Numerical solution of deformation of circular membrane of liquid lens under uniform hydrostatic pressure

Petr Pokorný; Filip Šmejkal; Pavel Kulmon; Antonín Mikš; Jiří Novák; Pavel Novák; Milan Jirásek; Martin Horák

doi:10.1117/12.2269505

26 June 2017 Numerical solution of deformation of circular membrane of liquid lens under uniform hydrostatic pressure

Petr Pokorný, Filip Šmejkal, Pavel Kulmon, Antonín Mikš, Jiří Novák, Pavel Novák, Milan Jirásek, Martin Horák

Proceedings Volume 10330, Modeling Aspects in Optical Metrology VI; 1033016 (2017) https://doi.org/10.1117/12.2269505
Event: SPIE Optical Metrology, 2017, Munich, Germany

Abstract

This paper is focused on a theoretical general description of membrane deformation in membrane liquid lenses, which is based on the theory of large deformations of thin plates under uniform hydrostatic loading. The general formulas are derived, leading to a system of differential equations that describe the shape of a deformed membrane. Since an analytical solution cannot be found, numerical methods are applied and the membrane shape is calculated for given practical examples. Further, the dependency of maximal deflection of the membrane on the applied hydrostatic pressure is analysed. For a better understanding and possibility of modelling the membrane shape in an optical design software, the shape is depicted as aspherical. Finally, the theoretical simulations are compared with experimental results for a given membrane and applied loadings. It is clearly seen that the shape of the membrane does not correspond to a sphere even under low applied pressures. Therefore, the presented analysis could have a significant impact in optical design. Using the results of the paper and numerical examples, one can easily model many cases of membrane liquid lenses and exploit the results of the simulation for precise description of optical systems with active components.

Citation Download Citation

Petr Pokorný, Filip Šmejkal, Pavel Kulmon, Antonín Mikš, Jiří Novák, Pavel Novák, Milan Jirásek, and Martin Horák "Numerical solution of deformation of circular membrane of liquid lens under uniform hydrostatic pressure", Proc. SPIE 10330, Modeling Aspects in Optical Metrology VI, 1033016 (26 June 2017); https://doi.org/10.1117/12.2269505

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