Abstract:
Visual acuity and refractive state probably are the two most basic or fundamental quantities that concern optometry, ophthalmology and vision science. Both of these variables are complicated and their mathematical and statistical use in research and other activities has been poorly understood. During particularly the last decade, modern statistical multivariate methods have become available to optometry and ophthalmology and this has assisted with the understanding of concepts such as refractive state (and its underlying nature, namely, dioptric power). It is now possible to transform measurements of refractive state from the conventional notation that is commonly used in the fields of optometry and ophthalmology to an orthodox mathematical form that can be understood by scientists and mathematicians. With this matrix form of refractive state it then is possible to use appropriate methods of linear algebra and multivariate statistics. Other theoretical approaches and analytical procedures or methods also have become accessible or have been developed recently as a consequence of this significant shift in thought as regards the fundamental nature of dioptric power. On the other hand, the scientific understanding of visual acuity (that is, the measurement of the resolving ability of the eye) perhaps has been somewhat neglected. Certainly there has been an abundance of research involving visual acuity and there also has been discussion concerning some of the difficulties that become apparent when measuring or attempting to interpret results from studies involving visual acuity. Visual acuity, unlike refractive state, can be represented by means of a single number and thus univariate, rather than multivariate, statistical methods are appropriate. And, of course, univariate statistics is less complicated than the multivariate form. But there are various difficulties with the understanding and researching of visual acuity. Some of these difficulties are relatively simple and thus can be solved more easily. For example, visual acuity measurements can be obtained from charts designed according to a logarithmic scale, or measurements from other charts can be transformed to a logarithmic scale. And thereby the ordinal nature of the basic or more common visual acuity scale is avoided and certain statistical methods become available that otherwise would not be possible. But more fundamentally visual acuity probably cannot truly be considered without the subject from which the measurement is obtained and, more particularly, the refractive state of the eye concerned. So the visual acuity and refractive state of an eye, perhaps, should be more appropriately regarded as a unitary concept that ideally should not be separated into two distinct parts. Thus to truly understand the relationship between visual acuity and refractive state we need to understand the 4-dimensional (mathematical) nature of the particular relationship involved. It follows then that the relationship between visual acuity and refractive state is a multivariate problem and that multivariate methods are best suited to its consideration. If we then begin to take into account other variables such as age or the ocular health, or say, iris aperture diameter of the eye then the complicated multivariate nature of the situation becomes even more obvious. In this dissertation an attempt is made to consider the possibilities of a modern multivariate approach to studies involving visual acuity, refractive state and other variables. The methodology used in this dissertation differs from those used in previous studies involving visual acuity and refractive state and other related variables. For example, here Jackson crossed cylinders are used extensively to produce dioptric blur or defocus in experimental subjects (positive and negative spheres also are used to a more limited extent). In previous published studies spherical or, less commonly, cylindrical lenses were used instead. Another difference between this dissertation and previous research studies is that the visual stimulus that the subjects observed, generally but not always, was a meridionally-independent or non-directional letter 0. The reasons for this choice is explained in the dissertation but in other research an enormous variety of visual stimuli have been used depending upon the interests of the researchers. But even more essentially this dissertation differs significantly from that of previous studies in terms of the manner in which the various experimental and other results (for instance, that from earlier researchers such as HB Peters) are presented. Entirely new, and largely unpublished, methods are used in many parts of this dissertation that probably represent a paradigmatic transition in understanding of visual acuity and its relation to refractive state. New terms such as decompensation and accompensation surfaces of constant visual acuity and antistigmatic ellipses are defined herein. (Briefly, one imagines starting from a state of compensation (of the refractive state of, say, an eye viewing a stimulus).