Double curvature membrane lens

Antonín Mikš; Petr Pokorný

doi:10.1364/AO.401892

Applied Optics
Vol. 59,
Issue 32,
pp. 9924-9930
(2020)
•https://doi.org/10.1364/AO.401892

Double curvature membrane lens

Antonín Mikš and Petr Pokorný

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Antonín Mikš and Petr Pokorný, "Double curvature membrane lens," Appl. Opt. 59, 9924-9930 (2020)

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Abstract

The paper presents a theoretical analysis of properties of a specific liquid membrane lens composed of two axially symmetric membranes of different thicknesses and double curvature. These membranes enclose a space where an optical liquid is filled. Mechanical and optical properties of the lens are then changed by varying the volume of the liquid. The paper presents new formulas for calculation of membrane deflections, radii of curvatures of the membranes, and axial geometry, which offer to minimize the third-order spherical aberration of the lens for an object at infinity. The presented theory is examined on specific examples.

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Equations (25)

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$f^{'} = 1 m m$ , $d = 0 m m$			$f^{'} = 1 m m$ , $d = 0.1 m m$
$n$	$r_{1} [m m]$	$r_{2} [m m]$	$n$	$r_{1} [m m]$	$r_{2} [m m]$
1.500	0.5833	−3.5000	1.500	0.5891	−3.1197
1.625	0.6561	−13.1818	1.625	0.6628	−10.3311
1.750	0.7143	15.0000	1.750	0.7217	18.0191
1.875	0.7614	5.8649	1.875	0.7696	5.9985
2.000	0.8000	4.0000	2.000	0.8088	3.9673

$H = 5 m m$ , $n = 1.333$ , $λ = 587 n m$ , $h_{1} = 0.5 m m$ , $h_{2} = 0.8 m m$ , $d_{k} = 2 m m$
$p [k P a]$	$X$	$f^{'} [m m]$	$d [m m]$	$r_{1} [m m]$	$r_{2} [m m]$	$1000 S_{I}$	$δ y^{'} [m m]$	$δ y_{O S L O}^{'} [m m]$	$w_{1} [m m]$	$w_{2} [m m]$
1.00	0.0735	75.4386	7.2779	45.9431	−53.2351	0.0111	−0.0524	−0.0508	2.8478	2.4301
4.00	0.0668	50.8614	10.4616	30.4838	−34.8445	0.0365	−0.1161	−0.1082	4.5723	3.8893
7.00	0.0618	44.3218	12.2750	26.2777	−29.7415	0.0554	−0.1536	−0.1390	5.5585	4.7165
10.00	0.0577	41.0056	13.6499	24.0992	−27.0491	0.0703	−0.1802	−0.1590	6.3086	5.3414

$p [k P a]$	$h_{1} [m m]$	$h_{2} [m m]$	$r_{1} [m m]$	$r_{2} [m m]$	$w_{1} [m m]$	$w_{2} [m m]$	$d_{t} [m m]$
1.00	0.0570	0.7503	11.1029	−25.9069	1.3676	0.5703	7.2548
4.00	0.2282	3.0009	11.1026	−25.9070	1.3677	0.5703	4.8329
7.00	0.3992	5.2520	11.1018	−25.9072	1.3678	0.5703	2.4107

$f^{'} = 1 m m$ , $d = 0 m m$			$f^{'} = 1 m m$ , $d = 0.1 m m$
$n$	$r_{1} [m m]$	$r_{2} [m m]$	$n$	$r_{1} [m m]$	$r_{2} [m m]$
1.500	0.5833	−3.5000	1.500	0.5891	−3.1197
1.625	0.6561	−13.1818	1.625	0.6628	−10.3311
1.750	0.7143	15.0000	1.750	0.7217	18.0191
1.875	0.7614	5.8649	1.875	0.7696	5.9985
2.000	0.8000	4.0000	2.000	0.8088	3.9673

$H = 5 m m$ , $n = 1.333$ , $λ = 587 n m$ , $h_{1} = 0.5 m m$ , $h_{2} = 0.8 m m$ , $d_{k} = 2 m m$
$p [k P a]$	$X$	$f^{'} [m m]$	$d [m m]$	$r_{1} [m m]$	$r_{2} [m m]$	$1000 S_{I}$	$δ y^{'} [m m]$	$δ y_{O S L O}^{'} [m m]$	$w_{1} [m m]$	$w_{2} [m m]$
1.00	0.0735	75.4386	7.2779	45.9431	−53.2351	0.0111	−0.0524	−0.0508	2.8478	2.4301
4.00	0.0668	50.8614	10.4616	30.4838	−34.8445	0.0365	−0.1161	−0.1082	4.5723	3.8893
7.00	0.0618	44.3218	12.2750	26.2777	−29.7415	0.0554	−0.1536	−0.1390	5.5585	4.7165
10.00	0.0577	41.0056	13.6499	24.0992	−27.0491	0.0703	−0.1802	−0.1590	6.3086	5.3414

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Applied Optics