Taming the Wild Wavefront – Part 1

How Misbehaving Wavefronts Influence Eyewear Satisfaction and What to Do About It

By Mark Mattison-Shupnick, ABOM

THE BUSINESS OF WAVEFRONT MANAGEMENT

In all kinds of eyewear (clear, sun, office), we are in the business of managing wavefront aberrations. Mostly we focus on the usual suspects—prism, defocus (sphere power) and astigmatism—but today a patient can get those corrected to some degree of adequacy almost anywhere. The key to excellence, differentiation and the resulting higher average selling price lies in detecting and managing the more subtle effects of aberrations that affect vision. Addressing the eye's wavefront aberrations, as well as the wavefront errors contributed by the chosen lens design and the way that lens is positioned in front of each eye can make the best pair of glasses. For many patients, this will make the difference between adequate vision and excellent vision.

WAVEFRONTS AND WAVEFRONT ABERRATIONS

The movement of light away from an object point can be represented either as diverging rays or as expanding spherical wavefronts centered on the object point. Wavefronts appear flat when viewed objects are at infinity and are more steeply curved from objects closer up. For example, the visibility of the candle (Fig. 1) is due to the many rays or waves that make up a wavefront. Conversely, light converging to a point can also be described as a wavefront that becomes continually smaller. It is in this converging process that we encounter wavefront aberrations.

Click on the image for animation.

In a perfect optical system, spherical wavefronts of light from an object point should converge to a single point focus at the desired image location, such as the retina of the eye. In the presence of optical aberrations, however, these wavefronts become either too steep, too flat or distorted from their ideal shape. Aberrated wavefronts do not converge to a single point focus but instead, form a smeared image pattern, resulting in blur. The wavefront error can be described as the difference between the actual wavefront and an ideal reference wavefront (Fig. 2). In the case of defocus and astigmatism, these errors are measured in diopters of sphere and cylinder, respectively.

Click on the image for animation.

The complicated shapes of aberrated wavefronts are often described as a sum of simpler aberration shapes. The most common method of describing these simpler aberrations relies on the use of special mathematical functions referred to as the Zernike polynomial series (Fig. 3).

These shapes are grouped into increasing "orders." First-order aberrations refer to a displacement of the wavefront, which are ignored for our purposes. Second order aberrations include defocus and different orientations of astigmatism. Third order aberrations include optical errors such as spherical aberration, trefoil, coma and so on. Second-order aberrations are called "low-order" aberrations, and third order aberrations and higher are called "high-order" aberrations.

What's the difference? In the simplest terms, the higher the order, the more their effects are dependent on pupil size. Low-order aberrations tend to reduce vision quality even when the pupil size is small. High-order aberrations, on the other hand, tend to reduce vision quality only when the pupil size is large, most commonly in low-light conditions. Fig. 4 shows the effects of these aberrations in the perception of a point of light at various pupil sizes.

A typical eye suffers from both low-order and high-order wavefront aberrations, although low-order aberrations are typically much greater. High-order aberrations generally do not become important to vision quality until the low-order aberrations are eliminated. A spectacle lens may also suffer from low-order aberrations, high-order aberrations or both.

The main purpose of spectacle lenses is to manage wavefront aberrations of an imperfect eye, specifically the second order aberrations defocus (corrected with sphere power) and astigmatism (corrected with cylinder power.) But other higher order aberrations also affect vision in low-light conditions when the pupil is larger. Addressing these aberrations with eye glass lenses will be the subject of Part 2 of this course, to appear next month.

While correcting wavefront aberrations of the eye, spectacle lenses may also produce their own low-order and high-order wavefront aberrations that result in blur in some areas of the lens. These can take two forms:

1. Aberrations in the lens design, and
2. Aberrations created by a mismatch between lens optics and the wearer's vision needs.

In the past, we had to live with many of these aberrations, and they are still significant in more basic types of lenses. But in recent years, new lens design and customization techniques have allowed us to reduce or eliminate these aberrations. Today, this defines the difference between adequate and premium vision solutions.

PROGRESSIVE LENS ABERRATIONS

Properly designed single vision and bifocal lenses typically produce only negligible amounts of low-order and high-order aberrations in most prescription powers. The optical limitations of progressive lenses, on the other hand, introduce meaningful levels of both aberrations. The peripheral blending of the distance zone into near zone produces significant levels of astigmatism and defocus, low-order aberrations. The progressive change in addition power and astigmatism produces coma and trefoil, high-order aberrations (Fig. 5A and 5B).

High-order aberrations in a progressive lens result from the change in power that occurs over the pupil of the eye. With a very small pupil, a bundle of rays are limited to a small-defined area of the lens. However, a large pupil would include more of the lens surface, over which power or cylinder is changing in a progressive. (Here you can see how the magnitude of this effect is dependent on pupil size.) The intermediate can mimic the effects of coma with a large pupil. Instead of a pinpoint focus, a V-shaped blur is produced. That same large pupil, when looking right and left like you might do when driving or walking, produces a cylinder change over the pupil diameter. The result is visible trefoil-like blurring that degrades vision quality through these areas.

These aberrations in progressive lenses can't be eliminated, but they can be managed. Modern design techniques can bring levels of unwanted defocus and astigmatism to near the mathematical minimum, and smooth power gradients manage coma and trefoil in the corridor and its periphery. As a result, many standard (non-customized) progressive lenses offer excellent vision in ideal circumstances.

ABERRATIONS AT THE LENS/ WEARER INTERFACE

The key to the last statement is "in ideal circumstances." As we know all too well, ideal circumstances are few and far between.

As soon as vision scientists were able to calculate off-axis lens errors, it was known that excellent vision, in a world of only sphero-cylinder curves, required a great many front base curves. However, the cost and manufacturability of so many base curves was prohibitive. As a result, limits to peripheral vision were accepted as unavoidable, within the constraints of the available technology. The result was a set of base curves; each used for a specific range of powers. This approach is still used for traditional lenses today.

What happens as the prescription deviates from a base curve's ideal power? Fig. 6 illustrates how optical performance deteriorates away from the ideal power using the same base curve. In the example, the plano lens is the targeted progressive lens design. As the power changes, the use of that same base curve degrades the optics by introducing oblique astigmatism, a low-order aberration, becoming worse in higher powers. In addition, a conventional lens design cannot address the aberrations produced simultaneously by both the sphere and cylinder power. The result is a further compromise for the astigmatic patient, especially in higher cylinders.

Click on the image for animation.

Moreover, as the pantoscopic and/or face-form tilt of the lens in the position of wear increases, optical performance deteriorates because of oblique astigmatism due to lens tilt. Fig. 7 illustrates how the power changes as tilt changes. The result is a lens whose effective powers become farther and farther from the prescribed powers. If one of these examples had been purchased by one of your patients from the Internet (in the mistaken belief that all lenses are probably the same), an understanding of these issues becomes an opportunity to deliver a better solution by better wavefront management.

Click on the image for animation.

LENS CUSTOMIZATION AND WAVEFRONT MANAGEMENT

To make lenses better and improve vision through them, low-order aberrations associated with off-axis vision and the position of wear, including defocus and obligue astigmatism, must be reduced or eliminated.

Fig. 8 compares different approaches to the management of low-order wavefront aberrations. Starting at the top, a premium but Conventional Lens (semi-finished design +2.00 add progressive) is made into a +3.00-1.50 x 135 prescription. The way that this person wears this lens with 12 degrees pantoscopic tilt and 12 degrees face-form wrap (position of wear) is not considered. Instead the calculations are done using an average fit. The design cannot account for the prescribed cylinder. The ray-traced astigmatic error as seen by the wearer is illustrated. Unwanted front surface astigmatism combines with the power errors produced by the prescription off-axis and by the tilt of the lens. This combination of errors degrades overall performance.

Next, asphericity or atoricity can be used to improve peripheral vision. By using an Atoric Lens (differing asphericity for both the sphere and cylinder power of the lens), the lens is improved by reducing off-axis oblique astigmatism. However, fit is still not considered at all, and the correction at every point on the lens is not optimized, so improvement is small.

The introduction of digital manufacturing technology, through which surface heights can be specified point by point, provides an opportunity to optimize the lens and customize the surfacing result when used in conjunction with advanced lens design software. The ideal optics of the lens design may be calculated, point-by-point, using the exact prescription and an assumed position of wear in order to provide more accurate vision correction over the entire lens. This custom lens design is then manufactured directly onto the lens blank using a precision free-form surfacing process.

Using this technology, the Rx Optimized Lens is better and from an astigmatic point of view improves both zone size and clarity. The ray-traced errors for the base curve are compensated, though the lens is still designed based on an average position of wear, rather than the specific way the patient wears the lenses. Because the patient's position of wear is not considered, the vision quality through the lens is still not ideal.

The Fully Customized Lens best produces a progressive with clear distance, mid-range and near. That's because the lens has been compensated for the predicted errors produced by both the prescription and the patient's specific position of wear (i.e., 12 degrees tilt and 12 degrees wrap). Therefore, lenses calculated to compensate for the low-order wavefront aberrations of power error and astigmatism for a particular base curve in the position of wear better deliver the intended design regardless of prescription. Zeiss Individual progressive and single vision lenses rely on this sophisticated technology to deliver lenses fully customized for the wearer.

CONCLUSION

Clearly (no pun intended), there's more to good vision than just an adequate pair of specs that have the right power as read by a lensometer. We've seen how advanced design techniques minimize wavefront aberrations in a progressive design, and how creating a lens design specifically for one individual eliminates aberrations resulting from a non-average individual wearing an average design. By addressing these issues, we go a long way up from a merely adequate vision correction to an outstanding, personalized visual experience.

Is that all we can do? No. As I mentioned earlier, eyes are subject to wavefront aberrations beyond prism, defocus and astigmatism. High-order aberrations of the eye affect vision in lower light conditions, and for many people, the impact on night vision is significant. These are also much more challenging from a vision-correction standpoint: A standard refraction won't detect them, and spectacle lenses can't correct them the way they correct low-order aberrations. However, new technology allows us to make spectacle lenses that can significantly improve night vision for many people by at least taking high-order aberrations into account. This will be the subject of Part 2 of this course.