{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T21:03:30Z","timestamp":1773435810273,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T00:00:00Z","timestamp":1612483200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The design of innovative reference aspheric and freeform optical elements was investigated with the aim of calibration and verification of ultra-high accurate measurement systems. The verification is dedicated to form error analysis of aspherical and freeform optical surfaces based on minimum zone fitting. Two thermo-invariant material measures were designed, manufactured using a magnetorheological finishing process and selected for the evaluation of a number of ultra-high-precision measurement machines. All collected data sets were analysed using the implemented robust reference minimum zone (Hybrid Trust Region) fitting algorithm to extract the values of form error. Agreement among the results of several partners was observed, which demonstrates the establishment of a traceable reference full metrology chain for aspherical and freeform optical surfaces with small amplitudes.<\/jats:p>","DOI":"10.3390\/s21041103","type":"journal-article","created":{"date-parts":[[2021,2,5]],"date-time":"2021-02-05T08:33:48Z","timestamp":1612514028000},"page":"1103","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Traceable Reference Full Metrology Chain for Innovative Aspheric and Freeform Optical Surfaces Accurate at the Nanometer Level"],"prefix":"10.3390","volume":"21","author":[{"given":"Yassir","family":"Arezki","sequence":"first","affiliation":[{"name":"Laboratoire Commun de M\u00e9trologie (LCM), Laboratoire National de M\u00e9trologie et d\u2019Essais (LNE), 1 Rue Gaston Boissier, 75015 Paris, France"},{"name":"Universit\u00e9 Paris-Saclay, Universit\u00e9 Sorbonne Paris Nord, ENS Paris-Saclay, LURPA, 91190 Gif-sur-Yvette, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0776-3716","authenticated-orcid":false,"given":"Rong","family":"Su","sequence":"additional","affiliation":[{"name":"Manufacturing Metrology Team, Faculty of Engineering, University of Nottingham (UNOTT), Nottingham NG8 1BB, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ville","family":"Heikkinen","sequence":"additional","affiliation":[{"name":"VTT Technical Research Centre of Finland Ltd., Centre for Metrology MIKES, Tekniikantie 1, 02150 Espoo, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7ois","family":"Leprete","sequence":"additional","affiliation":[{"name":"THALES LAS France, Etablissement de Saint Heand, Boulevard Ravel de Malval, 42570 Saint Heand, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pavel","family":"Posta","sequence":"additional","affiliation":[{"name":"TOPTEC, Institute of Plasma Physics of the Czech Academy of Sciences, Za Slovankou 1782\/3, 182 00 Praha, Czech Republic"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Youichi","family":"Bitou","sequence":"additional","affiliation":[{"name":"National Institute of Advanced Industrial Science and Technology (AIST), National Metrology Institute of Japan (NMIJ), Tsukuba, Ibaraki 305-8563, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christian","family":"Schober","sequence":"additional","affiliation":[{"name":"Institute of Applied Optics (ITO), University Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, 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China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7905-1817","authenticated-orcid":false,"given":"Yohan","family":"Kondo","sequence":"additional","affiliation":[{"name":"National Institute of Advanced Industrial Science and Technology (AIST), National Metrology Institute of Japan (NMIJ), Tsukuba, Ibaraki 305-8563, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christof","family":"Pruss","sequence":"additional","affiliation":[{"name":"Institute of Applied Optics (ITO), University Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vit","family":"Ledl","sequence":"additional","affiliation":[{"name":"TOPTEC, Institute of Plasma Physics of the Czech Academy of Sciences, Za Slovankou 1782\/3, 182 00 Praha, Czech 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