Abstract

Due to fabrication difficulties, separately-polished segmented mirrors cannot meet the co-phasing surface shape error requirements in the segmented telescope system. Applying the global radius of curvature (GRoC) actuation system for the individual segments has become an effective solution in space-based telescopes. In this paper, we designed a segmented mirror with a GRoC actuation system. The direct optimization by numerical simulations has low computational efficiency and is not easy to converge for optimizing the actuation point’s position on the segmented mirror. For this problem, three common surrogates, including polynomial response surface (PRS), radial basis function neural network (RBFNN), and kriging (KRG), were summed to propose the multiple surrogates (MS) which have the higher approximate ability. The surrogates were then optimized through the multi-island genetic algorithm (MIGA), and the segmented mirror met the design requirement. Compared with direct optimization through numerical simulations, the results show that the proposed multiple-surrogate-based optimization (MSBO) methodology saves computational cost significantly. Besides, it can be deployed to solve other complex optimization problems.

Highlights

  • There exist significant interest in using segmented mirrors instead of a monolithic primary mirror to build a large-aperture telescope

  • For the space telescope, taking the James Webb Space Telescope (JWST) as an example, a global radius of curvature (GRoC) actuation system was designed for the non-insistency in the radius of curvature of segmented mirrors

  • After removing the GRoC actuation system and supporting structures, the registered surface shape error is used as a target map for the finely-polished

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Summary

Introduction

There exist significant interest in using segmented mirrors instead of a monolithic primary mirror to build a large-aperture telescope. For the space telescope, taking the James Webb Space Telescope (JWST) as an example, a global radius of curvature (GRoC) actuation system was designed for the non-insistency in the radius of curvature of segmented mirrors This system has two main applications: (1) After rough polishing of the JWST primary mirror, use of the GRoC actuation system to adjust the GRoC to meet the requirements and record the surface shape error at this time. Based on the response surface method (RSM) surrogate, J.C. Hsiao et al carried out a multi-objective optimization design on the robot arm’s size parameters, which improved the computational efficiency by 90% compared with optimization by numerical simulation [12].

Multiple Surrogates
Procedure of Multiple-Surrogate-Based Optimization
Design Requirements
Problem Description
Procedure of the Actuation Point’s Position Optimization

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