38	+6.12
$\frac{1}{2} L_{A^{'} d}$	−3.38	−3.87	−3.33	−3.04	−2.63	−4.62	−3.27	−2.78	−2.62	−3.76
$\frac{1}{2} L_{dg}$	+5.23	+6.65	+5.25	+6.40	+5.13	+7.09	+6.25	+5.32	+5.34	+6.00

Abstract

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Equations (35)

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