A fast multiobjective optimization strategy for single-axis electromagnetic MOEMS micromirrors

Micro-opto-electro-mechanical (MOEMS) micromirrors are an enabling technology for mobile image projectors (pico-projectors). Low size and low power are the crucial pico-projector constraints. In this work, we present a fast method for the optimization of a silicon single-axis electromagnetic torsional micromirror. In this device, external permanent magnets provide the required magnetic field, and the actuation torque is generated on a rectangular multi-loop coil microfabricated on the mirror plate. Multiple constraints link the required current through the coil, its area occupancy, the operating frequency, mirror suspension length, and magnets size. With only rather general assumptions about the magnetic field distribution and mechanical behavior, we show that a fully analytical description of the mirror electromagnetic and mechanical behavior is possible, so that the optimization targets (the assembly size, comprising the mirror and magnets, and the actuation current) can be expressed as closed functions of the design parameters. Standard multiobjective optimization algorithms can then be used for extremely fast evaluation of the trade-offs among the various optimization targets and exploration of the Pareto frontier. The error caused by model assumptions are estimated by Finite Element Method (FEM) simulations to be below a few percent points from the exact solution.