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Micro/Nano Lithography

Novel focus-control mirrors move further under closed-loop control

Application of micro-electromechanical systems deformable mirrors improves the total range of motion by greater than 50%, thus significantly increasing focus-control capabilities.
21 April 2010, SPIE Newsroom. DOI: 10.1117/2.1201004.002921

At present, motors and cams translate (move) glass lenses to actively adjust focus or zoom in optical systems. This approach becomes increasingly challenging to implement for optical systems miniaturized to millimeter dimensions for endoscopes or ultrathin cell phones. Because of size constraints and power and cost considerations, most cell phone-cameras currently do not offer true optical-focus control. Without this, however, it is not possible to image with high resolution both up close and far away. Similarly, endoscopic microscopes, which perform in vivo imaging for disease diagnosis or to guide minimally invasive surgery, have no satisfactory way to adjust focus. This limits their usefulness for performing diagnostic microscopic imaging of tissue in the body.

We have shown that deformable-membrane mirrors, a class of optical micro-electromechanical systems (MEMS) devices, can also provide focus control.1 Unlike a moving lens, a circular membrane mirror is fixed on its perimeter but has freedom of movement in its center. As the mirror's curvature is altered, the focal point of the reflected light changes. Using deformable MEMS over translating glass lenses allows elimination of moving parts and the motors to drive them, resulting in a low-power solution that can be miniaturized easily.

Deformable membranes, like many MEMS devices, are electrostatically actuated. A voltage is applied between a flexible, reflective surface and a rigid substrate to generate an attractive force (see Figure 1). An air gap exists between membrane and substrate that provides the space necessary for membrane movement. Deformable membranes are limited to an electrostatically actuated range of motion of approximately 44%.2 This limitation is due to the mirror snapping down when the voltage reaches a critical level, causing the device to collapse. Being able to use more of the air gap with a larger range of motion would increase the range of focus possible for these devices.

Figure 1. Top and cross-sectional views of a 750μm (diameter) circular mirror. A voltage (V) is applied across the mirror's top and bottom for electrostatic actuation. SU-8 2002: Photopolymer. Cr/Au: Chromium/gold.

Figure 2. Feedback circuit for closed-loop control of an electrostatic device with variable capacitance CD. The loop provides a device voltage that is inversely and directly proportional to CD and the input signal (VQ), respectively, by means of a high-voltage amplifier (H. V. Amp). b: Difference amplifier. fdiff, fref, fsense: Frequency difference, and reference and operating frequencies.

The force controlling deflection depends on the charge on the membrane. As the membrane deflects, the structure's capacitance and charge increase proportionally. When a mirror reaches its instability point, charge continues to build even if the voltage remains constant or begins to decrease. With open-loop voltage control, the device is unstable and collapses. To address this problem, our feedback-control scheme relies on capacitive sensing to provide a terminal voltage that is inversely proportional to the actuator's capacitance. This effectively maintains a constant charge on the actuator (subject to the performance limitations of the feedback loop). This implementation of feedback control, therefore, exhibits characteristics of constant-charge control.

Figure 2 shows a simplified schematic of our closed-loop control scheme. A high-voltage amplifier drives the mirrors. As the mirrors deflect, they have an associated variable capacitance CD. The latter is coupled to a ring oscillator that is comprised of three inverters and located close to the device to minimize the effect of parasitics. Changes in capacitance minutely influence the operating frequency of the ring oscillator. A reference frequency is generated using an auxiliary oscillator constructed from gates on the same substrate as the sensing oscillator. A delay (or ‘D’) flip flop determines the frequency difference, which provides a viable measure of the device capacitance. The difference frequency is multiplied by the input reference voltage VQ, and the effect of a constant offset frequency is removed by a difference amplifier. The resulting voltage is proportional to VQ/CD, which is provided to the input of the high-voltage amplifier. Using this feedback-control scheme, a mirror made from a membrane of silicon nitride was operable to 69% of the air gap under closed-loop control (see Figure 3), compared to 47% of the air gap under open-loop conditions.3 A membrane made from the photopolymer SU-8 2002 was operable to 75% of the air gap under closed-loop control.4

Figure 3. Normalized displacement versus device voltage under open- and closed-loop conditions on a 2mm×2.8mm elliptical silicon nitride mirror. As the device approaches snap down, the voltage applied decreases under closed-loop control.

Using our capacitance sensing and 1/CD proportional feedback control, we observed stable closed-loop displacement of deformable-membrane mirrors beyond their open-loop pull-in instability point, thus significantly increasing the range of motion. In addition, we achieved better control of the membranes near and at snap down. An advantage of our feedback approach is the simplicity of implementation. The feedback configuration requires access only to the actuation terminals of the MEMS device and is, therefore, straightforward to implement, with no requirement for extra displacement sensors or external means of measurement. The approach should be broadly applicable to electrostatic MEMS devices and readily extendible to multiple-electrode devices such as deformable mirrors with several actuation zones. In the future, we intend to use this feedback-control technique to improve both the overall displacement and surface-shape accuracy of multizone mirrors to provide focus control for in vivo microscopy and other imaging applications.

We acknowledge support from the National Science Foundation (NSF) under projects DBR-0754608 and IIP-0810778. The test devices were fabricated with support from the Montana Microfabrication and the Stanford Nano-Fabrication Facilities. Sarah Lukes is supported by an NSF Graduate Research Fellowship.

Sarah Lukes, Steven R. Shaw, David L. Dickensheets
Montana State University
Bozeman, MT

Sarah Lukes is working on her MS en route to a PhD degree in electrical engineering, with emphasis on deformable-membrane mirrors for focus and closed-loop control techniques to extend device performance.

Steven Shaw received his doctoral degree in electrical engineering from the Massachusetts Institute of Technology in 2000. He is currently an associate professor with interests in system identification and controls, electromechanical systems, energy, and fuel cells.

David Dickensheets is a professor of electrical engineering. His research interests include optical imaging and spectroscopy of tissues, and applications of microfabrication technologies to develop miniature optical instruments for biomedical and industrial imaging.