Generic Zernike-based surface representation of measured corneal surface data

Meshes of points over the unit disk were found some years ago that ensure the discrete orthogonality of the Zernike functions. These meshes are referred in the paper as generic Zernike meshes. Presently, however, the corneal surface points are measured, e.g., with reflection-based corneal topographers, and computed, with their respective built-in surface(-point) reconstruction programs, at other, that is, non-generic Zernike meshes. In the present paper, the corneal surface points measured over conventional non-generic Zernike meshes are converted - via cubic spline-interpolation and appropriate re-sampling - to surface points over generic Zernike meshes. With these spatial points as input points, discrete Zernike transformation is carried out. The resulting Zernike coefficients are then used to geometrically reconstruct the optically smooth corneal surface. In the work reported herein, generic Zernike meshes of different cardinalities were used and the resulting surface representations were evaluated. Then, the error-surfaces were compared to the ones resulting from the Zernike-based reconstructions of a cornea-like mathematical surface that had been properly fitted to the input data.