Moiré Modeling in 3D Displays: A Dominant Component Approximation Using Indicial and Cosinusoidal Approaches

Moiré Modeling in 3D Displays: A Dominant Component Approximation Using Indicial and Cosinusoidal Approaches | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Moiré Modeling in 3D Displays: A Dominant Component Approximation Using Indicial and Cosinusoidal Approaches Tae Hee Lee, Young Ju Jeong This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7658681/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 16 Mar, 2026 Read the published version in Virtual Reality → Version 1 posted You are reading this latest preprint version Abstract Autostereoscopic 3D panels in augmented reality head-up displays use periodic optics to overlay pixel grids, creating a moiré effect. It is essential to predict this in advance to ensure display quality in virtual and augmented reality. The moiré effect in three-dimensional displays arises from the interference between the display panel’s pixel grid and periodic optical elements such as lenticular lenses or parallax barriers. While periodic gratings inherently exhibit infinitely many frequency components, analyzing them directly is impractical. In this work, we propose a dominant component approximation that models the moiré phenomenon using both indicial representation and cosinusoidal approximation, and demonstrate that these two approaches yield identical predictions for the moiré period and angle. We further validate the proposed approximation experimentally with two lenticular lenses at multiple slanted angles, achieving strong agreement between simulation and real-world measurements. moiré effect 3D displays dominant component approximation indicial representation cosinusoidal approximation lenticular lens Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 16 Mar, 2026 Read the published version in Virtual Reality → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7658681","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":524864728,"identity":"8c017597-a4b3-4c9f-ab28-84461ee344f0","order_by":0,"name":"Tae Hee Lee","email":"","orcid":"","institution":"Sungkyunkwan University","correspondingAuthor":false,"prefix":"","firstName":"Tae","middleName":"Hee","lastName":"Lee","suffix":""},{"id":524864729,"identity":"b0f220e3-4742-467e-be94-f23b16a1faf9","order_by":1,"name":"Young Ju Jeong","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA9klEQVRIiWNgGAWjYFCCAyDCBojZEGKMDYS1pJGkBQwOk6DF4ODhg48Lfp2352dvS93M23bHroH98APGmXvwaDlwLNl4Zt/txJk9x47d5m17ltzAk2bAuOEZPi1nzKR5e24nGNxIbwNqOZzMwJDDwPjgAD4t578BtZyzR2jhf0NIyxk2aZ4fBxg33EgDOeywHYME0JYNeLRIHjhmbMzbkAzyS9rNOecOJ7BJPDM4OAOPFr4bhx8+5vljBwoxsxtvyg7b8/MnP3zYg0eLwg2gJGMbhMPEw8CQCGLj0cDAIN/fACT/QDiMPxgY7PGpHgWjYBSMgpEJAC/SXwcIopHBAAAAAElFTkSuQmCC","orcid":"","institution":"Sookmyung Women's University","correspondingAuthor":true,"prefix":"","firstName":"Young","middleName":"Ju","lastName":"Jeong","suffix":""}],"badges":[],"createdAt":"2025-09-19 12:38:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7658681/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7658681/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s10055-026-01339-w","type":"published","date":"2026-03-16T15:58:22+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":92914781,"identity":"4dd3909d-1dbc-434b-ba33-2a69e615572f","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"json","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":3629,"visible":true,"origin":"","legend":"","description":"","filename":"e1c42c6c8f284833b9a6bbbe642162ef.json","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/5aacf47040828b31bee9c0a0.json"},{"id":92914785,"identity":"bd582e0c-0fd1-4286-bfd6-15d642dabc91","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"xml","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":69009,"visible":true,"origin":"","legend":"","description":"","filename":"e1c42c6c8f284833b9a6bbbe642162ef1enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/ef47129601638d89deb6ed00.xml"},{"id":92914909,"identity":"72f7764a-d48c-4569-8bfc-f798ec0dab3d","added_by":"auto","created_at":"2025-10-07 05:07:37","extension":"jpg","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":86831,"visible":true,"origin":"","legend":"","description":"","filename":"cosinespatial.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/a809965f78320842c0b1f4c4.jpg"},{"id":92914904,"identity":"29f7f3f2-e8b2-4b0e-b48a-4f98e70af77b","added_by":"auto","created_at":"2025-10-07 05:07:36","extension":"pdf","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":94594,"visible":true,"origin":"","legend":"","description":"","filename":"coverletter.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/9c780399d074201ed14cac2f.pdf"},{"id":92914784,"identity":"26631c15-73a5-47c0-a4d5-1bfa19184d07","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"png","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":510489,"visible":true,"origin":"","legend":"","description":"","filename":"expl1.png","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/f302c380a11191868c9c39d8.png"},{"id":92914794,"identity":"74b97187-5129-4c47-bc67-f99a8815940f","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"png","order_by":5,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":523978,"visible":true,"origin":"","legend":"","description":"","filename":"expl2.png","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/82af6fe1957f04c50159abb7.png"},{"id":92914782,"identity":"51dee45b-1a34-4214-a896-4f310c33dbb7","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"jpg","order_by":6,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":32165,"visible":true,"origin":"","legend":"","description":"","filename":"general.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/1bb3ffe0175cd633f3b08e65.jpg"},{"id":92914905,"identity":"e7a14c9d-a433-4f0a-a6b0-a0e9ddae748e","added_by":"auto","created_at":"2025-10-07 05:07:36","extension":"png","order_by":7,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":76940,"visible":true,"origin":"","legend":"","description":"","filename":"imsim.png","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/2fb130dadb42c8980aad11e7.png"},{"id":92914798,"identity":"6e50e32d-14e5-45d7-acad-facc14ed1fb4","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"jpg","order_by":8,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":60877,"visible":true,"origin":"","legend":"","description":"","filename":"indicialspatial.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/3ca376139ab4c6c2e1b5a452.jpg"},{"id":92914797,"identity":"fc9a1286-2c8b-4c59-b190-256472e452cf","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"png","order_by":9,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":101275,"visible":true,"origin":"","legend":"","description":"","filename":"mf.png","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/0a810b05cc4f5060c5d8d582.png"},{"id":92914908,"identity":"3c45c94b-63ea-4184-a3d7-f8903499e4ed","added_by":"auto","created_at":"2025-10-07 05:07:36","extension":"png","order_by":10,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":70663,"visible":true,"origin":"","legend":"","description":"","filename":"mfl1.png","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/cb49ba53086000ad197693e3.png"},{"id":92914906,"identity":"79cc5b61-4ae8-426e-b804-9178b7f9a3c2","added_by":"auto","created_at":"2025-10-07 05:07:36","extension":"png","order_by":11,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":73268,"visible":true,"origin":"","legend":"","description":"","filename":"mfl2.png","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/39f9034580cafaff199e7e86.png"},{"id":92914791,"identity":"a3aaddaf-7b7d-45cd-9ed8-7427bec27c4b","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"pdf","order_by":12,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":1603716,"visible":true,"origin":"","legend":"","description":"","filename":"moire.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/6ad8d2ad7e8c27b8483609ed.pdf"},{"id":92914788,"identity":"136dc0ba-9617-4fae-b784-f4a07f1a04a4","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"jpg","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":77488,"visible":true,"origin":"","legend":"","description":"","filename":"moireeffect1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/a4f082b4516192ccf6013c14.jpg"},{"id":92914910,"identity":"d47b4a8d-2a5c-4427-8097-b6fe5a093327","added_by":"auto","created_at":"2025-10-07 05:07:41","extension":"cls","order_by":14,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":55857,"visible":true,"origin":"","legend":"","description":"","filename":"snjnl.cls","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/390a638bc92262ac9bbec8f2.cls"},{"id":92914801,"identity":"ca44738e-fbd9-4c01-9a36-d87af1c4a281","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"bst","order_by":15,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":64164,"visible":true,"origin":"","legend":"","description":"","filename":"snmathphysnum.bst","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/d5af14d2a7856c11512ecd59.bst"},{"id":92914790,"identity":"dc5ce0fe-8f5f-41dd-967b-bafeed4931b4","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"png","order_by":23,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":60540,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinemfl1.png","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/6e50328a030fd2346e35292f.png"},{"id":92914799,"identity":"cf466a9c-e1d8-4f95-a142-b2f24b718c98","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"png","order_by":24,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":62294,"visible":true,"origin":"","legend":"","description":"","filename":"Onlinemfl2.png","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/479374a73f4e3e9b17fc12f0.png"},{"id":92914800,"identity":"7efd6ec0-7a07-4d47-a350-8011010fcf92","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"xml","order_by":26,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":73871,"visible":true,"origin":"","legend":"","description":"","filename":"e1c42c6c8f284833b9a6bbbe642162ef1structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/793bd25e4443323e81b8cc7b.xml"},{"id":92914795,"identity":"8f936b38-159b-48fb-a985-2b816b56bf18","added_by":"auto","created_at":"2025-10-07 04:59:36","extension":"html","order_by":27,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":87099,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1/7eb134ae560f6e4203aae515.html"},{"id":105223347,"identity":"64536456-cf65-43f2-80e3-99999fd2649b","added_by":"auto","created_at":"2026-03-23 16:04:33","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":768832,"visible":true,"origin":"","legend":"","description":"","filename":"moire.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7658681/v1_covered_9a41bd46-f2b9-497d-918d-ccc13cfc7310.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Moiré Modeling in 3D Displays: A Dominant Component Approximation Using Indicial and Cosinusoidal Approaches","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"moiré effect, 3D displays, dominant component approximation, indicial representation, cosinusoidal approximation, lenticular lens","lastPublishedDoi":"10.21203/rs.3.rs-7658681/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7658681/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eAutostereoscopic 3D panels in augmented reality head-up displays use periodic optics to overlay pixel grids, creating a moir\u0026eacute; effect. It is essential to predict this in advance to ensure display quality in virtual and augmented reality. The moir\u0026eacute; effect in three-dimensional displays arises from the interference between the display panel\u0026rsquo;s pixel grid and periodic optical elements such as lenticular lenses or parallax barriers. While periodic gratings inherently exhibit infinitely many frequency components, analyzing them directly is impractical. In this work, we propose a dominant component approximation that models the moir\u0026eacute; phenomenon using both indicial representation and cosinusoidal approximation, and demonstrate that these two approaches yield identical predictions for the moir\u0026eacute; period and angle. We further validate the proposed approximation experimentally with two lenticular lenses at multiple slanted angles, achieving strong agreement between simulation and real-world measurements.\u003c/p\u003e","manuscriptTitle":"Moiré Modeling in 3D Displays: A Dominant Component Approximation Using Indicial and Cosinusoidal Approaches","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-07 04:59:31","doi":"10.21203/rs.3.rs-7658681/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"30dcb6b2-1504-4543-af66-6e8c52b701f3","owner":[],"postedDate":"October 7th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2026-03-23T16:01:37+00:00","versionOfRecord":{"articleIdentity":"rs-7658681","link":"https://doi.org/10.1007/s10055-026-01339-w","journal":{"identity":"virtual-reality","isVorOnly":false,"title":"Virtual Reality"},"publishedOn":"2026-03-16 15:58:22","publishedOnDateReadable":"March 16th, 2026"},"versionCreatedAt":"2025-10-07 04:59:31","video":"","vorDoi":"10.1007/s10055-026-01339-w","vorDoiUrl":"https://doi.org/10.1007/s10055-026-01339-w","workflowStages":[]},"version":"v1","identity":"rs-7658681","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7658681","identity":"rs-7658681","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}