Objective refraction from aberrometry: theory.

A theoretical framework to formulate and solve the problem of obtaining the objective refraction of an eye from aberrometric data is presented. Matrix formalism was applied to represent lens power and beam vergences in standard clinical, sphere+cylinder (S+C) refraction, and to describe the vergence error of a general aberrated skew ray. The vergence error matrix of each ray passing through the pupil is obtained, and the global refractive error is obtained by simple pupil average. The 2 x 2 vergence error matrix of a skew ray can be decomposed into the sum of two even-symmetric and odd-symmetric contributions. The even symmetric part corresponds to classic S+C refractive errors. The odd component can not be corrected with standard lenses. All odd components have zero mean over pupil, and do not contribute to the global refractive error, which is completely determined by S+C components. The contributions of wavefront Zernike modes to the global vergence error were obtained: The contributions of odd orders are zero, but all even HOA, but spherical aberration, contribute to refractive error. The matrix formulation of power and vergence errors provided a direct, simple way to use aberrometers as objective refractometers.