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History and development of the apodized diffractive intraocular lens
J CATARACT REFRACT SURG - VOL 32, MAY 2006
LABORATORY SCIENCE
History and development of the apodized diffractive intraocular lens James A. Davison, MD, Michael J. Simpson, PhD
The ReSTOR intraocular lens presents a unique apodized diffractive design within a refractive foldable acrylic optic, which makes an unprecedented level of mulifocal optical performance available. We describe the history and principles of diffractive optics used in the development of this refractive–diffractive IOL. J Cataract Refract Surg 2006; 32:849–858 Q 2006 ASCRS and ESCRS
Human prosthetic lens replacements use simple and complex optical physics. One of the more complex ophthalmic lenses is the ReSTOR apodized diffractive intraocular lens (IOL) (Alcon Surgical). It is implanted in the eye to replace the natural crystalline lens to provide vision over a range of object distances through the provision of 2 primary lens powers. It combines various optical concepts into a unique design, and the optical properties of the lens are described here along with some historical background. Accommodation, in which the natural crystalline lens changes power by changing shape so that one can focus on distant and near objects, is an important property of the younger eye. Accommodation is gradually lost as a person ages, however, which typically becomes a problem for people in their mid- to late 40s. People find they can no longer focus on near objects, which is why the Franklin bifocal was adopted in the 18th century. Accommodation is also lost when the natural crystalline lens of the eye is removed during cataract surgery and is replaced with a monofocal IOL. Patients have had to choose whether they want to have their distance vision corrected by the IOL and wear reading glasses to see up close or to select Accepted for publication November 10, 2005. From the Wolfe Eye Clinic (Davison), Marshalltown and West Des Moines, Iowa, and the University of Utah, Salt Lake City, Utah, and Alcon Surgical (Simpson), Fort Worth, Texas, USA. Dr. Simpson is an employee of Alcon. Dr. Davison is a consultant for Alcon Surgical. Reprint requests to James A. Davison, MD, Wolfe Eye Clinic, 309 East Church Street, Marshalltown, Iowa 50158, USA. E-mail: [email protected]. Q 2006 ASCRS and ESCRS Published by Elsevier Inc.
a power that would permit them to be near-sighted through the IOL and wear a distance correction in their spectacles. A few patients also choose a monovision strategy in which 1 eye is implanted with an IOL for distance vision and the other with an IOL power that can provide some near vision without spectacle correction. To provide the ability to see at different distances again, multifocal IOLs with 2 primary focal points can be used. One power is used for distance vision, and the other power is used for near vision. The image from the second lens power is highly defocused and very faint, and it has been confirmed clinically, with several different designs, that the patient primarily perceives only the focused image.1–6 However, some patients may experience unwanted visual images such as glare, flare, streaks, and halos.7,8 Intermediate vision is provided by contributions from the defocus characteristics of both primary lens powers, with some lens designs attempting to direct additional light to an intermediate focus location (Figure 1).9 Three general optical principles have been used in multifocal IOLs: multizone refractive, diffractive, and aspheric lens designs. The multizonal refractive method is defined by 2 different powers that are incorporated into circular or annular (ring-shaped) refractive zones. Some early IOLs had 2 zones (Iolab NuVue1), 3 zones (Storz Tru Vista,4 Alcon AcuraSee, Ioptex,10 Morcher,11 Pharmacia12), 5 zones (AMO Array3), and 7 zones (Adatomed13). An example is the lens manufactured by Pharmacia that was implanted in 1989 (Figure 2). The 5-zone foldable silicone Array IOL (AMO), which was approved by the U.S. Food and Drug Administration (FDA) in 1997, is the most common contemporary example of this category. 0886-3350/06/$-see front matter doi:10.1016/j.jcrs.2006.02.006
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Figure 1. Multifocal IOLs provide 2 primary focal points; 1 for distance vision and the other for near vision. Each contributes to an intermediate vision function.
Multizone refractive IOLs differ from bifocal spectacle lenses because the IOL becomes an integral part of the eye, and the multiple zones are present across the pupil simultaneously at all times.1,14,15 Each lens zone has a different effective aperture, and this can affect the quality of the image that it provides because the pupil diameter changes in response to different illumination levels as well as with the accommodative reflex. The energy balance between the 2 images and the quality of the images vary with engineering design and environmental conditions. The second method to create a lens with 2 powers has been to use a diffractive surface on a refractive platform.2,16,17 These designs divide light between 2 images through the use of different diffractive orders, with an equal amount of light directed to the near and distant primary foci for all pupil diameters when the diffractive structure covers the whole lens surface. This design was introduced by 3M in 1988.2 The original IOL, which was typical of the time, featured a 3-piece, 6.0 mm diameter nonfoldable poly(methyl methacrylate) optic and with closed-loop haptics. Diffractive lens designs have also been used by
Figure 2. An early zonal multifocal lens from Pharmacia (1989).
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Pharmacia and Adatomed.18,19 The perception of halos and glare at night were a frequent clinical observation with these IOLs. The diffractive zones were very small, and light from all the zones went to both lens powers equally. Unlike the multizonal refractive optic, with these IOLs, the image quality and energy balance between the images were no longer dependent on pupil diameter. These were full-optic diffractive-refractive lenses that featured a diffractive surface across the entire anterior surface. A necessary artifact of any refractive–diffractive optical system including these is that a portion of the light energy about 18% is also directed into higher diffraction orders. This leaves about 82% of the light available to be divided between each of the 2 primary lens powers. The ReSTOR apodized refractive–diffractive design expands on these earlier diffractive lens designs. A third design method has been the use of aspheric optic regions that increase the depth of field of the lens. The addition of asphericity in this application does not provide an additional distinct focus but aims to expand the range of focus. However, this occurs at the expense of image contrast. Lenses that primarily used asphericity were the Progress lens from Domilens20 and the Nordan aspheric.21 Some zonal lenses also use a level of asphericity, such as the Ioptex 3-zone lens,10 with distinct aspheric regions between the zones. This article describes the optical principles and the history of both multizonal lenses and diffractive lenses and uses this background to describe the development of the ReSTOR apodized diffractive lens. During this development, a primary guiding principle was that near vision is less important in conditions of dim illumination when pupils are large. A second was that minimization of the perception of halos and glare in dim illumination was essential. A critically important coincidence of optical science is that these 2 characteristics are, in fact, complementary, and this allowed the use of a unique optical feature, apodization, in which the energy balance of the optical
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LABORATORY SCIENCE: HISTORY AND PRINCIPLES OF DIFFRACTIVE IOL
Figure 3. A: A large lighthouse lens. B: The underlying concept of a Fresnel lens: The original bulk of the dashed lens is reduced, leaving a thin lens whose surface slopes match the original lens. This example has equal step heights. C: A Fresnel lens with equal zone widths. A Fresnel lens is always a monofocal lens.
system varies with pupil diameter in a manner that is consistent with natural pupil responses to distance and near vision requirements under various lighting conditions and is compatible with the pupil accommodative reflex. FRESNEL LENSES
Zonal lenses can be traced back to the work of Augustin Fresnel, who improved lighthouse optics in the 1820s by segmenting large lenses to reduce their overall weight (Figure 3, A).22 Fresnel’s lighthouse design represented the first widespread use of a lens of this type, and Figure 3, B, illustrates the geometrical properties of what has come to be called a Fresnel lens. A large portion of the bulk of the lens is removed, but the general focusing properties are retained. There are no specific limitations on where zone boundaries need to be placed in a Fresnel lens, so boundary locations can vary with each application. One choice is to make the step heights constant, which requires that the zone widths will vary (Figure 3, B). Another choice is to give the zones a constant width, which requires that the step heights will vary (Figure 3, C). Both geometric and diffractive optical effects reduce potential image quality, although imaging is not important for the lighthouse application. In modern ophthalmology, temporary Fresnel prisms or lenses are sometimes attached to spectacle lenses and these typically use zone widths of at least 1.0 mm to minimize diffractive side effects. FRESNEL ZONES AND THE FRESNEL ZONE PLATE
Before creating the lighthouse lens, Fresnel had contributed to the concept of diffraction at a time when there were questions about whether light consisted of particles or waves and whether an ether existed to convey light from place to place.23 Huygen’s construction, in which each point on
a wavefront was taken to be the source of a new wavelet, was already well known at the time.23 The wavelets were drawn as circles centered on the original wavefront, and the propagating wavefront was determined by drawing a new smooth line that just grazed all the wavelets. Fresnel’s conceptual innovation in 1818 was to incorporate the ideas of amplitude, phase, and interference into the wavelet model of light propagation. This provided the potential for phase manipulations to have a significant effect on final wavefront characteristics. He described what came to be called Fresnel zones in 1818, and these are illustrated in (Figure 4, A), where a plane wavefront of light is seen moving from left to right. Working back from a distant point, the plane wavefront can be divided into zones by placing a zone boundary wherever the optical path increases by half a wavelength. If there is no diffracting obstacle, the light continues to propagate as a plane wave, but the theory indicates that if the central zone is obscured by an opaque object, a bright spot should appear in the shadow. This was found experimentally and called Arago’s spot24 and helped confirm the significance of Fresnel zones. Fresnel’s recognition of the importance of wavelength increments of the optical path distance between 2 points is the fundamental basis for a diffractive lens, but the first focusing structure, the diffractive zone plate, was not described until 50 years later in the 1870s. At that time, Lord Rayleigh observed that alternate half-period zones could be blocked to remove contributions from the second half of the wavelength cycle at the focus, and this led to the Fresnel zone plate structure depicted in (Figure 4, B).24,25 Light passing through 1 zone comes from the first half of a sinusoidal light wave, and light passing through the next zone comes from the second half. The circle that is centered on the image point describes a radius of constant phase, which is like a converging wavefront, and the
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Figure 4. A: Sketch of Fresnel zone construction. A plane wavefront moving from left to right is divided into zones using circles centered on a distant point P with radius increments of 1/2 wavelength. These divide the wavefront into Fresnel zones. B: Fresnel zone plate that obscures alternate half-period zones.
contributions of half the wavelength cycle are removed by making alternate zones opaque. This intensifies the light at the focal location because constructive interference at the image point is created, and components that would create destructive interference are eliminated. These focusing properties were confirmed experimentally since a Fresnel zone plate could be made photographically even in the 19th century. But the zone plate is not an efficient optical system because it only directs 10% of the light to the point of focus. Ten percent of the light is directed into a similar negative lens power, 50% of the light is absorbed by the opaque regions because the transmitting zones and blocking zones have equal areas, with 25% undiffracted, and 5% to higher lens powers. Lord Rayleigh provided further insight into diffractive lenses by considering what would happen if the phase of the light could be delayed in alternate zones by a half wavelength, rather than absorbing it using opaque zones. In Figure 4, this would be equivalent to shifting the sinusoidal waves that fall on the opaque zones by a half wavelength. The negative portion of the amplitude of the wave would be shifted into a positive portion that more closely matched the adjacent zone. This concept was evaluated experimentally by Wood26 by bleaching a photographic zone plate in 1898, and it was found to yield more light at the point of focus. This Wood zone plate, or phase-reversal zone plate, can direct about 40% of the light into each of 2 lens powers, with the remaining light wasted in higher diffractive orders. This is a predecessor to the modern multifocal diffractive lens. Since there are no opaque zones, no light is absorbed. MONOFOCAL DIFFRACTIVE LENSES COMPARED WITH FRESNEL LENSES
A monofocal diffractive lens can actually be thought of as a Fresnel lens with very special characteristics. For a lens in the first diffractive order, the zone boundaries have to be
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at the same locations as Fresnel zones that are created for full wavelength distances (rather than the half wavelength zones of the Fresnel zone plate), and the phase delay at the steps has to be 1 wavelength. This would not usually be the case for a refractive Fresnel lens, but a lens with such a controlled phase was described by Miyamoto27 in 1961, nearly 150 years after Fresnel’s original work, This type of lens has found increasing use in recent years, sometimes being named a kinoform.28,29 Because phase control between different zones is very challenging, the modern monofocal diffractive lens only became feasible with the development of high-precision lathes. At first glance, Fresnel lenses and monofocal diffractive lenses appear to be similar but they are actually very different. With the zonal Fresnel lens, each zone is considered to act separately to refract light. Adjacent zones usually have an arbitrary phase jump, and there is incidental and unwanted diffraction at the boundaries of the zone. With the diffractive lens, all the zones work together. The zone boundaries are strictly located where the optical path increases by 1 wavelength, and the phase jump at the zone boundary is strictly controlled. The control over the zone boundary locations and the phase delay at the steps permit a diffractive lens to provide high-quality imaging. It is interesting that 200 years ago, Fresnel did work that led to both refractive and diffractive zonal lenses. The very size of a lighthouse lens tells us that diffractive effects are not important for a Fresnel lens. Conversely, the control of Fresnel zones and phase delays to small fractions of a wavelength emphasize the features that are very important for modern diffractive lenses. FULL-OPTIC MULTIFOCAL DIFFRACTIVE INTRAOCULAR LENSES
Multifocal diffractive lenses have an important difference from their monofocal counterparts. Figure 5 shows
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LABORATORY SCIENCE: HISTORY AND PRINCIPLES OF DIFFRACTIVE IOL
Figure 5. Schematic drawings of full-optic multifocal diffractive lens in which there are w30 zones across a 6.0 mm lens diameter. A: Plan view. B: Magnified surface profile.
schematic drawings of a full-optic multifocal diffractive IOL in which there are about 30 diffractive zones across the lens surface. The zone boundary (or step) locations have a similar general appearance to those of the Fresnel zone plate because they are determined by full-wavelength Fresnel zone criterion. The defining difference between a monofocal diffractive lens and a multifocal (or bifocal) diffractive lens is the phase delay at the step. For a monofocal lens, the delay is usually 1 wavelength, and for the multifocal lens, it is typically a half wavelength. The zones between steps in a diffractive lens do not refract light so multifocal diffractive lenses cannot be described using a refractive description. If rays were conceptually traced through the zones using the assumption that they were refractive, they would focus halfway between the 2 primary lens powers. In reality, none of the light is concentrated at that location but is directed into the 2 primary lens powers instead. The use of ray tracing makes the refraction of light rays at a conventional lens surface seem obvious, but depictions of the properties of diffractive lenses are far less intuitive. However, if ray tracing is modified by appropriate calculations, it can be used to help explain diffractive lenses. Thirty years ago, Welford30 described a diffractive lens as a diffraction grating over a very small region. It was found that even though calculations for diffraction gratings assume that the gratings are very large, in practice, the redirection of a single ray can be calculated using a very localized grating spacing. This concept is beneficial for evaluating the general properties of a diffractive lens, and this capability has been a longtime standard in commercial ray-trace software. Figure 6 depicts diffractive ray tracing in comparison to the 2 other better-known methods of using lenses and mirrors. These are not rays refracted on the scale of the fine detail of the diffractive surface, but they represent the global effect of the local grating spacing. Modern raytracing programs allow the user to specify a diffractive surface in this manner, and the ray directions are calculated using diffraction grating equations. Other concepts can also be useful when thinking about diffraction. When light encounters an edge or discontinuity, it slows down and its direction changes slightly. This
is the effect of diffraction. Light can also be thought of as particles, rather than using the ray or wave pictures of light, where particles (ie, photons) constitute the wavefront of light energy. The light particle concept provides a more intuitive explanation of the simultaneous redirection of light energy to 2 separate foci, since adjacent particles can go in 2 different directions. Using the analogy of air handling louvers and diffusers, a moving stream of air molecules can be redirected into different directions. Common examples are the air vents found in automobile dashboards, which direct air to 1 location or another by changing the attitude of the air-control louvers, although other air diffusers can direct air into multiple directions. The redirection of air particles is similar to changing the direction of a stream of photons that encounters a set of diffractive discontinuities. The image quality of the full-optic multifocal diffractive IOL is generally higher than that of a multizonal refractive lens because light from all points in the aperture is directed to both foci. The diffraction that occurs at all the various steps creates the diffractive foci. The optical properties are relatively constant as the pupil diameter varies with approximately 41% of the light going to each focus
Figure 6. There are 3 methods to redirect light in a controlled manner: (a) Refraction: The refractive index difference between the 2 materials determines the angle. (b) Reflection: The reflected angle equals the incidence angle. (c) Diffraction: The grating period determines the diffracted angles, and the grating phase structure determines how much light goes into each diffraction order.
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at the design wavelength, with the additional 18% of light being wasted as it is directed into higher diffractive orders. For example, for an add power of 4 diopters (D), the higher diffraction orders represent add powers such as 8 D and 12 D and also ÿ4 D and ÿ8 D. These higher orders are focus locations where the optical path differences increase by integral numbers of wavelengths (2, 3, 4, etc.), and they are a consequence of the overall interaction of the light with the diffractive steps. The total of 82% transmission, 41% to each focal point in the example of a full-optic bifocal diffractive IOL, is the most efficient energy utilization that is possible for any diffractive optical system. It is not possible to direct 50% of the light to each of 2 foci. RESTOR APODIZED DIFFRACTIVE INTRAOCULAR LENS
The ReSTOR lens also has a diffractive design component, but it uses a new diffractive–refractive design concept to provide improved control energy distribution. The lens has 2 primary focal points, 1 at distance and the other at near. The near point is equivalent to approximately a 3.2 D add power in the spectacle plane. The base lens provides the distance power using its refractive shape and there are 12 diffractive discontinuities, or steps, that have been incorporated in the anterior surface of the cast-molded acrylic optic to provide the diffractive add power (Figure 7). These discontinuities cover the central 3.6 mm diameter of the IOL while the optic peripheral to the 3.6 mm diameter out to the 6.0 mm edge is comprised of a refractive surface dedicated to distance vision. Apodization has been used in the field of optics for many years,31 although it has not been used with diffractive lenses. Apodization was originally used to describe the optical effect created by variably absorbing filters. The filter would typically be transparent in the center of a circular
lens and would get gradually darker toward the lens periphery. With respect to a circular lens surface, apodization describes a change in a property of the lens or its function from center to periphery in a radial fashion. Contemporary use of the term describes filters that are used in an optical system to improve image quality (eg, filters that are placed at the back focus of a microscope objective to improve image quality are called apodizing filters, as are the slitlike opaque filters used in astronomy. The term apodization uses Greek words for ‘‘cutting off the feet’’. This describes the change in appearance of a plot of the intensity across a point image for conventional apodization, where the energy in the rings surrounding the central spot is reduced. The apodization property of the ReSTOR lens is radially symmetrical. It is defined by the gradual reduction in diffractive step heights from center to periphery, which results in an energy proportion continuum for light directed to the 2 primary foci. If the diffractive step heights were 1 wavelength high, the lens would behave in monofocal fashion and all the light would go to a single focus in the C1 diffraction order. If the steps were negligibly small, all the light would go to a lower-power monofocal lens focus at the 0 diffraction order. But when the steps are a half wavelength high, about 41% of the light goes into each of 2 foci. For other step-height values, the energy is divided between the 2 primary images in accordance with the step-height value. This optical effect can be modeled in a similar manner to the way that ray tracing can be used for diffractive lenses, as long as the grating spacing changes relatively slowly. The local grating spacing determines ray direction, and the local step height determines the diffraction efficiency of the light in each order. For the ReSTOR apodized diffractive–refractive IOL, the physical diffractive step heights reduce in height in an
Figure 7. Expanded cross-section of the ReSTOR apodized IOL. The heights of the diffractive steps have been magnified 400 times more than the lens diameter to make them visible on this drawing.
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almost continuously varying manner from 1.3 mm high centrally to 0.2 mm high peripherally (Figure 7). There are 12 zones, with the central outer zones having diameters of 0.75 mm and 3.6 mm, respectively. The central step heights create an approximate 0.5 wavelength of phase delay for light in aqueous. This divides the light energy fairly equally between the 2 lens powers, distance and near, for smaller pupils, with about 41% of the light going to each power. As the pupil aperture becomes larger, the increasingly exposed progressively decreasing step heights apportion more and more light to the distance power while less and less light is recruited for the near focal point. The cumulative energy balance as a function of pupil diameter is plotted in Figure 7. This happens because the step heights gradually reduce over the 12 steps, with the most peripheral shortest step being 0.2 mm high. This gradient in step heights results in a gradual change in energy balance. The outer region of the lens has no diffractive structure, so all the light goes to the distance power. This results in a distance-dominant lens for large pupils. It also means that more of the total light energy is used by the 2 primary images because none of the energy focused by the peripheral refractive portion is lost to higher diffractive orders. The apodized ReSTOR lens has some properties that are common to a full-optic multifocal diffractive lens, and some characteristics that are different. For both lenses, the radial location of the zone boundaries determines the add power. However, the step heights are the same for the full-optic multifocal diffractive lens while the ReSTOR lens has step heights that decrease with increasing distance from the lens center; ie, it is apodized, which gradually changes the proportion of energy directed to the 2 images as the pupil diameter changes. Apodization provides 2 necessary and complementary improvements to the older design of the 3M diffractive IOL: improved vision properties and reduced unwanted optical phenomena. Human beings normally function in a naturally or artificially lit photopic world, and our pupils are usually relatively small most of the time. For near tasks such as reading, we generally use bright light, which makes our pupils smaller. For near visual tasks, our accommodative reflex makes our pupils smaller too. Under these conditions, the earlier 3M diffractive IOL and the new ReSTOR IOL provide abundant light energy for distance and near vision. When we perform ambulatory distance-dominant activities in dimmer mesopic illumination, such as driving at night, the ReSTOR IOL provides relatively more available light energy for distance vision. The energy balance adjustment favoring distance vision that occurs when the pupil enlarges under dim mesopic situations resembles our normal physiology, because we normally do not attempt to accomplish complex reading or near tasks in dim illumination. Apodization also improves the quality of
vision under dim illumination by reducing unwanted secondary images, such as halos and glare, which had been frequently observed with the original 3M lens before apodization technology was available. Without apodization, there existed an equal contribution to distance and near across the entire optical surface for any pupil size. This resulted in energy being wasted under large-pupil mesopic conditions because half of it was unfortunately dedicated to near vision when it would have been more appropriate to strengthen distance vision under these conditions. Also, the low power of the add in the optic plane (3.5 D and some lenses with 2.5 D) of the 3M IOL led to smaller distance and near focal-point separation at the retina, which resulted in more perceived unwanted light images at night. A reduction in these perceptions is 1 of the reasons that the ReSTOR IOL features a 4.0 D add in the plane of the optic (3.2 D in the spectacle plane). The defocused image of a light at night from the second power of any multifocal IOL may sometimes be visible as a halo because it is on a dark background; to minimize this possibility, the diffractive structure of the ReSTOR lens only covers the central region (Figure 8). For larger pupils, more energy is directed to the distance focus and the outer region of the lens solely provides distance vision. The limited diffractive region limits the size and energy of defocused light under large-pupil conditions. Apodization also ensures that the redirection of light between the 2 images is gradual. This gradual change is very important optically because it avoids sudden optical boundaries, which can create unwanted diffractive effects. Figure 9 depicts the physical dimensions of the ReSTOR apodized diffractive lens. Unlike the standard depiction of Fresnel zones in textbooks in which collimated light enters from the left, light from the cornea is already converging strongly onto the IOL. This is focused by the base power of the IOL onto the fovea which is physically about 19 mm beyond the lens for an average eye. The zone boundaries of the diffractive portion of the lens are located where the optical path distance to the add power increases by 1 wavelength, with the physical distance being multiplied by the refractive index of aqueous to give the optical path distance. The phase delays at the optical steps are separate from the optical path distances. For steps near the center of the lens, the light travels about 3.0 wavelengths on one side of the step and 3.5 wavelengths on the other step, giving a delay of 0.5 wavelenghts. This phase delay is gradually reduced as the step heights get shorter for the more peripheral zones. The control of these features of the wavefront at the anterior optic surface creates the unique optical properties of the ReSTOR apodized diffractive lens. Figure 10 illustrates the diffraction of a plane wave using a small-scale computer simulation of an apodized diffractive lens. The scale of the lens has been reduced so
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Figure 8. Limiting the diameter of the diffractive region reduces the size and energy of halos surrounding a point source at night.
individual wavelengths are visible, and the diffraction and interference of the light can be seen. In the eye itself, many thousands of wavelengths are involved and the effects are difficult to calculate and evaluate. Here the calculation has been done for a very thin flat waveguide using software developed for telecommunications purposes. The size of the wavelength compared with the eye, and the separation between the images, are highly exaggerated. A plane wave enters the eye from the left, and it is focused by the cornea and the IOL, with the distance power of the IOL combined with the cornea in this simple model. The converging wavefront is divided by the diffractive structure into 2 primary components that create the 2 lens powers. The intensities of the wavefronts are adjusted in a nonlinear fashion moving from left to right to keep the
wavefronts visible because the light gets more intense as it moves toward a focus. The image shows the mutual interference between the 2 wavefronts when they are converted to intensity, although in practice, the wavefronts would never be visible because the material in the eye is transparent. The light can be seen to divide into 2 imaging components at the diffractive structure. The add power of the ReSTOR IOL is 4.0 D at the lens, which provides about 3.2 D of add power at the spectacle plane. This add power reduction at the cornea is due to the location of the IOL within the eye, and it is similar to the way the effective power of the base IOL is lower at the cornea.32 The use of this relatively high add power helps ensure that the second defocused image is as faint and unnoticeable as possible.
Figure 9. Scaling the apodized diffractive lens in wavelengths.
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Figure 10. Small-scale planar computer-generated simulation of diffraction at an apodized diffractive structure overlaid with a sketch of an eye.
IMPLEMENTING THE RESTOR INTRAOCULAR LENS
CONCLUSION
The fine diffractive surface structure of the ReSTOR lens is fabricated in the AcrySof (Alcon) foldable acrylic material using manufacturing precision that can control surface features down to 0.2 mm (200 nm) in a cast-molded process, making the IOL a visible example of contemporary nanotechnology. It is inserted through a small incision, which minimizes induced astigmatism to provide highquality uncorrected vision. The diffractive surface is not damaged during folding or compression of the anterior surface or by transient compression by the folded trailing haptic in the injector cartridge. There is consistent centration within the capsular bag, and Figure 11 shows images of lenses with both large and small pupil diameters. Even with a 2.5 mm pupil there are 4 to 5 diffractive zones across the pupil.
The ReSTOR apodized diffractive IOL brings together a variety of optical and physical features to provide vision over a range of object distances. The optical principles of a diffractive lens can be traced back to the early 1800s when the concept of the Fresnel zone was created to understand some of the fundamental properties of light. This work led to zone plates in the late 1800s, which for many years were used primarily as laboratory demonstrations of diffractive lenses. It was not until the final years of the 1900s that sophisticated diffractive lenses became possible with the introduction of computer-controlled high-precision lathes and other advances in the design, fabrication, and testing of diffractive lenses. Unlike Fresnel lenses, or zonal refractive multifocal IOLs, the scaling of the zones of the diffractive ReSTOR lens have to be controlled to
Figure 11. ReSTOR lenses with large and small pupil diameters.
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a fraction of the wavelength of light, and modern technologies make this possible. The ReSTOR apodized diffractive optical design utilizes the successful small-incision IOL lens platform, and it is implanted using standard surgical techniques. In the FDA clinical study, 80% of bilateral ReSTOR patients did not use glasses again and 85% achieved 20/25 and J2 vision uncorrected, while only 25% had some moderate perception of halos at night.33 These published clinical results are consistent with the theoretical lens design. REFERENCES 1. Keates RH, Pearce JL, Schneider RT. Clinical results of the multifocal lens. J Cataract Refract Surg 1987; 13:557–560 2. Lindstrom RL. Food and Drug Administration study update; one-year results from 671 patients with the 3M multifocal intraocular lens. Ophthalmology 1993; 100:91–97 3. Steinert RF, Aker BL, Trentacost DJ, et al. A prospective comparative study of the AMO Array zonal-progressive multifocal silicone intraocular lens and a monofocal intraocular lens. Ophthalmology 1999; 106:1243–1255 4. Knorz MC. Results of a European multicenter study of the True Vista bifocal intraocular lens. J Cataract Refract Surg 1993; 19:626–634 5. Avitabile T, Marano F. Multifocal intra-ocular lenses. Curr Opin Ophthalmol 2001; 12:12–16 6. Gimbel HV, Sanders DR, Raanan MG. Visual and refractive results of multifocal intraocular lenses. Ophthalmology 1991; 98:881–887; discussion by JT Holladay, 888 7. Hunkeler JD, Coffman TM, Paugh J, et al. Characterization of visual phenomena with the Array multifocal intraocular lens. J Cataract Refract Surg 2002; 28:1195–1204 8. Auffarth GU, Hunold W, Breitenbach S, et al. Langzeitergebnisse fu¨r Kontrastsehvermo¨gen und Blendungsempfindlichkeit bei Patienten mit diffraktiven Multifokallinsen. Klin Monatsbl Augenheilkd 1993; 203:336–340 9. Eisenmann D, Jacobi KW. Die ARRAY-multifokallinse – Funktionsprinzip und klinische Ergebnisse. Klin Monatsbl Augenheilkd 1993; 203:189–194 10. Christie B, Nordan L, Chipman R, Gupta A. Optical performance of an aspheric multifocal intraocular lens. J Cataract Refract Surg 1991; 17:583–591 11. Jacobi KW, Eisenmann D. Asymmetrische Mehrzonenlinsend ein neues Konzept multifokaler Intraokularlinsen. Klin Monatsbl Augenheilkd 1993; 202:309–314 12. Holladay JT, van Dijk H, Lang A, et al. Optical performance of multifocal intraocular lenses. J Cataract Refract Surg 1990; 16:413–422; erratum, 781
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13. Hessemer V, Eisenmann D, Jacobi KW. Multifokale Intraokularlinsen – eine Bestandsaufnahme. Klin Monatsbl Augenheilkd 1993; 203:19–33 14. Pearce JL. Multifocal intraocular lenses. Curr Opin Ophthalmol 1996; 7:2–10 15. Knorz MC, Koch DD, Martinez-Franco C, Lorger CV. Effect of pupil size and astigmatism on contrast acuity with monofocal and bifocal intraocular lenses. J Cataract Refract Surg 1994; 20:26–33 16. Simpson MJ. The diffractive multifocal intraocular lens. Eur J Implant Refract Surg 1989; 1:115–121 17. Walkow T, Liekfeld A, Anders N, et al. A prospective evaluation of a diffractive versus a refractive designed multifocal intraocular lens. Ophthalmology 1997; 104:1380–1386 18. Allen ED, Burton RL, Webber SK, et al. Comparison of a diffractive bifocal and a monofocal intraocular lens. J Cataract Refract Surg 1996; 22:446–451 19. Jacobi FK, Kammann J, Jacobi KW, et al. Bilateral implantation of asymmetrical diffractive multifocal intraocular lenses. Arch Ophthalmol 1999; 117:17–23 20. Bleckmann H, Schmidt O, Sunde T, Kaluzny J. Visual results of progressive multifocal posterior chamber intraocular lens implantation. J Cataract Refract Surg 1996; 22:1102–1107 21. Knorz MC, Claessens D, Seiberth V, et al. Kontrastsehscha¨rfe und Defokussierkurve mit verschiedenen Bifokal-IOLs. Ophthalmologe 1993; 90:352–359 22. Anicin BA, Babovic VM, Davidovic DM. Fresnel lenses. Am J Phys 1989; 57:312–316 23. Born M, Wolf E. Principles of Optics; Electromagnetic Theory of Propagation, Interference, and Diffraction of Light, 5th ed. New York, NY, Pergamon Press, 1975 24. Hecht E, Zajac A. Optics. Reading, MA, Addison-Wesley, 1974 25. Soret JL. Ueber die durch kreisgitter erzeugten Diffractionspha¨nomene. Ann Phys Chem 1875; 156:99 26. Wood RW. Phase-reversal zone-plates, and diffraction-telescopes. Phil Mag 1898; 45:511–522 27. Miyamoto K. The phase Fresnel lens. J Opt Soc Am 1961; 51:17–20 28. Buralli DA, Morris GM, Rogers JR. Optical performance of holographic kinoforms. Appl Opt 1989; 28:976–983 29. Sales TRM, Morris GM. Diffractive refractive behavior of kinoform lenses. App Optics 1997; 36:253–257 30. Welford WT. A vector raytracing equation for hologram lenses of arbitrary shape. Opt Commun 1975; 14:322–323 31. Wetherell WB. The calculation of image quality. In: Kingslake R, ed, Applied Optics and Optical Engineering. New York, NY, Academic Press, 1980; 171–315 32. Retzlaff J, Sanders DR, Kraff MC. Lens Implant Power Calculation; A Manual for Ophthalmologists and Biometrists, 3rd ed. Thorofare, NJ, Slack, 1990 33. Kohnen T, Allen D, Boureau C, et al. European multicenter study of the AcrySof ReSTOR apodized diffractive intraocular lens. Ophthalmology 2006; 113:584
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History and development of the apodized diffractive intraocular lens James A. Davison, MD, Michael J. Simpson, PhD
The ReSTOR intraocular lens presents a unique apodized diffractive design within a refractive foldable acrylic optic, which makes an unprecedented level of mulifocal optical performance available. We describe the history and principles of diffractive optics used in the development of this refractive–diffractive IOL. J Cataract Refract Surg 2006; 32:849–858 Q 2006 ASCRS and ESCRS
Human prosthetic lens replacements use simple and complex optical physics. One of the more complex ophthalmic lenses is the ReSTOR apodized diffractive intraocular lens (IOL) (Alcon Surgical). It is implanted in the eye to replace the natural crystalline lens to provide vision over a range of object distances through the provision of 2 primary lens powers. It combines various optical concepts into a unique design, and the optical properties of the lens are described here along with some historical background. Accommodation, in which the natural crystalline lens changes power by changing shape so that one can focus on distant and near objects, is an important property of the younger eye. Accommodation is gradually lost as a person ages, however, which typically becomes a problem for people in their mid- to late 40s. People find they can no longer focus on near objects, which is why the Franklin bifocal was adopted in the 18th century. Accommodation is also lost when the natural crystalline lens of the eye is removed during cataract surgery and is replaced with a monofocal IOL. Patients have had to choose whether they want to have their distance vision corrected by the IOL and wear reading glasses to see up close or to select Accepted for publication November 10, 2005. From the Wolfe Eye Clinic (Davison), Marshalltown and West Des Moines, Iowa, and the University of Utah, Salt Lake City, Utah, and Alcon Surgical (Simpson), Fort Worth, Texas, USA. Dr. Simpson is an employee of Alcon. Dr. Davison is a consultant for Alcon Surgical. Reprint requests to James A. Davison, MD, Wolfe Eye Clinic, 309 East Church Street, Marshalltown, Iowa 50158, USA. E-mail: [email protected]. Q 2006 ASCRS and ESCRS Published by Elsevier Inc.
a power that would permit them to be near-sighted through the IOL and wear a distance correction in their spectacles. A few patients also choose a monovision strategy in which 1 eye is implanted with an IOL for distance vision and the other with an IOL power that can provide some near vision without spectacle correction. To provide the ability to see at different distances again, multifocal IOLs with 2 primary focal points can be used. One power is used for distance vision, and the other power is used for near vision. The image from the second lens power is highly defocused and very faint, and it has been confirmed clinically, with several different designs, that the patient primarily perceives only the focused image.1–6 However, some patients may experience unwanted visual images such as glare, flare, streaks, and halos.7,8 Intermediate vision is provided by contributions from the defocus characteristics of both primary lens powers, with some lens designs attempting to direct additional light to an intermediate focus location (Figure 1).9 Three general optical principles have been used in multifocal IOLs: multizone refractive, diffractive, and aspheric lens designs. The multizonal refractive method is defined by 2 different powers that are incorporated into circular or annular (ring-shaped) refractive zones. Some early IOLs had 2 zones (Iolab NuVue1), 3 zones (Storz Tru Vista,4 Alcon AcuraSee, Ioptex,10 Morcher,11 Pharmacia12), 5 zones (AMO Array3), and 7 zones (Adatomed13). An example is the lens manufactured by Pharmacia that was implanted in 1989 (Figure 2). The 5-zone foldable silicone Array IOL (AMO), which was approved by the U.S. Food and Drug Administration (FDA) in 1997, is the most common contemporary example of this category. 0886-3350/06/$-see front matter doi:10.1016/j.jcrs.2006.02.006
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Figure 1. Multifocal IOLs provide 2 primary focal points; 1 for distance vision and the other for near vision. Each contributes to an intermediate vision function.
Multizone refractive IOLs differ from bifocal spectacle lenses because the IOL becomes an integral part of the eye, and the multiple zones are present across the pupil simultaneously at all times.1,14,15 Each lens zone has a different effective aperture, and this can affect the quality of the image that it provides because the pupil diameter changes in response to different illumination levels as well as with the accommodative reflex. The energy balance between the 2 images and the quality of the images vary with engineering design and environmental conditions. The second method to create a lens with 2 powers has been to use a diffractive surface on a refractive platform.2,16,17 These designs divide light between 2 images through the use of different diffractive orders, with an equal amount of light directed to the near and distant primary foci for all pupil diameters when the diffractive structure covers the whole lens surface. This design was introduced by 3M in 1988.2 The original IOL, which was typical of the time, featured a 3-piece, 6.0 mm diameter nonfoldable poly(methyl methacrylate) optic and with closed-loop haptics. Diffractive lens designs have also been used by
Figure 2. An early zonal multifocal lens from Pharmacia (1989).
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Pharmacia and Adatomed.18,19 The perception of halos and glare at night were a frequent clinical observation with these IOLs. The diffractive zones were very small, and light from all the zones went to both lens powers equally. Unlike the multizonal refractive optic, with these IOLs, the image quality and energy balance between the images were no longer dependent on pupil diameter. These were full-optic diffractive-refractive lenses that featured a diffractive surface across the entire anterior surface. A necessary artifact of any refractive–diffractive optical system including these is that a portion of the light energy about 18% is also directed into higher diffraction orders. This leaves about 82% of the light available to be divided between each of the 2 primary lens powers. The ReSTOR apodized refractive–diffractive design expands on these earlier diffractive lens designs. A third design method has been the use of aspheric optic regions that increase the depth of field of the lens. The addition of asphericity in this application does not provide an additional distinct focus but aims to expand the range of focus. However, this occurs at the expense of image contrast. Lenses that primarily used asphericity were the Progress lens from Domilens20 and the Nordan aspheric.21 Some zonal lenses also use a level of asphericity, such as the Ioptex 3-zone lens,10 with distinct aspheric regions between the zones. This article describes the optical principles and the history of both multizonal lenses and diffractive lenses and uses this background to describe the development of the ReSTOR apodized diffractive lens. During this development, a primary guiding principle was that near vision is less important in conditions of dim illumination when pupils are large. A second was that minimization of the perception of halos and glare in dim illumination was essential. A critically important coincidence of optical science is that these 2 characteristics are, in fact, complementary, and this allowed the use of a unique optical feature, apodization, in which the energy balance of the optical
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Figure 3. A: A large lighthouse lens. B: The underlying concept of a Fresnel lens: The original bulk of the dashed lens is reduced, leaving a thin lens whose surface slopes match the original lens. This example has equal step heights. C: A Fresnel lens with equal zone widths. A Fresnel lens is always a monofocal lens.
system varies with pupil diameter in a manner that is consistent with natural pupil responses to distance and near vision requirements under various lighting conditions and is compatible with the pupil accommodative reflex. FRESNEL LENSES
Zonal lenses can be traced back to the work of Augustin Fresnel, who improved lighthouse optics in the 1820s by segmenting large lenses to reduce their overall weight (Figure 3, A).22 Fresnel’s lighthouse design represented the first widespread use of a lens of this type, and Figure 3, B, illustrates the geometrical properties of what has come to be called a Fresnel lens. A large portion of the bulk of the lens is removed, but the general focusing properties are retained. There are no specific limitations on where zone boundaries need to be placed in a Fresnel lens, so boundary locations can vary with each application. One choice is to make the step heights constant, which requires that the zone widths will vary (Figure 3, B). Another choice is to give the zones a constant width, which requires that the step heights will vary (Figure 3, C). Both geometric and diffractive optical effects reduce potential image quality, although imaging is not important for the lighthouse application. In modern ophthalmology, temporary Fresnel prisms or lenses are sometimes attached to spectacle lenses and these typically use zone widths of at least 1.0 mm to minimize diffractive side effects. FRESNEL ZONES AND THE FRESNEL ZONE PLATE
Before creating the lighthouse lens, Fresnel had contributed to the concept of diffraction at a time when there were questions about whether light consisted of particles or waves and whether an ether existed to convey light from place to place.23 Huygen’s construction, in which each point on
a wavefront was taken to be the source of a new wavelet, was already well known at the time.23 The wavelets were drawn as circles centered on the original wavefront, and the propagating wavefront was determined by drawing a new smooth line that just grazed all the wavelets. Fresnel’s conceptual innovation in 1818 was to incorporate the ideas of amplitude, phase, and interference into the wavelet model of light propagation. This provided the potential for phase manipulations to have a significant effect on final wavefront characteristics. He described what came to be called Fresnel zones in 1818, and these are illustrated in (Figure 4, A), where a plane wavefront of light is seen moving from left to right. Working back from a distant point, the plane wavefront can be divided into zones by placing a zone boundary wherever the optical path increases by half a wavelength. If there is no diffracting obstacle, the light continues to propagate as a plane wave, but the theory indicates that if the central zone is obscured by an opaque object, a bright spot should appear in the shadow. This was found experimentally and called Arago’s spot24 and helped confirm the significance of Fresnel zones. Fresnel’s recognition of the importance of wavelength increments of the optical path distance between 2 points is the fundamental basis for a diffractive lens, but the first focusing structure, the diffractive zone plate, was not described until 50 years later in the 1870s. At that time, Lord Rayleigh observed that alternate half-period zones could be blocked to remove contributions from the second half of the wavelength cycle at the focus, and this led to the Fresnel zone plate structure depicted in (Figure 4, B).24,25 Light passing through 1 zone comes from the first half of a sinusoidal light wave, and light passing through the next zone comes from the second half. The circle that is centered on the image point describes a radius of constant phase, which is like a converging wavefront, and the
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Figure 4. A: Sketch of Fresnel zone construction. A plane wavefront moving from left to right is divided into zones using circles centered on a distant point P with radius increments of 1/2 wavelength. These divide the wavefront into Fresnel zones. B: Fresnel zone plate that obscures alternate half-period zones.
contributions of half the wavelength cycle are removed by making alternate zones opaque. This intensifies the light at the focal location because constructive interference at the image point is created, and components that would create destructive interference are eliminated. These focusing properties were confirmed experimentally since a Fresnel zone plate could be made photographically even in the 19th century. But the zone plate is not an efficient optical system because it only directs 10% of the light to the point of focus. Ten percent of the light is directed into a similar negative lens power, 50% of the light is absorbed by the opaque regions because the transmitting zones and blocking zones have equal areas, with 25% undiffracted, and 5% to higher lens powers. Lord Rayleigh provided further insight into diffractive lenses by considering what would happen if the phase of the light could be delayed in alternate zones by a half wavelength, rather than absorbing it using opaque zones. In Figure 4, this would be equivalent to shifting the sinusoidal waves that fall on the opaque zones by a half wavelength. The negative portion of the amplitude of the wave would be shifted into a positive portion that more closely matched the adjacent zone. This concept was evaluated experimentally by Wood26 by bleaching a photographic zone plate in 1898, and it was found to yield more light at the point of focus. This Wood zone plate, or phase-reversal zone plate, can direct about 40% of the light into each of 2 lens powers, with the remaining light wasted in higher diffractive orders. This is a predecessor to the modern multifocal diffractive lens. Since there are no opaque zones, no light is absorbed. MONOFOCAL DIFFRACTIVE LENSES COMPARED WITH FRESNEL LENSES
A monofocal diffractive lens can actually be thought of as a Fresnel lens with very special characteristics. For a lens in the first diffractive order, the zone boundaries have to be
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at the same locations as Fresnel zones that are created for full wavelength distances (rather than the half wavelength zones of the Fresnel zone plate), and the phase delay at the steps has to be 1 wavelength. This would not usually be the case for a refractive Fresnel lens, but a lens with such a controlled phase was described by Miyamoto27 in 1961, nearly 150 years after Fresnel’s original work, This type of lens has found increasing use in recent years, sometimes being named a kinoform.28,29 Because phase control between different zones is very challenging, the modern monofocal diffractive lens only became feasible with the development of high-precision lathes. At first glance, Fresnel lenses and monofocal diffractive lenses appear to be similar but they are actually very different. With the zonal Fresnel lens, each zone is considered to act separately to refract light. Adjacent zones usually have an arbitrary phase jump, and there is incidental and unwanted diffraction at the boundaries of the zone. With the diffractive lens, all the zones work together. The zone boundaries are strictly located where the optical path increases by 1 wavelength, and the phase jump at the zone boundary is strictly controlled. The control over the zone boundary locations and the phase delay at the steps permit a diffractive lens to provide high-quality imaging. It is interesting that 200 years ago, Fresnel did work that led to both refractive and diffractive zonal lenses. The very size of a lighthouse lens tells us that diffractive effects are not important for a Fresnel lens. Conversely, the control of Fresnel zones and phase delays to small fractions of a wavelength emphasize the features that are very important for modern diffractive lenses. FULL-OPTIC MULTIFOCAL DIFFRACTIVE INTRAOCULAR LENSES
Multifocal diffractive lenses have an important difference from their monofocal counterparts. Figure 5 shows
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Figure 5. Schematic drawings of full-optic multifocal diffractive lens in which there are w30 zones across a 6.0 mm lens diameter. A: Plan view. B: Magnified surface profile.
schematic drawings of a full-optic multifocal diffractive IOL in which there are about 30 diffractive zones across the lens surface. The zone boundary (or step) locations have a similar general appearance to those of the Fresnel zone plate because they are determined by full-wavelength Fresnel zone criterion. The defining difference between a monofocal diffractive lens and a multifocal (or bifocal) diffractive lens is the phase delay at the step. For a monofocal lens, the delay is usually 1 wavelength, and for the multifocal lens, it is typically a half wavelength. The zones between steps in a diffractive lens do not refract light so multifocal diffractive lenses cannot be described using a refractive description. If rays were conceptually traced through the zones using the assumption that they were refractive, they would focus halfway between the 2 primary lens powers. In reality, none of the light is concentrated at that location but is directed into the 2 primary lens powers instead. The use of ray tracing makes the refraction of light rays at a conventional lens surface seem obvious, but depictions of the properties of diffractive lenses are far less intuitive. However, if ray tracing is modified by appropriate calculations, it can be used to help explain diffractive lenses. Thirty years ago, Welford30 described a diffractive lens as a diffraction grating over a very small region. It was found that even though calculations for diffraction gratings assume that the gratings are very large, in practice, the redirection of a single ray can be calculated using a very localized grating spacing. This concept is beneficial for evaluating the general properties of a diffractive lens, and this capability has been a longtime standard in commercial ray-trace software. Figure 6 depicts diffractive ray tracing in comparison to the 2 other better-known methods of using lenses and mirrors. These are not rays refracted on the scale of the fine detail of the diffractive surface, but they represent the global effect of the local grating spacing. Modern raytracing programs allow the user to specify a diffractive surface in this manner, and the ray directions are calculated using diffraction grating equations. Other concepts can also be useful when thinking about diffraction. When light encounters an edge or discontinuity, it slows down and its direction changes slightly. This
is the effect of diffraction. Light can also be thought of as particles, rather than using the ray or wave pictures of light, where particles (ie, photons) constitute the wavefront of light energy. The light particle concept provides a more intuitive explanation of the simultaneous redirection of light energy to 2 separate foci, since adjacent particles can go in 2 different directions. Using the analogy of air handling louvers and diffusers, a moving stream of air molecules can be redirected into different directions. Common examples are the air vents found in automobile dashboards, which direct air to 1 location or another by changing the attitude of the air-control louvers, although other air diffusers can direct air into multiple directions. The redirection of air particles is similar to changing the direction of a stream of photons that encounters a set of diffractive discontinuities. The image quality of the full-optic multifocal diffractive IOL is generally higher than that of a multizonal refractive lens because light from all points in the aperture is directed to both foci. The diffraction that occurs at all the various steps creates the diffractive foci. The optical properties are relatively constant as the pupil diameter varies with approximately 41% of the light going to each focus
Figure 6. There are 3 methods to redirect light in a controlled manner: (a) Refraction: The refractive index difference between the 2 materials determines the angle. (b) Reflection: The reflected angle equals the incidence angle. (c) Diffraction: The grating period determines the diffracted angles, and the grating phase structure determines how much light goes into each diffraction order.
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at the design wavelength, with the additional 18% of light being wasted as it is directed into higher diffractive orders. For example, for an add power of 4 diopters (D), the higher diffraction orders represent add powers such as 8 D and 12 D and also ÿ4 D and ÿ8 D. These higher orders are focus locations where the optical path differences increase by integral numbers of wavelengths (2, 3, 4, etc.), and they are a consequence of the overall interaction of the light with the diffractive steps. The total of 82% transmission, 41% to each focal point in the example of a full-optic bifocal diffractive IOL, is the most efficient energy utilization that is possible for any diffractive optical system. It is not possible to direct 50% of the light to each of 2 foci. RESTOR APODIZED DIFFRACTIVE INTRAOCULAR LENS
The ReSTOR lens also has a diffractive design component, but it uses a new diffractive–refractive design concept to provide improved control energy distribution. The lens has 2 primary focal points, 1 at distance and the other at near. The near point is equivalent to approximately a 3.2 D add power in the spectacle plane. The base lens provides the distance power using its refractive shape and there are 12 diffractive discontinuities, or steps, that have been incorporated in the anterior surface of the cast-molded acrylic optic to provide the diffractive add power (Figure 7). These discontinuities cover the central 3.6 mm diameter of the IOL while the optic peripheral to the 3.6 mm diameter out to the 6.0 mm edge is comprised of a refractive surface dedicated to distance vision. Apodization has been used in the field of optics for many years,31 although it has not been used with diffractive lenses. Apodization was originally used to describe the optical effect created by variably absorbing filters. The filter would typically be transparent in the center of a circular
lens and would get gradually darker toward the lens periphery. With respect to a circular lens surface, apodization describes a change in a property of the lens or its function from center to periphery in a radial fashion. Contemporary use of the term describes filters that are used in an optical system to improve image quality (eg, filters that are placed at the back focus of a microscope objective to improve image quality are called apodizing filters, as are the slitlike opaque filters used in astronomy. The term apodization uses Greek words for ‘‘cutting off the feet’’. This describes the change in appearance of a plot of the intensity across a point image for conventional apodization, where the energy in the rings surrounding the central spot is reduced. The apodization property of the ReSTOR lens is radially symmetrical. It is defined by the gradual reduction in diffractive step heights from center to periphery, which results in an energy proportion continuum for light directed to the 2 primary foci. If the diffractive step heights were 1 wavelength high, the lens would behave in monofocal fashion and all the light would go to a single focus in the C1 diffraction order. If the steps were negligibly small, all the light would go to a lower-power monofocal lens focus at the 0 diffraction order. But when the steps are a half wavelength high, about 41% of the light goes into each of 2 foci. For other step-height values, the energy is divided between the 2 primary images in accordance with the step-height value. This optical effect can be modeled in a similar manner to the way that ray tracing can be used for diffractive lenses, as long as the grating spacing changes relatively slowly. The local grating spacing determines ray direction, and the local step height determines the diffraction efficiency of the light in each order. For the ReSTOR apodized diffractive–refractive IOL, the physical diffractive step heights reduce in height in an
Figure 7. Expanded cross-section of the ReSTOR apodized IOL. The heights of the diffractive steps have been magnified 400 times more than the lens diameter to make them visible on this drawing.
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almost continuously varying manner from 1.3 mm high centrally to 0.2 mm high peripherally (Figure 7). There are 12 zones, with the central outer zones having diameters of 0.75 mm and 3.6 mm, respectively. The central step heights create an approximate 0.5 wavelength of phase delay for light in aqueous. This divides the light energy fairly equally between the 2 lens powers, distance and near, for smaller pupils, with about 41% of the light going to each power. As the pupil aperture becomes larger, the increasingly exposed progressively decreasing step heights apportion more and more light to the distance power while less and less light is recruited for the near focal point. The cumulative energy balance as a function of pupil diameter is plotted in Figure 7. This happens because the step heights gradually reduce over the 12 steps, with the most peripheral shortest step being 0.2 mm high. This gradient in step heights results in a gradual change in energy balance. The outer region of the lens has no diffractive structure, so all the light goes to the distance power. This results in a distance-dominant lens for large pupils. It also means that more of the total light energy is used by the 2 primary images because none of the energy focused by the peripheral refractive portion is lost to higher diffractive orders. The apodized ReSTOR lens has some properties that are common to a full-optic multifocal diffractive lens, and some characteristics that are different. For both lenses, the radial location of the zone boundaries determines the add power. However, the step heights are the same for the full-optic multifocal diffractive lens while the ReSTOR lens has step heights that decrease with increasing distance from the lens center; ie, it is apodized, which gradually changes the proportion of energy directed to the 2 images as the pupil diameter changes. Apodization provides 2 necessary and complementary improvements to the older design of the 3M diffractive IOL: improved vision properties and reduced unwanted optical phenomena. Human beings normally function in a naturally or artificially lit photopic world, and our pupils are usually relatively small most of the time. For near tasks such as reading, we generally use bright light, which makes our pupils smaller. For near visual tasks, our accommodative reflex makes our pupils smaller too. Under these conditions, the earlier 3M diffractive IOL and the new ReSTOR IOL provide abundant light energy for distance and near vision. When we perform ambulatory distance-dominant activities in dimmer mesopic illumination, such as driving at night, the ReSTOR IOL provides relatively more available light energy for distance vision. The energy balance adjustment favoring distance vision that occurs when the pupil enlarges under dim mesopic situations resembles our normal physiology, because we normally do not attempt to accomplish complex reading or near tasks in dim illumination. Apodization also improves the quality of
vision under dim illumination by reducing unwanted secondary images, such as halos and glare, which had been frequently observed with the original 3M lens before apodization technology was available. Without apodization, there existed an equal contribution to distance and near across the entire optical surface for any pupil size. This resulted in energy being wasted under large-pupil mesopic conditions because half of it was unfortunately dedicated to near vision when it would have been more appropriate to strengthen distance vision under these conditions. Also, the low power of the add in the optic plane (3.5 D and some lenses with 2.5 D) of the 3M IOL led to smaller distance and near focal-point separation at the retina, which resulted in more perceived unwanted light images at night. A reduction in these perceptions is 1 of the reasons that the ReSTOR IOL features a 4.0 D add in the plane of the optic (3.2 D in the spectacle plane). The defocused image of a light at night from the second power of any multifocal IOL may sometimes be visible as a halo because it is on a dark background; to minimize this possibility, the diffractive structure of the ReSTOR lens only covers the central region (Figure 8). For larger pupils, more energy is directed to the distance focus and the outer region of the lens solely provides distance vision. The limited diffractive region limits the size and energy of defocused light under large-pupil conditions. Apodization also ensures that the redirection of light between the 2 images is gradual. This gradual change is very important optically because it avoids sudden optical boundaries, which can create unwanted diffractive effects. Figure 9 depicts the physical dimensions of the ReSTOR apodized diffractive lens. Unlike the standard depiction of Fresnel zones in textbooks in which collimated light enters from the left, light from the cornea is already converging strongly onto the IOL. This is focused by the base power of the IOL onto the fovea which is physically about 19 mm beyond the lens for an average eye. The zone boundaries of the diffractive portion of the lens are located where the optical path distance to the add power increases by 1 wavelength, with the physical distance being multiplied by the refractive index of aqueous to give the optical path distance. The phase delays at the optical steps are separate from the optical path distances. For steps near the center of the lens, the light travels about 3.0 wavelengths on one side of the step and 3.5 wavelengths on the other step, giving a delay of 0.5 wavelenghts. This phase delay is gradually reduced as the step heights get shorter for the more peripheral zones. The control of these features of the wavefront at the anterior optic surface creates the unique optical properties of the ReSTOR apodized diffractive lens. Figure 10 illustrates the diffraction of a plane wave using a small-scale computer simulation of an apodized diffractive lens. The scale of the lens has been reduced so
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Figure 8. Limiting the diameter of the diffractive region reduces the size and energy of halos surrounding a point source at night.
individual wavelengths are visible, and the diffraction and interference of the light can be seen. In the eye itself, many thousands of wavelengths are involved and the effects are difficult to calculate and evaluate. Here the calculation has been done for a very thin flat waveguide using software developed for telecommunications purposes. The size of the wavelength compared with the eye, and the separation between the images, are highly exaggerated. A plane wave enters the eye from the left, and it is focused by the cornea and the IOL, with the distance power of the IOL combined with the cornea in this simple model. The converging wavefront is divided by the diffractive structure into 2 primary components that create the 2 lens powers. The intensities of the wavefronts are adjusted in a nonlinear fashion moving from left to right to keep the
wavefronts visible because the light gets more intense as it moves toward a focus. The image shows the mutual interference between the 2 wavefronts when they are converted to intensity, although in practice, the wavefronts would never be visible because the material in the eye is transparent. The light can be seen to divide into 2 imaging components at the diffractive structure. The add power of the ReSTOR IOL is 4.0 D at the lens, which provides about 3.2 D of add power at the spectacle plane. This add power reduction at the cornea is due to the location of the IOL within the eye, and it is similar to the way the effective power of the base IOL is lower at the cornea.32 The use of this relatively high add power helps ensure that the second defocused image is as faint and unnoticeable as possible.
Figure 9. Scaling the apodized diffractive lens in wavelengths.
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Figure 10. Small-scale planar computer-generated simulation of diffraction at an apodized diffractive structure overlaid with a sketch of an eye.
IMPLEMENTING THE RESTOR INTRAOCULAR LENS
CONCLUSION
The fine diffractive surface structure of the ReSTOR lens is fabricated in the AcrySof (Alcon) foldable acrylic material using manufacturing precision that can control surface features down to 0.2 mm (200 nm) in a cast-molded process, making the IOL a visible example of contemporary nanotechnology. It is inserted through a small incision, which minimizes induced astigmatism to provide highquality uncorrected vision. The diffractive surface is not damaged during folding or compression of the anterior surface or by transient compression by the folded trailing haptic in the injector cartridge. There is consistent centration within the capsular bag, and Figure 11 shows images of lenses with both large and small pupil diameters. Even with a 2.5 mm pupil there are 4 to 5 diffractive zones across the pupil.
The ReSTOR apodized diffractive IOL brings together a variety of optical and physical features to provide vision over a range of object distances. The optical principles of a diffractive lens can be traced back to the early 1800s when the concept of the Fresnel zone was created to understand some of the fundamental properties of light. This work led to zone plates in the late 1800s, which for many years were used primarily as laboratory demonstrations of diffractive lenses. It was not until the final years of the 1900s that sophisticated diffractive lenses became possible with the introduction of computer-controlled high-precision lathes and other advances in the design, fabrication, and testing of diffractive lenses. Unlike Fresnel lenses, or zonal refractive multifocal IOLs, the scaling of the zones of the diffractive ReSTOR lens have to be controlled to
Figure 11. ReSTOR lenses with large and small pupil diameters.
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a fraction of the wavelength of light, and modern technologies make this possible. The ReSTOR apodized diffractive optical design utilizes the successful small-incision IOL lens platform, and it is implanted using standard surgical techniques. In the FDA clinical study, 80% of bilateral ReSTOR patients did not use glasses again and 85% achieved 20/25 and J2 vision uncorrected, while only 25% had some moderate perception of halos at night.33 These published clinical results are consistent with the theoretical lens design. REFERENCES 1. Keates RH, Pearce JL, Schneider RT. Clinical results of the multifocal lens. J Cataract Refract Surg 1987; 13:557–560 2. Lindstrom RL. Food and Drug Administration study update; one-year results from 671 patients with the 3M multifocal intraocular lens. Ophthalmology 1993; 100:91–97 3. Steinert RF, Aker BL, Trentacost DJ, et al. A prospective comparative study of the AMO Array zonal-progressive multifocal silicone intraocular lens and a monofocal intraocular lens. Ophthalmology 1999; 106:1243–1255 4. Knorz MC. Results of a European multicenter study of the True Vista bifocal intraocular lens. J Cataract Refract Surg 1993; 19:626–634 5. Avitabile T, Marano F. Multifocal intra-ocular lenses. Curr Opin Ophthalmol 2001; 12:12–16 6. Gimbel HV, Sanders DR, Raanan MG. Visual and refractive results of multifocal intraocular lenses. Ophthalmology 1991; 98:881–887; discussion by JT Holladay, 888 7. Hunkeler JD, Coffman TM, Paugh J, et al. Characterization of visual phenomena with the Array multifocal intraocular lens. J Cataract Refract Surg 2002; 28:1195–1204 8. Auffarth GU, Hunold W, Breitenbach S, et al. Langzeitergebnisse fu¨r Kontrastsehvermo¨gen und Blendungsempfindlichkeit bei Patienten mit diffraktiven Multifokallinsen. Klin Monatsbl Augenheilkd 1993; 203:336–340 9. Eisenmann D, Jacobi KW. Die ARRAY-multifokallinse – Funktionsprinzip und klinische Ergebnisse. Klin Monatsbl Augenheilkd 1993; 203:189–194 10. Christie B, Nordan L, Chipman R, Gupta A. Optical performance of an aspheric multifocal intraocular lens. J Cataract Refract Surg 1991; 17:583–591 11. Jacobi KW, Eisenmann D. Asymmetrische Mehrzonenlinsend ein neues Konzept multifokaler Intraokularlinsen. Klin Monatsbl Augenheilkd 1993; 202:309–314 12. Holladay JT, van Dijk H, Lang A, et al. Optical performance of multifocal intraocular lenses. J Cataract Refract Surg 1990; 16:413–422; erratum, 781
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