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. 2015 Apr-Jun;8(2):77-85.
doi: 10.1016/j.optom.2014.09.003. Epub 2014 Oct 19.

Third-order aberrations in GRIN crystalline lens: a new method based on axial and field rays

Arturo Díaz Del Río  1 , Carlos Gómez-Reino  1 , M Teresa Flores-Arias  2
Affiliations

Third-order aberrations in GRIN crystalline lens: a new method based on axial and field rays

Arturo Díaz Del Río et al. J Optom. 2015 Apr-Jun.

Abstract
in English, Spanish

This paper presents a new procedure for calculating the third-order aberration of gradient-index (GRIN) lenses that combines an iterative numerical method with the Hamiltonian theory of aberrations in terms of two paraxial rays with boundary conditions on general curved end surfaces and, as a second algebraic step has been presented. Application of this new method to a GRIN human is analyzed in the framework of the bi-elliptical model. The different third-order aberrations are determined, except those that need for their calculation skew rays, because the study is made only for meridional rays.

Este documento presenta un nuevo procedimiento para el cálculo de las aberraciones de tercer orden en los cristalinos con gradiente de índice (GRIN), que combina un método numérico iterativo con la teoría de Hamilton sobre aberraciones, en términos de dos rayos paraxiales con condiciones de contorno sobre superficies generales con límite curvado, y que se ha presentado como segundo paso algebraico. Se analiza la aplicación de este nuevo método al GRIN humano en el marco de un modelo bi-elíptico. Se determinan las diferentes aberraciones de tercer orden, excepto aquellas cuyo cálculo precisa de rayos inclinados, ya que el estudio se realiza únicamente para rayos meridionales.

Keywords: Aberraciones de tercer orden; Axial and field rays; Cristalino; Crystalline; Human eye; Ojo humano; Rayos axiales y de campo; Third-order aberrations.

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Figures

Figure 1
Figure 1
Evolution of the axial and field rays in a bi-elliptical GRIN medium.
Figure 2
Figure 2
Scheme of variables used to evaluate the third-order aberrations.
Figure 3
Figure 3
Structure of the refractive index of the human lens in the sagittal section considered as a bi-elliptical iso-indicial curves.
Figure 4
Figure 4
(a) Longitudinal spherical aberration (LSA) and (b) transversal spherical aberration (TSA) versus the input angle ϑ. Calculations have been made for the coefficients c0 = 1.406, c1 = −0.0201416, c2 = 0.0001423, c3 = −0.0000007 and c4 = 0, a1 = 1.7 mm and a2 = 1.9 mm and a lens semiaperture of 4.5 mm.
Figure 5
Figure 5
Comma versus the height of the input ray ρ0. Calculations have been made for the same parameter that Fig. 4, for the fovea, assuming it is at 5°.
Figure 6
Figure 6
Distortion versus the input angle ϑ. Calculations have been made for parameters of Fig. 4.
Figure 7
Figure 7
Meridional curvature versus the input angle ϑ. Calculations have been made for parameters of Fig. 4.
See this image and copyright information in PMC

References

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