Calculation of a surface shape of a pressure actuated membrane liquid lens

• New nonlinear differential equation for membrane deflection is derived.
• Numerical solution of the problem by optimization techniques is proposed.
• Comparison of proposed method with classical solution is given.
• The deviation between both methods is not negligible.
• The proposed method has to be used for surface shape calculation.

Our work is focused on the problem of theoretical evaluation of the surface shape of a variable focus membrane lens. In order to be able to determine the imaging properties of such a lens one has to know the shape of the membrane for a given pressure of the liquid inside the lens chamber with high accuracy. In our work a generalized nonlinear differential equation describing this problem is derived and the solution of this equation using expansion into series and transformation of the problem into constraint optimization problem is proposed. The proposed method enables us to calculate the shape of a membrane lens surface with satisfactory accuracy for further calculations such as e.g. calculation of aberrations of such a lens, imaging properties etc.