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.

To evaluate and compare the effect of misalignment and tilt on the optical performance of different aspheric intraocular lens (IOL) designs. Methods Three aspheric IOLs with a different quantity of spherical aberration (SA) have been designed and the effect of IOL misalignment and tilt on the imaging quality of an eye model has been numerically assessed using a commercial optical design software. The prototypes have been manufactured by lathe turning and tested in vitro using the same optical bench (PMTF, Lambda-X) that complies with International Organization for Standardization standard 11979-2 requirements. Image quality was evaluated from the modulation transfer functions (MTFs), through-focus modulation transfer functions (TF-MTFs), root mean square (RMS) values of defocus, astigmatism and coma, and images of the United States Air Force (USAF) target were taken. A comparison with the optical performance of spherical IOLs has also been performed. Results Intraocular lens misalignment and tilt increased wavefront aberrations; the effect of misalignment on root mean square (RMS) astigmatism and coma was positively correlated with the spherical aberration of the IOL. Aberration-free IOLs showed the highest MTF for all misalignment values and for IOLs with negative SA correction the MTF decays below 0.43 when they are decentered 0.50 mm. Conclusions Aspherical IOLs are more sensitive than spherical IOLs to misalignment or tilt, depending on their SA correction. The optical degradation caused by IOL misalignment had a greater effect on IOL designs with a higher amount of negative spherical aberration. In contrast, the effect of tilt on the optical performance was less sensitive to the IOL design.

The results show the usefulness of the proposed approach and point out the need for developing further adapted optimizations.