Direct transformation of Zernike eye aberration coefficients between scaled, rotated, and/or displaced pupils

Abstract

In eye aberrometry it is often necessary to transform the aberration coefficients in order to express them in a scaled, rotated, and/or displaced pupil. This is usually done by applying to the original coefficients vector a set of matrices accounting for each elementary transformation. We describe an equivalent algebraic approach that allows us to perform this conversion in a single step and in a straightforward way. This approach can be applied to any particular definition, normalization, and ordering of the Zernike polynomials, and can handle a wide range of pupil transformations, including, but not restricted to, anisotropic scalings. It may also be used to transform the aberration coefficients between different polynomial basis sets.

Six-Month Clinical Outcomes of Customized Treatments Minimized for Depth and Time in Laser Corneal Refractive Surgery

“…Coupling effects between different high-order aberration terms and between high-order-aberrations (HOAs) and manifest refraction have been found, [44][45][46] for example, between defocus and spherical aberration, or between third-order aberrations and low-order terms, between spherical aberration and coma, or between secondary and primary astigmatisms. These interactions may provide some relative visual benefits 47 but may as well contribute as sources of uncertainty in the conversion of wavefront aberration maps to refractive prescriptions.…”

Simulated effect of aspheric transition zone ablation profiles on optical aberrations after customized myopia ablation

“…Therefore, a Monte Carlo simulation was performed for simulating the treatment decentration in our study. In addition, the translation and rotation of ablation profile could be simulated theoretically by wavefront transformation [13].…”

Derivation of the propagation equations for higher order aberrations of local wavefronts

“…While there exist various publications dealing with analytical scaling transformations to a different pupil size [14][15][16][17][18][19][20][21], rotating the pupil [14,[20][21][22], displacing the pupil [14,15,[20][21][22], or deforming the pupil [21], only a few publications can be found that attempt to treat the wavefront propagation in an analytical way. In [14,23], an analytical method is described to calculate the propagation of a wavefront, but the method is still restricted by some approximations.…”