Algebraic solution for aplanatic cemented doublets with aspherical surfaces of second degree

Jiří Novák; Antonín Mikš

doi:10.1364/AO.496028

Applied Optics
Vol. 62,
Issue 25,
pp. 6697-6704
(2023)
•https://doi.org/10.1364/AO.496028

Algebraic solution for aplanatic cemented doublets with aspherical surfaces of second degree

Jiří Novák and Antonín Mikš

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Jiří Novák and Antonín Mikš, "Algebraic solution for aplanatic cemented doublets with aspherical surfaces of second degree," Appl. Opt. 62, 6697-6704 (2023)

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Abstract

An algebraic method of an initial design of the aplanatic cemented doublet with a unit focal length is described. Based on the third-order aberration theory, algebraic equations are derived for calculating the design parameters of an aplanatic thin cemented doublet with spherical surfaces and aspherical surfaces of the second degree. These equations make it easy to determine whether there exists a real solution of the doublet design for required parameters. The results of the calculations of selected cemented doublet solutions are presented in the examples. The obtained parameters can be used as the starting solution for the final optimization of doublet designs.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (28)

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$n_{2}$	$n_{3}$	$φ_{1}$	$r_{1}$	$r_{2}$	$r_{3}$
1,6000	1,5000	−1,2060	0,4300	0,2306	−13,1247
1,7000	1,5000	−1,0219	0,3996	0,2524	−12,2492
1,9000	1,5000	4,3616	0,1350	0,3904	0,1077
1,5000	1,6000	2,1380	0,5967	−0,3846	−1,4214
1,7000	1,6000	−1,3571	0,4833	0,2495	12,5826
1,8000	1,6000	−1,1434	0,4507	0,2741	13,2492
1,9000	1,6000	−1,0701	0,4294	0,2843	14,7728
1,5000	1,7000	1,9398	0,5952	−0,4547	−1,1672
1,6000	1,7000	2,2647	0,6512	−0,4466	−2,3135
1,8000	1,7000	−1,5061	0,5292	0,2651	5,2083
1,9000	1,7000	−1,2644	0,4953	0,2921	5,2915
1,5000	1,8000	1,8655	0,5923	−0,4896	−1,0409
1,6000	1,8000	2,0343	0,6500	−0,5399	−1,7885
1,7000	1,8000	2,3866	0,6958	−0,5071	−4,1862
1,9000	1,8000	−1,6536	0,5691	0,2782	3,6043
1,5000	1,9000	1,8307	0,5891	−0,5092	−0,9607
1,6000	1,9000	1,9440	0,6473	−0,5900	−1,5477
1,7000	1,9000	2,1255	0,6948	−0,6261	−2,8849
1,8000	1,9000	2,5043	0,7325	−0,5665	−10,6592

$φ_{1}$	$n_{2}$	$n_{3}$	$r_{1}$	$r_{2}$	$r_{3}$
2,0000	1,4000	1,5019	0,5291	−0,3215	−0,8948
2,0000	1,5000	1,6562	0,5961	−0,4306	−1,2523
2,0000	1,6000	1,8296	0,6492	−0,5577	−1,7016
2,5000	1,4000	1,4305	0,5262	−0,2299	−1,1551
2,5000	1,5000	1,5440	0,5948	−0,3013	−1,7813
2,5000	1,6000	1,6601	0,6502	−0,3804	−2,8074
2,5000	1,7000	1,7790	0,6953	−0,4688	−4,8130
2,5000	1,8000	1,9009	0,7326	−0,5682	−10,5442
3,0000	1,5000	1,5199	0,5908	−0,2322	−2,1700
3,0000	1,6000	1,6269	0,6464	−0,2896	−3,8026
3,0000	1,7000	1,7350	0,6920	−0,3520	−8,3524
3,0000	1,8000	1,8442	0,7298	−0,4202	−93,5113
3,0000	1,9000	1,9545	0,7614	−0,4951	13,2547
3,5000	1,5000	1,5109	0,5871	−0,1888	−2,4774
3,5000	1,6000	1,6147	0,6428	−0,2338	−4,7506
3,5000	1,7000	1,7190	0,6885	−0,2819	−14,1550
3,5000	1,8000	1,8240	0,7264	−0,3335	27,9520
3,5000	1,9000	1,4307	0,1687	0,4905	0,1275
4,0000	1,5000	1,5067	0,5840	−0,1590	−2,7270
4,0000	1,6000	1,6090	0,6396	−0,1960	−5,6581
4,0000	1,7000	1,7116	0,6853	−0,2350	−25,5070
4,0000	1,8000	1,4310	0,1405	0,4720	0,1101
4,0000	1,9000	1,4736	0,1473	0,4269	0,1152

$φ_{1}$	$n_{2}$	$n_{3}$	$r_{1}$	$r_{2}$	$r_{3}$
2,0000	1,4323	1,5500	0,5525	−0,3551	−1,0019
2,0000	1,4323	1,5500	0,5525	−0,3551	−1,0019
2,0000	1,4962	1,6500	0,5939	−0,4261	−1,2372
2,0000	1,5557	1,7500	0,6272	−0,4988	−1,4894
2,0000	1,6109	1,8500	0,6543	−0,5729	−1,7575
2,0000	1,6621	1,9500	0,6766	−0,6482	−2,0401
2,5000	1,5052	1,5500	0,5980	−0,3053	−1,8226
2,5000	1,5914	1,6500	0,6459	−0,3733	−2,6939
2,5000	1,6758	1,7500	0,6852	−0,4465	−4,1700
2,5000	1,7586	1,8500	0,7180	−0,5255	−7,2340
2,5000	1,8396	1,9500	0,7455	−0,6112	−17,5152
3,0000	1,5282	1,5500	0,6077	−0,2479	−2,5142
3,0000	1,6214	1,6500	0,6570	−0,3025	−4,3745
3,0000	1,7138	1,7500	0,6977	−0,3611	−9,7091
3,0000	1,8053	1,8500	0,7316	−0,4240	−176,9710
3,0000	1,8959	1,9500	0,7602	−0,4919	13,8310
3,5000	1,5377	1,5500	0,6094	−0,2054	−3,0992
3,5000	1,6339	1,6500	0,6592	−0,2497	−6,3138
3,5000	1,7296	1,7500	0,7004	−0,2968	−27,5372
3,5000	1,8247	1,8500	0,7348	−0,3469	17,1399
3,5000	1,9194	1,9500	0,7638	−0,4004	7,4533
4,0000	1,5424	1,5500	0,6089	−0,1744	−3,5981
4,0000	1,6400	1,6500	0,6589	−0,2113	−8,5631
4,0000	1,7373	1,7500	0,7003	−0,2502	334,6998
4,0000	1,8343	1,8500	0,7349	−0,2912	10,4305
4,0000	1,9310	1,9500	0,7641	−0,3347	5,8728

$n_{2}$	$n_{3}$	$φ_{1}$	$r_{1}$	$r_{2}$	$r_{3}$
1,6000	1,5000	−1,2060	0,4300	0,2306	−13,1247
1,7000	1,5000	−1,0219	0,3996	0,2524	−12,2492
1,9000	1,5000	4,3616	0,1350	0,3904	0,1077
1,5000	1,6000	2,1380	0,5967	−0,3846	−1,4214
1,7000	1,6000	−1,3571	0,4833	0,2495	12,5826
1,8000	1,6000	−1,1434	0,4507	0,2741	13,2492
1,9000	1,6000	−1,0701	0,4294	0,2843	14,7728
1,5000	1,7000	1,9398	0,5952	−0,4547	−1,1672
1,6000	1,7000	2,2647	0,6512	−0,4466	−2,3135
1,8000	1,7000	−1,5061	0,5292	0,2651	5,2083
1,9000	1,7000	−1,2644	0,4953	0,2921	5,2915
1,5000	1,8000	1,8655	0,5923	−0,4896	−1,0409
1,6000	1,8000	2,0343	0,6500	−0,5399	−1,7885
1,7000	1,8000	2,3866	0,6958	−0,5071	−4,1862
1,9000	1,8000	−1,6536	0,5691	0,2782	3,6043
1,5000	1,9000	1,8307	0,5891	−0,5092	−0,9607
1,6000	1,9000	1,9440	0,6473	−0,5900	−1,5477
1,7000	1,9000	2,1255	0,6948	−0,6261	−2,8849
1,8000	1,9000	2,5043	0,7325	−0,5665	−10,6592

$φ_{1}$	$n_{2}$	$n_{3}$	$r_{1}$	$r_{2}$	$r_{3}$
2,0000	1,4000	1,5019	0,5291	−0,3215	−0,8948
2,0000	1,5000	1,6562	0,5961	−0,4306	−1,2523
2,0000	1,6000	1,8296	0,6492	−0,5577	−1,7016
2,5000	1,4000	1,4305	0,5262	−0,2299	−1,1551
2,5000	1,5000	1,5440	0,5948	−0,3013	−1,7813
2,5000	1,6000	1,6601	0,6502	−0,3804	−2,8074
2,5000	1,7000	1,7790	0,6953	−0,4688	−4,8130
2,5000	1,8000	1,9009	0,7326	−0,5682	−10,5442
3,0000	1,5000	1,5199	0,5908	−0,2322	−2,1700
3,0000	1,6000	1,6269	0,6464	−0,2896	−3,8026
3,0000	1,7000	1,7350	0,6920	−0,3520	−8,3524
3,0000	1,8000	1,8442	0,7298	−0,4202	−93,5113
3,0000	1,9000	1,9545	0,7614	−0,4951	13,2547
3,5000	1,5000	1,5109	0,5871	−0,1888	−2,4774
3,5000	1,6000	1,6147	0,6428	−0,2338	−4,7506
3,5000	1,7000	1,7190	0,6885	−0,2819	−14,1550
3,5000	1,8000	1,8240	0,7264	−0,3335	27,9520
3,5000	1,9000	1,4307	0,1687	0,4905	0,1275
4,0000	1,5000	1,5067	0,5840	−0,1590	−2,7270
4,0000	1,6000	1,6090	0,6396	−0,1960	−5,6581
4,0000	1,7000	1,7116	0,6853	−0,2350	−25,5070
4,0000	1,8000	1,4310	0,1405	0,4720	0,1101
4,0000	1,9000	1,4736	0,1473	0,4269	0,1152

Abstract

Data Availability

Cited By

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Tables (3)

Equations (28)

Applied Optics