On The Pointing And Jitter Characterization Of MEMS Two-Axis (Tip-Tilt) Mirrors
Edwards, Clinton Lee
Davis, Christoper C
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This dissertation presents three first-principles analytic, closed-form models that describe the pointing characteristics of MEMS Two-Axis (Tip-Tilt) Mirrors: (1) a 2D Torque Model, (2) a Micro-mirror Pointing Model (MPM), and (3) a Micro-mirror Jitter Model (MJM). The 2D Torque Model accounts for all of the fundamental electrodynamics inherent in the operation of a MEMS Two-Axis (Tip-Tilt) Mirror. The 2D Torque Model is utilized in the MPM model and the MJM model and is a function of both axis angles. These three models provide explicit relationships between MEMS mirror physical, electrical, and environmental design parameters, and mirror performance. The MPM model, consisting of coupled damped harmonic oscillators with the 2D Torque Model as an input, is used to analyze the dynamics of the mirror. This formulation is imposed by Euler equations and the mirror's rigid structure. A generalized torque function, "G", is presented that utilizes symmetry in the torsional expressions to facilitate software implementation. A methodology is explained for determining the dynamic constants for the mirror as well as an "effective length" which accounts for electric field fringing. Since MEMS fabrication leads to variations in physical properties, the MPM model can be calibrated for a particular mirror to compensate for this variation. Experimental measurements and the MPM model results are in close agreement for steady-state and transient mirror dynamics. The MJM model was created using the MPM model to address the effects of mirror facet jitter. The MJM model provides an explicit relationship between noise sources and the resulting mirror jitter. It can be used to simulate the effects of mirror jitter as a function of the originating noise sources which are: (1) control voltage fluctuation, (2) platform vibration, (3) Brownian motion noise. A methodology is developed to validate the MJM model. Measurements from the resulting experimental apparatus support the model. Additionally, the experimental apparatus permitted pressure dependent measurements to be made. Mirror jitter was recorded and analyzed for varying pressure and tip-tilt angles. Damping constants (for both axes) were measured. Brownian motion generated jitter was isolated and its variance observed to be pressure invariant as the model predicted.