Reconstruction of the gradient refractive index of the crystalline lens with optimization methods

Resumo

The crystalline of the eye is the biconvex lens suspended behind the iris that contributes to around one third of the total power of the optical system of the eye. The crystalline lens can change its external shape to accommodate allowing the eye to focus to far and near objects in young subjects. The lens looses with age its ability to accommodate, and becomes opaque upon the development of cataract later in life. The optical properties of the crystalline lens depend not only on the geometry of the external shape, but also on its refractive index. In many species, the refractive index shows a non-homogeneous distribution, with higher index values in the nucleus than in the surface. The precise knowledge of the optics of the crystalline lens and its changes with accommodation and aging are currently limited by the challenges of estimating the gradient refractive index distribution. Understanding of the role of the gradient index distribution of the crystalline lens on the crystalline lens optics will allow not only to gain deeper insights into the optical properties of the lens, and their variation with accommodation and aging, but also to improve the imaging of the lens with optical techniques in which the posterior lens surface appears distorted by refraction from preceding ocular surfaces and GRIN. In this thesis we proposed and developed a novel method for reconstruction of the gradient refractive index distribution of non-spherical crystalline lenses and applied it experimentally in porcine and human lenses. We also studied the effects of GRIN on the visualization of the posterior lens surface The thesis has been organized by chapters which roughly correspond to the articles published on the topic of the thesis. The introductory chapter presents an extensive background, state of the art, and motivation of the thesis. Chapter 2 presents the developed method for GRIN reconstruction, which uses ray tracing or optical coherence tomography data as input data, as well as the experimental systems used to obtain experimental data from crystalline lenses. Chapter 3 presents the accuracy of the technique though computational simulations of the different experimental approaches using experimental estimates of data input errors. Chapter 4 presents the reconstruction of the gradient refractive index of a porcine crystalline lens three dimensionally using data obtained from a spectral OCT system in our laboratory. The relative contribution of the surface shape and GRIN on astigmatism and spherical aberration of these lenses is presented. Chapter 5 presents the reconstruction of the GRIN profile (in two dimensions) in a set of lenses of various ages. The variation of the values of surface and nucleus refractive indices, and in particular the shape of the GRIN profile, are discussed. Chapter 6 explores the optical distortion produced by the GRIN on the posterior surface shape of a young crystalline lens imaged by OCT. The impact of the assumption of a simple correction method on the geometrical parameters of the crystalline lens are discussed. Chapter 7 proposes a new optical distortion correction method considering the presence of GRIN in OCT images of the crystalline lens, which is applied on a set of human lenses in vitro.