Modeling and analysis of MEMS inertial sensors with grating-based interferometric optical readout
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Displacement detection using optical interferometric techniques allows for low minimum-detectable displacements which are unmatched by other displacement measurement methods as device sizes are scaled down. The use of microfabricated diffractive optical elements as beam splitters has proven an effective way to realize miniature and robust optical interferometers. However, models used to predict the optical performance of grating-based displacement sensors are frequently based on phase-varying aperture function, rooted in scalar diffraction theory, and fail to predict critical features of optical system behavior. A new computational model has been developed which includes several important physical effects, neglected in the varying-phase analysis, such as electromagnetic boundary effect, Talbot self-imaging effects, and the effect of incident beam divergence. Light propagation through the system is captured using a new scalar-vector hybrid technique, specifically designed to model grating-based displacement detection systems. Scalar Fourier optics methods are used to model the propagation of light over free-space regions, while computational electromagnetic methods such as rigorous coupled-wave analysis (RCWA) and finite-difference time-domain (FDTD) simulations are used to compute the interaction of the light with the diffraction gratings, where the vector nature of the electromagnetic field is important. Combining the scalar and vector approaches in a single model allows for much faster simulations than could be achieved with RCWA alone, which is important for undertaking parametric studies and optimizations which involve several varied parameters and many test cases. The model is then applied to understanding the impact of different design choices on system behavior, by varying one parameter at a time and examining the characteristics of resulting optical modulation curves. The most simple design for the optoelectronics in MEMS sensors involves a VCSEL source with no focusing optics. The optically-limited minimum detectable displacement for a lens-free system is investigated and determined to be 3.5 fm/√Hz for a system with 1 mW of incident light at a wavelength of 850 nm. Ronchi-ruled diffraction gratings have the most simple geometries to fabricate, but capturing all of the modulated light in the central beam diffracted by such a grating is difficult when a surface-normal source incidence is used. This can complicate the packaging of microfabricated devices with integrated optoelectronics. The development of a new multi-region diffraction grating is presented, which uses out-of-phase regions to eliminate the zeroth order beam via destructive interference. Prototype gratings were succesfully fabricated and tested. The measured sensitivity is similar to that of more conventional Ronchi-ruled gratings, demonstrating their suitability for grating-based interferometric sensors.