{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:49:08Z","timestamp":1760240948912,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T00:00:00Z","timestamp":1573084800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61801161, 61571175"],"award-info":[{"award-number":["61801161, 61571175"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003995","name":"Natural Science Foundation of Anhui Province","doi-asserted-by":"publisher","award":["1908085QF282"],"award-info":[{"award-number":["1908085QF282"]}],"id":[{"id":"10.13039\/501100003995","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Defense Science and Technology Project","award":["1816321TS00106401"],"award-info":[{"award-number":["1816321TS00106401"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Researchers have found that some animals can use the skylight polarization pattern for navigation. It is also expected to use the skylight polarization pattern for human navigating in the near future. However, the challenge is that the need for a more accurate and efficient model of the imaging of skylight polarization is always felt. In this paper, three improved models of imaging of skylight polarization are proposed. The proposed models utilize the analysis of the distribution of the skylight polarization pattern after the polarization imaging system. Given that the skylight polarization pattern after the polarization imaging system is distorted, the focus of this paper is on the degree of distortion of the skylight polarization pattern in these imaging models. Experiments in clear weather conditions demonstrate that the proposed model operates close to the actual acquired skylight polarization pattern.<\/jats:p>","DOI":"10.3390\/s19224844","type":"journal-article","created":{"date-parts":[[2019,11,7]],"date-time":"2019-11-07T06:52:36Z","timestamp":1573109556000},"page":"4844","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Improved Models of Imaging of Skylight Polarization Through a Fisheye Lens"],"prefix":"10.3390","volume":"19","author":[{"given":"Shaobo","family":"Sun","sequence":"first","affiliation":[{"name":"School of Computer and Information, Hefei University of Technology, Hefei 230009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jun","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Computer and Information, Hefei University of Technology, Hefei 230009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Daqian","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer and Information, Hefei University of Technology, Hefei 230009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tian","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Computer and Information, Hefei University of Technology, Hefei 230009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9291-3517","authenticated-orcid":false,"given":"Xin","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Computer and Information, Hefei University of Technology, Hefei 230009, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,11,7]]},"reference":[{"key":"ref_1","unstructured":"Coulson, K.L. (1988). Polarization and Intensity of Light in the Atmosphere, A. Deepak Publishing."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1007\/BF01338557","article-title":"Polarized skylight orientation in the desert ant Cataglyphis","volume":"158","author":"Fent","year":"1986","journal-title":"J. Comp. Physiol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1038\/424033a","article-title":"Animal behaviour: Insect orientation to polarized moonlight","volume":"424","author":"Dacke","year":"2003","journal-title":"Nature"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1016\/j.cub.2012.12.034","article-title":"Dung beetles use the Milky Way for orientation","volume":"23","author":"Dacke","year":"2013","journal-title":"Curr. Biol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"eaao6841","DOI":"10.1126\/sciadv.aao6841","article-title":"Bioinspired polarization vision enables underwater geolocalization","volume":"4","author":"Powel","year":"2018","journal-title":"Sci. Adv."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"619","DOI":"10.1098\/rstb.2010.0201","article-title":"Patterns and properties of polarized light in air and water","volume":"366","author":"Cronin","year":"2011","journal-title":"Philos. Trans. R. Soc. Lond. B Biol. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1098\/rstb.2010.0189","article-title":"Navigation by light polarization in clear and turbid waters","volume":"366","author":"Lerner","year":"2011","journal-title":"Philos. Trans. R. Soc. B Biol. Sci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"5193","DOI":"10.1364\/AO.53.005193","article-title":"Polarization transition between sunlit and moonlit skies with possible implications for animal orientation and Viking navigation: Anomalous celestial twilight polarization at partial moon","volume":"53","author":"Barta","year":"2014","journal-title":"Appl. Opt."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/BF01350213","article-title":"How bees analyse the polarization patterns in the sky","volume":"154","author":"Rossel","year":"1984","journal-title":"J. Comp. Physiol. A Neuroethol. Sens. Neural Behav. Physiol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1177\/105971239700600104","article-title":"An autonomous agent navigating with a polarized light compass","volume":"6","author":"Lambrinos","year":"1997","journal-title":"Adapt. Behav."},{"key":"ref_11","first-page":"745","article-title":"Investigation of atmospheric polarization measurement method imitating POL-neurons of cataglyphis","volume":"29","author":"Zhiguo","year":"2008","journal-title":"Chin. J. Sci. Instrum."},{"key":"ref_12","unstructured":"Usher, K., Ridley, P., and Corke, P. (2001, January 14\u201315). A camera as a polarized light compass: Preliminary experiments. Proceedings of the Australian Conference on Robotics and Automation, Sydney, Australia."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1117\/12.7976940","article-title":"Electro-optic camera system for measurement of the underwater radiance distribution","volume":"28","author":"Voss","year":"1989","journal-title":"Opt. Eng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"8753","DOI":"10.1364\/AO.36.008753","article-title":"Polarized radiance distribution measurement of skylight. II. Experiment and data","volume":"36","author":"Liu","year":"1997","journal-title":"Appl. Opt."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"543","DOI":"10.1364\/AO.41.000543","article-title":"Ground-based full-sky imaging polarimetry of rapidly changing skies and its use for polarimetric cloud detection","volume":"41","author":"Horvath","year":"2002","journal-title":"Appl. Opt."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1669","DOI":"10.1364\/JOSAA.21.001669","article-title":"How well does the Rayleigh model describe the E-vector distribution of skylight in clear and cloudy conditions? A full-sky polarimetric study","volume":"21","author":"Suhai","year":"2004","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"5470","DOI":"10.1364\/AO.45.005470","article-title":"Dual-field imaging polarimeter using liquid crystal variable retarders","volume":"45","author":"Pust","year":"2006","journal-title":"Appl. Opt."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"H190","DOI":"10.1364\/AO.47.00H190","article-title":"Digital all-sky polarization imaging of partly cloudy skies","volume":"47","author":"Pust","year":"2008","journal-title":"Appl. Opt."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"412","DOI":"10.1016\/j.jqsrt.2013.09.004","article-title":"vSmartMOM: A vector matrix operator method-based radiative transfer model linearized with respect to aerosol properties","volume":"133","author":"Sanghavi","year":"2014","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2321","DOI":"10.1364\/JOSAA.20.002321","article-title":"Comparison between the auxiliary function method and the discrete-ordinate method for solving the radiative transfer equation for light scattering","volume":"20","author":"Elias","year":"2003","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.jqsrt.2016.11.008","article-title":"A study of the radiative transfer equation using a spherical harmonics-nodal collocation method","volume":"189","author":"Capilla","year":"2017","journal-title":"J. Quant. Spectrosc. Radiat. Transf."},{"key":"ref_22","first-page":"6762","article-title":"Validation of a vector version of the 6S radiative transfer code for atmospheric correction of satellite data","volume":"45","author":"Kotchenova","year":"2006","journal-title":"Part I Path Radiance Appl. Opt."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1088\/1367-2630\/6\/1\/162","article-title":"Polarization singularities in the clear sky","volume":"6","author":"Berry","year":"2004","journal-title":"N. J. Phys."},{"key":"ref_24","unstructured":"Wilkie, A., Ulbricht, C., Tobler, R.F., Zotti, G., and Purgathofer, W. (2004, January 21\u201323). An analytical model for skylight polarization. Proceedings of the Eurographics Workshop on Rendering Techniques, The Eurographics Association, Nork\u00f6ping, Sweden."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"065601","DOI":"10.1088\/2040-8978\/18\/6\/065601","article-title":"An analytical model for the celestial distribution of polarized light, accounting for polarization singularities, wavelength and atmospheric turbidity","volume":"18","author":"Wang","year":"2016","journal-title":"J. Opt."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"B37","DOI":"10.1364\/AO.56.000B37","article-title":"Polarized skylight navigation","volume":"56","author":"Hamaoui","year":"2017","journal-title":"Appl. Opt."},{"key":"ref_27","unstructured":"Fleck, M.M. (1995). Perspective Projection: The Wrong Imaging Model, University of Iowa. Technical report."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1117\/12.405226","article-title":"Fish-eye lens designs and their relative performance","volume":"4093","author":"Kumler","year":"2000","journal-title":"Proc. SPIE"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1335","DOI":"10.1109\/TPAMI.2006.153","article-title":"A generic camera model and calibration method for conventional, wide-angle, and fish-eye lenses","volume":"28","author":"Kannala","year":"2006","journal-title":"IEEE T Pattern Anal."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"22252","DOI":"10.1364\/OE.20.022252","article-title":"Digital deformation model for fisheye image rectification","volume":"20","author":"Hou","year":"2012","journal-title":"Opt. Express"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"577","DOI":"10.1016\/j.solener.2003.12.003","article-title":"Solar position algorithm for solar radiation applications","volume":"76","author":"Reda","year":"2004","journal-title":"Sol. Energy"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"28589","DOI":"10.1364\/OE.26.028589","article-title":"Polarization patterns under different sky conditions and a navigation method based on the symmetry of the AOP map of skylight","volume":"26","author":"Zhao","year":"2018","journal-title":"Opt. Express"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"2347","DOI":"10.1364\/JOSAA.24.002347","article-title":"Polarization patterns of thick clouds: Overcast skies have distribution of the angle of polarization similar to that of clear skies","volume":"24","year":"2007","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"2933","DOI":"10.1242\/jeb.204.17.2933","article-title":"How the clear-sky angle of polarization pattern continues underneath clouds: Full-sky measurements and implications for animal orientation","volume":"4","author":"Pomozi","year":"2001","journal-title":"J. Exp. Biol."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/22\/4844\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:32:28Z","timestamp":1760189548000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/22\/4844"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,7]]},"references-count":34,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2019,11]]}},"alternative-id":["s19224844"],"URL":"https:\/\/doi.org\/10.3390\/s19224844","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2019,11,7]]}}}