A generalized electrostatic micro-mirror (GEM) model for a two-axis convex piecewise linear shaped MEMS mirror

C. L. Edwards; M. L. Edwards

doi:10.1117/12.818838

11 May 2009 A generalized electrostatic micro-mirror (GEM) model for a two-axis convex piecewise linear shaped MEMS mirror

C. L. Edwards, M. L. Edwards

Author Affiliations +

Proceedings Volume 7318, Micro- and Nanotechnology Sensors, Systems, and Applications; 73180W (2009) https://doi.org/10.1117/12.818838
Event: SPIE Defense, Security, and Sensing, 2009, Orlando, Florida, United States

Abstract

MEMS micro-mirror technology offers the opportunity to replace larger optical actuators with smaller, faster ones for lidar, network switching, and other beam steering applications. Recent developments in modeling and simulation of MEMS two-axis (tip-tilt) mirrors have resulted in closed-form solutions that are expressed in terms of physical, electrical and environmental parameters related to the MEMS device. The closed-form analytical expressions enable dynamic time-domain simulations without excessive computational overhead and are referred to as the Micro-mirror Pointing Model (MPM). Additionally, these first-principle models have been experimentally validated with in-situ static, dynamic, and stochastic measurements illustrating their reliability. These models have assumed that the mirror has a rectangular shape. Because the corners can limit the dynamic operation of a rectangular mirror, it is desirable to shape the mirror, e.g., mitering the corners. Presented in this paper is the formulation of a generalized electrostatic micromirror (GEM) model with an arbitrary convex piecewise linear shape that is readily implemented in MATLAB and SIMULINK for steady-state and dynamic simulations. Additionally, such a model permits an arbitrary shaped mirror to be approximated as a series of linearly tapered segments. Previously, "effective area" arguments were used to model a non-rectangular shaped mirror with an equivalent rectangular one. The GEM model shows the limitations of this approach and provides a pre-fabrication tool for designing mirror shapes.

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C. L. Edwards and M. L. Edwards "A generalized electrostatic micro-mirror (GEM) model for a two-axis convex piecewise linear shaped MEMS mirror", Proc. SPIE 7318, Micro- and Nanotechnology Sensors, Systems, and Applications, 73180W (11 May 2009); https://doi.org/10.1117/12.818838

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KEYWORDS

Mirrors

Micromirrors

Microelectromechanical systems

Cesium

Computer simulations

Curium

Simulink

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