{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T09:18:27Z","timestamp":1785403107973,"version":"3.56.0"},"reference-count":25,"publisher":"Optica Publishing Group","issue":"15","license":[{"start":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T00:00:00Z","timestamp":1784764800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2026,7,23]],"date-time":"2026-07-23T00:00:00Z","timestamp":1784764800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62127901"],"award-info":[{"award-number":["62127901"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2026,7,27]]},"abstract":"<jats:p>A computer-generated hologram (CGH) is a high-precision method for testing complex surfaces. However, its applicability is limited by the aperture constraints of the fabrication equipment, rendering it challenging to effectively measure large-aperture, high-precision freeform mirrors. In this study, we propose a hybrid compensation approach combining CGH and a spherical mirror for testing large-aperture low-sag freeform mirrors. By introducing a virtual equivalent surface, we developed a hybrid computational method to calculate the CGH phase function. An interferometric data-processing model was established by incorporating mapping distortion correction, surface error reconstruction, and spherical mirror error removal. Experimental validation was performed on a rounded rectangular off-axis freeform mirror with a clear aperture of 698\u2005mm\u2009\u00d7\u2009210\u2005mm, and comparative measurements were conducted using Dutch United Instruments. Root mean square density analysis shows that the hybrid compensation method achieves a low-frequency measurement accuracy of 3.6\u2005nm root mean square (RMS) and a clear aperture surface measurement accuracy of 8.3\u2005nm RMS. This method enables high-precision testing of large-aperture, low-sag freeform surfaces, and the spherical mirror compensator demonstrates a degree of general applicability.<\/jats:p>","DOI":"10.1364\/oe.587370","type":"journal-article","created":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T09:00:07Z","timestamp":1783501207000},"page":"28478","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hybrid compensation method for testing large-aperture low-sag freeform mirrors"],"prefix":"10.1364","volume":"34","author":[{"given":"Hongshi","family":"Li","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Advanced Manufacturing for Optical Systems"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Qiang","family":"Cheng","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Advanced Manufacturing for Optical Systems"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhuofei","family":"Ding","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Advanced Manufacturing for Optical Systems"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9774-7690","authenticated-orcid":true,"given":"Longxiang","family":"Li","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Advanced Manufacturing for Optical Systems"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jia","family":"Li","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Advanced Manufacturing for Optical Systems"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yushan","family":"Han","sequence":"additional","affiliation":[{"name":"Changchun Normal University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Donglin","family":"Xue","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Advanced Manufacturing for Optical Systems"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Xuejun","family":"Zhang","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/012rct222","id-type":"ROR","asserted-by":"publisher"}]},{"name":"University of Chinese Academy of Sciences"},{"name":"State Key Laboratory of Advanced Manufacturing for Optical Systems"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,7,23]]},"reference":[{"key":"oe-34-15-28478-R1","doi-asserted-by":"publisher","first-page":"36702","DOI":"10.1364\/OE.503494","type":"journal-article","volume":"31","author":"Wang","year":"2023","journal-title":"Opt. 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