Although light travels in a straight line, when it encounters the edge of an obstruction, it slows and spreads out slightly. This effect is called diffraction. It cannot be adequately explained with a ray-tracing model, because ray tracing should only be applied to smooth and continuous optical surfaces. Rays are normally perpendicular to a wavefront at every point, but, if the wavefront encounters an edge, simple ray tracing gives misleading results, because diffractive effects become dominant.
The Acrysof Restor refractive-diffractive IOL (Alcon Laboratories, Inc., Fort Worth, TX) uses a set of circular zones to focus light at two foci. The far focus is at the foveola, and the near focus is approximately 1mm in front of the foveola. There are a number of discontinuities, also known as diffractive steps or zone boundaries. There are zones between the discontinuities, but these do not act like the zones of a refractive multifocal IOL. That is, they do not alternate far-near-far-near. Instead, the diffractive effects created by the geometry of the steps combine with the refractive lens properties to create a unique design.
THE DESIGN IN DETAIL
The Restor's construction is inherently difficult to represent in a simple fashion for two reasons. First, there are the distractions of too much detail, such as the thickness of the optic, the range of wavelengths for visible light, the refractive indices of the media, and the anatomy of the fovea. Second, there is a huge number of light waves involved. Ignoring those distractions, Figure 1 schematically represents the distance from the lens to the foveola (19mm) and the distance from the lens to the point of near focus (18mm) in an emmetropic model eye.
The distances can be measured in wavelengths of light as well. Using green light as an example, there are approximately 46,000 wavelengths of 550-nm light in the vitreous from the lens to the foveola (the far image) and about 44,000 wavelengths from the lens to the add-power focus (the near image), which is approximately 1mm in front of the foveola. Starting at the first diffractive step of the Restor lens and moving radially outward, the location of the second zone boundary is where the difference of the distances between the two foci changes by just one wavelength on the IOL's optic. The other 11 zone boundaries are placed at additional, increasingly peripheral locations of one wavelength of change. As it turns out, in order to keep the same two points of focus (far and near) as zones are added, zone boundaries become progressively closer together peripherally. If the add power were lower, the second focus would move closer to the foveola (eg, it would be at 18.5mm for a 2.00D add), and the family of zones would move outward on the lens to maintain the one-wavelength requirement.
The magnitude of these numbers seems incredible, but changes in the optical path length of one wavelength of relating points that are thousands of wavelengths away specify the widths of the optical zones that lie within the zone boundaries. The engineering of the IOL with regard to these numbers is equally fascinating. That is, the company had to develop a cast-molding process that can reliably produce plastic lenses out of foldable Acrysof lens (Alcon Laboratories, Inc.) material that have step heights of approximately 1.3µm and gradually decrease in a stepwise fashion to 0.2µm peripherally. As 1.3µm equals 1,300nm, this is little more than two wavelengths of green light in air, or about three wavelengths in aqueous. Two-tenths of a micron is 200nm or one-half a wavelength of blue light in air.
The diffractive steps introduce phase delays for light at the zone boundaries. The height of the step is a measure of the phase delay, although the entire zone surface changes if the step height is altered. The reason is that, although the optical zones themselves have generally spherical surfaces, they are each composed of individually different curvatures that also differ from the underlying optical base curve of the lens. The characteristics of a diffractive IOL can be seen in the Restor lens' surface (Figure 2). The shape of the surface profile of each zone determines the predominant direction of light passing through the zone, while tiny steps at the zone boundaries adjust the phase of the light. The combination of the zone boundary's placement, the zone's surface profile, and the phase delay at the steps creates the overall optical properties.
The step height can be used as a simple descriptor of the overall optical properties of the Restor IOL. If there were no steps at the zone boundaries, for example, it would be a monofocal lens, and all the light would go to its base power. If the step heights all increased the optical path by one wavelength, then the lens would be monofocal, with all the light going to the add power; in this case, the curvatures of the individual zones would all be identical and similar to those of a refractive lens.
Something that is less obvious is that, if the step heights all increased the optical path by half a wavelength, then approximately 41% of the light would go to each of the two primary lens powers. This is theoretically and practically the best division of light that can be achieved by diffraction alone for two lens powers, and it results from the complex interaction between the zone boundaries' locations and the zonal structure. The step height essentially determines how much light goes to each image and provides control over energy balance. The additional light energy goes into other lens powers of -4.00, +8.00, -8.00, and +12.00D, powers that are related to other image distances that geometrically have integral multiples of optical path distance (three wavelengths, five wavelengths, etc.). The images are not perceived, because they are extremely defocused and their energy is very low.
Apodization refers to the change of a property across the optical surface from the center to periphery. The term could apply to a filter that is clear in the center and becomes increasingly opaque toward the periphery. In the case of the Restor's optic, the diffractive structure is apodized in order to control light energy's contribution to the two distant and near foci. This concept is illustrated in Figure 3, which compares the exaggerated surface with the approximate energy balance between the two images. Previous diffractive lenses have used the same step height for all the zone boundaries, a design that also makes all the zone curvatures similar to each other. For the Restor lens, with small pupils, the phase delay at the central steps is approximately half a wavelength, which divides the light energy fairly equally between the base and add powers. As pupils become larger, additional zones are used, with the step heights becoming progressively shorter and the zones less steeply curved. The phase delay at the steps is less, because the step heights get shorter, which results in less light's going to the add power and correspondingly more light's being used for far vision. The step heights actually straddle the base curve so that the calculation of the zone boundary's location is not affected by changes in step height.
Two factors are complementary when considering the design: the situations where near vision is used and the visibility of photic phenomena. In general, near vision is important primarily when the pupil is smaller because of normal high illumination levels for near work and the accommodative reflex. Photic phenomena due to the second image are more likely at night when the pupil is larger. The apodization profile for the Restor lens equally distributes energy between the two primary images for smaller pupils, but more light goes to the far lens power as the pupil becomes larger.
The peripherally decreasing step heights reduce the net contribution of energy to near and simultaneously increase the net contribution of energy to distance. In other words, depending on the pupillary diameter, the cumulative effect of the exposed zone surfaces and the step heights at the zone boundaries determines how much light goes to each of the two primary images.
The horizontal pattern of zone boundaries determines the 4.00D add power in the optic plane (3.20D in the spectacle plane). The fact that the space between boundaries gets progressively smaller from the optic's center to the periphery of the diffractive, 3.6-mm diameter is necessary to define the two focal points consistently across the optic. Put another way, the pattern of decreasing step widths is the necessary diffractive pattern to maintain the two focal points, both foveal and 1mm anterior to the fovea.
RANGE OF FOCUS
An increased depth of field can yield a pseudoaccommodative visual performance. The Restor lens has two fixed primary powers where retinal focus is sharpest and best acuity can be achieved. It also provides good visual acuity for two ranges of object distances. The midpoint of each range is each of the primary best-focusing distances. Figure 4 shows defocus curves measured in the phoropter that compare the Restor lens to a monofocal control. Far vision ranges are comparable for both lenses, but the Restor lens provides an additional range of vision around the best near focus of 32cm. Both primary lens powers of the Restor lens contribute to intermediate distance vision. With the Restor, the expanded performance of near and intermediate depths of field improves patients' vision of everything within arm's length.
The change in the intensity of defocused light varies with the type of object and other parameters. For a point source, the light from the second power has less than 1% of the intensity of the focused spot. For a line or other object, it may be 2% to 3%. The human visual system is designed to pick out structure in a scene and to ignore other optical phenomena, which arise normally in the phakic eye due to corneal tear film effects, dryness, and swelling; floaters; and other phenomena. Faint, secondary, defocused light is rarely noticeable, although it is more likely to be visible at night, when there are bright point sources against a dark background.
Restor patients do not report a loss of light, although the energy's focus is split between the two images. Human vision is very tolerant of the continual changes in light energy upon fluctuations in pupillary diameter and in illumination. The eye seeks details of interest and ignores modest changes in intensity. Objects are visible under luminance changes of more than a factor of 1 million, from a lighted office to outdoor sunshine. An intensity change of a factor of 2 is not normally noticeable.
Two analogies can describe diffraction. The first is sound waves traveling down a hall, encountering a corner, and then slowing and spreading out so that the sound wave travels around the corner and is heard 90º from the wave's original direction. The second analogy is not exactly correct but may be used to conceptualize light in its particulate form as photons and to compare it to atmospheric gas molecules as air. An air-vent diffuser in an automobile dashboard that directs air straight outward without deflection is analogous to distance vision, where the light is directed to the distance focal point at the fovea. The diffusers can be aimed downward to deflect the air stream in that direction, similar to if most of the light were deflected toward the shorter near focal point 1mm in front of the fovea. The diffuser can be placed in an in-between position so that half of the air is directed straight outward and half of it is deflected toward the near lower point. The Restor's refractive-apodized diffractive optic accomplishes the same objective in its most central zones by dividing the light wavefront so that half of it goes to the distance foveal focus point and half of it goes to the near point 1mm in front of it (Figure 5).
The Restor IOL represents a revolutionary integration of apodized diffractive structure on a platform with which ophthalmologists are familiar. Combined with the consistent centration of the Acrysof single-piece IOL, this new technology offers surgeons the opportunity to dramatically and almost immediately improve the quality of most patients' distance, near, and intermediate vision through lens replacement surgery.
James A. Davison, MD, FACS, is in private practice at the Wolfe Eye Clinic in Marshalltown and West Des Moines, Iowa, and he is Clinical Associate Professor of Ophthalmology at the University of Utah in Salt Lake City. He states that he holds no financial interest in the products or company mentioned herein. Dr. Davison may be reached at (800) 542-7956; firstname.lastname@example.org.