Extracting the zero-gravity surface figure of a mirror with data from three user-defined orientations

Jia Zhai; Fengtao Yan; Xiaoli Ren; Muxin Yu; Wenchuan Zhao; Haitao Liu

doi:10.1117/1.JATIS.5.3.034001

5 June 2019 Extracting the zero-gravity surface figure of a mirror with data from three user-defined orientations

Jia Zhai, Fengtao Yan, Xiaoli Ren, Muxin Yu, Wenchuan Zhao, Haitao Liu

Journal of Astronomical Telescopes, Instruments, and Systems, Vol. 5, Issue 3, 034001 (June 2019). https://doi.org/10.1117/1.JATIS.5.3.034001

Abstract

We present a method for extracting the zero-gravity surface figure of a mirror. If the structures and constraints of the mirror and its support mounts are invariable during measurement, we can use an algorithm to extract its zero-gravity surface figure by measured data obtained through three different orientations of the mirror. These orientations can be user-defined within the proposed rules, thereby reducing measuring constraints. The proposed algorithm is also available for the gravity-reversing method. To devise this algorithm, we propose and prove a nonlinear superposition property that the mirror system’s displacement of nodes at any gravity-included angle is equal to the sum of the projection of the displacement of nodes at θ = 0 and θ = π / 2. This method is verified through comparisons with a series of numerical stimulations.

Citation Download Citation

Jia Zhai, Fengtao Yan, Xiaoli Ren, Muxin Yu, Wenchuan Zhao, and Haitao Liu "Extracting the zero-gravity surface figure of a mirror with data from three user-defined orientations," Journal of Astronomical Telescopes, Instruments, and Systems 5(3), 034001 (5 June 2019). https://doi.org/10.1117/1.JATIS.5.3.034001

Received: 14 May 2018; Accepted: 15 May 2019; Published: 5 June 2019

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KEYWORDS

Mirrors

Finite element methods

Superposition

Data modeling

Mathematical modeling

Numerical analysis

Space mirrors

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