Salmon Wavefront

Many of you have seen demonstrations of the VISX Star S4 laser and WaveScan aberrometer that measures the total aberrations of your eye and then ablates your correction, including higher-order corrections, onto a slab of plastic. If you carefully center and correctly rotate this "PreView" lens in front of your eye, you will be able to appreciate the amazingly crisp vision that you can achieve with a wavefront-guided correction. (http://www.visx.com)

This course will provide you with a primer on the topic of aberrations, it will describe what higher-order aberrations are and how to measure them, and it will introduce you to the next generation of LASIK and contact lens generation systems that hold the promise for producing super-normal visual acuity.

Introduction and objectives
Modern science is providing doctors and their patients with exciting new ways to correct refractive errors. Laser vision correction was one of the most significant recent developments, but now we are entering a new era with the next major improvement in refractive surgery - wavefront-guided LASIK and PRK. This new technology has captured the public's attention because it has the potential to provide patients with so called, "super-normal vision."

Journal articles and experts at professional meetings are discussing new concepts such as wavefront aberrations or Zernike polynomials. Unfortunately, these terms are unfamiliar to most eye doctors who may feel inadequately prepared to understand them, much less explain them to patients. The purpose of this course is to give you a basic working knowledge of wavefront sensing (also known as aberrometry) so you will be able to keep up with these new advances.

First, let's consider higher-order aberrations. Optometrists routinely improve visual acuity by correcting refractive errors, and we are very good at it. We are so accustomed to measuring the refractive errors in terms of sphere, cylinder and axis that many optometrists (and ophthalmologists) assume that this is the complete refractive error of the eye (Fig. 1). Therefore, many doctors incorrectly assume that the best spherocylindrical prescription will perfectly and totally correct a patient's refractive error.

Figure 1. - Currently, clinicians usually measure spherocylindrical refractive errors only. The phoropter contains lenses that correct these refractive errors, but higher-order aberrations are routinely ignored.

But sphere and cylinder are not the only refractive errors of the eye; certain additional refractive errors, known as higher-order aberrations, also exist.

(Note that in this course we will discuss only monochromatic aberrations and disregard chromatic aberration, which is caused by the difference in refraction for light of different wavelengths. At this point, both wavefront sensors and wavefront-guided lasers essentially ignore chromatic aberration, but future research will probably investigate this effect more thoroughly.)

Until recently, essentially all optometrist and ophthalmologists typically ignored higher-order aberrations for three reasons.

Modern eye care, especially refractive surgery, has changed this, and now higher-order aberrations are a clinically significant consideration for many patients.

For three reasons that parallel those listed above, higher-order aberrations are now important to routine optometric practice.

In summary, higher order-aberrations are refractive errors beyond sphere and cylinder. They are important today because conventional refractive surgery patients may be experiencing poor vision due to uncorrected higher-order aberrations, and new patients will increasingly seek wavefront-guided treatments to optimize their visual acuities.

Super-normal vision
If we can correct not only sphere and cylinder but higher-order aberrations as well, it might be possible to provide patients with nearly perfect optical corrections and so called super-normal vision. Supernormal vision refers to the acuity that a person would have if he or she had perfect optics. In that case, visual acuity would no longer be limited by the eye's optics, but rather by the resolution limit of the retina. Super-normal optics would, in theory, allow a best-corrected visual acuity of 20/8, which is four lines of acuity better than 20/20!

Super-normal vision has captured the public's imagination and has been the subject of media reports including articles in Science News, Physics Today, Scientific American, and other journals. For doctors involved in refractive surgery, an excellent reference book is available entitled, "Customized Ablation-The Quest for SuperVision." For more information on this book, visit the Slack Web site (www.slackbooks.com/).

Figure 2 - Articles in the scientific literature since the late 1990s have made the public aware of new methods to measure optics of the human eye and the potential for super-normal vision (left three covers). A recent engineering book, "Recent Research Developments in Optics," included a chapter entitled, Optical Wavefront Sensing of the Human Eye (second from right), and a medical book entitled, "Customized Corneal Ablation - the Quest for SuperVision" was published in 2001 (far right).

What are wavefront sensors (aberrometers) and how do they measure higher-order aberrations?

Wavefront sensors, also known as aberrometers, are instruments designed to measure the entire refractive error of the eye, including sphere, cylinder, and the higher-order aberrations.

These sensors have come into clinical use via some interesting events in recent history. Initially, the Defense Department worked on them in the 1980s to support President Reagan's "Star Wars" ballistic missile defense program. The military needed a way to measure and correct the constantly fluctuating refractive power of the atmosphere so as to improve photographs of enemy satellites in space and to improve the accuracy of laser weapons. This led to the development of a branch of optical engineering known as adaptive optics, which involves the real-time measurement and correction of refractive errors such as those caused by atmospheric turbulence. Typically, this correction is accomplished by the use of a deformable mirror that can be rapidly bent or flexed to exactly compensate for the fluctuating refractive power of the atmosphere. The process involves flexing different portions of the mirror at different times in a very rapid manner under control of a high-speed computer.

Astronomers were also keenly interested in adaptive optics, because refractive errors caused by the turbulent atmosphere blurred their telescope images. (The reason for launching the Hubble Space Telescope was to avoid the atmospheric aberrations by putting the telescope above the atmosphere.) Adaptive optics allows them to accomplish the same thing from the ground by flexing their optical elements to negate the effects of the atmosphere's fluctuating refractive power. Since the late 1990s, all the world's largest telescopes have been fitted with adaptive optics systems that include a wavefront sensor to measure atmospheric aberrations and a deformable mirror to correct for them.

Figure 3 - Telescope photographs of Saturn without (left frame) and with (right frame) adaptive optics to correct for atmospheric aberrations. Adaptive compensation improves clarity to the point at which stripes are visible within the rings, and the moon Titan, faintly visible in the left frame, is clearly visible in the right frame. (Courtesy of the U.S. Air Force Philips Laboratory Starfire Optical Range.)

A century ago, Hartmann developed a test to evaluate the optical quality of telescope mirrors. The Hartmann test was the forerunner of the modern Shack-Hartmann wavefront sensor (a.k.a. Hartmann-Shack wavefront sensor). In the 1980s, while working on a project for the Air Force, University of Arizona Professor Roland Shack improved the Hartmann technique and developed what we now know as the Shack-Hartmann wavefront sensor (a.k.a. the Hartmann-Shack wavefront sensor). Shack-Hartmann aberrometry has become the most popular way to measure aberrations of the human eye in use today.

Figure 4 - Dr. Roland Shack, Professor at the University of Arizona Optical Sciences Center, helped develop the most popular device used today to measure higher-order optical aberrations-the Shack-Hartmann wavefront sensor.

From Astronomy to Eye Care
In 1990, scientists at the University of Heidelberg were developing the scanning laser ophthalmoscope to provide better retinal photographs, including three-dimensional images of the optic nerve head. This was the forerunner of the modern HRT (Heidelberg Retinal Tomograph) used in glaucoma management. (See the On-Line CE course titled "Use of the Heidelberg Retinal Tomograph II for Optic Nerve Head Documentation and Analysis" by Elliot M. Kirstein, O.D., F.A.A.O. in the Pacific On-Line course catalog.)

The Heidelberg scientists hoped to optimize the quality of fundus photographs by correcting the eye's complete refractive error, including higher-order aberrations. A Ph.D. student, Junzhong Liang, was the first person to measure aberrations of the human eye using a Shack-Hartmann wavefront sensor. His important work was published in 1994 and has become the most frequently cited paper in the field of ocular aberrometry.

Figure 5 - Dr. Junzhong Liang was the first person to measure higher-order aberrations of a human eye using a Shack-Hartmann wavefront sensor. He did this during his Ph.D. work at the University of Heidelberg, in Germany in about 1990.

Within a few years, other research laboratories around the world were building Shack-Hartmann sensors, including the one at Indiana University, where I worked. Figure 6 shows the large optical-table version of a Shack-Hartmann sensor I built in 1996.

Figure 6 - Photographs of the tabletop Shack-Hartmann wavefront sensor built by the author in 1996 at Indiana University.

By the late 1990s, the race was on between refractive laser companies to develop a commercial ophthalmic wavefront sensor (aberrometer) to guide their lasers for better PRK and LASIK surgery. The first commercial ophthalmic Shack-Hartmann aberrometer, the Complete Ophthalmic Analysis System (COAS), manufactured by WaveFront Sciences, Inc. (www.wavefrontsciences.com/) became available in early 2000 (Figure 7). Several other companies, including VISX and Alcon have also developed Shack-Hartmann-type aberrometers. In addition, a few commercial aberrometers have been developed that use a principle different from the Shack-Hartmann. (Additional information on these systems will be presented in the Clinical Applications section of this course.)

FIGURE 7 - Photograph of a modern ophthalmic Shack-Hartmann aberrometer, the Complete Ophthalmic Analysis System (COAS) manufactured by WaveFront Sciences, Inc. (www.wavefrontsciences.com)

Many aberrometers resemble autorefractors. In fact, you can think of a wavefront sensor, or aberrometer, as a super autorefractor that measures not only sphere and cylinder, but higher-order aberrations as well. Although several methods have been developed to measure aberrations of the eye, instruments based on the Shack-Hartmann principle are the most popular.

How do wavefront sensors work?
It is good for optometrists to understand the basic working principles of Shack-Hartmann aberrometry because this will provide better insight into aberrations and their place in modern eye care.

Figure 8 - Refractive errors of the eye can be described in terms of the shape of a wavefront of light that has passed through the eye's optics. With aberration-free optics, wavefronts exiting the eye are perfectly flat (top). Refractive errors, such as myopia, distort the wavefront (bottom). Other refractive errors, including higher-order aberrations, cause wavefront distortions that differ in shape from those seen in simple myopia. Aberrometers measure wavefront shape.

The purpose of an aberrometer is to measure the eye's complete refractive error, and a Shack-Hartmann device does so by measuring distortions in a wavefront of light emitted from the eye after it has passed through the eye's optics. Figure 8 shows the shape of an optical wavefront emitted from a point source on the retina and which has passed through the optics of an aberration-free, emmetropic eye (top), and an eye with simple myopia (bottom).

In an eye with no refractive error of any kind (Fig. 8-top), the optical wavefronts that pass out of the eye are perfectly flat. In the case of simple myopia (Fig. 8-bottom), the wavefronts are spherical surfaces that converge toward the far point. Other refractive errors, including higher-order aberrations, distort the wavefront emitted from the eye in other ways. One way to know the complete refractive error of the eye, including the higher-order aberrations, is to measure the shape of the optical wavefront emerging from the eye.

The goal of all aberrometers is to measure the shape of the optical wavefront that has been refracted by the eye's optics. Shack-Hartmann aberrometers measure the wavefront shape by measuring the distance between the wavefront surface and a reference plane located in the eye's entrance pupil. This distance, known as the wavefront error, is illustrated in Fig. 9.

Figure 9 - A Shack-Hartmann aberrometer measures the shape of a wavefront of light exiting the eye. It optically relays a real image of the wavefront into the plane of the lenslet array, which allows measurement of the wavefront.

In the right half of Figure 9, the straight vertical line represents the entrance pupil plane, and the curve is the optical wavefront exiting the eye, frozen in space with its center in the entrance pupil. The aberrometer measures the wavefront error, which is the distance between the wavefront and the reference plane, at many locations across the pupil. A Shack-Hartmann data set, therefore, consists of a large array of numbers (wavefront errors) for different pupil locations. As whole, the entire data set is sometimes called the wavefront aberration function.

To measure wavefront errors, the Shack-Hartmann apparatus uses a clever optical system that images the wavefront found in the eye's entrance pupil into an array of microscopic lenslets (Fig. 9-left). The lenslets are the heart of a Shack-Hartmann aberrometer. In addition to the wavefront, Figure 9-left shows several light rays, which indicate the direction of propagation for different parts of the wavefront.

FIGURE 10 - Schematic diagram of the sensor portion of a Shack-Hartmann aberrometer.

Figure 10 shows how light originating from a point on the retina passes out through the eye's optics, through two plus lenses in front of the eye, through the micro-lenslet array, and finally onto a video sensor (CCD). The illumination system that projects the tiny spot onto the retina is not shown.

Each tiny lenslet is a fraction of a millimeter across. The purpose of the lenslet array is to divide the broad beam of light exiting the eye into many sub-beams for measurement. Each lenslet focuses one of these sub-beams to a tiny spot on the surface of the video sensor (red dots), which records an image of the spots. By analyzing the position of each spot, we can determine the shape of the wavefront.

Recall that in an eye with perfect optics, parallel rays exit the eye. This is illustrated in Fig. 10, which shows that after passing through the Shack-Hartmann system, collimated rays (in an aberration-free eye) enter the lenslet array. Each of these tiny plus lenses gathers a collimated pencil of light and focuses it to a point on the video sensor (the red dots). Because light entering each lenslet is collimated, all entering rays are parallel, and they focus to a point on the optic axis of each lenslet. Therefore, in the case of an aberration-free eye, each spot will be centered with respect to its lenslet.

FIGURE 11 - The image recorded by the video sensor of a Shack-Hartmann aberrometer consists of a circular array of dots (left frame). If we add an overlay showing the geometry of the lenslet array (right frame), we see that, in the case of an aberration-free eye, each dot is centered with respect to its lenslet. If aberrations were present, the dots will be shifted away from their aberration-free positions.

The complete picture received by the video sensor consists of an array of dots (Fig. 11-left), one for each lenslet, and the dots will be arranged in a regular grid pattern that matches the geometry of the lenslet array. If aberrations are present, however, some of the dots will be shifted from their aberration-free positions. By analyzing the location of each dot, it is possible to reconstruct the shape of the optical wavefront exiting the eye. By doing so, we will can measure the wavefront aberration function, which contains complete information about the eye's refractive error, including sphere, cylinder, and higher-order aberrations.

FIGURE 12 - A magnified view of a single lenslet shows a portion of an aberrated wavefront (red curve) passing through. If the wavefront had been flat (aberration-free), it would have focused to a point on the video sensor (CCD) on the lenslet's optic axis (yellow dot). Refractive errors distort the wavefront out of a plane, so a wavefront portion (red curve) enters the lenslet curved and tilted . The light will therefore be focused to another place (red dot). The dot will be shifted by an amount that is in direct proportion to the wavefront tilt.

Figures 12 and 13 illustrate how the position of the dots can be used to compute the eye's wavefront aberration. Figure 12 is a magnified view of a single lenslet shown in Fig. 9, with a portion of the wavefront (red curve) passing through. Had the wavefront been aberration-free, it would have been flat and the light would have been focused straight ahead (yellow spot). Refractive errors (aberrations) however cause the wavefront to be tilted, as illustrated by the red curve. Following the blue rays, we can see that the light of an aberrated wavefront will focus to an off-center point. The distance that the focal point shifts is directly proportional to the local wavefront tilt.

FIGURE 13 - The geometry of Fig. 12 is simplified here. Based on the shift of the focal spot (delta y) and the lenslet focal length (f), we can easily computer the ray slope angle, which is equal to the local wavefront slope. This is repeated for many lenslets and enables a Shack-Hartmann aberrometer to measure local wavefront slopes across the pupil.

Figure 13 simplifies the geometry. In this example, the spot is deviated inferiorly in proportion to the wavefront tilt. Since distance f, the lenslet focal length, is known, and we can measure the spot deviation (delta y), we can easily compute the slope of the ray, which is equal to delta y/f. Because of the geometry, this is identical to the local wavefront tilt in the lenslet. By measuring the shift of each spot from the aberration-free reference position, we can compute the local wavefront slope in each lenslet. This is what the Shack-Hartmann sensor does - it measures wavefront slopes at multiple locations across the pupil.

FIGURE 14 - Wavefront data, like raw visual fields data (left), consist of an array of numbers in a circular window. A typical wavefront measurement can include hundreds of numbers, so it is easier to visualize the information by converting the data to a gray-scale or topographic map (upper right), or to a three-dimensional surface plot (lower right).

For each lenslet, the wavefront slopes are measured in the both x and y directions, and these data (the slopes) are mathematically integrated to compute the actual wavefront error at many points across the pupil. The result of these computations is a two-dimensional set of wavefront error values at multiple locations across the pupil.

The two-dimensional numerical array is similar to the arrangement of static perimetry data (Fig. 14). For example, the data from a Humphrey 30-2 visual field test consist of a circular array of 76 numbers as well as a gray-scale plot, which help to visualize the numbers. Likewise, the output from an aberrometer could be represented by a huge array of several hundred numbers, each of which is a wavefront error value. However, for the sake of visualization, it is better to convert the data array into a gray-scale or topographic map that indicates the values across the pupil (Fig. 14, upper right). It is also possible to create a surface plot, which gives a better three-dimensional perspective of the optical wavefront's shape (Fig. 14, lower right).

At this point, we know that wavefront sensors, also known as aberrometers, are super autorefractors that measure refractive errors of the eye, including sphere, cylinder, and higher-order aberrations. They do this by measuring wavefront slopes at multiple locations and then mathematically reconstruct the shape of the wavefront of light exiting the eye.

What are Zernike polynomials, and what do they tell us about refractive errors?

If we could see wavefronts exiting from different eyes, we would find that they have various shapes depending on the type and amount of refractive error. Because each wavefront is unique, raw wavefront data can be difficult to compare and categorize. There are just too many different possible surface shapes.

We currently describe lower-order refractive errors using only three numbers: sphere, cylinder, and axis.

How shall we specify the additional refractive errors contained in the higher-order aberrations? The Optical Society of America (OSA) recommended a system for describing ocular wavefront aberrations using what are known as Zernike polynomials sand this standard has been universally adopted by refractive surgeons and vision scientists.

Zernike polynomials allow us to break down any wavefront into a set of specific aberrations (referred to as Zernike modes) in which each mode represents one particular type of aberration. For example, there are modes for spherical defocus, astigmatism, coma, spherical aberration, etc.

Figure 15 - Examples of several Zernike modes, each of which represents a wavefront of light exiting the eye. Each has a defined shape. For example, spherical refractive error has a symmetric bowl-shaped wavefront, and an astigmatic wavefront is shaped like a saddle.

Figure 15 shows how several of the modes may be represented graphically. Each represents a particular aberration, that is, a kind of refractive error, which has a particular shape and specific mathematical definition. For example, spherical error looks like a bowl; astigmatism looks like a saddle; and the aberration known as trefoil has three lobes. Many of the other aberrations in the Zernike system have no names, but are identified by a double-number index such as Z₇^-3, or a single-number index such as Z₄₀.

FIGURE 16 - The top map shows total wavefront errors across the pupil for one particular eye. It is an irregularly shaped surface that can be re-expressed as the sum of the pre-defined surfaces below, each of which represents a Zernike mode, or one aberration.

Most eyes have a complex combination of refractive errors that may have an irregular, asymmetric shape, such as that shown in Fig. 16-top. In this example, a color topographic map is used to show one eye's wavefront aberration measured by a Shack-Hartmann aberrometer. Using Zernike analysis, the total refractive error in the wavefront can be broken down into the Zernike modes shown. Contained within this wavefront is a certain amount of sphere, cylinder, trefoil, coma, spherical aberration, Z₄₂, Z₄₄, and other aberrations which are not shown. A Zernike prescription would include numbers (Zernike coefficients) telling us the magnitude and sign of each of these aberrations.

Zernike Prescriptions
Conventional spectacle prescriptions look relatively simple because they describe the refractive error using just three values: sphere, cylinder, and axis. The refractive error pictured in Fig. 16-top, is best corrected using a spherocylindrical prescription of +0.19 –0.67 x 110. However this prescription provides no information about the higher-order aberrations. Zernike polynomials allow specification of sphere, astigmatism and higher-order aberrations for any wavefront to any level of detail. For greater detail, just include more modes. The Zernike prescription shown below includes twelve Zernike modes.

You may have noticed that in the prescription above there are two modes for astigmatism,
Z₂^-2 (45/135 astigmatism) and Z₂² (90/180 astigmatism). The standard OSA Zernike system specifies astigmatism in this way. Note that other aberrations also come in pairs: Z₃^-3 (vertical trefoil) and Z₃³ (oblique trefoil), Z₃^-1 (vertical coma) and Z₃¹(horizontal coma) and others.

Sometimes it is more convenient to combine the paired mode into a single mode, which will then have a magnitude and axis. For example, instead of having 0.04 microns of Z₃^-1 (vertical coma) paired with 0.03 microns of Z₃¹ (horizontal coma), you could combine them into one coma mode (labeled Z₃₁) with a magnitude of 0.05 microns and axis at 127 degrees.

Combined Zernike modes may be labeled with a subscript that is based on the original double index - for example, Z₃₁ (coma). (Note that this single index is different from the OSA single index used in Figs. 17 and 18.) This is what we displayed for the coma mode in Fig. 16. (For details about converting standard paired Zernike modes to a single combined mode, refer to the article by Campbell in the January, 2003 issue of Optometry and Vision Science.)

Pupil size is critical whenever we specify aberrations in terms of Zernike coefficients because the same eye will have a different set of coefficients for different pupil sizes, partially because aberrations become more pronounced as the peripherial aspects of the eye's optical system are uncovered. This differs from our usual modus operandi because optometrists normally don't include pupil size with conventional spectacle prescriptions. When diopters are used to specify the spherocylindrical refractive error, it is the same for all pupil sizes, but this is not true for Zernike coefficients.

Below the pupil size in the prescription example are two additional numbers, labeled, total RMS and higher-order RMS. The RMS values show how bad the aberrations are when multiple modes are lumped together. Total RMS indicates the magnitude of the total aberrations (lower- plus all higher-order aberrations), while the higher-order RMS shows the magnitude of the combined higher-order aberrations (third and fourth orders in this case). The RMS values can give you a feel for how bad the person's total and higher-order aberrations are.

As with the Zernike coefficients, the RMS values change with pupil size. For the same eye, both total and higher-order RMS wavefront error values decrease for smaller pupil sizes. Conversely, aberrations always increase with larger pupils. In general, for a 5.0-mm diameter pupil, the higher-order RMS value for a normal eye should be less than 0.2 µm.

Question: Why do you think patients with large post-LASIK aberrations have good vision during the day, but poor vision at night?

Answer: Large aberrations become more noticeable with a large pupil and can be nearly eliminated with a small pupil. This is why you can improve visual acuity for an uncorrected refractive error using a pinhole.

Question: What can you do to help a patient like this?

Answer: Prescribe a mild miotic such as Alphagan to reduce pupil size.

Simply assessing aberrations can often be extremely useful when working with a patient who has no spherical or cylindrical refractive errors but who complains of poor visual acuity. Using aberrometry, individuals with retinal, psychological, or other causes of real or presumed acuity reduction can be separated from those with demonstrable optical causes.

A stand-alone device such as the Wavefront Sciences COAS (Complete Ophthalmic Analysis System) aberrometer can also be used to assess and follow the optical effects of various conditions such as keratoconus (http://www.wavefrontsciences.com/pdf.html), irregular astigmatism, and other higher-order aberrations.

By one estimate, about half of the population has higher-order aberrations that produce a noticeable reduction in acuity and 15 percent would achieve a major benefit from having their aberrations corrected.

The effect of pupil size on acuity would depend on how significant the patient's aberrations were. For the half of the population with minimal aberrations, there would probably not be a noticeable change in acuity for a pupil dilation from 3 to 6 mm. For a normal eye with a higher spherocylindrical error, there would probably only be an acuity change of a few letters with dilation.

Acuity changes would be most noticeable for patients who have large aberrations of the type that could occur after refractive surgery. In these cases, acuity for high contrast targets might change from 20/20 to 20/30 (or possibly worse) with pupil dilation from 3 to 6 mm. Patients might also experience significant visual loss that is not easily detectable with standard Snellen acuity tests. For example acuity measured with low contrast targets would show more of a loss and contrast sensitivity might also be significantly worse.

Pupil size changes can have major effects on patients with significant aberrations.

Clinical Case 1 - Assessing uncorrectable poor vision after conventional LASIK

A 24-year-old male with a highly myopic refractive error had LASIK performed on both eyes, followed by several enhancement surgeries. The procedures corrected most of his myopia, as summarized by the refraction data below:

Although he was glad to be less dependent on spectacles or contact lenses, the patient was troubled by the following visual symptoms:

The patient refused to consider wearing spectacles or contact lenses to help correct his residual error and was referred to the Northeastern State University College of Optometry for detailed analysis of his vision.

The following tables and figures summarize the results of our visual acuity and optical quality tests:

Aberrations

Eye

RMS Wavefront Error (um)

Total

OD

1.97

Higher-Order

OD

0.51

Total

OS

2.37

Higher-Order

OS

0.51

FIGURE 17 - Graph showing the magnitude of individual Zernike modes (higher-order aberration) for the patient's right eye (blue bars) compared to normal values (red grid). Pupil size was 5.5 mm. Modes #7 (Z₃^-1; vertical coma), #8 (Z₃¹; horizontal coma), #12 (Z₄⁰; spherical aberration) and #17 (Z₅^-1) were much larger than normal.

FIGURE 18 - Graph showing the magnitude of individual Zernike modes (higher-order aberration) for the patient's left eye (blue bars) compared to normal values (red grid). Pupil size was 5.5 mm. Modes #8 (Z^₃1; horizontal coma), #9 (Z₃³; oblique trefoil), #12 (Z₄⁰; spherical aberration), #18 (Z₅¹) and #24 (Z₆⁰) were much larger than normal.

FIGURE 19 - Color topographic map showing the higher-order aberrations for the right eye of the patient. This shows the shape of the optical wavefront in the eye's pupil, assuming lower order aberrations (sphere and astigmatism) have been perfectly corrected. An aberration-free eye would have a flat wavefront with a value of zero across the entire pupil. The irregular contour could not be corrected using a spherical or toric lens. Contour lines indicate quarter micrometer intervals.

FIGURE 20 - Color topographic map showing the higher-order aberrations for the left eye of the patient. This shows the shape of the optical wavefront in the eye's pupil, assuming lower order aberrations (sphere and astigmatism) have been perfectly corrected. An aberration-free eye would have a flat wavefront with a value of zero across the entire pupil. The irregular contour would be could not be corrected using a spherical or toric lens. Contour lines indicate quarter micrometer intervals.

Aberrometry revealed significant lower- and higher-order aberrations that could account for the patient's symptoms. If the patient would be willing to wear spectacles, this would correct a large portion of his residual refractive error. However, larger-than-normal higher-order aberrations would still remain, and these would probably cause some visual problems, especially in low-light situations. These could be partially corrected by prescribing a mild miotic, such as Alphagan, to reduce pupil size.

Re-treatment with a wavefront-guided refractive laser might correct also the residual aberrations, but good stable vision cannot be guaranteed. Also, it was questionable whether he had enough corneal thickness remaining to allow additional ablative procedures.

Clinical Case 2 - Determining whether reduced acuity is due to optical or sensory problems

A 72-year-old male patient complained of blurred and distorted vision OD that was uncorrectable with glasses. He had visited several optometrists and ophthalmologists, but no one was able to completely correct his vision.

He had mild nuclear sclerosis OU, and very slight (stage 0) epiretinal membrane OD that, according to a retinal specialist, should not have affected his vision. Because the referring doctor could find no pathology that could account for his reduced visual acuity with best spectacles, he referred the patient to the Northeastern State University College of Optometry for aberrometry and other tests.

In this case, aberrometry revealed that the patient had completely normal higher-order aberrations. Because no optical error could explain his reduced visual acuity, it was concluded that his visual symptoms were caused by the early epiretinal membrane, OD, and the patient was returned to the retinal specialist for further care.

These examples demonstrate how aberrometry can be used to assess the cause of a patient's reduced acuity. Aberrometry can provide useful information for any patient with visual blur that cannot be corrected by conventional spectacles and that cannot be attributed to cataracts, pathology or amblyopia. Wavefront sensors can also measure complex optical systems, such as aspheric or progressive lenses (http://www.wavefrontsciences.com/pdf.html).

Correcting Aberrations
In the past only spherical and regular astigmatic (lower-level) aberrations of the eye's optical system were corrected by using lenses or reshaping the cornea with an excimer laser (LASIK). Today, aberrometers can be coupled with excimer lasers to ablate corneal tissue point by point so as to compensate for both lower- and higher-order aberrations.

Currently, almost all major manufacturers of LASIK equipment offer aberrometer-guided (a.k.a., wavefront-guided) devices that use outputs from an aberrometer to determine the depth of corneal ablation on a point by point basis. A partial list of manufacturers, along with the types of lasers and aberrometers used, is provided below:

Among the aberrometers listed in the Table, the COAS (WaveFront Sciences, Inc.) and the OPD Scan (Nidek) are available as stand-alone instruments, similar to table-top autorefractors. The COAS is a high-resolution Shack-Hartmann aberrometer, whereas the OPD Scan uses automated retinoscopy to assess aberrations. (The OPD scan includes a videokeratoscope in the same instrument.) The VISX and ALCON systems use proprietary aberrometers to assess the eye's optics.

In theory, an aberration-guided excimer laser could create an eye with perfect optics and provide the patient with super-normal vision limited only by the resolution of the retina (about 20/8 in a healthy young person).

For patients who do not want to undergo LASIK, it is also possible to reduce or remove aberrations using an aberrometer-guided contact lens generation system. (http://research.opt.indiana.edu/library/waveGuidedLens/waveGuidedLens.html) With an aberrometer and a special contact lens generating device, customized contact lenses with the patient's "visual fingerprint" could be made to theoretically produce super-vision. Of course ballasting or other means would be required to keep these lenses from rotating because rotation would reduce the ability of the lens to compensate for the eye's aberrations.

In addition to contact lenses, wavefront-guided intraocular lenses (IOL) could also be made so that pseudophakes could theoretically experience aberration free vision. A problem with these lenses might be that the aberrations of the eye could be very different before versus after the surgical procedure and lens extraction. Perhaps it will be possible to modify IOLs by use of a laser or other means after they have been implanted.

Unfortunately, it is more difficult to conceive of how spectacles with wavefront-corrected lenses would work because the lenses would either have to move as the eye moved to keep the optical axes of the lenses aligned with the eyes, or the shapes of the lenses would have to be constantly changed to maintain the proper alignment with the eyes. Neither alternative seems feasible at the present time.

Clearly (pun intended), the use of aberrometer-based assessment, and wavefront-guided corrections offer a great potential for increasing, perhaps to super-levels, the visual acuity for a significant proportion of the patients typically seen by optometrists.

The main points of this course are reviewed in the following questions and answers.

Q. What are higher-order aberrations, and why are they important?
A. They are refractive errors beyond sphere and cylinder. In some patients they may be significant enough to affect vision. Modern wavefront-guide lasers are programmed to correct sphere, cylinder, and the higher-order aberrations.

Q. What are wavefront sensors (a.k.a. aberrometers)?
A. They are super-autorefractors that measure the complete refractive error, including sphere, cylinder, and higher-order aberrations.

Q. How do aberrometers work?
A. They measure wavefront slopes and mathematically reconstruct the shape of the wavefront of light exiting the eye.

Q. What are Zernike polynomials, and what do they tell us about refractive errors?
A. They form a system for recording refractive errors, including sphere, cylinder, and higher-order aberrations. Zernike polynomials tell us what kind of refractive errors (aberrations) are present and how much of each is present.

Q. What important numbers are typically reported following an aberrometer measurement?
A. A Zernike coefficient for each of the various modes, pupil size, and total and higher-order RMS wavefront error values.

1. Atchison DA, Scott DH, Cox MJ. Mathematical Treatment of Ocular Aberrations: a User's Guide. Vision Science and Its Applications, 2000:110-30.

2. Campbell CE. A New Method for Describing the Aberrations of the Eye Using Zernike Polynomials. Optom Vis Sci 2003;80:79-83.

3. Fugate RQ, Wild WJ. Untwinkling the stars - part I. Sky & Telescope 1994;May issue.

4. Goss DA, West RW. Introduction to the Optics of the Eye. Boston: Butterworth-Heinemann, 2002.

5. Howland HC. The History and Methods of Ophthalmic Wavefront Sensing. J Ref Surg 2000;16:S552-3.

6. Liang J, Grimm B, Goelz S, Bille JF. Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor. J Opt Soc Am A 1994;11:1949-57.

7. Liang J, Williams DR. Aberrations and retinal image quality of the normal human eye. J Opt Soc Am A 1997;14:2873-83.

8. Liang J, Williams DR, Miller DT. Supernormal vision and high-resolution retinal imaging through adaptive optics. J Opt Soc Am A 1997;14:2884-92.

9. MacRae SM, Krueger RR, Applegate RA. Customized Corneal Ablation - The Quest for SuperVision. Thorofare, NJ: SLACK, Inc., 2001.

10. Maguire LJ. Keratorefractive Surgery, Success and the Public Health. Am J Ophthalmol 1994;117:394-8.

11. Marcos S. Aberrations and Visual Performance Following Standard Laser Vision Correction. J Ref Surg 2001;17:S596-601.

12. Miller DT. Retinal Imaging and Vision at the Frontiers of Adaptive Optics. Physics Today 2000;53:31-6.

13. Platt B, Shack R. History and Principles of Shack-Hartmann Wavefront Sensing. J Ref Surg 2001;17:S573-7.

14. Salmon TO, West RW. Optical Wavefront Sensing of the Human Eye. In: Pandalai S, ed. Recent Research in Optics, Fort, Trivandrum, India: Research Signpost, 2002:183-214.

15. Salmon TO, West RW. Measurement of Refractive Errors in Young Myopes Using the COAS Shack-Hartmann Aberrometer. Optom Vis Sci 2003;80:6-14.

17. Thibos LN, Applegate RA, Marcos S. Aberrometry: The Past, Present and Future of Optometry. Optom Vis Sci 2003;80:1-2.

18. Thibos LN, Applegate RA, Schwiegerling JT, Webb R, Members VST. Standards for Reporting teh Optical Aberrations of the Eye. Vision Science and Its Applications, 2000:232-44.

19. Thibos LN, Hong X. Clinical Applications of the Shack-Hartmann Aberrometer. Optom Vis Sci 1999;76:817-25.

20. Wild WJ, Fugate RQ. Untwinkling the stars - part II. Sky & Telescope 1994;May issue.

21. Yoon GY, Williams DR. Visual performance after correcting the monochromatic and chromatic aberrations of the eye. J Opt Soc Am A 2002;19:266-75.

22. Thibos LN, Cheng X, Bradley A. Design Principles and Limitations of Wavefront-guided Contact Lenses. http://research.opt.indiana.edu/library/waveGuidedLens/waveGuidedLens.html

Pacific University College of Optometry provides On-Line CE as a service to optometrists. The college does not endorse or recommend any products, equipment, or services that might be discussed in the courses. Courses are prepared by individuals believed to be experts in their areas of specialization who are compensated for their efforts. The College relies on their expertise to produce accurate and timely courses. Questions or concerns about courses should be directed to the individual authors and/or to the Continuing Education Department at the College of Optometry at kundart@pacificu.edu

Type of Acuity Test	OD	OS	Pupil Diameter (mm)
Unaided	10/25	20/35	4
Pinhole	20/20	20/15	1
Low Contrast (10 %)	20/46	20/58	4
Low Contrast (10 %) with Pinhole	20/36	20/40	1

A Primer on Using Wavefront Analysis for Refractive Surgery and Other Ophthalmic Applications

Thomas O. Salmon, O.D., Ph.D., F.A.A.O.

COPE Certificate 10260-RS, Expires December 1, 2006

Aberrations	Eye	RMS Wavefront Error (um)
Total	OD	1.97
Higher-Order	OD	0.51
Total	OS	2.37
Higher-Order	OS	0.51