Third-order aberration theory for weak gradient-index lenses

Analytical surrogate model for the aberrations of an arbitrary GRIN lens

Current analytical expressions between Gradient-Index (GRIN) lens parameters and optical aberrations are limited to paraxial approximations, which are not suitable for realizing GRIN lenses with wide fields of view or small f-numbers. Here, an analytical surrogate model of an arbitrary GRIN lens ray-trace evaluation is formulated using multivariate polynomial regressions to correlate input GRIN lens parameters with output Zernike coefficients, without the need for approximations. The time needed to compute the resulting surrogate model is over one order-of-magnitude faster than traditional ray trace simulations with very little losses in accuracy, which can enable previously infeasible design studies to be completed.

Refractive power of a multilayer rotationally symmetric model of the human cornea and tear film

Optical models of the human cornea and tear film typically employ a single homogeneous cornea with an average refractive index. I propose to use a more realistic multilayer model based on morphological data from the literature. The mathematical methodology to derive the refractive power equation of this model is presented. Special attention is given to the axial gradient index of the refraction structure of the stroma layer because of its optical implications. The importance of considering this multilayer model is quantified in a specific example (orthokeratology) with the help of the derived power equation.