Dr. Chernyak: The goal of wavefront-driven surgery is to correct all optical aberrations of the eye. In order to do that, first, we need to make sure that the shape being measured by the aberrometer is in fact an accurate representation of the optics of the eye. We wondered if there could be an alternative to Zernike polynomials that more precisely reconstructed the wavefront. We thought of Fourier transforms, because that method has several properties that are appropriate for use with Hartmann-Shack sensors. One such property is that the Fourier method samples the wavefront over fixed intervals of space that correspond to the equal spacing of the lenslets in the sensor's lenslet array. In other words, Fourier is designed to work on an evenly spaced grid, which is exactly what a Hartmann-Shack sensor is. It is based on a phenomenon called the Nyquist sampling rate, which ensures that the signal is reconstructed to the maximum fidelity present in the raw data.
After identifying Fourier as a potential algorithm for wavefront-guided surgery, we tried to evaluate its residual error by comparing it with the residual error caused by the Zernike reconstruction. We converted the reconstructed wavefront back into the raw data, which, with a Hartmann-Shack sensor, are the local tilt of the wavefront at any given location. We then compared the raw data with the reconstructed data. In every case, the residual error was smaller for the Fourier reconstruction than for the sixth-order Zernike. Next, we thought that using higher-order Zernike expressions would produce less residual error. Although it did produce less residual error, we still achieved better results with Fourier reconstruction for the majority of cases, especially in highly aberrated eyes.
Another benefit of using the Fourier transform is that it is not limited to a circular reconstruction. Most of the pupil aperture of the eye is not circular but elliptical. Zernike tries to fit a circular pattern to the pupil area and thus leaves some of the area out of the reconstruction. The Fourier transform does not have from this drawback because it can use all the data that come through the aperture of the pupil (Figure 1). Another advantage of Fourier is that it does not require surgeons to specify the order of the reconstruction, as Zernike does. The problem with this specification is that the amount of raw data changes as the pupil changes size. The larger the pupil is, the more data points there are in the Hartman-Shack sensor. Surgeons could potentially use more orders of Zernike, but they would have to dynamically adjust that number based on the pupil size aperture. Staying within a fixed order, such as the fourth or sixth order of Zernike, produces more smoothing in the reconstruction of a large pupil. Again, the Fourier reconstruction does not have that problem because it uses all the data present in the reconstruction. These are some of the differences between the two approaches that led us to believe that the Fourier approach is more precise and more versatile for generating wavefront reconstructions on human eyes.CRST: How do you address the claims that Fourier is too sensitive and adds erroneous data (such as the tear film) into the measurement?
Dr. Chernyak: Because the reconstruction of a wavefront is only as good as the raw signal that the sensor receives, we have to be very careful in choosing data that are of high quality, regardless of the reconstruction method used. In conjunction with developing the Fourier reconstruction for use with our laser platform, we implemented additional checks to make sure that the quality of each spot in the Hartmann-Shack spot image passes the thresholds that we deemed appropriate for that type of data. We also tested the repeatability of the wavefront reconstruction for any given patient, specifically for sensitivity to tear film fluctuations. We conducted several experiments in which we repeatedly measured patients over an extended period of time to make sure that the tear film was not an issue. Each patient was measured, as per Wavescan user instructions, within a few seconds from an eye blink. We also used different time intervals after the patients blinked to take the scan. We found that both Zernike and Fourier reconstructions are very repeatable, meaning that they image the same features over and over. That would not be the case if a patient's tear film were unstable (Figure 2).
Dr. Harner: If there is tear film breakup, both Zernike and Fourier reconstructions lose resolution as a result of poor spot quality. It is a case of garbage-in, garbage-out. The Visx Wavescan Fourier approach incorporates strict criteria to prevent inclusion of poor spot quality.CRST: How will you get surgeons who are used to Zernike to accept this new platform?
Dr. Chernyak: The primary message that we want physicians to understand is that the new Fourier upgrade on the Star S4 laser platform does not at all change the process of performing an ablation procedure. To users, this new wavefront reconstruction method is transparent.
We have conducted studies in which we reconstructed point-spread functions based on both Zernike and Fourier maps and compared them with patients' drawings of their vision when they were looking at a point source of light such as an LED. We found that the point-spread functions derived from the Fourier reconstructive maps were much more similar to the subjective drawings of the patients than the Zernike maps. Therefore, the Fourier algorithm will give surgeons and patients an additional level of comfort by comparing the similarity of the subjective symptoms and the objective derived point-spread function. Also, the ability to cut a Prevue lens will allow patients to see what their vision might be like without their higher-order aberrations as measured by the sensor.CRST: What feedback have you received from users thus far?
Ms. Mitchell: We are excited about the results our surgeons are achieving with the new Fourier algorithms. Anecdotal comments from various practices are confirming great surgical success and excellent outcomes. We would not have undertaken such a shift in our reconstruction algorithm if we did not truly believe that it was going to improve outcomes. Based on extensive testing conducted by our research team, we feel strongly that moving toward a Fourier algorithm is a key incremental surgical improvement over previous technologies.
Dimitri A. Chernyak, PhD, is Manager of Scientific Research at Visx, Inc. He may be reached at (408) 773-7368; email@example.com. Carol F. H. Harner, PhD, is Senior Vice President of Research and Development at Visx, Inc. She may be reached at (408) 773-7114; firstname.lastname@example.org.
Yari Mitchell is Senior Professional Education Specialist at Visx, Inc. She may be reached at (408) 773-7174; email@example.com.