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D.Phil. / Under certain conditions the human visual system accommodates and postures at a position classically known as the dark focus. The dark focus is usually presented as a spherical phenomenon. The characteristics of the dark focus that can be conveyed by its spherical presentation are limiting: little representation can be given of the characteristics of the variation that occurs when measurements are taken of the dark focus (for example under dark conditions); no indication can be given of any antistigmatic (non-spherical) change or variation; differences in variation between light and dark conditions cannot be shown or detected using classical methods of analysis; meridional characteristics of the dark focus cannot be represented, and so on. In this thesis I have preferred to coin and use the term dark refraction shift (defined here as: 8F = F dark- Flight) for what has classically been known as the dark focus. I have done so because I believe that the term is a better description of what happens to the human visual system under dark conditions. Multivariate methods of analysis allow for a much more detailed, and complete, presentation ofthe dark refraction shift and its variation. The limitations of methods used previously and mentioned above are overcome when multivariate methods are used to analyze and present dark refraction shift data. This thesis presents the dark refraction shift and its various characteristics, making use of multivariate methods that are used for this purpose for the first time. A Hoya AR550 autorefractor, set to measure refractive state to the nearest 0.01 D, was used to take 50 measurements at a time of the refractive state of twenty subjects under varying conditions ofluminance. The autorefractor was re-focused after each measurement. In the light condition, the subject was positioned in front of the autorefractor, the room lights were left switched on and the fixation target inside the instrument was visible to the subject. 50 measurements were then taken under these conditions. A second set of measurements was then taken under the dark condition. In the dark condition measurements the subject was left in complete darkness for five minutes to allow the accommodative system to settle at the dark focus. No fixation target was visible to the subject who remained in complete darkness for the duration of the dark condition measurements. 50 autorefractor measurements were taken under these conditions. Two measurement sessions were conducted where the order of the light and dark conditions were reversed. In the case of each subject the order of light versus dark condition measurements was determined randomly for the initial session and reversed in the second session. Subjects had to fulfill certain selection criteria; the refractive state had to have a cylinder equivalent dioptric strength of less than or equal to 6 D, the visual acuity had to be 6/6 or better in the right eye, subjects with strabismus were eliminated and subjects with any observable ocular pathology were not accepted. Ten of the subjects were aged between 21 and 35 years of age. They constituted the prepresbyopic group. The other ten subjects were aged between 40 and 65 years of age and constituted the presbyopic group. Each subject had a total of 200 measurements taken, 100 measurements taken in the light condition and 1 00 taken in the dark condition.

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Over the past few decades, short-period giant planets have been discovered in extrasolar planetary systems, allowing for new tests of planetary evolution theories. Many of these giant exoplanets have high temperatures (>1000 K) and do not directly resemble Jupiter or Saturn. Only in the past few years have exoplanets akin to the cold (~100 K) gas giants in the solar system been identified. In this dissertation, I investigated giant gaseous planets through comparative studies of Saturn and exoplanets. Saturn has been the target of numerous high-precision observations, making it the ideal candidate for comparative studies. I simulated transit observations of a Saturn-analog exoplanet and determined that cold exoplanet atmospheres are amenable to characterization via transmission spectroscopy. By casting Saturn as an exoplanet, I demonstrated the potential for exoplanets to place the solar system in a Galactic context. The transit spectrum of Saturn also highlighted the importance of atmospheric refraction in transit observations. Refraction alters the path of light propagating in an atmosphere. I showed that out-of-transit refracted light provides an opportunity to identify and characterize the atmospheres of cold transiting and non-transiting exoplanets. I searched exoplanet parameter space to locate the maximal effect and derived a criterion that predicts which atmospheres produce detectable refracted light signatures. My consideration of exoplanetary refraction also included a parallel study of Saturn's atmosphere. I developed a novel method to measure atmospheric refractivity from distorted images of the Sun. I used this method to infer Saturn's atmospheric structure for more than a dozen Saturn solar occultations and to identify seasonal variations in Saturn's stratospheric temperature. Lastly, I obtained ground-based observations of the long-period transiting exoplanet Kepler-421b to refine its transit ephemeris. Without accurate transit ephemerides, long-period exoplanet characterization with large space-based observatories cannot occur. My unique observations represent the first step toward ensuring that long-period exoplanets are characterized in the near future. In summary, this dissertation lays the foundation for investigations of cold giant exoplanets, which exist in an almost entirely unexplored regime of exoplanetary science. Using Saturn to provide context and motivation, I began confronting the challenges facing this new discipline of exoplanetary science.

This dissertation deals with the characterization of the nonlinear absorption and refraction of two representative metallophthalocyanine dyes: chloro aluminum phthalocyanine dissolved in methanol, referred to as CAP, and a silicon naphthalocyanine derivative dissolved in toluene, referred to as SiNc. Using the Z-scan technique, the experiments are performed on both the picosecond and nanosecond timescales at a wavelength of 0.532 μm.

D.Phil. / 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).

The torque exerted by a beam of polarized light on a half-wave plate which alters its state of polarization is calculated for several laser wavelengths and intensities using electromagnetic theory. The second-order torque that arises through the nonlinear interaction is formulated and the numerical values are calculated for the 42m crystal class. The experiment used to detect the existence of the torque is reviewed and a demonstration experiment is suggested.

Myopia is a refractive condition and develops because either the optical power of the eye is abnormally great or the eye is abnormally long, the optical consequences being that the focal length of the eye is too short for the physical length of the eye. The increase in axial length has been shown to match closely the dioptric error of the eye, in that a lmm increase in axial length usually generates 2 to 3D of myopia. The most common form of myopia is early-onset myopia (EO M) which occurs between 6 to 14 years of age. The second most common form of myopia is late-onset myopia (LOM) which emerges in late teens or early twenties, at a time when the eye should have ceased growing. The prevalence of LOM is increasing and research has indicated a link with excessive and sustained nearwork. The aim of this thesis was to examine the ocular biometric correlates associated with LOM and EOM development and progression. Biometric data was recorded on SO subjects, aged 16 to 26 years. The group was divided into 26 emmetropic subjects and 24 myopic subjects. Keratometry, corneal topography, ultrasonography, lens shape, central and peripheral refractive error, ocular blood flow and assessment of accommodation were measured on three occasions during an ISmonth to 2-year longitudinal study. Retinal contours were derived using a specially derived computer program. The thesis shows that myopia progression is related to an increase in vitreous chamber depth, a finding which supports previous work. The myopes exhibited hyperopic relative peripheral refractive error (PRE) and the emmetropes exhibited myopic relative PRE. Myopes demonstrated a prolate retinal shape and the retina became more prolate with myopia progression. The results show that a longitudinal, rather than equatorial, increase in the posterior segment is the principal structural correlate of myopia. Retinal shape, relative PRE and the ratio of axial length to corneal curvature have been indicated, in this thesis, as predictive factors for myopia onset and development. Data from this thesis demonstrates that myopia progression in the LOM group is the result of an increase in anterior segment power, owing to an increase in lens thickness, in conjunction with posterior segment elongation. Myopia progression in the EOM group is the product of a long posterior segment, which over-compensates for a weak anterior segment power. The weak anterior segment power in the EOM group is related to a combination of crystalline lens thinning and surface flattening. The results presented in this thesis confirm that posterior segment elongation is the main structural correlate in both EOM and LOM progression. The techniques and computer programs employed in the thesis are reproducible and robust providing a valuable framework for further myopia research and assessment of predictive factors.