Towards non-invasive optical reconstruction of the human eye’s crystalline lens

Light propagation in non-homogenous media with varying refractive index is challenging to analyse, even with knowledge of the gradient index (GRIN) structure n(x,y,z). Differential equations can be used to describe the path light rays take when travelling through a medium. In this project, a differential ray equation is used to calculate the effective focal length (EFL) and back focal distance (BFD) of a GRIN lens, with an emphasis on quadratic refractive index profiles commonly used to describe the crystalline lens of the human eye. The estimated values for EFL and BFD are then compared to the output of an optical design software, Zemax OpticStudio, which performs numerical ray-tracing through the lens. Ray-tracing in GRIN media is very difficult, and usually not possible without numerical methods, however for several types of GRIN lenses, the analytical solution exists. By extending the ray-tracing from the paraxial region (near the axis) to a broader region, a general differential ray equation has been derived, enabling the analysis of rays propagating through the GRIN lens at finite heights. From this, the back focal distances for rays entering the lens at varying initial heights can be calculated, and thus, the longitudinal spherical aberration can be estimated. The solution to the general differential equation enables one to calculate the refractive indices along the ray. The BFDs obtained using the paraxial method, the along-ray method, and numerical ray-tracing in Zemax OpticStudio software have all been compared, showing consistent results. The EFL of the lens was estimated using the derived ray equation and then compared with the numerical solution in Zemax OpticStudio; the discrepancy in the values of the EFL did not exceed one-tenth of the wavelength of light. The proposed ray-tracing methods have been applied to models of crystalline lenses found in nature, with specific interest on the lens in an octopus eye and Liou and Brennan model of a human eye. Reconstructing the refractive index profile of the crystalline lens presents a major challenge in representing the lens as a GRIN medium with a specific profile defined by polynomial functions of radial and axial distances. Without prior knowledge of the polynomial functions for a given lens, reconstructing the refractive index profile depends on predicting the path of light within the GRIN medium. This project explores a systematic approach to solving the GRIN reconstruction problem for symmetric and asymmetric lenses by utilizing the geometry of the lens's outer surface and the solution from the proposed ray equation based on the Frobenius method.

Funder

Hardiman Scholarship, University of Glaway

Publisher

University of Galway

Rights

CC BY-NC-ND

cbn

Collections

University of Galway Theses (PhD Theses)