Analytical ray transfer matrix for the crystalline lens

Date

2022

Authors

Navarro, Rafael
Lockett-Ruiz, Verónica

Director

Publisher

OSA Publishing
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión publicada / Argitaratu den bertsioa

Project identifier

  • AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2019-107058RB-I00/ES/ recolecta
  • AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-095795B-I00/ES/ recolecta
  • European Commission/Horizon 2020 Framework Programme/956720/ openaire
Impacto
No disponible en Scopus

Abstract

We 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.

Description

Keywords

ABCD matrix, GRIN lenses

Department

Estadística, Informática y Matemáticas / Estatistika, Informatika eta Matematika

Faculty/School

Degree

Doctorate program

item.page.cita

Navarro, 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.466374

item.page.rights

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