{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,12]],"date-time":"2026-03-12T09:52:09Z","timestamp":1773309129864,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2023,8,1]],"date-time":"2023-08-01T00:00:00Z","timestamp":1690848000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union with the European Regional Development Fund","award":["ELSAT2020"],"award-info":[{"award-number":["ELSAT2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Topographic maps are composed of pixels associated with coordinates (x, y, z) on a surface. Each pixel location (x, y) is linked with fluctuations in a measured height sample (z). Fluctuations here are uncertainties in heights estimated from multiple topographic measurements at the same position. Height samples (z) are measured at individual locations (x, y) in topographic measurements and compared with gradients on topographies. Here, gradients are slopes on a surface calculated at the scale of the sampling interval from inclination angles of vectors that are normal to triangular facets formed by adjacent height samples (z = z(x, y)). Similarities between maps of gradients logs and height fluctuations are apparent. This shows that the fluctuations are exponentially dependent on local surface gradients. The highest fluctuations correspond to tool\/material interactions for turned surfaces and to regions of maximum plastic deformation for sandblasted surfaces. Finally, for abraded, heterogeneous, multilayer surfaces, fluctuations are dependent on both abrasion and light\/sub-layer interactions. It appears that the natures of irregular surface topographies govern fluctuation regimes, and that regions which are indicative of surface functionality, or integrity, can have the highest fluctuations.<\/jats:p>","DOI":"10.3390\/ma16155408","type":"journal-article","created":{"date-parts":[[2023,8,2]],"date-time":"2023-08-02T11:17:17Z","timestamp":1690975037000},"page":"5408","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Height Fluctuations and Surface Gradients 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":"U.R Concept, 59300 Valenciennes, France"},{"name":"Valutec, Univ. Polytechnique Hauts-de-France, CEDEX 9, 59314 Valenciennes, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Clement","family":"Moreau","sequence":"additional","affiliation":[{"name":"Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH-Laboratoire d\u2019Automatique de M\u00e9canique et d\u2019Informatique Industrielles et Humaines, F-59313 Valenciennes, France"},{"name":"Digital Surf, 25000 Besan\u00e7on, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raphael","family":"Deltombe","sequence":"additional","affiliation":[{"name":"Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH-Laboratoire d\u2019Automatique de M\u00e9canique et d\u2019Informatique Industrielles et Humaines, F-59313 Valenciennes, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joseph","family":"Martin","sequence":"additional","affiliation":[{"name":"ESSILOR, Centre Innovation et Technologies CIT3, 94000 Creteil, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fran\u00e7ois","family":"Blateyron","sequence":"additional","affiliation":[{"name":"Digital Surf, 25000 Besan\u00e7on, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maxence","family":"Bigerelle","sequence":"additional","affiliation":[{"name":"Univ. Polytechnique Hauts-de-France, CNRS, UMR 8201-LAMIH-Laboratoire d\u2019Automatique de M\u00e9canique et d\u2019Informatique Industrielles et Humaines, F-59313 Valenciennes, France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1016\/j.measurement.2015.04.001","article-title":"Influence of Argon Pollution on the Weld Surface Morphology","volume":"70","author":"Krolczyk","year":"2015","journal-title":"Measurement"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Lemesle, J., Moreau, C., Deltombe, R., Blateyron, F., Martin, J., Bigerelle, M., and Brown, C.A. (2023). Top-down Determination of Fluctuations in Topographic Measurements. Materials, 16.","DOI":"10.3390\/ma16020473"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Dainty, J.C. (1975). Laser Speckle and Related Phenomena, Springer. Topics in Applied Physics.","DOI":"10.1007\/978-3-662-43205-1"},{"key":"ref_4","unstructured":"(2019). Surface Texture (Surface Roughness, Waviness, and Lay) (Standard No. ASME B46.1)."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"753906","DOI":"10.3389\/fmech.2021.753906","article-title":"Surface Metrology Principles for Snow and Ice Friction Studies","volume":"7","author":"Brown","year":"2021","journal-title":"Front. Mech. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kr\u00f3lczyk, G., Kacalak, W., and Wieczorowski, M. (2021). 3D Parametric and Nonparametric Description of Surface Topography in Manufacturing Processes. Materials, 14.","DOI":"10.3390\/ma14081987"},{"key":"ref_7","unstructured":"(2012). Geometrical Product Specifications (GPS)\u2014Surface Texture: Areal\u2014Part 2: Terms, Definitions and Surface Texture Parameters (Standard No. ISO 25178-2)."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Tchoundjeu, S., Bigerelle, M., Robbe-Valloire, F., Da Silva Botelho, T., and Jarnias, F. (2020). How to Select 2D and 3D Roughness Parameters at Their Relevant Scales by the Analysis of Covariance. Materials, 13.","DOI":"10.3390\/ma13071526"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1078\/0030-4026-00369","article-title":"Optimization of White Light Interferometry on Rough Surfaces Based on Error Analysis","volume":"115","author":"Richter","year":"2004","journal-title":"Optik"},{"key":"ref_10","unstructured":"Mills, L.N. (2014). Hierarchical Markov Chain Monte Carlo for Pavement Roughness Estimation. [Master\u2019s Thesis, University of Delaware]."},{"key":"ref_11","unstructured":"(1998). Geometrical Product Specification (GPS)\u2014Surface Imperfections\u2014Terms, Definitions and Parameters. (Standard No. ISO 8785)."},{"key":"ref_12","unstructured":"Brown, C.A. (2007, January 26\u201328). Uncertainty and Quality in the Measurement and Characterization of the Texture of Abrasive Media. Proceedings of the ISAAT 2007\/SME International Grinding Conference, Dearborn, MI, USA."},{"key":"ref_13","first-page":"195","article-title":"Reduced Measurement Uncertainty of White-Light Interferometry on Rough Surfaces","volume":"Volume 6341","author":"Gross","year":"2006","journal-title":"Speckle06: Speckles, from Grains to Flowers"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2941","DOI":"10.1364\/AO.47.002941","article-title":"White-Light Interferometry on Rough Surfaces\u2014Measurement Uncertainty Caused by Surface Roughness","volume":"47","year":"2008","journal-title":"Appl. Opt."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"766","DOI":"10.1364\/AO.43.000766","article-title":"Measurement of the Influence of Dispersion on White-Light Interferometry","volume":"43","author":"Soubusta","year":"2004","journal-title":"Appl. Opt."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1364\/OL.17.000898","article-title":"Chromatic Dispersion Effects in Coherent Absolute Ranging","volume":"17","year":"1992","journal-title":"Opt. Lett."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Leach, R. (2013). Characterisation of Areal Surface Texture, Springer.","DOI":"10.1007\/978-3-642-36458-7"},{"key":"ref_18","unstructured":"Blunt, L., and Jiang, X. (2003). Advanced Techniques for Assessment Surface Topography: Development of a Basis for 3D Surface Texture Standards \u201cSURFSTAND\u201d, Elsevier Inc."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1016\/0043-1648(94)90128-7","article-title":"Comprehensive Study of Parameters for Characterising Three-Dimensional Surface Topography: IV: Parameters for Characterising Spatial and Hybrid Properties","volume":"178","author":"Dong","year":"1994","journal-title":"Wear"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1243\/JMES_JOUR_1978_020_021_02","article-title":"Slope Measurement in Surface Texture Analysis","volume":"20","author":"Chetwynd","year":"1978","journal-title":"J. Mech. Eng. Sci."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1007\/s41871-020-00057-4","article-title":"Noise Reduction in Coherence Scanning Interferometry for Surface Topography Measurement","volume":"3","author":"Gomez","year":"2020","journal-title":"Nanomanuf. Metrol."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"50","DOI":"10.3389\/fmech.2020.00050","article-title":"Sdq-Sdr Topological Map of Surface Topographies","volume":"6","author":"Czifra","year":"2020","journal-title":"Front. Mech. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1002\/sca.4950250405","article-title":"Quantification of Dental Microwear by Tandem Scanning Confocal Microscopy and Scale-Sensitive Fractal Analyses","volume":"25","author":"Ungar","year":"2003","journal-title":"Scanning"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Lemesle, J., Robache, F., Goic, G., Mansouri, A., Brown, C., and Bigerelle, M. (2020). Surface Reflectance: An Optical Method for Multiscale Curvature Characterization of Wear on Ceramic\u2013Metal Composites. Materials, 13.","DOI":"10.3390\/ma13051024"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/0040-6090(82)90590-9","article-title":"Optical Properties of Thin Films","volume":"89","author":"Aspnes","year":"1982","journal-title":"Thin Solid Films"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"032001","DOI":"10.1088\/1361-6501\/abb54f","article-title":"Metrological Characteristics for the Calibration of Surface Topography Measuring Instruments: A Review","volume":"32","author":"Leach","year":"2021","journal-title":"Meas. Sci. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"8670","DOI":"10.1364\/AO.54.008670","article-title":"Estimation of Measurement Uncertainty Caused by Surface Gradient for a White Light Interferometer","volume":"54","author":"Liu","year":"2015","journal-title":"Appl. Opt."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"1809","DOI":"10.1364\/AO.42.001809","article-title":"Theoretical Measurement Uncertainty of White-Light Interferometry on Rough Surfaces","volume":"42","author":"Soubusta","year":"2003","journal-title":"Appl. Opt."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1364\/AO.51.000465","article-title":"White-Light Interferometry on Rough Surfaces\u2014Measurement Uncertainty Caused by Noise","volume":"51","year":"2012","journal-title":"Appl. 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