Algebraic method for finding the initial design parameters of a two-element optical system with an afocal meniscus lens

Antonín Mikš; Jiří Novák

doi:10.1364/JOSAA.476478

Journal of the Optical Society of America A
Vol. 40,
Issue 1,
pp. 108-115
(2023)
•https://doi.org/10.1364/JOSAA.476478

Algebraic method for finding the initial design parameters of a two-element optical system with an afocal meniscus lens

Antonín Mikš and Jiří Novák

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Antonín Mikš and Jiří Novák, "Algebraic method for finding the initial design parameters of a two-element optical system with an afocal meniscus lens," J. Opt. Soc. Am. A 40, 108-115 (2023)

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Abstract

This work introduces an algebraic method of the calculation of an initial design of a two-element optical system composed of a thick afocal meniscus lens and a thin lens element, which can be formed, for example, by a cemented doublet. The third-order aberration theory is used to find the fundamental parameters of the starting configuration of a given optical system. The method gives results that make it possible to obtain a good starting design for further optimization of such imaging systems using optical design software. The proposed method is presented on two examples of finding the initial design parameters of the objective with an afocal meniscus lens and a cemented doublet.

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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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Glass 1	Glass 2	${\bar{M}}_{3}$	${\bar{N}}_{3}$	$r_{1}$	$r_{2}$	$r_{3}$
SF2	P-SF67	−5.78896	−0.26580	4.11930	−0.23486	−0.46583
N-BAK2	N-LAF7	−5.75199	−0.26580	2.51095	−0.21799	−0.42904
N-BAK1	LAFN7	−5.78307	−0.26580	2.93105	−0.21461	−0.45976
N-BAF4	N-SF10	−5.75410	−0.26580	3.39517	−0.20286	−0.51047
KZFS12	SF11	−5.76415	−0.26580	5.13754	−0.19311	−0.59243
N-SK5	N-BAF52	−5.78498	−0.26580	2.53232	−0.12743	−0.66073

Surface	$r_{i}$	$d_{i}$	$n_{i}$
			1.0000
1	−16.8574	8	1.51872
2	−19.5898	0	1.0000
3	251.095	6	1.54212
4	−21.799	2	1.75460
5	−42.904		1.0000

$r_{1}$	$r_{2}$	$d$	$n$	$Δ s_{\tan}$	$Δ s_{s a g}$	$S_{I V}$	${\bar{M}}_{1}$	${\bar{N}}_{1}$	$C_{I}$
11.0284	9.3617	5.0000	1.5000	−0.0396	−0.0396	0.0008	−33.5115	1.6135	0.0100
11.3966	9.5633	5.5000	1.5000	−0.0283	−0.0283	0.0006	−32.4901	1.4135	0.0104
11.7288	9.7288	6.0000	1.5000	−0.0165	−0.0165	0.0003	−31.7311	1.2283	0.0108
12.0284	9.8617	6.5000	1.5000	−0.0042	−0.0042	0.0001	−31.1862	1.0540	0.0112
12.2981	9.9648	7.0000	1.5000	0.0087	0.0087	−0.0002	−30.8218	0.8876	0.0116
12.5403	10.0403	7.5000	1.5000	0.0223	0.0223	−0.0004	−30.6147	0.7267	0.0120
12.7567	10.0900	8.0000	1.5000	0.0367	0.0367	−0.0007	−30.5489	0.5693	0.0124

Required Parameters: ${\bar{M}}_{1} = - 31.19$ , ${\bar{N}}_{1} = 1.054$ , $C_{I} = 0.0112$
Glass 1	Glass 2	${\bar{M}}_{1}$	${\bar{N}}_{1}$	$r_{1}$	$r_{2}$	$r_{3}$
N-LAK7	N-LASF43	−31.11039	1.05400	4.36163	−0.14297	−0.41686
LF5	N-SF10	−31.14127	1.05400	3.08252	−0.14029	−0.39146
N-FK51A	N-KZFS2	−31.27525	1.05400	1.77056	−0.11671	−0.41578

Surface	$r_{i}$	$d_{i}$	$D / 2$	Glass
1	308.252	3.0		LF5
2	–14.029	1.0	7.00	SF10
3	–39.146	0.5	7.00	AIR
4	12.0284	6.50	7.00	BK3
5	9.8617		5.94	AIR
	$s_{F^{'}}^{'} = 63.499$		$y_{0}^{'} = 9.607$

Abstract

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Equations (42)

Journal of the Optical Society of America A