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Design and Analysis of Hemispherical Electrostatic Micro Deformable Focusing Mirror

[+] Author Affiliations
Shang-Wei Tsai, Meng-Ju Lin

Feng Chia University, Taichung, Taiwan, R.O.C.

Paper No. ESDA2004-58265, pp. 497-503; 7 pages
  • ASME 7th Biennial Conference on Engineering Systems Design and Analysis
  • Volume 3
  • Manchester, England, July 19–22, 2004
  • ISBN: 0-7918-4175-8 | eISBN: 0-7918-3741-6
  • Copyright © 2004 by ASME


For uniform deformation, based on bulk microfabrication with isotropic etching, two types of hemispherical electrostatic micro deformable focusing mirror are designed. One of the focusing mirrors is center-anchored, and the other is circular clamped. Using theory of shells, theoretical solution of deformation under uniform electrostatic force is derived. For more detail analysis of the electrostatic and elastic forces coupling problem, finite element is used to analyze the deformation of the mirror structure. Applying electrostatic force, the profile of micro focusing mirror will be not the spherical and change to become a curve like parabolic surface. Using least square method, the curve is fitted as a parabolic curve and the focal lengths of the focusing micro mirror are obtained. The result shows the focal length without applying electrostatic force can be determined by different micro mirror radius and isotropic etching depth. When the electrostatic forces are applied, the deformation and the focal length change differently between the two types of focusing mirror. For circular clamped micro mirror, the deformation is larger near circular clamped region and uniform in the center regime. Therefore, the relation of focal length and applying voltage is a concave curve with minimum values. That is, the focusing length decreasing as the applying voltage increasing and reaches a limit values. When the applying voltage continues increasing after reaching the minimum value, the focal length increases fast. It also shows the thicker structure layer needs larger applied voltage. But the focal length changes in larger stroke. The pull-in voltage is about 100 volt when the structure layer are both 2 μm. However, the pull-in voltage increases nonlinearly as gap increasing. When the gap increases to 4 μm, the pull-in voltage is about 300 volt. The result shows center-anchored micro mirror has better performance. The deformation is more uniform and the focal length increases nonlinearly as applied voltage increasing. It is found the stroke of focal length is larger and the applied voltage is less. The results shows even when the gap and structure layer is 4 and 2 μm, the pull-in voltage is about 62 volts. However, the stoke changes from 990 to about 1320 μm when applying voltage is from 0 to 60 volts. Therefore, with low applied voltage and large focal length stoke, the center-anchored micro mirror has good performance.

Copyright © 2004 by ASME
Topics: Design , Mirrors



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