{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,9]],"date-time":"2026-06-09T15:52:16Z","timestamp":1781020336881,"version":"3.54.1"},"reference-count":29,"publisher":"Optica Publishing Group","issue":"3","license":[{"start":{"date-parts":[[2023,1,13]],"date-time":"2023-01-13T00:00:00Z","timestamp":1673568000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR"},{"start":{"date-parts":[[2023,1,13]],"date-time":"2023-01-13T00:00:00Z","timestamp":1673568000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"State Key Laboratory of Applied Optics"}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Appl. Opt."],"published-print":{"date-parts":[[2023,1,20]]},"abstract":"<jats:p>To reduce the surface figure error induced by mechanical strains during the integration process of a high-precision mirror, a cost-efficient compensation method by spring preloads is proposed. The study is based on the primary mirror of a Ritchey\u2013Chr\u00e9tien space telescope with a focal length of 1200\u00a0mm. First, the surface figure degradation of the mirror during the assembly process is expressed and analyzed. Then, a finite element model of the mirror and its mounting structure is established, and surface deformations caused by different preloading forces are simulated. An optimized combination of different preloads was obtained through data fitting, and the influence of the combined preload on the mirror was analyzed. The simulation results show that ring preloads mainly affect spherical aberration and high-order spherical aberrations, while quadrupole preloads mainly affect astigmatism, and the optimized preload can compensate for the surface figure error from <jats:inline-formula>\n      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n\t<mml:mrow class=\"MJX-TeXAtom-ORD\">\n\t  <mml:mn>0.120<\/mml:mn>\n\t<\/mml:mrow>\n\t<mml:mi>\u03bb<\/mml:mi>\n      <\/mml:math>\n    <\/jats:inline-formula> RMS to <jats:inline-formula>\n      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n\t<mml:mrow class=\"MJX-TeXAtom-ORD\">\n\t  <mml:mn>0.088<\/mml:mn>\n\t<\/mml:mrow>\n\t<mml:mi>\u03bb<\/mml:mi>\n      <\/mml:math>\n    <\/jats:inline-formula> RMS. Last, the surface figure error of the mirror is measured by experiments under optimized preloads, and the result is <jats:inline-formula>\n      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"inline\">\n\t<mml:mrow class=\"MJX-TeXAtom-ORD\">\n\t  <mml:mn>0.084<\/mml:mn>\n\t<\/mml:mrow>\n\t<mml:mi>\u03bb<\/mml:mi>\n      <\/mml:math>\n    <\/jats:inline-formula> RMS, which verifies the correctness of the analysis process and effectiveness of the compensation method.<\/jats:p>","DOI":"10.1364\/ao.477606","type":"journal-article","created":{"date-parts":[[2022,12,21]],"date-time":"2022-12-21T15:00:08Z","timestamp":1671634808000},"page":"635","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Surface figure compensation of the primary mirror in a Ritchey\u2013Chr\u00e9tien space telescope by spring preloads"],"prefix":"10.1364","volume":"62","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4167-4178","authenticated-orcid":true,"given":"Shuqiang","family":"Jia","sequence":"first","affiliation":[{"name":"Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Science"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wei","family":"Huang","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mingfei","family":"Xu","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xin","family":"Qin","sequence":"additional","affiliation":[{"name":"Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Science"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2023,1,13]]},"reference":[{"key":"ao-62-3-635-R1","doi-asserted-by":"publisher","first-page":"115109","DOI":"10.1117\/1.OE.54.11.115109","volume":"54","author":"Lin","year":"2015","journal-title":"Opt. 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