{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:33:22Z","timestamp":1760240002278,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2019,3,3]],"date-time":"2019-03-03T00:00:00Z","timestamp":1551571200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100012329","name":"European Association of National Metrology Institutes","doi-asserted-by":"publisher","award":["EMPIR 17IND03"],"award-info":[{"award-number":["EMPIR 17IND03"]}],"id":[{"id":"10.13039\/100012329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper is concerned with backscattered luminous signals, coming from a particular class of dielectric spheres illuminated by a coherent source. The purpose is to measure the lateral position of the sphere serving as an optical target, to achieve an overall contactless sensor of lateral position in space. Traditional approaches and theories such as ray-tracing and Mie scattering\u2014as implemented in dedicated software\u2014are applied to investigate their fitness for purpose in this application. No previous literature was found dealing with this specific case. Unfortunately, our observations did not match the theories\u2019 predictions to an acceptable degree, and these approaches proved to be unsatisfactory. The rest of the paper focusses then on the development and comparison of suitable algorithms to compute the image coordinates of a representative point, which was in fact the true motivation of this work. Two original algorithms are proposed and discussed. Their robustness and repeatability are benchmarked under noisy conditions and at different distances from the target, with simulated as well as real images. Both resulted capable of sub-pixel accuracy.<\/jats:p>","DOI":"10.3390\/s19051082","type":"journal-article","created":{"date-parts":[[2019,3,4]],"date-time":"2019-03-04T05:45:36Z","timestamp":1551678336000},"page":"1082","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["High-Index Glass Ball Retroreflectors for Measuring Lateral Positions"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3472-0853","authenticated-orcid":false,"given":"Andrea","family":"Egidi","sequence":"first","affiliation":[{"name":"INRiM\u2014National Institute of Research in Metrology, Division of Applied Metrology and Engineering, 10135 Torino, Italy"}]},{"given":"Alessandro","family":"Balsamo","sequence":"additional","affiliation":[{"name":"INRiM\u2014National Institute of Research in Metrology, Division of Applied Metrology and Engineering, 10135 Torino, Italy"}]},{"given":"Marco","family":"Pisani","sequence":"additional","affiliation":[{"name":"INRiM\u2014National Institute of Research in Metrology, Division of Applied Metrology and Engineering, 10135 Torino, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,3]]},"reference":[{"key":"ref_1","unstructured":"Beck, A. (1887). Ueber einige neue Anwendungen ebener Spiegel. Zeitschrift f\u00fcr Instrumentenkunde, Vol.7: Organ f\u00fcr Mittheilungen aus dem Gesammten Gebiete der Wissenschaftlichen Technik, Springer."},{"key":"ref_2","unstructured":"Crabb, H. (1903). Improvements in and Means for Signalling and Indicating Position of Objects. (GB190321856A), Patent."},{"key":"ref_3","unstructured":"Olsen, J.C., and Percy, O.K. (1965). Multi-Directional Optical Target. (US3188739A), Patent."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"N87","DOI":"10.1088\/0957-0233\/10\/7\/403","article-title":"Whole-viewing-angle cat\u2019s-eye retroreflector as a target of laser trackers","volume":"10","author":"Takatsuji","year":"1999","journal-title":"Meas. Sci. Technol."},{"key":"ref_5","unstructured":"Yang, B., and Friedsam, H. (2019, January 17). Ray-Tracing Studies for a Whole-Viewing-Angle Retroreflector. International Workshop on Accelerator Alignment IWAA99; Grenoble (France). Available online: https:\/\/inis.iaea.org\/collection\/NCLCollectionStore\/_Public\/31\/047\/31047197.pdf."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1016\/0736-5845(85)90110-3","article-title":"Robot performance measurements using automatic laser tracking techniques","volume":"2","author":"Lau","year":"1985","journal-title":"Robot. Comput. Integr. Manuf."},{"key":"ref_7","unstructured":"Lau, K.C., and Hocken, R.J. (1987). Three and Five Axis Laser Tracking Systems. (US4714339A), Patent."},{"key":"ref_8","unstructured":"Balsamo, M.C. (2014, January 3\u20135). Cartesian approach to large scale co-ordinate measurement: InPlanT. Proceedings of the 11th IMEKO Symposium LMPMI2014 Laser Metrology for Precision Measurement, Tsukuba, Japan."},{"key":"ref_9","unstructured":"Bohren, C.F., and Huffman, D.R. (2007). Absorption and Scattering of Light by Small Particles, WILEY-VCH Verlag GmbH & Co. KGaA. Chapter 7.2."},{"key":"ref_10","unstructured":"Wriedt, T., and Hellmers, J. (2019, January 16). Light Scattering Software. Available online: https:\/\/scattport.org\/index.php\/light-scattering-software."},{"key":"ref_11","unstructured":"Flatau, P. (2019, January 16). Mie Codes. Available online: http:\/\/scatterlib.wikidot.com\/mie."},{"key":"ref_12","unstructured":"Sumlin, B. (2019, January 16). Python Mie Scattering Package (PyMieScatt). Available online: https:\/\/pymiescatt.readthedocs.io\/en\/latest\/#."},{"key":"ref_13","unstructured":"Laven, P. (2019, January 16). MiePlot. Available online: http:\/\/www.philiplaven.com\/mieplot.htm."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"68","DOI":"10.1038\/scientificamerican0112-68","article-title":"The Science of the Glory","volume":"306","author":"Nussenzveig","year":"2012","journal-title":"Sci. Am."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"5675","DOI":"10.1364\/AO.44.005675","article-title":"How are glories formed?","volume":"44","author":"Laven","year":"2005","journal-title":"Appl. Opt."},{"key":"ref_16","unstructured":"Sorensen, C.M., and Fischbach, D.J. (2000). Patterns in Mie Scattering, Kansas State University. Program for Complex Fluid Flows and Department of Physics."},{"key":"ref_17","unstructured":"Hulst, H.C., and van de Hulst, H.C. (1981). Light Scattering by Small Particles, Dover Publications. Chapter 13.31."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/S0370-1573(01)00076-X","article-title":"The mathematical physics of rainbows and glories","volume":"356","author":"Adam","year":"2002","journal-title":"Phys. Rep."},{"key":"ref_19","unstructured":"(2019, January 16). OpenCV (Open Source Computer Vision Library). Available online: https:\/\/opencv.org\/."},{"key":"ref_20","unstructured":"(2019, January 24). Zemax OpticStudio. Available online: https:\/\/www.zemax.com\/products\/opticstudio."},{"key":"ref_21","unstructured":"(2019, January 16). NVIDIA\u00ae CUDA\u00ae Toolkit. Available online: https:\/\/developer.nvidia.com\/cuda-toolkit."},{"key":"ref_22","unstructured":"(2019, January 24). LaVA\u2014Large Volume Metrology Applications. Available online: https:\/\/www.euramet.org\/research-innovation\/search-research-projects\/details\/?eurametCtcp_project_show%5Bproject%5D=1530&eurametCtcp_project%5Bback%5D=1081&cHash=620ac747fd4d4c27a6c1292add5cccfe."},{"key":"ref_23","unstructured":"(2019, January 24). LUMINAR\u2014Large Volume Metrology in Industry. Available online: http:\/\/projects.npl.co.uk\/luminar\/."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/5\/1082\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:35:57Z","timestamp":1760186157000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/5\/1082"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,3,3]]},"references-count":23,"journal-issue":{"issue":"5","published-online":{"date-parts":[[2019,3]]}},"alternative-id":["s19051082"],"URL":"https:\/\/doi.org\/10.3390\/s19051082","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,3,3]]}}}