{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,29]],"date-time":"2026-10-29T05:49:51Z","timestamp":1793252991366,"version":"4.5.0"},"reference-count":15,"publisher":"Optica Publishing Group","issue":"12","license":[{"start":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T00:00:00Z","timestamp":1780876800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/doi.org\/10.1364\/OA_License_v2#VOR-OA"},{"start":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T00:00:00Z","timestamp":1780876800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/opg.optica.org\/policies\/opg-tdm-policy.json"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["62505059"],"award-info":[{"award-number":["62505059"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"},{"id":"https:\/\/ror.org\/01h0zpd94","id-type":"ROR","asserted-by":"publisher"}]}],"content-domain":{"domain":["opg.optica.org"],"crossmark-restriction":false},"short-container-title":["Opt. Express"],"published-print":{"date-parts":[[2026,6,15]]},"abstract":"<jats:p>\n                    The cat-eye effect provides strong retro-reflected echoes that are widely exploited for laser active detection, yet in long-range scenarios, the echo-field morphology can be jointly distorted by atmospheric turbulence and oblique incidence. In the present work, the experimental validation is carried out within a moderate off-axis range that is directly supported by the measurement system. Here, we develop an analytical\u2013numerical unified framework to predict the three-dimensional (3D) echo field of a cat-eye target illuminated by a multiband Gaussian probe under turbulent propagation and oblique incidence. The analytical model combines a four-interval matrix-optics formulation with the Collins diffraction integral, incorporates turbulence statistics via the Rytov approximation, and maps oblique incidence to an equivalent transverse shift using a rotated coordinate system; hard-edge apertures are further treated by a complex-Gaussian expansion for efficient evaluation. In parallel, round-trip propagation is simulated using split-step Fourier propagation of the parabolic wave equation with a multi-phase-screen method, where phase screens are synthesized by FFT-based spectral inversion with subharmonic compensation. Angle-scan experiments in free space show consistent trends among measurements, analytical predictions, and numerical simulations in terms of echo-spot morphology, peak decay, and centroid drift. By varying the refractive-index structure constant\n                    <jats:italic>\n                      C\n                      <jats:sub>n<\/jats:sub>\n                    <\/jats:italic>\n                    <jats:sup>2<\/jats:sup>\n                    , we further observe turbulence-induced speckle formation, spot broadening, and beam wander, and the analytical and numerical models agree in their overall trends. This framework enables echo-field prediction and supports pointing assessment and tracking of cat-eye targets in complex atmospheric environments.\n                  <\/jats:p>","DOI":"10.1364\/oe.592936","type":"journal-article","created":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T04:00:07Z","timestamp":1779249607000},"page":"22009","update-policy":"https:\/\/doi.org\/10.1364\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Unified analytical\u2013numerical modeling and experimental validation of 3D cat-eye echo fields under turbulence and oblique incidence"],"prefix":"10.1364","volume":"34","author":[{"given":"Zhe","family":"Lv","sequence":"first","affiliation":[{"name":"Hangzhou Institute for Advanced Study University of Chinese Academy of Sciences"},{"name":"University of Chinese Academy of Sciences"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0295-701X","authenticated-orcid":true,"given":"Xiaojian","family":"Hao","sequence":"additional","affiliation":[{"id":[{"id":"https:\/\/ror.org\/047bp1713","id-type":"ROR","asserted-by":"publisher"}]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"285","published-online":{"date-parts":[[2026,6,8]]},"reference":[{"key":"oe-34-12-22009-R1","doi-asserted-by":"publisher","first-page":"108044","DOI":"10.1016\/j.optlastec.2022.108044","type":"journal-article","volume":"151","author":"Lv","year":"2022","journal-title":"J. Opt. Laser Technol."},{"key":"oe-34-12-22009-R2","doi-asserted-by":"publisher","first-page":"25993","DOI":"10.1364\/OE.494618","type":"journal-article","volume":"31","author":"Lv","year":"2023","journal-title":"Opt. Express"},{"key":"oe-34-12-22009-R3","doi-asserted-by":"publisher","first-page":"053110","DOI":"10.1117\/1.OE.56.5.053110","type":"journal-article","volume":"56","author":"Gong","year":"2017","journal-title":"Opt. Eng."},{"key":"oe-34-12-22009-R4","doi-asserted-by":"publisher","first-page":"2","DOI":"10.3788\/COL202523.020101","type":"journal-article","volume":"23","author":"Fu","year":"2025","journal-title":"Chin. Opt. Lett."},{"key":"oe-34-12-22009-R5","doi-asserted-by":"publisher","first-page":"28","DOI":"10.1117\/1.OE.64.5.058102","type":"journal-article","volume":"64","author":"Bachmann","year":"2025","journal-title":"Opt. Eng."},{"key":"oe-34-12-22009-R6","doi-asserted-by":"publisher","first-page":"3726","DOI":"10.1364\/AO.389121","type":"journal-article","volume":"59","author":"Chen","year":"2020","journal-title":"Appl. Opt."},{"key":"oe-34-12-22009-R7","doi-asserted-by":"publisher","first-page":"738","DOI":"10.1364\/JOSAA.385754","type":"journal-article","volume":"37","author":"Charnotskii","year":"2020","journal-title":"J. Opt. Soc. Am. A"},{"key":"oe-34-12-22009-R8","doi-asserted-by":"publisher","first-page":"1168","DOI":"10.1364\/JOSA.60.001168","type":"journal-article","volume":"60","author":"Collins","year":"1970","journal-title":"J. Opt. Soc. Am."},{"key":"oe-34-12-22009-R9","author":"Chahine","year":"2020"},{"key":"oe-34-12-22009-R10","doi-asserted-by":"publisher","first-page":"478","DOI":"10.1007\/s11801-011-1055-2","type":"journal-article","volume":"7","author":"Zhao","year":"2011","journal-title":"J. Optoelectron Lett."},{"key":"oe-34-12-22009-R12","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1016\/j.optcom.2018.05.069","type":"journal-article","volume":"426","author":"He","year":"2018","journal-title":"Opt. Commun."},{"key":"oe-34-12-22009-R13","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1364\/AO.57.001218","type":"journal-article","volume":"57","author":"He","year":"2018","journal-title":"Appl. Opt."},{"key":"oe-34-12-22009-R14","doi-asserted-by":"publisher","first-page":"1339","DOI":"10.1364\/JOSAA.429928","type":"journal-article","volume":"38","author":"Muschinski","year":"2021","journal-title":"J. Opt. Soc. Am. A"},{"key":"oe-34-12-22009-R15","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1088\/0959-7174\/2\/3\/003","type":"journal-article","volume":"2","author":"Lane","year":"1992","journal-title":"Waves in Random Media"},{"key":"oe-34-12-22009-R16","doi-asserted-by":"publisher","first-page":"6153","DOI":"10.1038\/s41598-023-32805-z","type":"journal-article","volume":"13","author":"Wang","year":"2023","journal-title":"Sci. Rep."}],"container-title":["Optics Express"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/opg.optica.org\/viewmedia.cfm?URI=oe-34-12-22009&seq=0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T15:58:00Z","timestamp":1780934280000},"score":1,"resource":{"primary":{"URL":"https:\/\/opg.optica.org\/abstract.cfm?URI=oe-34-12-22009"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6,8]]},"references-count":15,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2026]]},"published-print":{"date-parts":[[2026]]}},"URL":"https:\/\/doi.org\/10.1364\/oe.592936","relation":{},"ISSN":["1094-4087"],"issn-type":[{"value":"1094-4087","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,6,8]]},"assertion":[{"value":"Optica Publishing Group","name":"publisher","label":"This article is maintained by"},{"value":"https:\/\/doi.org\/10.1364\/OE.592936","name":"articlelink","label":"Crossref DOI link to publisher maintained version"},{"value":"research-article","name":"content_type","label":"Article type"},{"value":"Screened by Similarity Check","name":"cross_check","label":"Similarity check"},{"value":"Yes","order":0,"name":"peer_reviewed","label":"Peer reviewed","group":{"name":"peer_review","label":"Peer review"}},{"value":"Single blind","order":1,"name":"review_process","label":"Review process","group":{"name":"peer_review","label":"Peer review"}},{"value":"6 February 2026","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"18 May 2026","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"8 June 2026","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}},{"value":"\u00a9 2026 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement","name":"copyright","label":"Copyright"}]}}