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The central theme of my research program is the role of the eye's optical system and neural retina in determining the quality of our visual experience and in setting the limits to visual performance. I have approached this broad theme from several different directions, using a variety of experimental paradigms, techniques, and models. As a graduate student at Berkeley, and subsequently as a postdoctoral fellow and eventually as Research Fellow at the Australian National University (JCSMR), I concentrated on neurophysiological investigations of retinal information processing in animal models. After moving to Indiana University in 1983 I expanded into the domain of human experimentation and broadened my interests to include the optical system of the eye. Throughout these changes, the ultimate goal remained the same: to understand how the physiology of the eye determines the way we see, when we see clearly, and explains the failure to see, when we see poorly.
The narrative which follows is organized into three broad categories: peripheral vision, optical limits to vision, and visual optics. Although it is useful to make these distinctions here, such a division is somewhat artificial in practice since the same experiment often bears upon more than one issue. For each of these topics I provide a brief summary of the results of several related lines of investigation which address the same general questions. Most of the work described below has been done in collaboration with Dr. Arthur Bradley and our several, mutual graduate students.
The most important discovery of my early years at Indiana University was the unexpected finding that spatial patterns much too fine to be resolved by the peripheral retina were nevertheless quite visible. The very idea that vision might exist beyond the resolution limit was exciting because it was totally outside the conventional framework for thinking about peripheral vision that had existed, unchallenged, for over a century of vision research. Over the past five years we have developed our initial observations of this phenomenon, which we call aliasing, into a coordinated attack from a variety of angles onto the basic question of how the architecture of peripheral retina establishes limits upon the quality of spatial vision in man. At the same time, we have been forced to deal with the related issue of retinal image quality in peripheral vision in order to clearly distinguish between optical and retinal limits to visual perception in the periphery.
Retinal factors have long been suspected of limiting human visual performance for fundamental tasks like pattern resolution and pattern detection. A rigorous account of these ideas is possible by applying the sampling theory of communications engineering to this neurophysiological system1I. Such analysis predicts that if the spatial filtering effects of the eye's optical system are avoided, then visual resolution should be limited by the spacing of retinal sampling units. Thus the density of the retinal mosaic of neurons places a fundamental limit, called the Nyquist limit, on spatial vision. Since ganglion cells form a sparser array than do the photoreceptors, we predicted early on that visual resolution should vary with stimulus eccentricity from the fovea in accordance with the spacing between retinal ganglion cells. Initial results supported this prediction, which led to further tests of the hypothesis. In one experiment, Roger Anderson, Mike Wilkinson, and I were able to reveal a subtle asymmetry of the retina known as the visual streak.31 This term refers to the slightly elevated density of retinal ganglion cells near the horizontal meridian. By using the sampling-limited acuity task developed in earlier experiments, we were able to reveal the presence of a visual streak in our own eyes that was consistent with what is known about human retinal neuroanatomy.
Following these initial successes, Mike Wilkinson and I took on a much more ambitious project to map the resolving power of the human eye throughout the visual field. This was a very demanding parametric study which represents the first systematic study of peripheral visual acuity since Wertheim's classic, textbook study published in 1894. In contrast to Wertheim, our experiment was explicitly designed to reveal sampling-limited behavior. Thus, from our data we were able to infer the sampling density of the human retinal mosaic throughout the peripheral field. Quantitative comparisons between our results and neuroanatomical data recently published for human retina indicate that visual resolution is closely correlated with the spacing of primate beta ganglion cells, a class of neurons which provides the major retinal input to visual cortex. Although these exciting new results have been presented on several occasions to the scientific community at various meetings and seminars, the completion and publication of this excellent doctoral thesis has been delayed significantly by the return of LTCDR Wilkinson to active duty following the expiration of his 3-year doctoral program sponsored by the US Navy.
Human retina is characterized by the presence of both rod photoreceptors (for night-time scotopic vision) and cone photoreceptors (for day-time photopic vision). One controversial area of current research in visual neuroscience is whether the changeover from cones to rods during dark adaptation is accompanied by a changeover from one visual pathway (the P-pathway via the parvocellular layers of the lateral geniculate nucleus) to another (the M-pathway via the magnocellular layers of the lateral geniculate nucleus). Since the M-pathway is served by a class of retinal ganglion cells that cover the visual field with a very low sampling density, this model has gained some acceptance because it predicts a marked loss of visual acuity for scotopic peripheral vision. To test the idea experimentally, Mike Wilkinson and I repeated his study of visual acuity in the periphery under a wide range of background illumination levels (7 orders of magnitude). Amazingly, his results showed that, contrary to popular belief, visual acuity in the periphery is largely independent of illumination provided that the experiment is not contaminated by the poor optical quality of the retinal image that normally occurs as the pupil dilates under dim illumination. This is an important proviso because poor optics become the limiting factor (instead of the sampling density of the retinal mosaic) when the pupil dilates and exposes the large optical aberrations of the eye.
Visual sensitivity to spatial contrast is a fundamental attribute of the visual system which is important from the point of view of basic mechanisms and clinical applications. Despite its importance, the contrast sensitivity of the peripheral visual system has not received much attention experimentally and consequently is poorly understood. One popular view (called M-scaling) is that peripheral vision is essentially the same as central vision, except for spatial scale, which can be compensated simply by making visual targets larger. Implicit in such a model lies a definition of the resolution limit as that spatial frequency for which contrast sensitivity falls to the theoretical minimum (unity). In other words, this model excludes the possibility of vision beyond the resolution limit and therefore is incompatible with our previous demonstrations of aliasing. To demonstrate this point directly, David Still, Arthur Bradley, and I performed a series of experiments to measure the contrast sensitivity of peripheral vision with improved methodology. Our results dispel the conventional view by demonstrating qualitative differences in the shape of the contrast sensitivity functions for central and peripheral vision. These results form part of Still's doctoral thesis, and some of the ideas and data have been published [refs] and two more manuscripts are planned. (Full p ublication has been delayed significantly by the return of LTCDR Still to active duty in the US Navy immediately upon completion of his 3-year degree program).
The longest thread of my research career is the investigation of amblyopia, one of the most intriguing visual dysfunctions known to clinical optometry. Amblyopia is characterized by a loss of visual acuity for no apparent reason. As a freshman graduate student at Berkeley I undertook a project directed by R.D. Freeman which indicated that the amblyopic defect lies in the early stages of the visual pathways, perhaps the retina. Some years later, I was awarded an N.I.H. postdoctoral fellowship to join W.R. Levick in Australia to test this idea in the cat animal model. Although we ended up rejecting the retinal hypothesis in the cat, the idea re-surfaced yet again when Arthur Bradley and I began our collaboration at Indiana University a few years ago. My work on aliasing due to retinal undersampling in human peripheral vision reminded Prof. Bradley of the scrambled drawings which amblyopic individuals produce when asked to sketch their subjective perceptions of simple periodic patterns. Additional experimental results we have gathered suggest to us that amblyopia may be due in part to neural aliasing at some early stage of the visual system.44
An important class of retinal disorders are the acquired disease processes. Cats are particularly susceptible to dietary insufficiency of the amino acid taurine which leads to photoreceptor death and blindness in the central region of the retina. As a research fellow in Australia many years ago, I joined Prof. Levick's long-term neurophysiological and histological study of this disease with the goal of understanding the consequences of photoreceptor death and the loss of photic input to retinal ganglion cells. Although my role in that project was interrupted when I moved to Indiana, I had the opportunity recently to return to Australia on an "archeological" expedition. Digging through ancient laboratory notes and records from those halcyon days allowed Prof. Levick and me to reconstruct (and publish) a series of fascinating results which demonstrated that ganglion cells outside the photoreceptor lesion have normal response properties, cells inside the lesion are blind, and cells on the border of the lesion have abnormal sensitivity and unusual receptive fields. Surprisingly, conduction of nerve action potentials by optic nerve fibers was normal despite the fact that some cells had probably not generated an action potential spontaneously for several years prior to our experiments.43
The optical system of the eye presents a low-pass filter at the front end of the visual system and thus represents a potential limiting factor for any visual task. Optical limitations are especially likely in the peripheral field because of the presence of off-axis aberrations. In general, the primary optical factors of interest are diffraction and aberrations. Chief among these is chromatic aberration, which is manifest in three distinctly different forms in which the focus, magnification, and/or position of the retinal image varies with the wavelength of light. The result is image degradation which has the potential to limit vision in two general modes of viewing: Keplerian and Maxwellian. The former is the usual case where external objects are focused onto the retina by the eye's optical system, whereas the latter is a special kind of viewing that occurs when a visual instrument projects an image onto the retina by first focusing the light into a small portion of the eye's pupil.
Using a simple optical model of the eye which we call the Chromatic Eye,32 we have shown that visual performance can be hampered significantly by ocular chromatic aberration.28 For example, chromatic difference of focus can account quantitatively for the small, but well-known loss of foveal acuity in white light (as compared to monochromatic light). The same model also accounts for the much more severe loss of foveal acuity which occurs when viewing through a pupil which is displaced laterally from the visual axis. In this case the loss of acuity is due to chromatic difference of position which induces phase shifts that led to reduced image contrast.
Interestingly, attempts to reduce losses of visual performance by optically correcting the eye's chromatic aberration have been largely unsuccessful for a variety of reasons.29 Principal among these is the unavoidable introduction of chromatic parallax which reduces image quality, again because of phase shifts which degrade image contrast.26 Since chromatic parallax is inherent in the achromatizing method itself,26 there seems to be little hope for correcting the many aspects of ocular chromatic aberration by conventional means. However, other techniques based on diffractive optics may prove more effective.37, 42
The effect of chromatic aberration on peripheral vision is more difficult to demonstrate since (as we have shown previously) peripheral resolution acuity is limited by retinal rather than optical factors. Nevertheless, using a contrast detection task that extends the range of vision to well beyond the resolution limit, former student Frank Cheney and I measured a 3-fold loss of detection acuity in the mid-periphery as predicted by our optical model. Thus chromatic aberration may play a major role in limiting the amount of aliasing present in peripheral vision under normal viewing conditions.
An important experimental technique called "isoluminance" is commonly used to isolate those neural channels which convey color information through the visual system. An isoluminant visual stimulus is one which has uniform luminance everywhere, but which varies in color (e.g. a spatial pattern made of alternating red and green stripes of equal brightness). Through careful calibration procedures, color vision scientists take great pains to produce such stimuli in order to investigate the characteristics of the color system in isolation. Unfortunately, there is no direct method of verifying that the retinal image of the stimulus is also isoluminant. In fact, there is good reason to believe that the image will not be isoluminant because of luminance artifacts introduced by the eye's chromatic aberration. Using our Chromatic Eye model, and the notion of chromatic parallax developed in the context of achromatizing methodologies, we have shown that the eye's chromatic aberration can introduce significant luminance artifacts which can be more visible than the original chromatic contrast in the pattern.33 These results have considerable importance for the interpretation of the color vision literature, and also for the design of new experiments in color vision.
One of the most fundamental visual tasks is to establish the visual direction of objects in space. To achieve this basic visual function, individual retinal neurons must "learn" (or perhaps are genetically programmed) which part of visual space corresponds to their specific location in the retinal mosaic. The geometrical optics notion of point-to-point correspondence between retinal locations and visual directions is so pervasive in vision science that one rarely thinks to question it. However, as a result of our investigations into the chromatic aberration of the eye, we came to realize that each retinal point corresponds to many different visual directions, one for each wavelength of light. We introduced the term chromatic diplopia to describe this phenomenon, which is simply explained on the basis of chromatic difference of position caused by transverse chromatic aberration. Furthermore, since stereoscopic depth perception is based on the small, systematic differences in visual direction of objects with respect to the two eyes, it follows that chromatic aberration has a potentially powerful effect on depth perception. In fact, objects of different color but at the same distance frequently appear to be at different distances, a phenomenon known as chromostereopsis.
To develop this line of investigation for her doctoral thesis, Ming Ye decided to experimentally test the hypothesis that chromosteropsis is directly attributable to chromatic differences of visual direction, which are in turn directly attributable to the chromatic aberration of the eye. Her initial experiments, which employed small artificial pupils to introduce controlled amounts of transverse chromatic aberration, verified this basic hypothesis.30 However, when large pupils were used instead, we found a much reduced degree of chromostereopsis and a corresponding reduction of chromatic diplopia. In effect, the apparent visual direction of objects was being modulated by the pupil diameter! Following a considerable amount of experimentation and advanced theoretical calculations, Ye was eventually able to explain her experimental results by invoking the Stiles-Crawford effect as a mechanism for shaping the profile of the blurred retinal images upon which judgments of visual direction depend.36
In order to examine visual function without the normal optical limitations imposed by diffraction and aberrations of the eye, clinical optometrists and vision scientists have adopted and modified the technique known as Maxwellian view.34 Diffraction effects are avoided by focusing all of the light into a small spot which fits well within the pupil of the eye. This is useful clinically, for example, to direct a beam of light around a localized opacity to measure visual acuity in cataract patients. The effects of ocular aberrations can also be avoided for a special configuration in which two mutually coherent spots of light are focused in the pupil plane. In this case the retinal distribution of light consists of sinusoidal interference fringes which have high contrast regardless of whether the eye is aberrated or out of focus. For these reasons, the Maxwellian view interferometer is often described as a method for "bypassing the optical imperfections of the eye". However, this is a naive view which has led to serious design errors in clinical and research instrumentation.24 The problem arises when objects more complex than simple, monochromatic sinusoidal fringes are to be produced on the retina. For such stimuli, the distribution of light in the pupil plane is more than just two points of light, and can be a very complex spatial distribution of polychromatic light. We have argued from a theoretical viewpoint,23 and have demonstrated experimentally,24,25,39 that defocus and ocular chromatic aberration have a major influence on retinal contrast produced by such devices.
As a result of our finding that detection acuity in peripheral vision is limited by retinal image quality, it became apparent that to fully appreciate the limits to visual performance requires an understanding of off-axis optical performance of the human ocular system. Although several of the chief optical aberrations which affect peripheral vision have been studied by others, no thorough assessment of ocular chromatic aberration had previously been attempted. To fill this gap, we began by developing the theory of ocular chromatic aberration through analysis of a simple model of the eye's optical system. The goal was to devise a realistic model capable of making explicit, quantitative predictions suitable for experimental testing. At the same time we undertook experiments to directly measure the modulation transfer of the eye for peripheral parts of the visual field.
The classical psychophysical method (Campbell & Green 1965) used to measure the modulation transfer function of the human eye involves the measurement of contrast sensitivity functions for natural viewing and again with the Maxwellian view interferometer. Under the assumption that optical imperfections of the eye are the sole factors responsible for the difference in these two functions, their ratio is equal to the modulation transfer function of the eye. Since David Still had obtained both of these functions in his study of contrast sensitivity of peripheral vision, we were able to demonstrate experimentally the relatively high quality of peripheral optics. In fact, Still's results show that, provided refractive errors are corrected, peripheral optical quality is nearly as good as central optical quality. As a control experiment we applied the same methodology to central vision and thus provided the first confirmation of the widely quoted results of Campbell & Green's classic study.
Our theoretical modeling of the optical system of the eye has provided for the first time a unified treatment of both the transverse and longitudinal components of ocular chromatic aberration.22 This was achieved through analysis of a model eye consisting of a volume of water with a single, spherical refracting surface and an internal aperture. An important conceptual result of the analysis was the identification of a new reference axis, called the achromatic axis, which is of crucial importance in specifying the magnitude of transverse chromatic aberration. We call the angle between the achromatic and visual axes Y in honor of Indiana University. We have shown that angle Y is the primary determinant of how much transverse chromatic aberration is present for foveal vision. When present, chromatic aberration of the eye reduces image contrast for two reasons. First, the longitudinal aberration defocuses the image by an amount which varies with wavelength. Second, the transverse aberration induces a phase shift that varies with wavelength which also results in a loss of contrast. Given this formulation of the problem, it is possible to compute polychromatic modulation transfer functions for the eye which were essential to account for visual performance in a variety of recent studies.23,25,26,28,33
Although the traditional, reduced eye model was useful early on, limitations of the model soon became apparent. First, the model failed to account for the degree of chromatic aberration at short wavelengths. Second, the traditional model has large amounts of spherical aberration which is not present in real eyes. Third, and most important, the traditional model lacks a pupil. This is a major limitation since the location of the pupil relative to the visual axis of the eye is the key determinant of the amount of transverse chromatic aberration at the fovea, and therefore of image quality for central vision. To improve upon each of these three deficiencies, a new model dubbed the Chromatic Eye was developed using parametric data collected in our laboratory and from the published literature.32 Another useful variant, called the Indiana Eye , includes spherical aberration.46
The Chromatic Eye model of ocular chromatic aberration makes quantitative predictions about the magnitude of both the transverse and the longitudinal chromatic aberrations of the eye. Although measurements of the longitudinal component are available in the literature, no useful measurements have been reported for the transverse component. We therefore devised an experimental method for measuring transverse chromatic aberration based on a two-color, vernier-alignment task. The results closely followed theoretical predictions thus supporting the postulated model. Unexpectedly, our measurements indicate that angle Y is nearly zero in the majority of subjects examined. The implication of this result is that, although the eye has substantial chromatic aberration, the pupil is positioned so as to minimize the transverse component of the aberration for central vision, thereby optimizing image quality for foveal viewing of polychromatic objects.22 This tantalizing result has led to additional experiments on a much larger population currently underway by Maurice Rynders and two optometry students, Lidke and Chisholm.
Theory predicts that retinal image size should vary with wavelength in direct proportion to the magnitude of longitudinal chromatic aberration (i.e. the chromatic difference of focus).27 The constant of proportionality in this linear relationship is the axial distance between the entrance pupil of the eye and the anterior nodal point. Because this distance is so small in human eyes, retinal magnification is likely to vary by less than 1% over the visible spectrum. This probably accounts for why the chromatic difference in magnification has been difficult to measure experimentally. However, by using a stereoscopic technique which is sensitive to very small amounts of interocular difference in magnification, Xiaoxiao Zhang was able to measure the chromatic variation of magnification for the first time as part of his doctoral thesis. Those experiments confirmed theoretical expectations and went on to show how and why the use of artificial pupils greatly magnify the effect. On the basis of his results, it was possible for the first time to infer the location of the anterior nodal point in human eyes.38
Bifocal contact lenses which employ diffractive optics to form images at two different distances are characterized by chromatic aberration which is opposite in sign to the chromatic aberration of the eye. This suggested that diffractive contact lenses might be used to correct the eye's chromatic aberration without introducing the additional complications of chromatic parallax associated with conventional dioptric methods. Using commercially available contact lenses, we verified experimentally that the chromatic aberration of the eye is in fact reduced when wearing this kind of lens.37,42 Thus hopes were raised about the possibility of improving retinal image quality by neutralizing ocular chromatic aberration. However, in the course of these experiments subjects frequently commented on the presence of double images in the test eye. This monocular diplopia appeared to degrade image quality more than the improvement gained by neutralizing chromatic aberration, hence a net loss in image quality. To get a better grasp of this phenomenon, we devised a theoretical and experimental model of simultaneous bifocal vision to examine the effects of monocular diplopia on vision. Preliminary experiments have demonstrated that diplopia may cause a significant loss of contrast sensitivity (> 100%) for the recognition of small and medium sized letters.40
For many real-world tasks there is considerable pressure to increase the amount of information presented to human observers through optical instruments, displays, and other high-tech devices that design engineers call "visually-coupled system interfaces". Inevitably this demand leads to overload of central (foveal) vision and so new strategies must be considered. One such strategy is to shift information from central to peripheral vision, for example in the design of visual instrumentation in aircraft displays. From a clinical perspective, a shift of visual function from central to peripheral vision is unavoidable in patients who have diminished central vision due to disease, injury, or the normal aging process. Another strategy is to somehow avoid the optical imperfections of the eye which normally limit the amount of information (i.e. spatial bandwidth) that can be imaged on the retina. Clearly, our basic research into the mechanisms which limit the quality of spatial vision in the periphery provide a framework in which to analyze clinical conditions and engineering design strategies which aim to optimize the transfer of visual information to the human observer. It was for this reason that our group was invited on two separate occasions to address the Society for Information Display2I, 3I (an engineering group) and also the American Academy of Optometry44 (a clinical audience) regarding this general issue which has culminated in two textbook chapters [refs].
Current research in my laboratory centers around the doctoral research of Roger Anderson, Yizhong Wang, and Maurice Rynders. Anderson is interested in applying some of our recent advances in understanding of peripheral vision to important problems in clinical optometry. Since letter acuity is the single most important clinical test of foveal visual function, he is making systematic measurements of peripheral acuity for letters with a view to establishing whether performance is sampling limited. If so, then letter acuity may become a valuable non-invasive method for assessing the effective sampling density of the retinal mosaic. Such a method would be of great importance in monitoring the development of retinal diseases such as glaucoma and optic neuritis.
Yizhong Wang is interested in more basic questions concerning the functional significance of the aliasing portion of the spatial frequency spectrum. Although we know that the aliasing zone can be very wide (e.g. 3 to 30 cyc/deg in the mid-periphery), it is unknown whether aliased stimuli are a help or a hindrance to spatial vision. In his preliminary experiments Wang demonstrated that aliased stimuli can be used to discriminate two spatial patterns which differ only for those spatial frequency components beyond the Nyquist limit. Thus he has established that under certain circumstances aliased stimuli can be useful. Future work will examine the range of circumstances consistent with that preliminary conclusion, and the degree to which those results can be generalized across stimulus parameters.
Maurice Rynders is interested in the application of modern diffractive optics technology to the design of new ophthalmic devices. He has a novel idea for a diffractive bifocal contact lens which he is exploring for his doctoral research and for which he has won an outside equipment grant. Although contact lens design is not one of my major areas of interest, Rynders has asked me to supervise his project because of my background and interest in visual optics.
Prof. Horner is investigating the effect of a newly designed contact lens treatment on the reduction of myopia. I am contributing to that research effort by helping to develop new ways of visualizing the multidimensional nature of refractive error and its statistical analysis.45