Modelling accommodation and ageing of the crystalline lens in the human eye

This thesis is a study on the optical properties of the human eye; specifically, optical modelling of the human lens with accommodation and ageing. The idiosyncratic nature of the human eye provides a hindrance to modelling efforts in terms of model construction and verification. For this reason, generic data---while lacking useful individual information---prove very useful. Hence, a comprehensive review of the literature on age-related changes in spherical aberration was performed, with the goal of using spherical aberration as an important constraint for developing more realistic generic optical eye models. An analytical method to describe the accommodative changes in the human crystalline lens has been proposed. The method is based on the geometry-invariant lens model, in which the GRIN iso-indicial contours are coupled to the external shape. This coupling enables definition of the GRIN structure if the radii and asphericities of the external lens surfaces are known. As an example, the accommodative changes in lenticular radii and central thickness were taken from the literature, while the asphericities of the external surfaces were derived analytically by adhering to the basic physical conditions of constant lens volume and its axial position. The resulting changes in lens geometry are consistent with experimental data, and the optical properties are in line with expected values for optical power and spherical aberration. This provides an anatomically and optically accurate lens model that is valid for 3 mm pupils and can be used as a new tool for better understanding of accommodation. Second, a new age-dependent model of the human lens is proposed, with two GRIN power distributions (axial and radial) which, together with a logarithmic model of the lens core, allow decoupling of three fundamental optical characteristics of the lens, namely axial optical path length, optical power and third-order spherical aberration, without changing the external shape of the lens. The spherical aberration calculated by exact raytracing is shown to be in line with experimental data. Conversely, the near-surface GRIN structure conforms to the external shape of the lens, which is necessary for accommodation modelling. The proposed model is compared to previous GRIN models from the literature, and it is concluded that the features of the new model will be useful for GRIN reconstruction in future experimental studies; in particular, studies of the accommodation-dependent properties of the ageing human eye. The extra flexibility of this model is highlighted in the concluding section, where the lens paradox is examined. The requirement of a smooth equatorial join of the anterior and posterior lens surfaces imparts anatomical relevance to the models. While importantly allowing volume specification, this formulation has many more applications, purely because of its physical significance. This will form the basis for a joined optical and bio-mechanical model of the lens using finite element methods