Mr. Long-jun Jiang Profile

Long-jun Jiang

at Soochow Univ

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Proceedings Article | 19 December 2013 Paper

Design and analysis of multi-electrodes distribution for shaping of electrostatic stretched membrane mirror

Long-jun Jiang, Xiao-ru Wei, Bin Yang, Min-xue Tang

Proceedings Volume 9046, 90460N (2013) https://doi.org/10.1117/12.2034662

KEYWORDS: Mirrors, Shape analysis, Electrodes, Finite element methods, Protactinium, Error analysis, Optics manufacturing, Space mirrors, Imaging systems, Zernike polynomials

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One of the key technologies which need to be solved in developing membrane mirror is the surface shape control of the mirror. The pressure distribution and calculation method for the shape of a membrane paraboloidal mirror are studied in this paper. According to Karman equation in circular membrane theory, the analytic expression of the radial continuous distributed pressure load used to form a membrane paraboloidal mirror with certain aperture and F number is solved out under certain radial displacement condition. Taking the example of membrane paraboloidal mirror with diameters of 200mm, 300mm, 500mm, and F number of 10, the number and the radial width of sub-electrodes are optimized. It is founded that by using multi-electrodes distribution mode that the radial width of center sub-electrode is 1.6 times longer than that of the rest concentric annulus electrodes with same radial width, the deviation between the membrane mirror shape and the standard paraboloid surface shape can be effectively reduced. The surface shape of a membrane mirror in 300mm diameter and F/10 that is formed by electrostatic stretching through a multi-electrodes plate with insulation intervals among sub-electrodes or not are simulated by using finite element analysis. It may provide a theoretical basis for practical control of membrane mirror shape.

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