Cover photo. Visualization of the array of liquid crystal cells in an adaptive optics device programmed to function as a +1 diopter spherical lens.
Optometric practitioners routinely measure and correct just three types of optical imperfections of eyes: defocus, astigmatism, and prismatic deviation. Not surprisingly, the biological optical system of the eye has numerous other refractive aberrations such as coma, spherical aberration, and oblique astigmatism, plus many other irregular anomalies peculiar to each individual eye. Although many of these "higher-order" refractive aberrations have been measured in research laboratories using a variety of psychophysical1-3 and objective4,5 techniques, they have been largely ignored by the optometric profession for two main reasons. First, these diagnostic methods used in the laboratory are too demanding for routine clinical practice and, second, suitable ophthalmic lenses for correcting these higher-order aberrations have been unavailable. However, recent advances in visual optics research have shown a way to overcome both of these limitations to current optometric practice. These advances pave the way for an expanded scope of practice in optometry's traditional domain of strength in visual optics and ophthalmic corrective lenses.
The most promising of the new methodologies for characterizing eyes obtains a detailed measurement of a hundred or more refractive aberrations in addition to the three fundamental aberrations of defocus, astigmatism, and prismatic deviation. All this information may be obtained in the fraction of a second required to take a single flash photograph of reflected light from a laser beam focused on the retina. This dramatic increase in the scope of ophthalmic evaluation of eyes is achieved using a new type of objective aberrometer based on the Shack-Hartmann principle of optical metrology. Developed extensively by astronomers for measuring the optical aberrations of the atmosphere which interfere with terrestrial telescopes, the Shack-Hartmann technique was adapted recently for measuring aberrations of eyes by Liang et al.5 Since then the technique has undergone further refinement and evaluation at research laboratories at the University of Rochester,6,7 the University of Waterloo, and in our laboratories at Indiana University.8 In the near future we expect to see these research efforts yield new clinical instruments that will allow fast, patient-friendly, detailed measurement of the refractive anomalies of human eyes on a routine clinical basis.
Given these exciting prospects for routine comprehensive measurement of refractive errors of eyes, our attention shifts to the question of aberration correction. Fortunately, there are several new technologies, collectively known as "adaptive optics", which have the potential to correct even the highly irregular, idiosyncratic aberrations of human eyes. One of these technologies uses a deformable mirror placed in the optical path from eye to object. This is the same technology used in astronomy to correct atmospheric aberrations. Although deformable mirrors are currently too expensive and bulky to be considered for clinical use, they have been used successfully in the research laboratory to demonstrate the feasibility of correcting the higher-order aberrations of eyes. Previously, one of us (Miller) had shown that the eye's optical aberrations are the primary limiting factor which prevents high-resolution diagnostic imaging of the human fundus.9 This conclusion was demonstrated dramatically when, for the first time, individual human photoreceptors in living human eyes were photographed with a specially designed, high-resolution fundus camera. Those initial results were obtained from eyes with unusually small optical aberrations but subsequently the fundus camera has been augmented with adaptive optics, making it possible to achieve high-resolution images also in eyes with more typical levels of aberrations.6 Furthermore, when the fundus camera was replaced by a visual test pattern so that the patient was given the opportunity to experience vision through an eye corrected by the adaptive optical system, dramatic improvements in visual contrast sensitivity were obtained.7 As a result of this aberration correction by adaptive optics, the observer achieved super-normal visual performance that approached the ultimate limit expected of an optical system limited only by diffraction.
Although deformable mirrors and other reflective technologies (such as micro-mirrors and reflective liquid crystals of the kind used in digital watches and laptop computer screens) may have a bright future in the creation of a new generation of ophthalmic instruments, they seem unlikely to develop into the spectacles of the next century. However, at least one new technology does have the potential for providing an entirely new kind of optical element for 21st century spectacles. This technology uses transparent liquid-crystals deposited on a glass substrate to produce an optical medium with variable refractive-index.10 At Indiana University we have been exploring the potential of this technology for producing a new kind of "electronic spectacle" based on a programmable optical element that can dynamically alter its characteristics as required by the patient (e.g. to obtain a "variable-add" for presbyopic individuals). Furthermore, when the crystals are subdivided into an array of cells that can be individually addressed by an integrated circuit controller, it becomes possible to conceive of an advanced spectacle lens which will correct not only the traditional parameters of sphere, cylinder, and prism, but also the higher order, irregular aberrations peculiar to any individual eye. Thus the electronic spectacles of the future may provide a customized correction of the refractive anomalies of the patient's eye. If successful, the result will serve optometry in two major ways. First, when used in a clinical environment, it will provide the clinician with a high-resolution diagnostic view of the internal structures of the patient's eye. Second, when used by the patient for daily wear, it will provide an exceptionally high contrast view of the world implicit in the term "super-normal vision".
The principle of operation of a lens fabricated from an array of liquid crystals is contrasted with a conventional lens in Fig. 1. A conventional lens is an optical medium of variable thickness formed from a transparent material of constant refractive index. This variable-thickness feature of conventional lenses causes planar wavefronts of light from a distant object point to be re-shaped into spherical wavefronts so that they will focus onto a point image. To understand how this re-shaping of the wavefront happens, we must first recall that a wavefront of light is defined as the locus of points which are equidistant from the source, where distance is measured in terms of wavelengths of light. Since the wavelength of light shortens when the light enters a medium with a higher refractive index, we need to measure optical distances with a ruler that takes refractive index into account. For this reason the concept of an "optical path length" is defined as the product of physical distance and refractive index. For example, a physical distance of 1 meter in air (n=1.0) has the same optical path length as 2/3 meter in a medium with refractive index n=3/2 because in both cases light must oscillate the same number of times to traverse the distance.
Figure 1. Wavefront shaping with conventional lenses (top), gradient-index lenses (middle), and liquid-crystal lenses (bottom).
To see how a wavefront changes shape as it propagates through a conventional lens, we trace a ray from each point on a given wavefront and follow it for a fixed optical path distance. The terminal ends of these rays locate the wavefront at some later point in time. For example, to see how a planar wavefront that is tangent to the lens at its vertex emerges from the lens, we trace all rays that have an optical path length equal to nd, where n is the refractive index of the material and d is the thickness of the lens at the vertex. For an off-axis ray, the path has three segments as shown in Fig. 1. Segments a and c are in air, while segment b is in the medium of the lens. Thus the optical path length for these rays is nd=a+nb+c. Clearly the physical distance a+b+c must be larger than the physical distance d because the refractive index n is greater than 1 for the lens. Furthermore this inequality grows larger as the ray gets further from the optical axis of the lens, hence the emerging wavefront must be curved. Further analysis would be required to verify that the curved wavefront has a spherical shape, but the main point of our argument is that a lens is able to focus light by using its shape to create a medium of variable optical path length.
An intermediate step to lenses fabricated from liquid crystals is shown in the middle diagram of Fig. 1. Contrary to the lens example just described, this optical element has constant thickness but has a refractive index which varies systematically with distance from the optical axis. Computing optical path length in this case is a little more complicated because a ray will follow a curved path as it propagates through the gradient-index material.11 Nevertheless, the concept of an optical path length still applies and is computed by integrating the product of refractive index and the infinitesimal distance along the curved path a. Given the appropriate gradient of the refractive index, the optical path length for each ray could be made the same as for corresponding rays in a conventional lens. Thus it is clear that curved surfaces usually associated with optical lenses are not strictly required for focusing light since a gradient-index lens achieves the same end by varying refractive index rather than thickness to control the optical path length.
A lens built from an array of cells filled with liquid crystals is shown in the bottom diagram of Fig. 1. Each cell contains a thin layer of liquid crystal molecules sandwiched between two parallel glass plates. The molecules are oriented in parallel, as in a crystal, which causes the cell to be birefringent. Consequently, when light passes through the crystal it is subjected to a different refractive index when polarized in a direction parallel to the molecules, compared to when it is polarized in the orthogonal direction. The molecules are free to rotate, as in a liquid, by increasing amounts when an electric field of increasing strength is applied to transparent, conductive electrodes located on the inside of the glass plates. Consequently, an applied voltage can be used to vary the refractive index experienced by light of fixed polarization when transmitted through the cell. Thus when programmed to be a simple lens, each cell will have a different refractive index similar to the gradient-index lens. The difference is that each individual cell has finite size and a fixed refractive index, which means that the gradient of refractive index follows a step-wise profile rather than a smooth, continuous profile. Thus the emerging wavefront has a segmented appearance, which would make an increasingly accurate approximation to a smooth, spherical wavefront as the density of the cells increases. Although not shown in the diagram, the step-wise discontinuities are also smothed by diffraction effects as the wavefront propagates forward.
A photograph of the prototype liquid-crystal lens we have been evaluating at Indiana University is shown in the cover illustration. The device was manufactured by Meadowlark Optics of Longmont, CO and has 127 individual cells packed in an hexagonal array. Since the device is completely transparent, to obtain the photo we sandwiched it between crossed polarizing filters in order to visualize the cells and to display their refractive index with a grey-scale code. Although the electrical connections to each cell are visible in the photo, they would normally be eliminated from the light path with a circular mask. The photo was taken when the device was programmed to be a +1 diopter lens inside a 3 mm pupil, which requires that the optical path length through the center of the lens be 2 wavelengths longer than the optical path at the margin of the lens. Our experiments have verified that the device works well as a simple spherical or cylindrical lens, provided it is programmed to provide no more than 1.5 diopters of refractive power. This practical limitation is set by the number of individual cells in the array and therefore we can expect to see a wider operating range achieved as the manufacturing process improves to produce future generations of the device with higher spatial density of cells.
We suspect that the most useful form of the liquid-crystal technology for ophthalmic applications may be a hybrid lens, rather like a doublet, in which ordinary glass is used to correct the sphero-cylindrical refractive error of an eye and the liquid crystals are used to correct the residual, higher order aberrations. One of the first applications of such a lens would be to provide high-resolution diagnostic imaging of the internal structures of the eye. As illustrated in Fig. 2, wavefronts reflected from anatomical structures of interest are defocused and aberrated as a result of the imperfections of the patient's eye. By passing these distorted wavefronts through the hybrid liquid-crystal lens, the wavefront can be reshaped into a perfect wavefront for imaging by an ophthalmoscope or fundus camera. To use the same lens to correct the patient's vision, wavefronts from visual objects would be pre-distorted by the liquid-crystal lens by an amount which is equal, but opposite, to the aberrations in the eye. In this way the optical path length of light passing through all points in the pupil will be equal, thus ensuring aberration-free retinal images limited only by the unavoidable diffraction effects of a finite pupil size. Because the power of the lens is electronically programmable, the liquid-crystal lens seems particularly well suited for auto-focus applications such as correcting presbyopia or perhaps for a new generation of computer-controlled, electronic phoropters. One aim of future research will be to overcome potential problems (e.g. alignment and control of the variable-focus spectacle lens) associated with various potential applications.
Figure 2. Electronic spectacles made from a programmable array of liquid crystal cells may be used to correct aberrated wavefronts emerging from the eye (diagnostic retinal imaging) or to pre-distort wavefronts to compensate for the eye's aberrations (vision correction).
The correction of higher-order aberrations offers the possibility of increased visual acuity for everyone, perhaps beyond typical limit of 20/15. In theory, diffraction-limited optical cutoffs for 3 mm and 8 mm pupils would be high enough to yield retinal images of letter targets as small as 20/6.7 and 20/2.5, respectively. To illustrate what the retinal image would be like with super-normal optics, imagine yourself viewing the Statue of Liberty at a distance of 3 kilometers from a boat in the New York Harbor. Under optimal viewing conditions and 20/15 vision (i.e. a normal 3 mm pupil), your retinal image of the statue would look like Fig. 3A. If you view the statue through the liquid-crystal lens, programmed to fully correct all ocular aberrations across your 3 mm pupil, then the retinal image of the statue would look like Fig. 3B. Notice the finer detail and higher contrast in the retinal image when the eye's aberrations are corrected. This illustrates that retinal image quality can be noticeably increased even for pupil sizes as small as 3 mm. Maximum retinal image quality can be obtained with the largest physiological pupil diameter (8 mm) and full correction of all ocular aberrations. This situation is depicted in Fig. 3C, which shows that the theoretical maximum optical bandwidth that can be achieved with the human eye is six times greater than the optical cutoff of a normal eye with a 3 mm pupil.
Figure 3. Simulation of the improvement in retinal image quality expected by correcting the optical aberrations of the eye. (A) Normal optics, 3mm pupil. (B) Corrected optics, 3mm pupil. (C) Corrected optics, 8mm pupil.
Improving the quality of the retinal image is an important first step towards achieving super-normal visual acuity, but it may not be sufficient. This is because when optical limitations have been removed, visual performance now becomes constrained by neural factors.12 Specifically, the spacing between retinal photoreceptors represents a neural limitation to visual resolution which is only slightly higher than the optical limit. Consequently, increasing the quality of the retinal image will probably not yield a major increase in resolution acuity, although it could have a large impact on detection acuity. In this respect, fitting the eye with super-normal optics for foveal vision would be similar to the normal situation in peripheral vision. In the periphery, the eye's optical quality is nearly as good as for central vision but the neural architecture of the peripheral retina is dramatically different. The large increase in spacing between neural elements in the periphery severely reduces resolution acuity (e.g. 20/200 in the mid-periphery). However, the size of neural receptive fields remains relatively small and, as a result, detection acuity may remain as high as 20/20.13 This tenfold difference between resolution acuity and detection acuity in the periphery occurs because the spacing between neural sampling elements (Minimum Angle of Resolution Å 10' at 30° eccentricity) is much larger than their radius (Minimum Angle of Detection Å 1' at 30° eccentricity).14 To the contrary, only a twofold difference between detection acuity and resolution acuity would be expected in the fovea because foveal cones are tightly packed,which makes the spacing between cones just twice their radius.
Figure 4. An enlargement of the image of Figure 3C is overlaid with an hexagonally-packed mosaic of circles that represent the foveal cone mosaic. This neural mosaic is relatively coarse compared to the retinal image, which may introduce artifacts into the neural image and ultimately cause a kind of mis-perception called "aliasing".
Although there are many potential benefits of super-normal visual optics, there is at least one expected penalty. Given a dramatic increase in optical quality of the retinal image, the photoreceptor mosaic will appear relatively coarse by comparison, as shown in Fig. 4. As a result of this mismatch, very fine spatial details in the retinal image will be smaller than the distance between neighboring cones and therefore will not be registered properly in the neural image. This mis-representation of the image due to neural undersampling by a relatively coarse array of photoreceptors is called "aliasing". Research indicates that the ambiguity introduced by aliasing is the primary factor which limits resolution acuity in normal peripheral vision,13 and the same is true for central vision when optical limitations are removed.15 However, for everyday vision the penalty of aliasing is likely to be outweighed by the reward of higher contrast sensitivity and higher detection acuity. Therefore we anticipate that correcting the eye's optical aberrations will yield a net increase in the quality of the patient's visual experience and therefore is worth pursuing. Indeed, our preliminary observations indicate that stimuli seen through adaptive optics have a strikingly crisp appearance expected of an eye with supernormal optical quality, which is consistent with the sixfold increase in contrast sensitivity measured experimentally.7
In summary, we forecast major advances in spectacle lenses in the early part of the 21st century which will combine the power of adaptive optics technologies with the flexibility of electronic circuitry. The result will be a new generation of "smart spectacles" capable of adapting to the specific requirements of individual eyes to produce customized optical correction of unprecedented quality. However, to make this prediction come true will require an optometric community that is committed to building upon its traditional strength in visual optics by supporting research aimed at applying modern technologies to solve important optometric problems.