Abstract

This paper presents a complete model for analysis of the deformed shape of a prestressed circular axisymmetric membrane of a liquid lens. The governing equations are derived using the exact relation between displacements and the Green–Lagrange strains combined with the Saint Venant–Kirchhoff material law, which postulates a linear relation between the Green–Lagrange strains and the second Piola–Kirchoff stresses. A numerical solution based on minimization of potential energy is illustrated by an example, and the dependence of the maximum membrane deflection on material properties and initial prestress is analyzed. The theoretical model is then experimentally validated. It is shown that the model is suitable for large-strain analysis of liquid lens membranes and provides sufficiently accurate results that can be used in further analyses and simulations of imaging properties of active optical elements based on liquid lenses.

© 2017 Optical Society of America

Calculation of nonlinearly deformed membrane shape of liquid lens caused by uniform pressure

Petr Pokorný, Filip Šmejkal, Pavel Kulmon, Pavel Novák, Jiří Novák, Antonín Mikš, Martin Horák, and Milan Jirásek
Appl. Opt. 56(21) 5939-5947 (2017)

Dependence of the imaging properties of the liquid lens with variable focal length on membrane thickness

Antonín Mikš and Filip Šmejkal
Appl. Opt. 57(22) 6439-6445 (2018)

Double curvature membrane lens

Antonín Mikš and Petr Pokorný
Appl. Opt. 59(32) 9924-9930 (2020)

Surface profiling of an aspherical liquid lens with a varied thickness membrane

Zengqian Ding, Chinhua Wang, Zhixiong Hu, Zhenggang Cao, Zhen Zhou, Xiangyu Chen, Hongyu Chen, and Wen Qiao
Opt. Express 25(4) 3122-3132 (2017)

Spherical aberration free liquid-filled tunable lens with variable thickness membrane

Pengpeng Zhao, Çağlar Ataman, and Hans Zappe
Opt. Express 23(16) 21264-21278 (2015)