Validity of scaling zernike coefficients to a larger diameter for refractive surgery

To investigate the validity of a Zernike rescaling algorithm to a larger wavefront diameter.

Using 4256 preoperative wavefront examinations, the variability of inter-examination wavefront root-mean-square (RMS) was compared to the error induced due to scaling Zernike coefficients to a larger diameter. The validity of scaling Zernike coefficients was set when the error due to the scaling was the same as the variability of the inter-examination wavefronts. The inter-examination variability was calculated from eyes having at least 3 same-day, preoperative examinations over the same diameters. Error from scaling Zernike coefficients to a larger diameter was calculated by comparing the wavefront for a (scaled-up) set of Zernike coefficients to the wavefront of the average of Zernike coefficient sets at a larger diameter for the same eye. Wavefront diameters of 5, 5.5, 6, 6.5, and 7 mm were considered.

No significant difference was found for the variability for different pupil sizes. The error due to scaling Zernike coefficients to a larger pupil size was generally smaller than the inter-examination variability when the new diameter was 0.25 mm larger than the original diameter. The error was comparable to the inter-examination variability when the new diameter was 0.5 mm larger. The error became larger when the new diameter was >0.75 mm larger than the original diameter.

Rescaling Zernike coefficients from a smaller diameter to a larger one has practical applications in optical zone extension for wavefront-guided refractive surgery.