Single function crystalline lens capable of mimicking ciliary body accommodation

Abstract

The lens is a complex optical component of the human eye because of its physiological structure: the surface is aspherical and the structural entities create a gradient refractive index (GRIN). Most existent models of the lens deal with its external shape independently of the refractive index and, subsequently, through optimization processes, adjust the imaging properties. In this paper, we propose a physiologically realistic GRIN model of the lens based on a single function for the whole lens that accurately describes different accommodative states simultaneously providing the corresponding refractive index distribution and the external shape of the lens by changing a single parameter that we associate with the function of the ciliary body. This simple, but highly accurate model, is incorporated into a schematic eye constructed with reported experimental biometric data and accommodation is simulated over a range of 0 to 6 diopters to select the optimum levels of image quality. Changes with accommodation in equatorial and total axial lens thicknesses, as well as aberrations, are found to lie within reported biometric data ranges.

Modified Poisson-Gauss Single-Function to Describe the GRIN of the Human Lens

“…(1)a. This key feature has been exploited to describe another asymmetric distribution, that of the GRIN of the human lens [18]. By multiplying the Poisson distribution times a Gaussian, the Poisson-Gauss function can be obtained:…”

“…where r = x 2 + y 2 is the radial distance in cylindrical coordinates, z is the axial coordinate, and l, a 1 , a 2 , a r are parameters [18]. Furthermore, the Poisson-Gauss function is able to describe the GRIN structure of the lens through the following expression…”

“…Several GRIN lens models have been proposed over the last three decades following two main approaches: to describe the GRIN using one or two functions, since the lens is asymmetric [2,[4][5][6][7][8][9][10][11][12][13][14][15][16][17]. Recently, a single function model, that was inspired by quantum notions, has been proposed to describe the whole lens in a simple fashion with optical performance within experimental range [18,19].…”

Generation of Lens Progenitor Cells and Lentoid Bodies from Pluripotent Stem Cells: Novel Tools for Human Lens Development and Ocular Disease Etiology

“…One of these challenges relates to the precise 3D lens shape and its control via a combination of processes governing lens growth, optic, and mechanical stretching to generate a gradient refractive index underlying physiological lens function [ 457 ] that may not be possible without complex tissue engineering to mimic functionally active lens ciliary muscles and zonules [ 458 , 459 ].…”

Gabor superlens with variable focus

“…A change like this shifts the focal distance of the lens [7] . This process has several similitudes with the accommodation of the human eye [8] due to the fact that the human crystalline lens adjusts its shape to correctly focus the eye in response to visual demand [8][9][10] rather than shifting its position as other mechanical systems. For this reason, the tunable liquid lens has been considered as an option for developing bionic eyes to mimic the function of the human crystalline lens [11] .…”