{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T10:00:26Z","timestamp":1787997626015,"version":"build-2784847793"},"reference-count":45,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T00:00:00Z","timestamp":1672790400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"ELSAT2020 project"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>A top-down method is presented and studied for quantifying topographic map height (z) fluctuations directly from measurements on surfaces of interest. Contrary to bottom-up methods used in dimensional metrology, this method does not require knowledge of transfer functions and fluctuations of an instrument. Fluctuations are considered here to be indicative of some kinds of uncertainties. Multiple (n), successive topographic measurements (z = z(x,y)) are made at one location without moving the measurand relative to the measurement instrument. The measured heights (z) at each position (x,y) are analyzed statistically. Fluctuation maps are generated from the calculated variances. Three surfaces were measured with two interferometric measuring microscopes (Bruker ContourGT\u2122 and Zygo NewView\u2122 7300). These surfaces included an anisotropic, turned surface; an isotropic, sandblasted surface; and an abraded, heterogeneous, multilayer surface having different, complex, multiscale morphologies. In demonstrating the method, it was found that few non-measured points persisted for all 100 measurements at any location. The distributions of uncertainties are similar to those of certain features on topographic maps at the same locations, suggesting that topographic features can augment measurement fluctuations. This was especially observed on the abraded ophthalmic lens; a scratch divides the topographic map into two zones with different uncertainty values. The distributions of fluctuations can be non-Gaussian. Additionally, they can vary between regions within some measurements.<\/jats:p>","DOI":"10.3390\/ma16020473","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T04:28:17Z","timestamp":1672806497000},"page":"473","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Top-down Determination of Fluctuations in Topographic Measurements"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6119-8725","authenticated-orcid":false,"given":"Julie","family":"Lemesle","sequence":"first","affiliation":[{"name":"Valutec, Universit\u00e9 Polytechnique Hauts-de-France, CEDEX 9, 59314 Valenciennes, France"},{"name":"Universit\u00e9 Polytechnique Hauts-de-France, CNRS UMR 8201\u2014LAMIH\u2014Laboratoire d\u2019Automatique, de M\u00e9canique et d\u2019Informatique Industrielles et Humaines, 59313 Valenciennes, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Clement","family":"Moreau","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Polytechnique Hauts-de-France, CNRS UMR 8201\u2014LAMIH\u2014Laboratoire d\u2019Automatique, de M\u00e9canique et d\u2019Informatique Industrielles et Humaines, 59313 Valenciennes, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Raphael","family":"Deltombe","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Polytechnique Hauts-de-France, CNRS UMR 8201\u2014LAMIH\u2014Laboratoire d\u2019Automatique, de M\u00e9canique et d\u2019Informatique Industrielles et Humaines, 59313 Valenciennes, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fran\u00e7ois","family":"Blateyron","sequence":"additional","affiliation":[{"name":"Digital Surf, 16 rue Lavoisier, 25000 Besan\u00e7on, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Joseph","family":"Martin","sequence":"additional","affiliation":[{"name":"ESSILOR, Centre Innovation et Technologies CIT3, 94000 Creteil, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Maxence","family":"Bigerelle","sequence":"additional","affiliation":[{"name":"Universit\u00e9 Polytechnique Hauts-de-France, CNRS UMR 8201\u2014LAMIH\u2014Laboratoire d\u2019Automatique, de M\u00e9canique et d\u2019Informatique Industrielles et Humaines, 59313 Valenciennes, France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9355-4824","authenticated-orcid":false,"given":"Christopher A.","family":"Brown","sequence":"additional","affiliation":[{"name":"Surface Metrology Laboratory, Worcester Polytechnic Institute, Worcester, MA 01609, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,4]]},"reference":[{"key":"ref_1","unstructured":"(2021). 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