Modeling framework for piezoelectrically actuated MEMS tunable lenses

Abstract

WWe report a modeling framework for evaluating the performance of piezoelectrically actuated MEMS tunable lenses. It models the static opto-electromechanical coupling for symmetric configurations of piezoelectric actuators based on the laminated-plate theory, linear piezoelectricity, and ray tracing. With these assumptions, it helps to find geometrical parameters for actuators on clamped square or circular diaphragms that give a diffraction-limited tunable lens with minimum F-number. The tunable lens' optical performance and its focusing capability, alone and in combination with a paraxial fixed lens, were calculated in terms of object distance and actuation voltage. Using the modeling framework, we confirmed that the modulation transfer function for objects located at different distances remains the same after voltage adjustment.

Optical performance of piezoelectrically actuated MEMS tunable lenses with various pupil geometries

“…For case 6, with all γ values of interest, we have previously found that N ¼ 28 is sufficient to obtain less than 10% l 2 relative error norm when comparing the displacement from the variational solution against FEM. 15 This observation still holds for the other polygonal-shaped pupils.…”

“…In a previous research work, 15 we have developed a variational formulation based on the classical laminated plate theory, linear piezoelectricity, quasielectrostatic conditions, and a thin film approximation. Originally, it was used to predict the displacement profile of the transparent membrane in case 6 [refer to Fig.…”

“…Weighted Gegenbauer polynomials were chosen as basis functions in order to satisfy the clamped boundary conditions of zero deflection and zero slope along the diaphragm edges. 15 In addition, they are orthogonal and easily mapped to Zernike polynomials, which suits an optical representation of wavefronts. For case 6, with all γ values of interest, we have previously found that N ¼ 28 is sufficient to obtain less than 10% l 2 relative error norm when comparing the displacement from the variational solution against FEM.…”

“…15 for further details). The flexural rigidity varies over the diaphragm due to the difference in layer structures between the actuator and the pupil areas.…”

“…The first part of this framework is to model the static electromechanical performance based on variational methods introduced in a previous work. 15 For verification of the electromechanical model, we compare the lens displacement from the variational solutions against the finite element method (FEM). The The second part is to quantitatively investigate the tunable lens's optical performance using ray tracing by analyzing its F-number (F#), RMS wavefront error (RMSWFE), and modulation transfer function (MTF).…”