Weighted Zernike polynomial fitting in steep corneas sampled in Cartesian grid

Abstract

Surfaces with radial structure do not fit well to squared detectors or sampling matrices. Cartesian grid sampling provides a different density of nodes in sectors. Zernike polynomials are a complete set of orthogonal polynomials defined on a unit disk often used as an expansion of such surfaces. In the fitting process, the sampling distribution is not usually taken into account and might have undesirable effects on the final parameter estimates. We propose applying weighted least-squares regression that compensates the unequal influence of sectors due to the sampling distribution, assigning a weight function to the nodes grid and thus providing a better fit in the central optical zone.

Keywords:

• corneal surface reconstruction
• Zernike polynomials
• weighted least-squares fitting

Acknowledgements

This work has been supported by the Generalitat Valenciana project no. GV/2009/002. J. Espinosa acknowledges the support of the Generalitat Valenciana through the project BEST/2010/209.