Generalised models of the vertebrate eye.

Purpose: To present a set of closed-form analytical equations to create a consistent eye model balance based on clinically measured input parameters in a single step. These models complement the existing iterative approaches in the literature.

Methods: Two different approaches are presented, both considering the cornea and lens as equivalent thin lenses. The first, called the Gaussian model, starts by defining the refractive error as the difference between the axial power (or dioptric distance) and the whole eye power, which can be expanded by filling in the formulas for each power. The resulting equation can be solved for either the refractive error, axial length, corneal power, lens power or the distance between the cornea and the lens as a function of the other four parameters. The second approach uses vergence calculations to provide alternative expressions, assuming that the refractive error is located at the corneal plane. Both models are explored for a biometric range typically found in adult human eyes.

Results: The Gaussian and vergence models each instantly balance the input data into a working eye model over the human physiological range and far beyond as demonstrated in various examples. The equations of the Gaussian model are more complicated, while the vergence model experiences more singularities, albeit in trivial or highly unlikely parameter combinations.

Conclusions: The proposed equations form a flexible and robust platform to create eye models from clinical data. Possible applications lie in creating animal eye models or providing a generic reference for real biometric data and the relationships between the ocular dimensions.