Wavefront Measurement Sufficiency

A combination of lower-order aberrations (such as tilt, defocus, and astigmatism) and higher-order aberrations (such as trefoil, coma, quadrafoil, secondary astigmatism, and spherical aberration) contribute to optical aberrations. Aberrometry facilitates the measurement of higher-order aberrations and provides the necessary information for wavefront-driven customized ablation. This data is important because higher-order aberrations have been associated with various visual distortions that are bothersome to patients. These aberrations (sphere, coma, etc.) are measured in the fourth through sixth orders.

The majority of today's aberrometry software, including the Ladarwave aberrometer (Alcon Laboratories, Inc., Fort Worth, TX), relies on the Zernike polynomial to describe the wavefront of each patient's aberrations. Introduced in 1934, this mathematical expression of shapes essentially provides the blueprint for a customized ablation.

The Fourier mathematical method, which was developed more than 100 years earlier than the Zernike, has recently been cast as an alternative to the Zernike model for the Visx Wavescan system (Visx, Inc., Santa Clara, CA.) The Fourier method, as proposed, is roughly equal to that of a 20th-order Zernike fit.

TOO MUCH INFOrmation?
A crucial question remains: is it possible to have too much information? A review of the relative merits and disadvantages of the Zernike polynomial and the Fourier method can provide the answer.

Both the Zernike and Fourier models work by adding increasingly complex patterns to describe a desired shape, and each can describe any wavefront shape found in the eye. In an instance when it is necessary to describe all of the details of a measurement, including noise and artifacts, a very high Zernike order or Fourier equivalent would be appropriate. For the purposes of refractive surgery, however, this is not only inappropriate, but, it could be detrimental. If excessively higher orders are included in the wavefront description, then noise and artifacts—most notably the ever-changing tear film—will be included in the wavefront description and will be ablated onto the eye.

Wavefront-driven customized ablation demands a technique that accurately describes the true aberrations of the eye, while minimizing the impact of noise and error. It is not desirable to use a technique that mimics exact descriptions of the data at a point in time that is irrelevant to the patient's overall vision. Variations in the data occur between two points in time (eg, artifacts, tear-film break-up, etc.).

HIGHER, NOT BETTER
An unpublished study of 100 normal and complex eyes was designed to identify the optimal fidelity necessary to describe optical wavefront errors. It showed that, even for highly complex eyes, a sixth-order description is more than adequate (Figure 1). Further support of this finding comes from analysis of a highly aberrated keratoconic eye, with a very large amount of RMS higher-order error (Figure 2). In this scenario, a second-order polynomial resulted in major errors, but increasing to a fourth- or fifth-order polynomial decreased those errors significantly. Moreover, a sixth-order description resulted in an extremely accurate fit to the Shack-Hartmann data. Continuing to the 20th Zernike order—the equivalent of the proposed Fourier-based method—would not be beneficial, even in this highly complex case.

These examples show that, although Fourier and Zernike at the 20th order both provide a higher degree of fidelity than at the traditional sixth-order Zernike, they do not provide a better wavefront fit. The reason is the noise in the data increases beyond the sixth order. The higher the Zernike or Fourier level is, the better the odds are that the wavefront description will erroneously fit to noise and artifacts. These artifacts (including floaters, corneal disruptions, tear film break-up time, tear film debris, and tear film pooling) can have a significant effect on the Shack-Hartmann image. This noise is an unavoidable everyday occurrence, but it is easily circumvented through the use of most aberrometers, such as the Ladarwave, which uses a logical Zernike order.

The impact of a normal sixth-order description versus a very high Zernike or Fourier equivalent on a young healthy eye with a minor tear film disruption illustrates how artifacts and biological changes in the eye can adversely affect wavefront maps (Figure 3). At the sixth order, the higher-order aberrations have been slightly affected. At the 12th-order description of the same data, the higher-order aberrations show severe undulations, and the total wavefront is highly irregular (Figure 4). Going to even higher (beyond the sixth-order) Zernike orders or the Fourier equivalent would worsen this. It is also important to note that this type of irrelevant data will not be consistently reproducible. If these data were used for surgery, a very irregular and clinically irrelevant shape would be ablated onto the cornea. It would also require a precise delivery of a very fine laser spot with very short latency to minimize further noise's being induced.1

CONCLUSION
Even in highly complex eyes, a sixth-order Zernike fit provides all of the information, or fidelity, necessary to describe the wavefront of each aberration. Too much information can, in fact, be detrimental to the outcome and result in the “correction” of noise and/or artifacts.

James P. McCulley, MD, is Professor and Chairman of the Department of Ophthalmology, University of Texas Southwestern Medical School, Dallas. He is a paid consultant for Alcon Laboratories, Inc., but states that he holds no financial interest in any product or other company mentioned herein. Dr. McCulley may be reached by fax at (214) 648-9061; james.mcculley@utsouthwestern.edu.

1. Krueger R, MacRaes, Applegate R. The future of customization. In: Wavefront Customized Visual Correction: The Quest for Super Vision II. Thorofare, NJ: Slack Inc.; 2004: 181-193.