This dissertation discusses the fundamental limits of scanning mirror design, focusing on the limitations due to the interaction between mechanical properties (mirror flatness and dynamic deformation), and optical properties (beam divergence and optical resolution). The performance criteria for both resonant-scanning mirrors and steady-state, beam-positioning mirrors are related to the mirror geometries, desired optical resolution, material properties, and mechanical resonant frequencies. The optical resolution of the scanning mirror is linearly dependent on the mirror length, so longer mirrors should provide higher-resolution scanners. However, when undergoing an angular acceleration mirrors exhibit dynamic deformation, which is shown to be proportional to the fifth power of the length. The mirror length that gives the highest resolution for a desired resonant frequency is derived by matching the dynamic deformation to the Rayleigh limit; mirrors designed to satisfy this equality provide nearly diffraction-limited optical resolution at the highest possible resonant frequency.
Using this formulation there is a maximum achievable resonant frequency for a desired optical resolution that depends on the mirror material properties, its thickness, and the maximum scan angle. If the maximum achievable resonant frequency is higher than a few kilohertz, only MEMS-scale mirrors can achieve it. Therefore, we show that MEMS provides an enabling technology for new optical-scanner applications at multi-kHz frequencies.
Two different implementations of MEMS scanning mirrors are presented: polysilicon surface-micromachined mirrors and a new design we call the Staggered Torsional Electrostatic Combdrive (STEC) micromirror. The surface-micromachined mirrors are shown to be capable of reliable operation, but they have significant performance limitations caused by the limited thickness obtainable with the LPCVD-polysilicon structures. Calculations show that surface-micromachined mirrors of thickness 1.5 um and diameter 550 um are only capable of scanning +/-10 degrees at 251 Hz while retaining diffraction-limited optical performance.
The STEC micromirrors, designed to overcome the limitations of the surface-micromachined mirrors, are capable of much higher-speed scanning (up to 61 kHz) without performance-limiting dynamic deformation of the mirror surface. A 550 um-diameter mirror was scanned +/-3.92 degrees at 9.24 kHz with only 40 nm of dynamic deformation. The STEC micromirror structure also eliminates the need for post-fabrication assembly that has been problematic in producing surface-micromachined mirrors, and eliminates hinges that can cause unwanted and uncontrollable mirror motion during operation.
The STEC micromirror fabrication process is extended to create Tensile Optical Surface (TOS) micromirrors -- mirrors with thick silicon rib support structures and thin membranes that provide the reflective surface. TOS mirrors are designed for high-speed steady-state beam steering, so they have low inertia, high-torque actuators, and maintain optical flatness below the Rayleigh limit under static and dynamic conditions.
An application of scanning mirrors is presented: a raster-scanning video display. This demonstration uses two surface-micromachined mirrors scanning in orthogonal directions to reflect a modulated laser beam in a raster pattern. By interfacing this raster-scanning system with a computer video card, we demonstrate a full-motion video system with resolution of 41 x 52 pixels and grayscale capability. The dynamic deformation of the surface-micromachined MEMS mirrors used in this video display is shown to be the factor that limits its optical resolution.