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Stephen G. Odaibo; Photon Trajectory in the Human Cornea. Invest. Ophthalmol. Vis. Sci. 2012;53(14):127.
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To determine the trajectory of a photon in the human cornea. Prior to experimental evidence of the cornea's gradient refractive index (GRIN) nature, schematic eye models used a constant or average as the corneal refractive index. A few recent models respect the intra-corneal GRIN, but are based on the paraxial approximation, and thereby have limited validity in peripheral visual field analysis and non-paraxial photon tracking. Here, in a model respectful of the cornea's GRIN nature, we set out to determine the intra-corneal trajectory of a photon which is not restricted to the paraxial regime.
To achieve our objective, we design the Trajectron algorithm. It uses a closed form solution of the ray equation of constant axial GRIN media, and evaluates over piece-wise constant axial GRIN. Discrete measurements of corneal refractive indices are obtained from the literature, and a continuous distribution is generated by curve fitting. Trajectron is prototyped in MATLAB (The MathWorks Inc., Natick, MA). [A pre-print of Trajectron and the current work is available on the arXiv pre-print server at http://arxiv.org/abs/1110.0081].
In this work, we have provided the first quantitative demonstration of non-paraxial light-bending within the human cornea. We have also introduced the Trajectron algorithm for computing photon trajectories in the human cornea.And we have initiated steps towards describing the angular domain over which the paraxial approximation is clinically applicable. These demonstrations have significant implications in the development of refractive surgery algorithms.
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