Study On Shape Of Membrane Mirror Applied By Uniform Load

With the development of space optics, the optical systems with large apertures are required. As the diameter and the weight of an optical element made by traditional technology restrict mutually, and are limited by the payload of transport equipments, new materials and technologies are needed to be adopted and developed for the manufacture of large and light-weight optical components. The membrane mirror with a substrate of flexible film has characteristics of lightweight, compact-deployable and low cost compared to the traditional one. And it is prospected to be applied in future large space optical systems.However, there are very big differences between the design and manufacture of the membrane mirror and that of the traditional mirror. In this thesis, the shape of the membrane mirror applied by uniform load is studied and analyzed theoretically. The following aspects are included.Firstly, the development history of the membrane mirror and the recent research situation in domestic and oversea are introduced briefly.Secondly, the mathematics model of the shape of membrane mirror is established through the analysis and comparison of several thin film models and their solutions, such as Hencky's circle-film series solution, Sergey A.Dimakov's model and solution and semi-sphere model and solution, which is derived from the shell model. It is shown that Dimakov's solution is closest to the standard parabolic equation, and than it is used as a theoretical basis for the further studies.Then, based on finite element method (FEM) and by using finite element analysis software, the shapes of membrane mirrors with different diameters, different F numbers, and applied by uniform load are studied. Combining with the aberration theory, 37 Zernike coefficients are achieved by fitting the discrete data got from the analysis result of FEM. These Zernike coefficients correspond to the aberrations of the shaped membrane mirror and each kind of aberration can be separated. The calculation and analysis results show that the main aberration of the shaped membrane mirror applied by uniform loads is the spherical aberration. For the membrane mirrors with same apertures, the larger the F number is, the less the spherical aberration will be. If the spherical aberration is removed, the shape of the membrane mirror will be approach to that of a standard parabolic one. And the membrane mirror can be used in practical optical system.In conclusion,the aberration value of a membrane mirror can be obtained by combining finite element analysis method and aberration theory. The research results supply a foundation for further design and shape control of membrane mirrors.