30 resultados para Coma

em Queensland University of Technology - ePrints Archive


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Familial hemiplegic migraine is a severe, rare subtype of migraine. Gene mutations on chromosome 19 have been identified in the calcium channel, voltage-dependent, P/Q type, alpha-1A subunit gene (chromosome 19p13) for familial hemiplegic migraine. Recently a gene mutation (Serine-218-Leucine) for a dramatic syndrome associated with familial hemiplegic migraine, commonly named “migraine coma”, has implicated exon 5 of this gene. The occurrence of trivial head trauma, in such familial hemiplegic migraine patients, may also be complicated by severe, sometimes even fatal, cerebral edema and coma occurring after a lucid interval. Sporadic hemiplegic migraine shares a similar spectrum of clinical presentation and genetic heterogeneity. The case report presented in this article implicates the involvement of the Serine-218-Leucine mutation in the extremely rare disorder of minor head trauma–induced migraine coma. We conclude that the Serine-218-Leucine mutation in the calcium channel, voltage-dependent, P/Q type, alpha-1A subunit gene is involved in sporadic hemiplegic migraine, delayed cerebral edema and coma after minor head trauma.

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We investigate the potential for the third-order aberrations coma and trefoil to provide a signed cue to accommodation. It is first demonstrated theoretically (with some assumptions) that the point spread function is insensitive to the sign of spherical defocus in the presence of odd-order aberrations. In an experimental investigation, the accommodation response to a sinusoidal change in vergence (1–3 D, 0.2 Hz) of a monochromatic stimulus was obtained with a dynamic infrared optometer. Measurements were obtained in 10 young visually normal individuals with and without custom contact lenses that induced low and high values of r.m.s. trefoil (0.25, 1.03 μm) and coma (0.34, 0.94 μm). Despite variation between subjects, we did not find any statistically significant increase or decrease in the accommodative gain for low levels of trefoil and coma, although effects approached or reached significance for the high levels of trefoil and coma. Theoretical and experimental results indicate that the presence of Zernike third-order aberrations on the eye does not seem to play a crucial role in the dynamics of the accommodation response.

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PURPOSE. This study was conducted to determine the magnitude of pupil center shift between the illumination conditions provided by corneal topography measurement (photopic illuminance) and by Hartmann-Shack aberrometry (mesopic illuminance) and to investigate the importance of this shift when calculating corneal aberrations and for the success of wavefront-guided surgical procedures. METHODS. Sixty-two subjects with emmetropia underwent corneal topography and Hartmann-Shack aberrometry. Corneal limbus and pupil edges were detected, and the differences between their respective centers were determined for both procedures. Corneal aberrations were calculated using the pupil centers for corneal topography and for Hartmann-Shack aberrometry. Bland-Altmann plots and paired t-tests were used to analyze the differences between corneal aberrations referenced to the two pupil centers. RESULTS. The mean magnitude (modulus) of the displacement of the pupil with the change of the illumination conditions was 0.21 ± 0.11 mm. The effect of this pupillary shift was manifest for coma corneal aberrations for 5-mm pupils, but the two sets of aberrations calculated with the two pupil positions were not significantly different. Sixty-eight percent of the population had differences in coma smaller than 0.05 µm, and only 4% had differences larger than 0.1 µm. Pupil displacement was not large enough to significantly affect other higher-order Zernike modes. CONCLUSIONS. Estimated corneal aberrations changed slightly between photopic and mesopic illumination conditions given by corneal topography and Hartmann-Shack aberrometry. However, this systematic pupil shift, according to the published tolerances ranges, is enough to deteriorate the optical quality below the theoretically predicted diffraction limit of wavefront-guided corneal surgery.

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Suggestions that peripheral imagery may affect the development of refractive error have led to interest in the variation in refraction and aberration across the visual field. It is shown that, if the optical system of the eye is rotationally symmetric about an optical axis which does not coincide with the visual axis, measurements of refraction and aberration made along the horizontal and vertical meridians of the visual field will show asymmetry about the visual axis. The departures from symmetry are modelled for second-order aberrations, refractive components and third-order coma. These theoretical results are compared with practical measurements from the literature. The experimental data support the concept that departures from symmetry about the visual axis in the measurements of crossed-cylinder astigmatism J45 and J180 are largely explicable in terms of a decentred optical axis. Measurements of the mean sphere M suggest, however, that the retinal curvature must differ in the horizontal and vertical meridians.

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Purpose: To investigate the effect of orthokeratology on peripheral aberrations in two myopic volunteers. Methods: The subjects wore reverse geometry orthokeratology lenses overnight and were monitored for 2 weeks of wear. They underwent corneal topography, peripheral refraction (out to ±34° along the horizontal visual field) and peripheral aberration measurements across the 42° × 32° central visual field using a modified Hartmann-Shack aberrometer. Results: Spherical equivalent refraction was corrected for the central 25° of the visual fields beyond which it gradually returned to its preorthokeratology values. There were increases in axial coma, spherical aberration, higher order root mean square aberrations, and total root-mean-squared aberrations (excluding defocus). The rates of change of vertical and horizontal coma across the field changed in sign. Total root mean square aberrations showed a quadratic rate of change across the visual field which was greater subsequent to orthokeratology. Conclusion: Although orthokeratology can correct peripheral relative hypermetropia it induces dramatic increases in higher-order aberrations across the field

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PURPOSE: To compare the repeatability within anterior corneal topography measurements and agreement between measurements with the Pentacam HR rotating Scheimpflug camera and with a previously validated Placido disk–based videokeratoscope (Medmont E300). ------ SETTING: Contact Lens and Visual Optics Laboratory, School of Optometry, Queensland University of Technology, Brisbane, Queensland, Australia. ----- METHODS: Normal eyes in 101 young adult subjects had corneal topography measured using the Scheimpflug camera (6 repeated measurements) and videokeratoscope (4 repeated measurements). The best-fitting axial power corneal spherocylinder was calculated and converted into power vectors. Corneal higher-order aberrations (HOAs) (up to the 8th Zernike order) were calculated using the corneal elevation data from each instrument. ----- RESULTS: Both instruments showed excellent repeatability for axial power spherocylinder measurements (repeatability coefficients <0.25 diopter; intraclass correlation coefficients >0.9) and good agreement for all power vectors. Agreement between the 2 instruments was closest when the mean of multiple measurements was used in analysis. For corneal HOAs, both instruments showed reasonable repeatability for most aberration terms and good correlation and agreement for many aberrations (eg, spherical aberration, coma, higher-order root mean square). For other aberrations (eg, trefoil and tetrafoil), the 2 instruments showed relatively poor agreement. ----- CONCLUSIONS: For normal corneas, the Scheimpflug system showed excellent repeatability and reasonable agreement with a previously validated videokeratoscope for the anterior corneal axial curvature best-fitting spherocylinder and several corneal HOAs. However, for certain aberrations with higher azimuthal frequencies, the Scheimpflug system had poor agreement with the videokeratoscope; thus, caution should be used when interpreting these corneal aberrations with the Scheimpflug system.

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Aberrations affect image quality of the eye away from the line of sight as well as along it. High amounts of lower order aberrations are found in the peripheral visual field and higher order aberrations change away from the centre of the visual field. Peripheral resolution is poorer than that in central vision, but peripheral vision is important for movement and detection tasks (for example driving) which are adversely affected by poor peripheral image quality. Any physiological process or intervention that affects axial image quality will affect peripheral image quality as well. The aim of this study was to investigate the effects of accommodation, myopia, age, and refractive interventions of orthokeratology, laser in situ keratomileusis and intraocular lens implantation on the peripheral aberrations of the eye. This is the first systematic investigation of peripheral aberrations in a variety of subject groups. Peripheral aberrations can be measured either by rotating a measuring instrument relative to the eye or rotating the eye relative to the instrument. I used the latter as it is much easier to do. To rule out effects of eye rotation on peripheral aberrations, I investigated the effects of eye rotation on axial and peripheral cycloplegic refraction using an open field autorefractor. For axial refraction, the subjects fixated at a target straight ahead, while their heads were rotated by ±30º with a compensatory eye rotation to view the target. For peripheral refraction, the subjects rotated their eyes to fixate on targets out to ±34° along the horizontal visual field, followed by measurements in which they rotated their heads such that the eyes stayed in the primary position relative to the head while fixating at the peripheral targets. Oblique viewing did not affect axial or peripheral refraction. Therefore it is not critical, within the range of viewing angles studied, if axial and peripheral refractions are measured with rotation of the eye relative to the instrument or rotation of the instrument relative to the eye. Peripheral aberrations were measured using a commercial Hartmann-Shack aberrometer. A number of hardware and software changes were made. The 1.4 mm range limiting aperture was replaced by a larger aperture (2.5 mm) to ensure all the light from peripheral parts of the pupil reached the instrument detector even when aberrations were high such as those occur in peripheral vision. The power of the super luminescent diode source was increased to improve detection of spots passing through the peripheral pupil. A beam splitter was placed between the subjects and the aberrometer, through which they viewed an array of targets on a wall or projected on a screen in a 6 row x 7 column matrix of points covering a visual field of 42 x 32. In peripheral vision, the pupil of the eye appears elliptical rather than circular; data were analysed off-line using custom software to determine peripheral aberrations. All analyses in the study were conducted for 5.0 mm pupils. Influence of accommodation on peripheral aberrations was investigated in young emmetropic subjects by presenting fixation targets at 25 cm and 3 m (4.0 D and 0.3 D accommodative demands, respectively). Increase in accommodation did not affect the patterns of any aberrations across the field, but there was overall negative shift in spherical aberration across the visual field of 0.10 ± 0.01m. Subsequent studies were conducted with the targets at a 1.2 m distance. Young emmetropes, young myopes and older emmetropes exhibited similar patterns of astigmatism and coma across the visual field. However, the rate of change of coma across the field was higher in young myopes than young emmetropes and was highest in older emmetropes amongst the three groups. Spherical aberration showed an overall decrease in myopes and increase in older emmetropes across the field, as compared to young emmetropes. Orthokeratology, spherical IOL implantation and LASIK altered peripheral higher order aberrations considerably, especially spherical aberration. Spherical IOL implantation resulted in an overall increase in spherical aberration across the field. Orthokeratology and LASIK reversed the direction of change in coma across the field. Orthokeratology corrected peripheral relative hypermetropia through correcting myopia in the central visual field. Theoretical ray tracing demonstrated that changes in aberrations due to orthokeratology and LASIK can be explained by the induced changes in radius of curvature and asphericity of the cornea. This investigation has shown that peripheral aberrations can be measured with reasonable accuracy with eye rotation relative to the instrument. Peripheral aberrations are affected by accommodation, myopia, age, orthokeratology, spherical intraocular lens implantation and laser in situ keratomileusis. These factors affect the magnitudes and patterns of most aberrations considerably (especially coma and spherical aberration) across the studied visual field. The changes in aberrations across the field may influence peripheral detection and motion perception. However, further research is required to investigate how the changes in aberrations influence peripheral detection and motion perception and consequently peripheral vision task performance.

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On-axis monochromatic higher-order aberrations increase with age. Few studies have been made of peripheral refraction along the horizontal meridian of older eyes, and none of their off-axis higher-order aberrations. We measured wave aberrations over the central 42°x32° visual field for a 5mm pupil in 10 young and 7 older emmetropes. Patterns of peripheral refraction were similar in the two groups. Coma increased linearly with field angle at a significantly higher rate in older than in young emmetropes (−0.018±0.007 versus −0.006±0.002 µm/deg). Spherical aberration was almost constant over the measured field in both age groups and mean values across the field were significantly higher in older than in young emmetropes (+0.08±0.05 versus +0.02±0.04 µm). Total root-mean-square and higher-order aberrations increased more rapidly with field angle in the older emmetropes. However, the limits to monochromatic peripheral retinal image quality are largely determined by the second-order aberrations, which do not change markedly with age, and under normal conditions the relative importance of the increased higher-order aberrations in older eyes is lessened by the reduction in pupil diameter with age. Therefore it is unlikely that peripheral visual performance deficits observed in normal older individuals are primarily attributable to the increased impact of higher-order aberration.

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Purpose: Poor image quality in the peripheral field may lead to myopia. Most studies measuring the higher order aberrations in the periphery have been restricted to the horizontal visual field. The purpose of this study was to measure higher order monochromatic aberrations across the central 42º horizontal x 32º vertical visual fields in myopes and emmetropes. ---------- Methods: We recruited 5 young emmetropes with spherical equivalent refractions +0.17 ± 0.45D and 5 young myopes with spherical equivalent refractions -3.9 ± 2.09D. Measurements were taken with a modified COAS-HD Hartmann-Shack aberrometer (Wavefront Sciences Inc). Measurements were taken while the subjects looked at 38 points arranged in a 7 x 6 matrix (excluding four corner points) through a beam splitter held between the instrument and the eye. A combination of the instrument’s software and our own software was used to estimate OSA Zernike coefficients for 5mm pupil diameter at 555nm for each point. The software took into account the elliptical shape of the off-axis pupil. Nasal and superior fields were taken to have positive x and y signs, respectively. ---------- Results: The total higher order RMS (HORMS) was similar on-axis for emmetropes (0.16 ± 0.02 μm) and myopes (0.17 ± 0.02 μm). There was no common pattern for HORMS for emmetropes across the visual field where as 4 out of 5 myopes showed a linear increase in HORMS in all directions away from the minimum. For all subjects, vertical and horizontal comas showed linear changes across the visual field. The mean rate of change of vertical coma across the vertical meridian was significantly lower (p = 0.008) for emmetropes (-0.005 ± 0.002 μm/deg) than for myopes (-0.013 ± 0.004 μm/deg). The mean rate of change of horizontal coma across the horizontal meridian was lower (p = 0.07) for emmetropes (-0.006 ± 0.003 μm/deg) than myopes (-0.011 ± 0.004 μm/deg). ---------- Conclusion: We have found differences in patterns of higher order aberrations across the visual fields of emmetropes and myopes, with myopes showing the greater rates of change of horizontal and vertical coma.

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Aim: To measure the influence of spherical intraocular lens implantation and conventional myopic laser in situ keratomileusis on peripheral ocular aberrations. Setting: Visual & Ophthalmic Optics Laboratory, School of Optometry & Institute of Health and Biomedical Innovation, Queensland University of Technology, Brisbane, Australia. Methods: Peripheral aberrations were measured using a modified commercial Hartmann-Shack aberrometer across 42° x 32° of the central visual field in 6 subjects after spherical intraocular lens (IOL) implantation and in 6 subjects after conventional laser in situ keratomileusis (LASIK) for myopia. The results were compared with those of age matched emmetropic and myopic control groups. Results: The IOL group showed a greater rate of quadratic change of spherical equivalent refraction across the visual field, higher spherical aberration, and greater rates of change of higher-order root-mean-square aberrations and total root-mean-square aberrations across the visual field than its emmetropic control group. However, coma trends were similar for the two groups. The LASIK group had a greater rate of quadratic change of spherical equivalent refraction across the visual field, higher spherical aberration, the opposite trend in coma across the field, and greater higher-order root-mean-square aberrations and total root-mean-square aberrations than its myopic control group. Conclusion: Spherical IOL implantation and conventional myopia LASIK increase ocular peripheral aberrations. They cause considerable increase in spherical aberration across the visual field. LASIK reverses the sign of the rate of change in coma across the field relative to that of the other groups. Keywords: refractive surgery, LASIK, IOL implantation, aberrations, peripheral aberrations

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Purpose: To investigate the influence of keratoconus on peripheral ocular aberrations. Methods: Aberrations of 7 mild and 5 moderate keratoconics were determined over a 42°horizontal x 32° vertical visual field with a modified COAS-HD aberrometer. Control data were obtained from an emmetropic group. Results: Most aberrations in keratoconics showed field dependence predominately along the vertical meridian. Mean spherical equivalent M, oblique astigmatism J45 and regular astigmatism J180 refraction components and total root mean square aberrations (excluding defocus) had high magnitudes in the inferior visual field. The rates of change of aberrations were higher in moderate than in mild keratoconics. Coma was the dominant peripheral higher-order aberration in both emmetropes and keratoconics; for the latter it had high magnitudes in the centre and periphery of the visual field. Conclusion: Greater rates of change of aberrations across the visual field occurred for the keratoconic groups than for the emmetropic control group. Moderate keratoconics had more rapid changes in, and higher magnitudes of aberrations across the visual field than mild keratoconics. The dominant higher-order aberration for the keratoconics across the visual field was vertical coma.

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PURPOSE. To measure tear film surface quality in healthy and dry eye subjects using three noninvasive techniques of tear film quality assessment and to establish the ability of these noninvasive techniques to predict dry eye. METHODS. Thirty four subjects participated in the study, and were classified as dry eye or normal, based on standard clinical assessments. Three non-invasive techniques were applied for measurement of tear film surface quality: dynamic-area high-speed videokeratoscopy (HSV), wavefront sensing (DWS) and lateral shearing interferometry (LSI). The measurements were performed in both natural blinking conditions (NBC) and in suppressed blinking conditions (SBC). RESULTS. In order to investigate the capability of each method to discriminate dry eye subjects from normal subjects, the receiver operating curve (ROC) was calculated and then the area under the curve (AUC) was extracted. The best result was obtained for the LSI technique (AUC=0.80 in SBC and AUC=0.73 in NBC), which was followed by HSV (AUC=0.72 in SBC and AUC=0.71 in NBC). The best result for DWS was AUC=0.64 obtained for changes in vertical coma in suppressed blinking conditions, while for normal blinking conditions the results were poorer. CONCLUSIONS. Non-invasive techniques of tear film surface assessment can be used for predicting dry eye and this can be achieved in natural blinking as well as suppressed blinking conditions. In this study, LSI showed the best detection performance, closely followed by the dynamic-area HSV. The wavefront sensing technique was less powerful, particularly in natural blinking conditions.

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There are several noninvasive techniques for assessing the kinetics of tear film, but no comparative studies have been conducted to evaluate their efficacies. Our aim is to test and compare techniques based on high-speed videokeratoscopy (HSV), dynamic wavefront sensing (DWS), and lateral shearing interferometry (LSI). Algorithms are developed to estimate the tear film build-up time TBLD, and the average tear film surface quality in the stable phase of the interblink interval TFSQAv. Moderate but significant correlations are found between TBLD measured with LSI and DWS based on vertical coma (Pearson's r2=0.34, p<0.01) and higher order rms (r2=0.31, p<0.01), as well as between TFSQAv measured with LSI and HSV (r2=0.35, p<0.01), and between LSI and DWS based on the rms fit error (r2=0.40, p<0.01). No significant correlation is found between HSV and DWS. All three techniques estimate tear film build-up time to be below 2.5 sec, and they achieve a remarkably close median value of 0.7 sec. HSV appears to be the most precise method for measuring tear film surface quality. LSI appears to be the most sensitive method for analyzing tear film build-up.

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Purpose: We compared subjective blur limits for defocus and the higher-order aberrations of coma, trefoil, and spherical aberration. ---------- Methods: Spherical aberration was presented in both Zernike and Seidel forms. Black letter targets (0.1, 0.35, and 0.6 logMAR) on white backgrounds were blurred using an adaptive optics system for six subjects under cycloplegia with 5 mm artificial pupils. Three blur criteria of just noticeable, just troublesome, and just objectionable were used.---------- Results: When expressed as wave aberration coefficients, the just noticeable blur limits for coma and trefoil were similar to those for defocus, whereas the just noticeable limits for Zernike spherical aberration and Seidel spherical aberration (the latter given as an “rms equivalent”) were considerably smaller and larger, respectively, than defocus limits.---------- Conclusions: Blur limits increased more quickly for the higher order aberrations than for defocus as the criterion changed from just noticeable to just troublesome and then to just objectionable.

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The depth of focus (DOF) can be defined as the variation in image distance of a lens or an optical system which can be tolerated without incurring an objectionable lack of sharpness of focus. The DOF of the human eye serves a mechanism of blur tolerance. As long as the target image remains within the depth of focus in the image space, the eye will still perceive the image as being clear. A large DOF is especially important for presbyopic patients with partial or complete loss of accommodation (presbyopia), since this helps them to obtain an acceptable retinal image when viewing a target moving through a range of near to intermediate distances. The aim of this research was to investigate the DOF of the human eye and its association with the natural wavefront aberrations, and how higher order aberrations (HOAs) can be used to expand the DOF, in particular by inducing spherical aberrations ( 0 4 Z and 0 6 Z ). The depth of focus of the human eye can be measured using a variety of subjective and objective methods. Subjective measurements based on a Badal optical system have been widely adopted, through which the retinal image size can be kept constant. In such measurements, the subject.s tested eye is normally cyclopleged. Objective methods without the need of cycloplegia are also used, where the eye.s accommodative response is continuously monitored. Generally, the DOF measured by subjective methods are slightly larger than those measured objectively. In recent years, methods have also been developed to estimate DOF from retinal image quality metrics (IQMs) derived from the ocular wavefront aberrations. In such methods, the DOF is defined as the range of defocus error that degrades the retinal image quality calculated from the IQMs to a certain level of the possible maximum value. In this study, the effect of different amounts of HOAs on the DOF was theoretically evaluated by modelling and comparing the DOF of subjects from four different clinical groups, including young emmetropes (20 subjects), young myopes (19 subjects), presbyopes (32 subjects) and keratoconics (35 subjects). A novel IQM-based through-focus algorithm was developed to theoretically predict the DOF of subjects with their natural HOAs. Additional primary spherical aberration ( 0 4 Z ) was also induced in the wavefronts of myopes and presbyopes to simulate the effect of myopic refractive correction (e.g. LASIK) and presbyopic correction (e.g. progressive power IOL) on the subject.s DOF. Larger amounts of HOAs were found to lead to greater values of predicted DOF. The introduction of primary spherical aberration was found to provide moderate increase of DOF while slightly deteriorating the image quality at the same time. The predicted DOF was also affected by the IQMs and the threshold level adopted. We then investigated the influence of the chosen threshold level of the IQMs on the predicted DOF, and how it relates to the subjectively measured DOF. The subjective DOF was measured in a group of 17 normal subjects, and we used through-focus visual Strehl ratio based on optical transfer function (VSOTF) derived from their wavefront aberrations as the IQM to estimate the DOF. The results allowed comparison of the subjective DOF with the estimated DOF and determination of a threshold level for DOF estimation. Significant correlation was found between the subject.s estimated threshold level for the estimated DOF and HOA RMS (Pearson.s r=0.88, p<0.001). The linear correlation can be used to estimate the threshold level for each individual subject, subsequently leading to a method for estimating individual.s DOF from a single measurement of their wavefront aberrations. A subsequent study was conducted to investigate the DOF of keratoconic subjects. Significant increases of the level of HOAs, including spherical aberration, coma and trefoil, can be observed in keratoconic eyes. This population of subjects provides an opportunity to study the influence of these HOAs on DOF. It was also expected that the asymmetric aberrations (coma and trefoil) in the keratoconic eye could interact with defocus to cause regional blur of the target. A dual-Badal-channel optical system with a star-pattern target was used to measure the subjective DOF in 10 keratoconic eyes and compared to those from a group of 10 normal subjects. The DOF measured in keratoconic eyes was significantly larger than that in normal eyes. However there was not a strong correlation between the large amount of HOA RMS and DOF in keratoconic eyes. Among all HOA terms, spherical aberration was found to be the only HOA that helped to significantly increase the DOF in the studied keratoconic subjects. Through the first three studies, a comprehensive understanding of DOF and its association to the HOAs in the human eye had been achieved. An adaptive optics system was then designed and constructed. The system was capable of measuring and altering the wavefront aberrations in the subject.s eye and measuring the resulting DOF under the influence of different combination of HOAs. Using the AO system, we investigated the concept of extending the DOF through optimized combinations of 0 4 Z and 0 6 Z . Systematic introduction of a targeted amount of both 0 4 Z and 0 6 Z was found to significantly improve the DOF of healthy subjects. The use of wavefront combinations of 0 4 Z and 0 6 Z with opposite signs can further expand the DOF, rather than using 0 4 Z or 0 6 Z alone. The optimal wavefront combinations to expand the DOF were estimated using the ratio of increase in DOF and loss of retinal image quality defined by VSOTF. In the experiment, the optimal combinations of 0 4 Z and 0 6 Z were found to provide a better balance of DOF expansion and relatively smaller decreases in VA. Therefore, the optimal combinations of 0 4 Z and 0 6 Z provides a more efficient method to expand the DOF rather than 0 4 Z or 0 6 Z alone. This PhD research has shown that there is a positive correlation between the DOF and the eye.s wavefront aberrations. More aberrated eyes generally have a larger DOF. The association of DOF and the natural HOAs in normal subjects can be quantified, which allows the estimation of DOF directly from the ocular wavefront aberration. Among the Zernike HOA terms, spherical aberrations ( 0 4 Z and 0 6 Z ) were found to improve the DOF. Certain combinations of 0 4 Z and 0 6 Z provide a more effective method to expand DOF than using 0 4 Z or 0 6 Z alone, and this could be useful in the optimal design of presbyopic optical corrections such as multifocal contact lenses, intraocular lenses and laser corneal surgeries.