Zonal integration of circular Hartmann and Placido patterns with non-rotationally symmetric aberrations

Placido disk methods for corneal topography use a target with concentric rings in order to obtain measurements of the corneal surface, codifying the topography from the deformations of the rings' image. Knowing exactly how the corneal surface departs from a rotational symmetric shape is difficult by using Placido rings. This is due to the fact that any ray deviations in the angular direction (sagittal transverse aberrations) are not easily detected and measured. This is the so-called skew ray error. For that reason, this technique has been considered as limited, especially when one tries to measure corneal aberrations with large rotational symmetry errors. However, we considered that the Placido disk topography has the potential to obtain a full description of the corneal surface as long as the skew ray error is fixed. Here, we present a solution based in the assumption that a corneal topography calculated with the presence of the skew ray error has hidden information that can be extracted by applying some basis of the classical Hartmann test. To achieve that solution, we improve some aspects of the Hartmann test to be later applied in the processing of Placido disk images. Our solution gives us the ability to solve the skew ray error in a simple and direct method, with an effectiveness that is probed by the computing of some simulated representative surfaces without rotational symmetry and the performance of our algorithm.