Method for expressing clinical and statistical significance of ocular and corneal wave front error aberrations

Abstract

Purpose: The significance of ocular or corneal aberrations may be subject to misinterpretation whenever eyes with different pupil sizes or the application of different Zernike expansion orders are compared. A method is shown that uses simple mathematical interpolation techniques based on normal data to rapidly determine the clinical significance of aberrations, without concern for pupil and expansion order.

Methods: Corneal topography maps (TOMEY, Inc, Nagoya, Japan) from 30 normal corneas were collected, and the corneal wave front error was analyzed by Zernike polynomial decomposition into specific aberration types for pupil diameters of 3, 5, 7, and 10 mm and Zernike expansion orders of 6, 8, 10, and 12. Using this 4 × 4 matrix of pupil sizes and fitting orders, the best-fitting 3-dimensional functions were determined for the mean and standard deviation of the root-mean-square error for specific aberrations. The functions were encoded into a software application to determine the significance of data acquired from nonnormal cases.

Results: The best-fitting functions for 6 types of aberrations were determined: defocus, astigmatism, prism, coma, spherical aberration, and all higher-order aberrations. A clinical screening method of color coding the significance of aberrations in normal, postoperative laser in situ keratomileusis, and keratoconus cases having different pupil sizes and different expansion orders is demonstrated.

Conclusions: A method to calibrate wave front aberrometry devices using a standard sample of normal cases was devised. This method could be potentially useful in clinical studies involving patients with uncontrolled pupil sizes or in studies that compare data from aberrometers that use different Zernike fitting-order algorithms.

Figure 1

Mean value of six different aberrations as a function of pupil size and Zernike order number. Aberrations selected for analysis include defocus (top left); prism (top right); 2^nd order astigmatism (center left); 3^rd order coma (center right); 4^th order spherical aberration (lower left); and all higher order aberrations above the 2^nd order (lower right). Note the use of a floating Z-axis scale in all graphs.

Figure 2

Standard deviation of the mean value of six different aberrations as a function of pupil size and Zernike order number. Aberrations selected for analysis include defocus (top left); prism (top right); 2^nd order astigmatism (center left); 3^rd order coma (center right); 4^th order spherical aberration (lower left); and all higher order aberrations above the 2^nd order (lower right). Note the use of a floating Z-axis scale in all graphs.

Figure 3

Example of how the calibrated aberration analysis method can be used to indicate a normal corneal wavefront. Upper left: corneal topography map; upper right: corneal wavefront in the Smolek-Klyce absolute scale; lower right: corneal wavefront in the ANSI scale; lower left: close-up view of the hexagonal warning label system described in the text. All aberrations are less than 2 standard deviations from the normal mean as specified during calibration. Note that the ANSI color mapping method uses a floating numerical scale that overemphasizes non-significant amounts of spherical aberration.

Figure 4

Example of how the calibrated aberration analysis method can be used with a post-LASIK case. Upper left: corneal topography map; upper right: corneal wavefront in the Smolek-Klyce absolute scale; lower right: corneal wavefront in the ANSI scale; lower left: close-up view of the hexagonal warning label system described in the text. The defocus value is between 2 and 3 standard deviations above normal, while the value for spherical aberration is 4 standard deviations or more above normal.

Figure 5

Example of how the calibrated aberration analysis method can be used with a mild keratoconus case. Upper left: corneal topography map; upper right: corneal wavefront in the Smolek-Klyce absolute scale; lower right: corneal wavefront in the ANSI scale; lower left: close-up view of the hexagonal warning label system described in the text.

Figure 6

Example of how the calibrated aberration analysis method can be used with a mild central keratoconus case. Upper left: corneal topography map; upper right: corneal wavefront in the Smolek-Klyce absolute scale; lower right: corneal wavefront in the ANSI scale; lower left: close-up view of the hexagonal warning label system described in the text.