Analytical ray transfer matrix for the crystalline lens

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dc.contributor.authorNavarro, Rafael
dc.contributor.authorLockett-Ruiz, Verónica
dc.contributor.authorLópez García, José Luis
dc.contributor.departmentEstadística, Informática y Matemáticases_ES
dc.contributor.departmentEstatistika, Informatika eta Matematikaeu
dc.date.accessioned2023-02-21T11:23:13Z
dc.date.available2023-02-21T11:23:13Z
dc.date.issued2022
dc.date.updated2023-02-21T10:15:27Z
dc.description.abstractWe present the formulation of a paraxial ray transfer or ABCD matrix for onion-type GRIN lenses. In GRIN lenses, each iso-indicial surface (IIS) can be considered a refracting optical surface. If each IIS is a shell or layer, the ABCD matrix of a GRIN lens is computed by multiplying a typically high number of translation and refraction matrices corresponding to the K layers inside the lens. Using a differential approximation for the layer thickness, this matrix product becomes a sum. The elements A, B, C, and D of the approximated GRIN ray transfer matrix can be calculated by integrating the elements of a single-layer matrix. This ABCD matrix differs from a homogeneous lens matrix in only one integration term in element C, corresponding to the GRIN contribution to the lens power. Thus the total GRIN lens power is the sum of the homogeneous lens power and the GRIN contribution, which offers a compact and simple expression for the ABDC matrix. We then apply this formulation to the crystalline lens and implement both numerical and analytical integration procedures to obtain the GRIN lens power. The analytical approximation provides an accurate solution in terms of Gaussian hypergeometric functions. Last, we compare our numerical and analytical procedures with published ABCD matrix methods in the literature, and analyze the effect of the iso-indicial surface’s conic constant (Q) and inner curvature gradient (G) on the lens power for different lens models.en
dc.description.sponsorshipMinisterio de Ciencia e Innovación (PID2019-405 107058RB-100, PGC2018-095795B-I00); HORIZON EUROPE Marie Sklodowska-Curie Actions (956720).en
dc.format.mimetypeapplication/pdfen
dc.identifier.citationNavarro, R., Lockett-Ruiz, V., & López, J. L. (2022). Analytical ray transfer matrix for the crystalline lens. Biomedical Optics Express, 13(11), 5836. https://doi.org/10.1364/BOE.466374en
dc.identifier.doi10.1364/BOE.466374
dc.identifier.issn2156-7085
dc.identifier.urihttps://academica-e.unavarra.es/handle/2454/44742
dc.language.isoengen
dc.publisherOSA Publishingen
dc.relation.ispartofBiomedical Optics Express 13(11) 5836-5848en
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107058RB-I00/ES/
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095795B-I00/ES/
dc.relation.projectIDinfo:eu-repo/grantAgreement/European Commission/Horizon 2020 Framework Programme/956720/
dc.relation.publisherversionhttps://doi.org/10.1364/BOE.466374
dc.rights© 2022 Optica Publishing Group. Users may use, reuse, and build upon the article, or use the article for text or data mining, so long as such uses are for non-commercial purposes and appropriate attribution is maintained. All other rights are reserved.en
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.subjectABCD matrixen
dc.subjectGRIN lensesen
dc.titleAnalytical ray transfer matrix for the crystalline lensen
dc.typeinfo:eu-repo/semantics/article
dc.type.versioninfo:eu-repo/semantics/publishedVersion
dspace.entity.typePublication
relation.isAuthorOfPublicatione6cd33c5-6d5e-455c-b8da-32a9702e16c8
relation.isAuthorOfPublication.latestForDiscoverye6cd33c5-6d5e-455c-b8da-32a9702e16c8

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