{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,17]],"date-time":"2026-01-17T14:35:04Z","timestamp":1768660504195,"version":"3.49.0"},"reference-count":38,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T00:00:00Z","timestamp":1768435200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Program of Education Department of Shaanxi Province","award":["24JK0484"],"award-info":[{"award-number":["24JK0484"]}]},{"DOI":"10.13039\/501100017596","name":"Natural Science Basic Research Program of Shaanxi Province","doi-asserted-by":"publisher","award":["2025JC-YBQN-109"],"award-info":[{"award-number":["2025JC-YBQN-109"]}],"id":[{"id":"10.13039\/501100017596","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Postdoctoral Research Project of Shaanxi Province","award":["2024BSHSDZZ150"],"award-info":[{"award-number":["2024BSHSDZZ150"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The surface tension of a liquid droplet can be determined by fitting its actual profiles using the Young\u2013Laplace equation, effectively reducing the measurement of surface tension to an accurate determination of the droplet\u2019s profiles. Spectral confocal sensors are high-precision, interference-resistant, non-contact measurement systems for droplet surface profiling, employing a light source together with a dispersive objective lens and a spectrometer to acquire depth-dependent spectral information. The accuracy and stability of surface tension measurements can be effectively enhanced by spectral confocal sensors measuring the droplet surface profile. Although existing spectral confocal sensors have significantly improved measurement range and accuracy, their angular measurement performance remains limited, and deviations may arise at droplet edges with large inclinations or pronounced surface profile variations. This study presents the optical design of a large-angle spectral confocal sensor. By theoretically analyzing the conditions for generating linear axial dispersion in the dispersive objective lens, a front-end dispersive objective lens was designed by combining positive and negative lenses. Based on a Czerny\u2013Turner (C-T) configuration, the back-end spectrometer was designed under the astigmatism-free condition, taking into account both central and edge wavelength effects. Zemax was employed for simulation optimization and tolerance analysis of each optical module. The results show that the designed system achieves an axial dispersion of 1.5 mm over the 430\u2013700 nm wavelength range, with a maximum allowable object angle of \u00b140\u00b0 and a theoretical resolution of 3 \u03bcm. The proposed spectral confocal sensor maintains high measurement accuracy over a wide angular range, facilitating precise measurement of droplet surface tension at large inclination angles.<\/jats:p>","DOI":"10.3390\/s26020599","type":"journal-article","created":{"date-parts":[[2026,1,15]],"date-time":"2026-01-15T16:21:13Z","timestamp":1768494073000},"page":"599","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optical Design of a Large-Angle Spectral Confocal Sensor for Liquid Surface Tension Measurement"],"prefix":"10.3390","volume":"26","author":[{"given":"Lingling","family":"Wu","sequence":"first","affiliation":[{"name":"School of Optoelectronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tingting","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Optoelectronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-1543-161X","authenticated-orcid":false,"given":"Fang","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Optoelectronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Optoelectronic Engineering, Xi\u2019an Technological University, Xi\u2019an 710021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fei","family":"Xi","sequence":"additional","affiliation":[{"name":"Xi\u2019an Guide Technology Co., Ltd., Xi\u2019an 710065, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinsong","family":"Lv","sequence":"additional","affiliation":[{"name":"Huazhong Institute of Electro-Optics-Wuhan National Laboratory for Optoelectronics, Wuhan 430223, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"6722","DOI":"10.1021\/acs.langmuir.1c00668","article-title":"Surfactant adsorption to different fluid interfaces","volume":"37","author":"Bergfreund","year":"2021","journal-title":"Langmuir"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"116735","DOI":"10.1016\/j.geoderma.2023.116735","article-title":"Effect of surfactant surface and interfacial tension reduction on infiltration into hydrophobic porous media","volume":"441","author":"Ogunmokun","year":"2024","journal-title":"Geoderma"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"102541","DOI":"10.1016\/j.cis.2021.102541","article-title":"Emulsion characterization via microfluidic devices: A review on interfacial tension and stability to coalescence","volume":"299","author":"Ho","year":"2022","journal-title":"Adv. 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