{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T04:46:53Z","timestamp":1791866813197,"version":"4.3.4"},"reference-count":23,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T00:00:00Z","timestamp":1790726400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100018933","name":"Clausthal University of Technology","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100018933","id-type":"DOI","asserted-by":"publisher"}]},{"id":[{"id":"https:\/\/ror.org\/04qb8nc58","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Fiber-optic shape sensors require accurate calibration of the spatial orientation and effective core distances of their sensing planes. We present a rotation-angle correction procedure for sinusoidal calibration of multicore fiber Bragg grating (MCF-FBG) shape sensors. The method is demonstrated using a constant-radius groove template and a single rotation stage. Within the groove fixture, groove\u2013fiber friction, finite torsional stiffness, and non-ideal boundary conditions may contribute to deviations between the local sensor-plane rotation and the motor-imposed angle, resulting in distorted sinusoidal wavelength responses and biased curvature estimation. The proposed method addresses deviations from the assumed sinusoidal response by jointly correcting the effective rotation angle assigned to the four FBG responses in each sensor plane while leaving the measured wavelength shifts unchanged. The method was demonstrated using a 20 cm four-core single-mode fiber containing 200 femtosecond-laser-inscribed FBGs arranged in 50 sensor planes at 4 mm spacing. Quantitative validation with planar constant-curvature templates showed tip-position errors of approximately 2\u20135 mm, compared with approximately 6\u201313 mm for conventional sine calibration. An additional endpoint-position test of the 50-plane sensor yielded a mean error of 11.28 mm and an RMSE of 13.73 mm, compared with 19.03 mm and 21.55 mm, respectively, for conventional sine calibration. Additional non-planar bending tests qualitatively illustrated the sensor\u2019s three-dimensional reconstruction capability. The results show that rotation-angle correction can improve calibration accuracy while retaining a single-rotation-stage groove fixture.<\/jats:p>","DOI":"10.3390\/s26196214","type":"journal-article","created":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T14:19:37Z","timestamp":1790777977000},"page":"6214","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Groove-Based Calibration of Multicore Fiber Bragg Grating Shape Sensors with Rotation-Angle Correction"],"prefix":"10.3390","volume":"26","author":[{"given":"Yi","family":"Jiang","sequence":"first","affiliation":[{"name":"Institute for Energy Research and Physical Technologies (IEPT), Clausthal University of Technology, Am Stollen 19B, 38640 Goslar, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3147-8918","authenticated-orcid":false,"given":"Martin","family":"Angelmahr","sequence":"additional","affiliation":[{"name":"Department of Fiber Optical Sensor Systems, Fraunhofer Heinrich Hertz Institute, Am Stollen 19H, 38640 Goslar, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ahmad","family":"Abdalwareth","sequence":"additional","affiliation":[{"name":"Institute for Energy Research and Physical Technologies (IEPT), Clausthal University of Technology, Am Stollen 19B, 38640 Goslar, Germany"},{"name":"Department of Fiber Optical Sensor Systems, Fraunhofer Heinrich Hertz Institute, Am Stollen 19H, 38640 Goslar, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yannick","family":"Willer","sequence":"additional","affiliation":[{"name":"Institute for Energy Research and Physical Technologies (IEPT), Clausthal University of Technology, Am Stollen 19B, 38640 Goslar, Germany"},{"name":"Department of Fiber Optical Sensor Systems, Fraunhofer Heinrich Hertz Institute, Am Stollen 19H, 38640 Goslar, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0225-1976","authenticated-orcid":false,"given":"G\u00fcnter","family":"Flachenecker","sequence":"additional","affiliation":[{"name":"Department of Fiber Optical Sensor Systems, Fraunhofer Heinrich Hertz Institute, Am Stollen 19H, 38640 Goslar, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wolfgang","family":"Schade","sequence":"additional","affiliation":[{"name":"Institute for Energy Research and Physical Technologies (IEPT), Clausthal University of Technology, Am Stollen 19B, 38640 Goslar, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,9,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"106508","DOI":"10.1016\/j.optlaseng.2020.106508","article-title":"Fiber Optic Shape Sensors: A Comprehensive Review","volume":"139","author":"Floris","year":"2021","journal-title":"Opt. Lasers Eng."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Wu, J., Li, B., Li, C., Qiu, Y., Zhang, Z., Lyu, W., Ali, A., Mohsan, S.A.H., Ge, W., and Tong, Z. (2020, January 16\u201318). Fiber Bragg Grating-Based Shape Sensing: A Review and Perspective. Proceedings of the Global Intelligent Industry Conference 2020, Guangzhou, China.","DOI":"10.1117\/12.2590684"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Waltermann, C. (2014, January 2\u20136). Femtosecond Laser Aided Processing of Optical Sensor Fibers for 3D Medical Navigation and Tracking (FiberNavi). Proceedings of the 23rd International Conference on Optical Fibre Sensors, Santander, Spain.","DOI":"10.1117\/12.2059599"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1002\/phvs.201900013","article-title":"Shaping Spectra within Optical Fibers: Embedding High-Resolution Spectrometers into the Cores of Optical Fibers","volume":"16","author":"Waltermann","year":"2019","journal-title":"PhotonicsViews"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3109","DOI":"10.1364\/OL.40.003109","article-title":"Cladding Waveguide Gratings in Standard Single-Mode Fiber for 3D Shape Sensing","volume":"40","author":"Waltermann","year":"2015","journal-title":"Opt. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Waltermann, C., Doering, A., Koch, J., G\u00fchlke, P., and Lena, A. (2016). Femtosecond Laser Written Cladding Waveguides and Gratings for 3D Shape Sensing Applications. Bragg Gratings, Photosensitivity, and Poling in Glass Waveguides, Optica Publishing Group.","DOI":"10.1364\/BGPP.2016.BTh4B.1"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.optlaseng.2014.03.005","article-title":"Fiber-Bragg-Grating-Based Ultrathin Shape Sensors Displaying Single-Channel Sweeping for Minimally Invasive Surgery","volume":"59","author":"Moon","year":"2014","journal-title":"Opt. Lasers Eng."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Lenke, P., Wendt, M., Krebber, K., and Gl\u00f6tzl, R. (2011, January 15\u201319). Highly Sensitive Fiber Optic Inclinometer: Easy to Transport and Easy to Install. Proceedings of the 21st International Conference on Optical Fiber Sensors, Ottawa, ON, Canada.","DOI":"10.1117\/12.884695"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1115","DOI":"10.1109\/TMECH.2013.2269836","article-title":"Three-Dimensional Needle Shape Reconstruction Using an Array of Fiber Bragg Grating Sensors","volume":"19","author":"Roesthuis","year":"2014","journal-title":"IEEE\/ASME Trans. Mechatron."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"8619","DOI":"10.1364\/OE.26.008619","article-title":"All-Fiber 3D Vector Displacement (Bending) Sensor Based on an Eccentric FBG","volume":"26","author":"Bao","year":"2018","journal-title":"Opt. Express"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4670","DOI":"10.1109\/JLT.2017.2750407","article-title":"Femtosecond Laser Inscription of Fiber Bragg Grating in Twin-Core Few-Mode Fiber for Directional Bend Sensing","volume":"35","author":"Yang","year":"2017","journal-title":"J. Light. Technol."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Xiao, X., He, J., Xu, B., Du, B., Xu, X., and Wang, Y. (2021, January 23\u201327). Multicore Fiber Bragg Gratings Array Shape Sensor Fabricated with an Auto-Alignment Femtosecond Laser Point-by-Point Technology. Proceedings of the 2021 19th International Conference on Optical Communications and Networks (ICOCN), Qufu, China.","DOI":"10.1109\/ICOCN53177.2021.9563665"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5878","DOI":"10.1109\/JSEN.2019.2905010","article-title":"Multi-Core Optical Fibers with Bragg Gratings as Shape Sensor for Flexible Medical Instruments","volume":"19","author":"Khan","year":"2019","journal-title":"IEEE Sens. J."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"210055","DOI":"10.29026\/oea.2022.210055","article-title":"Advances in Femtosecond Laser Direct Writing of Fiber Bragg Gratings in Multicore Fibers: Technology, Sensor and Laser Applications","volume":"5","author":"Wolf","year":"2022","journal-title":"Opto-Electron. Adv."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1273","DOI":"10.1364\/OL.516067","article-title":"OFDR Shape Sensor Based on a Femtosecond-Laser-Inscribed Weak Fiber Bragg Grating Array in a Multicore Fiber","volume":"49","author":"Fu","year":"2024","journal-title":"Opt. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"2137","DOI":"10.1007\/s11548-019-02059-0","article-title":"Fiber Optical Shape Sensing of Flexible Instruments for Endovascular Navigation","volume":"14","author":"Eixmann","year":"2019","journal-title":"Int. J. Comput. Assist. Radiol. Surg."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"3909","DOI":"10.1109\/JLT.2024.3363171","article-title":"Multicore Fiber Shape Sensing Based on Optical Frequency Domain Reflectometry Parallel Measurements","volume":"42","author":"Meng","year":"2024","journal-title":"J. Light. Technol."},{"key":"ref_18","first-page":"227","article-title":"Fiber-Optical 3D Shape Sensing","volume":"189","author":"Marowsky","year":"2014","journal-title":"Planar Waveguides and Other Confined Geometries"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"102319","DOI":"10.1016\/j.yofte.2020.102319","article-title":"Characterization and Calibration of Shape Sensors Based on Multicore Optical Fibre","volume":"61","author":"Idrisov","year":"2021","journal-title":"Opt. Fiber Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"111844","DOI":"10.1016\/j.measurement.2022.111844","article-title":"Self-Calibration Method of Optical Fiber Shape Sensor Placement Angle Deviation Based on GA","volume":"202","author":"Tan","year":"2022","journal-title":"Measurement"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2260","DOI":"10.1364\/OL.593283","article-title":"Synchronous Azimuth Calibration of Helical Multicore Fibers in Shape Sensing","volume":"51","author":"Zhang","year":"2026","journal-title":"Opt. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Kashyap, R. (2010). Fiber Bragg Gratings, Academic Press. [2nd ed.].","DOI":"10.1016\/B978-0-12-372579-0.00007-7"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"38421","DOI":"10.1364\/OE.380816","article-title":"Durable Shape Sensor Based on FBG Array Inscribed in Polyimide-Coated Multicore Optical Fiber","volume":"27","author":"Bronnikov","year":"2019","journal-title":"Opt. Express"}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/19\/6214\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T04:12:43Z","timestamp":1791864763000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/26\/19\/6214"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9,30]]},"references-count":23,"journal-issue":{"issue":"19","published-online":{"date-parts":[[2026,10]]}},"alternative-id":["s26196214"],"URL":"https:\/\/doi.org\/10.3390\/s26196214","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,9,30]]}}}