{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,28]],"date-time":"2026-03-28T22:17:34Z","timestamp":1774736254029,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,18]],"date-time":"2021-09-18T00:00:00Z","timestamp":1631923200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012166","name":"National Key Research and Development Program of China","doi-asserted-by":"publisher","award":["2019YFB2005401"],"award-info":[{"award-number":["2019YFB2005401"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 91860207"],"award-info":[{"award-number":["No. 91860207"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Taishan Scholar Foundation and Shandong Provincial Key Research and Development Program (Major Scientific and Technological Innovation Project)","award":["No.2020CXGC010204"],"award-info":[{"award-number":["No.2020CXGC010204"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The emissivity is an important surface property parameter in many fields, including infrared temperature measurement. In this research, a symmetry theoretical model of directional spectral emissivity prediction is proposed based on Gaussian random rough surface theory. A numerical solution based on a matrix method is determined based on its symmetrical characteristics. Influences of the index of refraction n and the root mean square (RMS) roughness \u03c3rms on the directional spectrum emissivity \u03b5 are analyzed and discussed. The results indicate that surfaces with higher n and lower \u03c3rms tend to have a peak in high viewing angles. On the contrary, surfaces with lower n and higher \u03c3rms tend to have a peak in low viewing angles. Experimental verifications based on infrared (IR) temperature measurement of Inconel 718 sandblasted surfaces were carried out. This model would contribute to understand random rough surfaces and their emitting properties in fields including machining, process controlling, remote sensing, etc.<\/jats:p>","DOI":"10.3390\/sym13091733","type":"journal-article","created":{"date-parts":[[2021,9,21]],"date-time":"2021-09-21T22:35:20Z","timestamp":1632263720000},"page":"1733","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Theoretical Modeling and Analysis of Directional Spectrum Emissivity and Its Pattern for Random Rough Surfaces with a Matrix Method"],"prefix":"10.3390","volume":"13","author":[{"given":"Jianrui","family":"Hu","sequence":"first","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key National Demonstration Center for Experimental Mechanical Engineering Education\/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4790-0052","authenticated-orcid":false,"given":"Zhanqiang","family":"Liu","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key National Demonstration Center for Experimental Mechanical Engineering Education\/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China"}]},{"given":"Jinfu","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key National Demonstration Center for Experimental Mechanical Engineering Education\/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China"}]},{"given":"Bing","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key National Demonstration Center for Experimental Mechanical Engineering Education\/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9792-9988","authenticated-orcid":false,"given":"Qinghua","family":"Song","sequence":"additional","affiliation":[{"name":"School of Mechanical Engineering, Shandong University, Jinan 250061, China"},{"name":"Key National Demonstration Center for Experimental Mechanical Engineering Education\/Key Laboratory of High Efficiency and Clean Mechanical Manufacture of MQE, Jinan 250061, China"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/S0143-8166(97)00108-5","article-title":"Effective spectral emissivity measurements of superalloys and YSZ thermal barrier coating at high temperatures using a 1.6 \u03bcm single wavelength pyrometer","volume":"30","author":"Alaruri","year":"1998","journal-title":"Opt. 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