Design of zoom systems composed of lenses with variable focal length

Antonín Mikš; Petr Pokorný

doi:10.1364/AO.410891

Applied Optics
Vol. 59,
Issue 34,
pp. 10838-10845
(2020)
•https://doi.org/10.1364/AO.410891

Design of zoom systems composed of lenses with variable focal length

Antonín Mikš and Petr Pokorný

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Antonín Mikš and Petr Pokorný, "Design of zoom systems composed of lenses with variable focal length," Appl. Opt. 59, 10838-10845 (2020)

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Abstract

This paper develops a methodology for a design of zoom-systems, which are composed of thin optical components with a variable focal length (e.g., membrane lenses). The proposed procedure allows us to design not only the outer parameters of the system (focal lengths and separation of lenses), but the inner structure of individual components of the system can be calculated as well (radii of curvature, thicknesses, and refractive indices) i.e., the starting values of the mentioned parameters can be calculated and used for the next optimization.

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$S_{I}$	$S_{I I}$	$S_{I, 0}$	$S_{I I, 0}$	$r_{1}$	$r_{4}$	$d_{2}$	$f^{'}$	Error [%]
1.8357e−04	−1.4925e−03	1.8951e−04	−1.5252e−03	20.00	−20.00	1.00	3.0027e $+$ 01	−3.2333e $+$ 00
2.3315e−05	−3.7720e−04	2.3689e−05	−3.8129e−04	40.000	−40.00	1.00	6.0053e $+$ 01	−1.6019e $+$ 00
6.9449e−06	−1.6825e−04	7.0189e−06	−1.6946e−04	60.000	−60.00	1.00	9.0080e $+$ 01	−1.0647e $+$ 00
2.9377e−06	−9.4811e−05	2.9611e−06	−9.5322e−05	80.000	−80.00	1.00	1.2011e $+$ 02	−7.9727e−01
1.5065e−06	−6.0744e−05	1.5161e−06	−6.1006e−05	100.00	−100.00	1.00	1.5013e $+$ 02	−6.3723e−01

$f^{'}$	$f_{1}^{'}$	$f_{2}^{'}$	$f_{3}^{'}$	$s_{p}$	$s_{p}^{'}$	$h_{1}$	$h_{2}$	$h_{3}$	${\bar{h}}_{1}$	${\bar{h}}_{3}$
55.0000	730.3056	−34.8367	36.5817	20.5631	−78.9646	4.9107	4.7762	8.0357	−0.9347	1.1684
82.5000	75.4234	−26.7195	41.3782	27.2172	−63.1605	7.3661	5.4128	8.0357	−0.8248	1.0310
110.0000	57.9037	−27.4887	52.3328	30.5531	−47.8663	9.8214	6.4291	8.0357	−0.6944	0.8680
137.5000	53.7200	−31.8809	78.4208	31.8624	−36.6996	12.2768	7.7061	8.0357	−0.5793	0.7241
165.0000	55.6694	−45.2755	242.4949	31.2141	−27.8736	14.7321	9.4394	8.0357	−0.4729	0.5912

Member	$\bar{M}$	$\bar{N}$	${\bar{M}}_{0}$	${\bar{N}}_{0}$
$f_{min}^{'} = 55 mm$ , $f_{max}^{'} = 165 mm$
1	4.5753	1.7281	2.1792	0.4181
2	6.4526	−0.6185	8.7496	−1.9285
3	1.5348	−0.9450	4.4848	−2.2550
$f_{min}^{'} = 82.5 mm$ , $f_{max}^{'} = 137.5 mm$
1	2.8988	1.2723	1.4141	−0.0377
2	1.7536	−0.2572	3.3280	−1.5672
3	1.2975	−0.7042	3.7659	−2.0142

$n_{1} = 1.3330$ , $n_{2} = 1.8052$ , $ν_{1} = 57.07$ , $ν_{2} = 25.43$ , $n_{3} = n_{1}$ , $ν_{3} = ν_{1}$
	$f^{'} = 55$	$f^{'} = 82.5$	$f^{'} = 137.5$	$f^{'} = 165$	$d$
	$r / 730.3056$	$r / 74.4234$	$r / 53.7200$	$r / 55.6694$	$d$
1	0.4181	0.4510	0.4510	0.4181
2	−0.4188	−0.3612	−0.3612	−0.4188
3	−0.7195	−0.5649	−0.5649	−0.7195
4	−0.5190	−0.4545	−0.4545	−0.5190
	$- r / 34.8367$	$- r / 26.7195$	$- r / 31.8809$	$- r / 45.2755$	20
5	0.6656	0.7102	0.7102	0.6656
6	−0.3808	−0.2777	−0.2777	−0.3808
7	−0.6142	−0.3841	−0.3841	−0.6142
8	−0.3430	−0.3323	−0.3323	−0.3430
	$r / 36.5817$	$r / 41.3782$	$r / 78.4208$	$r / 242.4949$	25
9	1.0007	0.8843	0.8843	1.0007
10	−0.2404	−0.2492	−0.2492	−0.2404
11	−0.3163	−0.3318	−0.3318	−0.3163
12	−0.2925	−0.3042	−0.3042	−0.2925

$S_{I}$	$S_{I I}$	$S_{I, 0}$	$S_{I I, 0}$	$r_{1}$	$r_{4}$	$d_{2}$	$f^{'}$	Error [%]
1.8357e−04	−1.4925e−03	1.8951e−04	−1.5252e−03	20.00	−20.00	1.00	3.0027e $+$ 01	−3.2333e $+$ 00
2.3315e−05	−3.7720e−04	2.3689e−05	−3.8129e−04	40.000	−40.00	1.00	6.0053e $+$ 01	−1.6019e $+$ 00
6.9449e−06	−1.6825e−04	7.0189e−06	−1.6946e−04	60.000	−60.00	1.00	9.0080e $+$ 01	−1.0647e $+$ 00
2.9377e−06	−9.4811e−05	2.9611e−06	−9.5322e−05	80.000	−80.00	1.00	1.2011e $+$ 02	−7.9727e−01
1.5065e−06	−6.0744e−05	1.5161e−06	−6.1006e−05	100.00	−100.00	1.00	1.5013e $+$ 02	−6.3723e−01

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Applied Optics