After Theo Seiler, MD, PhD, first treated a patient with wavefront technology in July 1999, we have embarked as ophthalmologists and scientists on the quest for perfect vision through the application of wavefront data. This article aims to provide an update on the status of our efforts from a scientific standpoint with appropriate clinical applications. As in the article I organized in February 2003 for Cataract & Refractive Surgery Today, I posed several difficult questions to leaders in the field. Their answers are thought-provoking but also relevant to the everyday application of wavefront technology.

WHERE ARE WAVEFRONT APPLICATIONS WITH REGARD TO OPHTHALMIC TREATMENTS?
Isaac Lipshitz, MD, expresses concern about current technology's role in clinical treatment. He remains unconvinced that different systems provide equally reliable results and adds that the same platform can produce varying data for one patient.

?The use of aberrometry to create customized ablations is still in the experimental phase,? comments Guy Kezirian, MD, FACS. ?Several questions remain unanswered. Which aberrations should be treated? Which should be ignored? Does optical alignment of the cornea and natural lens limit the treatment of higher-order aberrations to those that arise from the cornea? The technology will not be ready for routine use until these and other basic issues are resolved.?

ARE ZERNIKE POLYNOMIALS AND RMS ADEQUATE FOR MEASURING OCULAR ABERRATIONS?

Zernike Polynomials
Michael Smolek, PhD, asserts that there are several drawbacks to the use of Zernike polynomials, including its generation of “many irrelevant terms that are not significant by themselves and that compete with one another through phase differences. A second problem is that the accuracy of Zernike fitting decreases as the aberrations increase … Third, there is still no error standard in ophthalmology by which Zernike fitting can be judged. Only when you know what RMS error level constitutes an acceptable fit can you determine the number of polynomial terms needed. Finally, … Zernike fitting routine fails to record all visually significant surface features, and this in itself should tell us to consider other fitting routines.” Dr. Smolek believes that methods of analysis such as the Fourier technique will soon replace Zernike polynomials.

By contrast, David Williams, PhD, and Scott MacRae, MD, stipulate that “much of the frustration with Zernikes has to do with their apparent complexity” to clinicians. They add that, although the polynomials “will remain central to the automated computations that generate the appropriate wavefront correction,” Zernike polynomials will eventually be invisible to clinicians, “just as physicians using MRI do not need to understand the basis functions that result in tomographic reconstruction of MRI images.”

Moreover, Drs. Williams and MacRae provide several reasons to continue using these polynomials. They cite research showing that Zernike polynomials were nearly as efficient as principle components analysis for describing the wave aberrations of a large patient population.1 Further, Drs. Williams and MacRae observe that these polynomials are widely used in the field of optics and are the basis for the Optical Society of America standard description of wave aberrations. Additionally, they note that second- to fourth-order aberrations usually predominate in the average human eye and those with irregular astigmatism. Because the largest aberrations in human eyes are also lower-order Zernike modes, Drs. Williams and MacRae say that a relatively small number of Zernike terms can account for the most important aberrations.

[Surgeons' transition from conventional to wavefront-guided ablations] involves steady technological improvement, clinician education, and inertia in the marketplace. Ultimately, wavefront technology will play a key role in contact lens, IOL, and spectacle design as well as refractive surgery. Wavefront sensors will replace autorefractors, and adaptive optics systems will replace phoropters for refracting the eye. None of the technological, sociological, and economic hurdles that remain are prohibitive. In principle, wavefront-based methods must be superior to conventional methods for vision correction simply because they allow more accurate measurement [of the optical system] and correction of a larger number of aberrations in the eye. But, it will take years to fully translate theory into practice.

—David R. Williams, PhD, and Scott M. MacRae, MD
The relief on a new [US] penny includes many sharp edges and corners that demarcate ? [Abraham] Lincoln's head and the words In God We Trust. Fitting the topographic map of a penny with smooth functions [including Zernike polynomials] is bound to give disappointing results, because smooth functions have a hard time representing step-like changes in elevation. But, the normal eye is not a copper penny! If the post-LASIK eye does have ? discontinuous topography like a copper [penny], then the industry has a far more serious problem on its hands than finding a replacement for Zernike fitting functions.

—Larry N. Thibos, PhD

RMS
Although he finds RMS to be an acceptable method of describing error, Dr. Smolek stipulates that clinicians need to realize that (1) not all aberrations affect vision equally,2,3 (2) two terms with large RMS errors can combine into a low RMS error, and (3) the RMS error value does not indicate the difficulty level of correcting the aberration.

Commenting that mounting evidence suggests that RMS wavefront error is not an effective descriptor of a patient's image quality, Drs. Williams and MacRae expand on Dr. Smolek's first point. For example, they state that an RMS wavefront error of 0.2 µm in the form of secondary coma or astigmatism would disturb a patient far more than an equivalent amount of quadrafoil or pentafoil.

Dr. Lipshitz argues that the point spread function is a better way to present the total effect of all aberrations on the eye. Michael Mrochen, PhD, meanwhile, recommends representing the results of a wavefront measurement in terms of image quality measures such as the modulation transfer function/Strehl ratio. For clinical use, he thinks that representation in diopters might be simpler.

WHAT ROLE DOES COMPUTED TOPOGRAPHY PLAY IN CUSTOMIZED ABLATION?
Several of the participants agree that topographic information is useful for determining the amount of aberration present in the cornea versus the crystalline lens. Dr. Kezirian comments that understanding the location of aberrations will allow refractive surgeons to determine which should be treated with ablation (those in the cornea) and which should not (those in the lens). Drs. Williams and MacRae, meanwhile, note that separating out aberration information on the cornea will allow the customization of IOLs in the future. For Raymond Applegate, OD, PhD, subtracting measurements of the patient's preoperative from his postoperative corneal elevations will indicate whether the desired surgical result has been achieved.

Dr. Mrochen believes that topography-guided treatments will be particularly valuable in eyes with significant corneal surface irregularities due to disease, injury, or ophthalmic surgery. He asserts that these treatments are inappropriate in virgin eyes, however, because topography cannot represent the optical quality of the total eye. In particular, the physician cannot determine an eye's total spherical aberrations without knowing the optics of the intraocular structure.

Published data2-4 from our laboratory have demonstrated that RMS wavefront error cannot explain the fact that different Zernike modes affect visual performance (high contrast letter acuity) in significantly different manners. Neither can RMS wavefront error explain interactions between modes. Larry Thibos, David Williams, and I have been collaborating to develop better single-value metrics … [that] are several times better than RMS in predicting visual performance.

—Raymond Applegate, OD, PhD

DOES CURRENT WAVEFRONT TECHNOLOGY PROVIDE REPEATABLE, PREDICTABLE MEASUREMENTS?
Most participants believe that measurements are generally predictable and repeatable in normal eyes but much less so in abnormal ones. Drs. Williams and MacRae point to results from a 1997 study demonstrating early Hartmann-Shack sensors' repeatability on real eyes of better than 0.05 µm.5 They add that “the fact that these measurements can also be used to guide the correction of the wave aberrations with a deformable mirror6 to improve vision beyond that possible with spectacles tends to confirm the accuracy of the measurements.”

To Dr. Kezirian, however, current technology is overly dependent upon the user and requires too much cooperation from patients. As a result, he says, “accommodation, misalignment, defocus, and other errors are present in many images, and the images are not reproducible.” Dr. Kezirian believes that more automated technology will yield more accurate, reproducible images.

SHOULD OPHTHALMOLOGISTS TREAT ALL HIGHER-ORDER ABERRATIONS?
Dr. Applegate2,3 has shown that aberrations near the center of the Zernike tree (eg, secondary astigmatism and spherical aberration) affect vision the most. Several participants agree that surgeons should generally aim to eliminate optical aberrations. Drs. Williams and MacRae acknowledge many physicians' concern that “this strategy will greatly narrow the depth of field,” but they argue that current technology leaves behind a sufficient amount of aberrations to avoid this problem. They do note two cases for not eliminating all aberrations, however: (1) highly aberrated eyes of patients whose nervous systems could not adapt to nearly perfect optics and (2) patients who would benefit from a deliberately increased depth of field (eg, presbyopes).

Dr. Lipshitz comments that pupil size is a definite determinant of treatment. He says that, whereas eliminating fourth-order aberrations would achieve supervision in the presence of a 4-mm pupil, a 7-mm pupil might require the treatment of all aberrations up to the eighth order. Larry Thibos, PhD, meanwhile, emphasizes that it is impossible to discuss the effect of one aberration in isolation from the others.4 For example, he says, a clinician cannot determine if spherical or astigmatic defocus is more important without knowing the amount of each. The point, he asserts, is that “different aberrations interact with each other, so their effects in isolation may have no bearing on their effects in the presence of other aberrations.”

I have doubts about Zernike [polynomials], but I am very much convinced that RMS has no meaning at all and should be replaced as soon as possible. There is no logic in calculating an average of different aberrations. Some are positive, some are negative, [and] their influence on vision ? differs from one eye to another. —Isaac Lipshitz, MD

ARE A DILATED PUPIL AND/OR CYCLOPLEGIA REQUIRED FOR WAVEFRONT MEASUREMENTS?
Most of the participants feel that pupil dilation is beneficial but object to cycloplegia, which they argue induces artifactual aberrations. Dr. Kezirian asserts that dilation is necessary because most higher-order aberrations occur in the periphery. He adds that the illumination required to image the eye under mesopic conditions causes the pupil to constrict, so clinicians should employ mild pharmacologic dilation such as 2.5% phenylephrine with 0.5% tropicamide.

Drs. Williams and MacRae dilate the pupil with 2.5% Neo-Synephrine (Bayer Corporation, West Haven, CT) and 0.5% tropicamide and collect wavefront data under low-light conditions (<0.5 lux). They add the tropicamide because Neo-Synephrine alone sometimes produces asymmetrical dilation. They use the limbus or iris features to ensure treatment alignment. Drs. Williams and MacRae state that performing wavefront measurements without pharmacologic dilation allows the loss of light from the lenslets around the pupil and prohibits the use of a larger ablation zone. They note that ablation zones of 6.5 to 7.0 mm versus 6.0 mm provide patients with superior postoperative contrast sensitivity and a greater reduction in higher-order aberrations.

Dr. Smolek points to one caveat with dilation: “If the natural pupil is abnormal (eg, aniridia), then the wavefront analysis with simulated pupils will lack correlation to vision through the abnormal pupil.” To Dr. Lipshitz, pupil dilation introduces data on aberrations that have no significance to normal vision. He prefers to measure the eye under scotopic conditions.

HOW DOES THE TEAR FILM COME INTO PLAY, AND HOW DO YOU REDUCE ARTIFACT?
All the participants believe that the tear film is an important factor. Dr. Mrochen comments that it is the eye's first refractive surface, and its breaking up reduces image quality. He applies a drop of hyaluronic acid approximately 15 minutes before the wavefront measurement, asks patients to blink several times, and examines the tear film just before performing the measurement. Similarly, Dr. Kezirian recommends using a dilute preparation of hyaluronic acid pre- and postoperatively.

Newer lasers with fast, accurate trackers and a 0.95-mm spot size are probably adequate to treat most visually significant aberrations in virgin eyes. The answer is different for eyes that have had prior treatments where the demands are much higher.

—Guy M. Kezirian, MD, FACS

HOW DO THE LENS, AGING, AND ACCOMMODATION AFFECT WAVEFRONT MEASUREMENTS AND TREATMENT?
Dr. Smolek comments that aging increases the amount of aberrations by altering the corneal shape and producing the physiologic changes associated with presbyopia. Both he and Dr. Lipshitz assert that accurate wavefront analysis requires information on the patient's pupil size and accommodative state at the time of data collection.

Drs. Williams and MacRae note that young people's crystalline lenses possess negative spherical aberration, which partially compensates for the positive spherical aberration of the cornea,7 but its compensatory effect is lost during aging. They emphasize the importance of avoiding accommodation during wavefront measurements, because accommodation increases the lens' negative spherical aberration.8

DO CURRENT LASERS POSSESS SUFFICIENT ACCURAcy AND SPATIAL RESOLUTION TO TREAT HIGHER-ORDER ABERRATIONS?
Dr. Mrochen states that current lasers can correct for third-order, coma-like aberrations and fourth-order spherical aberration, and Drs. Williams and MacRae cite a study9 showing that current laser spots of 1 mm in diameter or less can correct up to fifth-order aberrations, ?the most important aberrations in typical human eyes.?

In a similar vein, Dr. Thibos raises the issue of whether current aberrometers have adequate resolution. He believes they do for presurgical eyes but perhaps not for postsurgical eyes.

Although he says some new lasers are capable of achieving good results on a theoretical surface, Dr. Lipshitz stresses10 that “the cornea is not a piece of plastic.” He argues that mechanical (eg, tracking and registration), biological (eg, wound healing and intraeye biological differences), and surgeon-dependent problems prevent lasers from adequately treating higher-order errors.11

Dr. Smolek notes the submicron precision of femtosecond lasers, which have been used to replicate LASIK-style surgery, but he adds that it remains undetermined whether they will be as practical as excimer lasers.

“Even if one can generate smaller laser spots to create a precise ablation, one still has to deal with accurately measuring wavefront error, alignment (which will be even more critical with higher-precision lasers), controlling the effects of wound healing, and other problems,” he says.

CAN CURRENT TECHNOLOGIES MANAGE CYCLOTORSION?
According to Dr. Mrochen, none of the currently available systems can track or compensate for cyclotorsion with accuracy sufficiently high to provide aberration-free correction, but some can compensate for the extreme eye rotation that may occur when the patient is measured while upright and treated under a laser. Drs. Williams and MacRae assert that, because current systems do not automatically compensate for cyclotorsion, surgeons must mark the cornea in order to ensure proper alignment. They believe that cyclotorsion is an important consideration, not just with regard to correcting higher-order aberrations, but also for the correction of astigmatism, “which is usually of greater magnitude and more sensitive than the most common higher-order aberration in the normal population (namely third-order coma). Fortunately, virtually all of the next-generation trackers, including [those of] VISX, Inc. [Santa Clara, CA], Bausch & Lomb [Rochester, NY], as well as Alcon [Laboratories, Inc., Fort Worth, TX], will have an automatic tracker.”

Dr. Kezirian believes that avoidance is the best way in which to manage cyclotorsion. He says that most studies12 examining cyclotorsion combined it with head-tilt and that it is easy to ensure proper alignment of the patient's head. He advises setting guiding beams on the instruments to bony landmarks as a means for avoiding cyclotorsion.

Dr. Lipshitz believes an automated unit will correct both the change in ocular position in an upright versus recumbent patient and minor cyclotorsive movements visible under the microscope while the patient is supine. He says surgeons cannot manually compensate for the latter type, however.

[All laser ablations should be wavefront-guided] if all other clinical factors allow a treatment and the measurements fulfill the clinical protocol. [The biggest benefits are] the objective determination of the optical quality of the eye before and after surgery, individualized ablation profiles [and] optimized treatment planning, [and] possibly better outcomes for vision under mesopic conditions. [The risks introduced by wavefront-guided procedures include] possible errors during wavefront measurements, possible communication errors between the wavefront sensor and laser, [and] centration errors.

—Michael Mrochen, PhD

WHAT PERCENTAGE OF VIRGIN EYES CAN CURRENT LASER SYSTEMS TREAT?
Drs. Williams and MacRae state that approximately 50% of patients are candidates for conventional LASIK with currently available technology, but they assert that the average outcome for the entire population is better with customized treatment. They say that wavefront-guided procedures can treat up to 10.00 D of myopic sphere and 3.00 D of cylinder, but they add that each surgeon must adjust the spherical nomogram when performing customized ablation.

“Each system has its own fingerprint, and each surgeon is encouraged to start conservatively with lower amounts of myopia for the first 10 to 20 cases until an initial spherical adjustment factor can be derived,” say Drs. Williams and MacRae.

Dr. Kezirian emphasizes that using an aberrometer to capture patients' refractive errors does not change the basic facts that all lasers and surgeons are different and require nomogram adjustment. He adds that it is only possible with current methodology, which uses Zernike polynomials, to adjust the basic defocus (sphere) portion of the treatment.

Dr. Lipshitz asserts that laser treatments based solely on wavefront data will be unsuccessful. He advises correcting “anything that can be corrected from the topographic map and only then perform[ing] the minor touch-ups according to wavefront maps.”

SHOULD ALL ABLATIONS BE WAVEFRONT-GUIDED WHEN AN IMAGE CAN BE OBTAINED? WHAT ARE THE BENEFITS AND RISKS?
Drs. Williams and MacRae comment that some experienced surgeons use wavefront-guided treatments for 80% to 90% of their patients, but they say most physicians need time to grow comfortable with the technology. They believe that customized ablations most benefit eyes with large amounts of higher-order aberrations, but they caution against performing wavefront-guided treatments on patients whose wavefront and manifest refractions differ greatly.

In cases of severe spherical aberration or coma, Dr. Lipshitz believes that wavefront-guided treatments are necessary. He stipulates that the currently available technology is not the answer for all patients, however.

Dr. Smolek utters a “qualified yes” on using wavefront-guided ablations on all normal eyes and a “qualified no” regarding abnormal eyes. The biggest benefits in the former group, he says, are that results will typically be superior to those of a spherocylindrical correction alone and induce less higher-order aberration. In particular, he says customized ablations will produce less iatrogenic spherical aberration and coma than standard LASIK, but wavefront-guided procedures require precise eye tracking. Dr. Smolek argues that the accuracy of Zernike fitting in wavefront-guided treatments is much worse with abnormal eyes, so the chance of poor surgical outcomes rises depending on the severity of the aberrations.

“The biggest temptation here is to use wavefront-guided procedures for retreatment eyes, which are not normal eyes,” he says. “Retreatments require more terms than normal eyes, and [surgeons should] expect the residual error to increase because of the inaccuracy of the Zernike fit.”

Wavefront error measurements and wavefront-guided treatments are always going to be at odds with the dynamic nature of the eye. We can continue to fine-tune this technology to its physical limits, but we have to accept that a normal physiologic shift can quickly throw all of our precise surgical planning out the window.

—Michael K. Smolek, Phd

DOES THE EMPEROR HAVE NEW CLOTHES? IN OTHER WORDS, HAS WAVEFRONT TECHNOLOGY DELIVERED ON ITS PROMISE, AND WILL IT IN THE FUTURE?
Among the overall positive responses, Dr. Smolek voiced a dissenting opinion, largely owing to his opinions on the limitations of Zernike fitting. He believes that current technology is only a stepping stone to something better, including better fitting algorithms.

Although he acknowledges the unreasonable expectations created by excessive marketing hype, Dr. Thibos believes that wavefront aberrometry is essential for characterizing the optical effects of any refractive treatment. Similarly, Dr. Lipshitz remarks that not being able to achieve everything desired “does not decrease the importance of this technology for our patients.” For his part, Dr. Mrochen believes that wavefront technology will become a part of clinical routine and have applications in the areas of contact lenses, IOLs, and diagnostics.

Drs. Williams and MacRae comment that “the value of wavefront has never been in question” and patients with abnormal, highly aberrated eyes stand to benefit greatly from the technology. At issue, they say, is what fraction of the patient population will wavefront technology aid. Although the answer is presently unknown, they say that the size of that fraction will increase as technology improves.

Dr. Kezirian compares the development of wavefront-driven LASIK to the US space program, which “cost billions of dollars, lost lives, and left us with a few moon rocks. At the same time, space program spin-offs advanced technologies and improved life for everyone. The race to wavefront LASIK has led to [a] better understanding of aberrations, visual function, and laser technologies.”

In addition to its clinical and scientific applications, respondents' answers reveal that wavefront technology continues to evolve. To quote Antoine de Saint-Exupéry, “A rock pile ceases to be a rock pile the moment a single man contemplates it, bearing within him the image of a cathedral.” As with any scientific endeavor, it is the quest that inspires perfection. Sometimes when we fall short of our idealistic goals, the knowledge that we have gained in the process improves the world in which we live and work.

—Karl G. Stonecipher, MD
Raymond A. Applegate, OD, PhD, is Professor and Borish Chair of Optometry for the College of Optometry at the University of Houston. He is a consultant for Alcon Laboratories, Inc.; Sarver and Associates, Inc.; and PolyVue, Inc. Dr. Applegate may be reached at (713) 743-1957; rapplegate@optometry.uh.edu.
Guy M. Kezirian, MD, FACS, is a board-certified ophthalmologist. He is President of SurgiVision Consultants, Inc., an ophthalmic consulting company in Thousand Oaks, California, and a partner in SurgiVision Refractive Consultants, LLC, the company that conducted the US clinical trials leading to FDA approval of the ALLEGRETTO WAVE Excimer Laser System (WaveLight Technologie AG, Erlangen, Germany). Dr. Kezirian may be reached at (805) 493-4200; guy1000@surgivision.biz.
Isaac Lipshitz, MD, is Director of the Ophthalmic Health Center in Tel Aviv, Israel. He does not hold a financial interest in any of the technologies or companies mentioned herein. Dr. Lipshitz may be reached at +97 23 643 79 25; lipshitz@netvision.net.il.
Scott M. MacRae, MD, is Professor of Ophthalmology and Professor of Visual Science at the University of Rochester in New York. He is a consultant to Bausch & Lomb and NIDEK, Inc. Dr. MacRae may be reached at (585) 273-2020; scott_macrae@urmc.rochester.edu.
Michael Mrochen, PhD, is a research fellow at the Swiss Federal Institute of Technology and University of Zürich Institute of Biomedical Engineering in Switzerland. He does not hold a financial interest in any of the technologies or companies mentioned herein. Dr. Mrochen may be reached at +41 1 632 4583; michael.mrochen@greenmail.ch.
Michael K. Smolek, PhD, is Assistant Research Professor, Ophthalmology, LSU Eye Center in New Orleans. He does not hold a financial interest in any of the technologies or companies mentioned herein. Dr. Smolek may be reached at (504) 412-1360; msmole@lsuhsc.edu.
Karl G. Stonecipher, MD, is Director of Refractive Surgery at Southeastern Eye Center in Greensboro, North Carolina. He does not hold a financial interest in any of the technologies or companies mentioned herein. Dr. Stonecipher may be reached at (800) 632-0428; stonenc@aol.com.
Larry N. Thibos, PhD, is Professor of Optometry at the Indiana University School of Optometry in Bloomington. He does not hold a financial interest in any of the technologies or companies mentioned herein. Dr. Thibos may be reached at (812) 855-9842; thibos@indiana.edu.
David R. Williams, PhD, is Director of the Center for Visual Science and William G. Allyn Professor of Medical Optics at the University of Rochester in New York. He does not hold a financial interest in any of the technologies or companies mentioned herein. Dr. Williams may be reached at (585) 275-8672; david@cvs.rochester.edu.
1. Porter J, Guirao A, Cox IG, Williams DR. Monochromatic aberrations of the human eye in a large population. J Opt Soc Am A. 2001;18:8:1793-1803.
2. Applegate RA, Sarver EJ, Khemsara V. Are all aberrations equal? J Refract Surg. 2002;18(suppl):556-562.
3. Applegate RA, Ballentine C, Gross H, et al. Visual acuity as a function of zernike mode and level of RMS error. Optom Vis Sci. 2003;80:97-105.
4. Applegate RA, Marsack J, Ramos R. Interaction between aberrations can improve or reduce visual performance. J Cataract Refract Surg. 2003;29:1487-1495.
5. Liang J, Williams DR. Aberrations and retinal image quality of the normal human eye. J Opt Soc Am A. 1997;14:11:2873-2883.
6. Liang J, Williams DR, Miller DT. Supernormal vision and high-resolution retinal imaging through adaptive optics. J Opt Soc Am A. 1997:14:11:2884-2892.
7. Artal P, Guirao A, Berrio E, Williams DR. Compensation of corneal aberrations by the internal optics in the human eye. J Vis. 2001;1:1:1-8.
8. Williams DR, Yoon GY, Guirao A, et al. How far can we extend the limits of human vision? In: MacRae SM, Krueger RR, Applegate RA, eds. Customized Corneal Ablation: The Quest for Supervision. Thorofare, NJ: Slack, Inc.; 2001:11-32.
9. Guirao A, Williams DR, MacRae SM. Effect of beam size on the expected benefit of customized laser refractive surgery. J Refract Surg. 2003;19:15-23.
10. Roberts C. The cornea is not a piece of plastic. J Refract Surg. 2000;16:407-413.
11. Lipshitz I. Thirty-four challenges to meet before excimer laser technology can achieve super vision. J Refract Surg. 2002;18:740-743.
12. Swami AU, Steinert RF, Osborne WE, White AA. Rotational malposition during laser in situ keratomileusis. Am J Ophthalmol. 2002;133:561-562.