spotlight on technology & technique
A New Alternative to Zernike?
Fourier analysis promises to improve the precision of wavefront ablations, especially in aberrated eyes.
By Kay T. Adams, Managing Editor

The Fourier Wavefront Upgrade for the VISX CustomVue platform, which will be released soon, is another step toward improving the precision of wavefront-guided laser ablations and reducing the aberrations typically induced by LASIK.

The new software incorporates a Fourier algorithm with Zernike diagnostic images in the WaveScan system and generates a treatment table for the laser that can be used for all custom surgical procedures.

A Fourier-based wavefront provides improved data resolution.

What is Fourier Analysis?

Fourier analysis is a mathematical problem-solving tool widely used in engineering and scientific disciplines such as linear systems analysis, random process modeling, quantum physics, and, more pertinent, astronomy where it is used to measure light aberrations of the atmosphere that interfere with terrestrial telescopes.

In refractive surgery, Fourier analysis is used to fully map Hartmann-Shack data to derive a precise ablation shape. Simply put, it does this by defining a slope at various spots in each lenslet of the aberrometer and fitting the slopes together to derive a "best fit," producing the optimum shape.

Fourier uses all of the approximately 240 Hartmann-Shack spots in a 7-mm pupil to generate a wavefront ablation -- the detail is equivalent to 20th order Zernikes. In contrast, Zernike will use 6th order, or only about 26 data points, to generate a shape.

How is Fourier Different From Zernike?

Zernike polynomials are also mathematical calculations that have long been used in optical systems technology. The choice of Zernike for analyzing optical wavefronts in customized laser surgery came about primarily because the system works well for the more common lower-order and intuitive shapes such as sphere, cylinder, and coma.

However, Zernike can be used only with circular patterns, as in a circular pupil. Most people have elliptical pupils, so any peripheral data outside the circular pattern is not used. Linear defects cannot be characterized, and aberrations are smoothed out as a pattern becomes more complex. So Zernike loses fidelity in mapping a highly aberrated eye. Because Fourier is not restricted to circular patterns, it can resolve complex patterns such as those that occur in highly irregular aberrations in the eyes.

Here's a practical example: Fourier analysis can provide more data on the small but measurable features and discrepancies that determine what a farsighted patient looking at a car headlight at night is really seeing. If that patient has a discrepancy such as a binocular defocal or vague double image in one eye, Fourier analysis, but not Zernike, will pick it up.

Fourier vs. Zernike reconstruction.

Is All Fourier Data Useful?

One criticism of Fourier analysis has been that it provides too much data, much of which may just be tear film breakup or "noise in the system" and not useful. But the repeatability factor indicates otherwise, according to Capt. Steve C. Schallhorn, M.D., director of Cornea and Refractive Surgery at the Navy Medical Center, San Diego. He says, "If dry eye is causing erroneous aberrations, for example, the wavefront pattern should be different with each blink. But it has been shown that Fourier reconstruction has the same repeatability as a Zernike reconstruction."

Dr. Schallhorn sees other potential benefits with Fourier. "All our understanding of aberrations so far is based on Zernike orders," he explains. "We don't have enough information yet based on Fourier data to know how a normal eye may benefit. A Fourier-based ablation pattern is not treating noise but real and repeatable aberrations, so it would appear to be no worse, and could be better in eyes that are aberrated. I tell patients it's another step. Wavefront was a big step, and now Fourier is another. All these steps should give us better and better outcomes."

Douglas D. Koch, M.D., professor, and the Allen, Mosbacher, and Law chair, Cullen Eye Institute, Baylor College of Medicine, Texas, agrees that Fourier will give us more useful data. "We are using Fourier analysis in the VISX clinical trials for high myopia. The results are great, and, importantly, we are getting highly reproducible wavefront data, so I don't think Fourier introduces 'noise.' It just enhances the precision of clinically valuable data.

"This may have relatively little impact for normal eyes, although I suspect that we will see further advances in reducing aberrations with this approach. However, for complicated eyes such as asymmetric ablations and grafts, Fourier should enable us to more accurately characterize and treat irregular astigmatism and address patient symptoms much more effectively."

Will Fourier Replace Zernike in Everyday Practice?

Stephen D. Klyce, Ph.D., professor of Ophthalmology and Anatomy/Cell Biology, Louisiana State University Eye Center, sees Zernike and Fourier as serving two separate purposes: corneal sculpting and clinical diagnostics.

"The Zernike approach excels at extracting meaningful diagnostic information regarding low-order aberrations, and the fit to wavefront aberrations is quite accurate for most eyes, but substantially less accurate for those that have significant distortions, such as corneal transplants, cones, and decentered refractive surgical procedures," he says. "In these cases, the Zernike approach fails to capture all the aberrations that diminish visual function; that is, it suffers in those cases where customization of treatment is most needed (bringing the 20/100 eye best corrected to 20/30 or better). (Smolek MK, Klyce SD. Zernike polynomials are inadequate to represent higher-order aberrations in the eye. Invest Ophthalmol Vis Sci. 2003; 44:4676-4681). Fourier analysis has been introduced to provide a more precise methodology for fitting wavefronts, not only for otherwise normal myopic or hyperopic eyes, but also for those with complex higher-order wavefronts. At this point in time, it appears that the Zernike approach has the edge for clinical diagnostics, and the Fourier methodology is more advantageous for sculpting the cornea. Both methodologies have a niche in clinical practice."

As technology for measuring wavefronts improves, more higher-order aberrations will be detected and treated. Does that mean Fourier analysis and subsequent advances will require additional education and training of refractive specialists, for example in accurate data registration?

As Dr. Klyce explains "Careful registration of wavefront data to the corneal plane is always in issue regardless of which mathematical technique is used for fitting. Since wavefront data represents the optics of the eye at the pupil plane and the sculpting is done on the curved corneal surface, registration of optical axes, transformation of wavefront data to sculpting instructions, and mapping these onto the corneal surface are not trivial concepts."

Dr. Klyce says that accurate treatment registration will become even more crucial as wavefront measurement become more complex.

Other Features of the VISX Upgrade

VISX's Fourier Wavefront Upgrade has several other new features for more accurate data profiling and treatments:

• WaveScan data capture out to 7mm
• corneal marking and iris registration capability
• increase of 4.5% in CustomVue WaveScan power (The boost is added to the number of pulses delivered in the treatment to compensate for an average undercorrection in VISX's clinical trails of 4.5%.)
• point spread function display that better represents what a patient actually sees
• percentage nomogram adjustment to compensate for individual differences in practice environmental conditions and surgical techniques
• offline programming of ablation plans.

For More Information

To find out more about the VISX Fourier Wavefront Upgrade, call (800) 246-VISX or contact your VISX representative.