Abstract This paper performs an analysis to the systematic surface figure error influenced by three factors including errors of faceted paraboloids, fabrication imperfection and random thermal strains in orbit. Firstly, the computational formulas for root-mean-square surface deviations caused by these factors are presented respectively. The stochastic finite element method is applied to derive the computational formulas of fabrication imperfection and random thermal strains, by which the sensitivity of surface accuracy to component imperfection can be revealed. Then the Monte Carlo simulation method is introduced to obtain the surface figure by sampling test on random errors. Finally, the analytical method is applied to the research on the surface figure error of AstroMesh deployable reflector. The results show that the deviations between the root-mean-square surface errors calculated by the proposed formulas with less consuming time and those by the Monte Carlo simulation method are less than 2%, which indicates that the proposed method is efficient and receivable enough to analyze systematic surface figure error of a large deployable antenna. Moreover, further investigations on the relationship between surface RMS deviation and the antenna parameters including aperture and the number of subdivisions are presented in the end.

Highlights • The sources of surface errors are investigated. • The formulas of random errors based on probabilistic finite element method are proposed. • The sensitivity analysis of surface accuracy to component imperfection is presented. • The relevance of surface RMS errors to antenna parameters is revealed.