Goodness-of-prediction of Zernike polynomial fitting to corneal surfaces

A 4th-order Zernike polynomial appeared reliable for modeling the normal cornea, but using a 4th-order fitting routine with an abnormal corneal surface caused a loss of fine-detail shape information. As more Zernike terms were added, the accuracy of the fit improved, and the result approached the minimum error found with normal corneas. Unless sufficient higher-order Zernike terms are included when analyzing irregular surfaces, some diagnostic applications of Zernike coefficients may not be rigorous. This conclusion also suggests that wavefront shape analysis is similarly dependent on the number of orders used. Current surgical corrections based on normal-eye wavefronts may fail to capture all visually relevant aberrations in abnormal eyes, such as those having laser retreatments or experiencing corneal warpage from contact lens wear. A clinical goodness-of-fit or goodness-of-prediction index would indicate whether the number of terms in use has fully accounted for all of the visually significant aberrations present in the eye.