{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,23]],"date-time":"2026-10-23T20:50:21Z","timestamp":1792788621091,"version":"4.5.0"},"reference-count":31,"publisher":"Optica Publishing Group","issue":"20","license":[{"start":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T00:00:00Z","timestamp":1790553600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2026,9,28]],"date-time":"2026-09-28T00:00:00Z","timestamp":1790553600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"name":"National Natural Science Foundation of China","award":["J0017-2326-QT"],"award-info":[{"award-number":["J0017-2326-QT"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China Young Scientists Fund","award":["52305519"],"award-info":[{"award-number":["52305519"]}],"id":[{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"crossref"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2026,10,5]]},"abstract":"<jats:p>The grazing-incidence operating mode of large-aperture X-ray mirrors imposes bidirectional anisotropic requirements on surface figure accuracy: extremely stringent in the meridional direction, while relatively relaxed in the sagittal direction. The strict meridional accuracy requirement necessitates the use of small-beam deterministic figuring processes, making machining efficiency a critical bottleneck to be overcome. To address this issue, this paper proposes a spatially decoupled figuring strategy based on a bidirectionally anisotropic elliptical diaphragm. By exploiting the disparity in accuracy requirements between the meridional and sagittal directions, a non-axisymmetric ion-beam removal function is designed. First, a multi-objective collaborative optimization model is established, and the diaphragm dimensions are optimized using the Non-dominated Sorting Genetic Algorithm II (NSGA-II) with an elitist strategy. An optimal structural parameter of 4\u2005mm (meridional) \u00d7 7\u2005mm (sagittal) is determined. The geometric decoupling characteristics and stability of the bidirectionally anisotropic removal function are then verified through multiphysics-field simulations and fixed-point calibration experiments. Finally, figuring simulations and experimental validation are conducted on a \u03a6100\u2005mm monocrystalline silicon substrate. Compared with the conventional high-precision scheme using a \u03a64\u2005mm circular diaphragm, the proposed strategy increases the volumetric removal rate to 304%, reduces the machining time to 32.3%, while achieving a meridional slope error converged to 0.28 \u00b5rad and a surface figure height RMS error converged to 1.850\u2005nm. The figuring capability is comparable to that of the high-precision scheme. This work not only theoretically elucidates the formation mechanism of bidirectionally anisotropic removal functions, but also provides an engineering-feasible technological pathway for the fabrication of large-aperture, high-precision X-ray mirrors.<\/jats:p>","DOI":"10.1364\/oe.589965","type":"journal-article","created":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T07:00:08Z","timestamp":1779260408000},"page":"37618","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Research on ultra-fast fabrication method of bidirectionally anisotropic Ion beam figuring for large-aperture nanoradian X-ray mirrors"],"prefix":"10.1364","volume":"34","author":[{"given":"Yusheng","family":"Wang","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05d2yfz11","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Hunan Key Laboratory of Ultra-Precision Machining Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yifan","family":"Dai","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05d2yfz11","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Hunan Key Laboratory of Ultra-Precision Machining Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chaoliang","family":"Guan","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05d2yfz11","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Hunan Key Laboratory of Ultra-Precision Machining Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3289-3563","authenticated-orcid":true,"given":"Chunyang","family":"Du","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05d2yfz11","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Hunan Key Laboratory of Ultra-Precision Machining Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Meng","family":"Liu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05d2yfz11","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Hunan Key Laboratory of Ultra-Precision Machining Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jie","family":"Hu","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/05d2yfz11","id-type":"ROR","asserted-by":"publisher"}]},{"name":"Hunan Key Laboratory of Ultra-Precision Machining Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,9,28]]},"reference":[{"key":"oe-34-20-37618-R1","first-page":"18","type":"journal-article","volume":"2","author":"Geng","year":"2025","journal-title":"Acta Optica Sinica(Online)"},{"key":"oe-34-20-37618-R2","first-page":"351","type":"journal-article","volume":"61","author":"Li","year":"2024","journal-title":"Laser & Optoelectronics Progress"},{"key":"oe-34-20-37618-R3","doi-asserted-by":"publisher","first-page":"82","DOI":"10.1038\/s42005-023-01195-z","type":"journal-article","volume":"6","author":"Raimondi","year":"2023","journal-title":"Commun. 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