Decentred optical axes and aberrations along principal visual field meridians

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.

Limits of spherical blur determined with an adaptive optics mirror

We extended an earlier study (Vision Research, 45, 1967–1974, 2005) in which we investigated limits at which induced blur of letter targets becomes noticeable, troublesome and objectionable. Here we used a deformable adaptive optics mirror to vary spherical defocus for conditions of a white background with correction of astigmatism; a white background with reduction of all aberrations other than defocus; and a monochromatic background with reduction of all aberrations other than defocus. We used seven cyclopleged subjects, lines of three high-contrast letters as targets, 3–6 mm artificial pupils, and 0.1–0.6 logMAR letter sizes. Subjects used a method of adjustment to control the defocus component of the mirror to set the 'just noticeable', 'just troublesome' and 'just objectionable' defocus levels. For the white-no adaptive optics condition combined with 0.1 logMAR letter size, mean 'noticeable' blur limits were ±0.30, ±0.24 and ±0.23 D at 3, 4 and 6 mm pupils, respectively. White-adaptive optics and monochromatic-adaptive optics conditions reduced blur limits by 8% and 20%, respectively. Increasing pupil size from 3–6 mm decreased blur limits by 29%, and increasing letter size increased blur limits by 79%. Ratios of troublesome to noticeable, and of objectionable to noticeable, blur limits were 1.9 and 2.7 times, respectively. The study shows that the deformable mirror can be used to vary defocus in vision experiments. Overall, the results of noticeable, troublesome and objectionable blur agreed well with those of the previous study. Attempting to reduce higher-order aberrations or chromatic aberrations, reduced blur limits to only a small extent.

Effect of orthokeratology on peripheral aberrations of the eye

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

Describing ocular aberrations with wavefront vergence maps

A common optometric problem is to specify the eye’s ocular aberrations in terms of Zernike coefficients and to reduce that specification to a prescription for the optimum sphero-cylindrical correcting lens. The typical approach is first to reconstruct wavefront phase errors from measurements of wavefront slopes obtained by a wavefront aberrometer. This paper applies a new method to this clinical problem that does not require wavefront reconstruction. Instead, we base our analysis of axial wavefront vergence as inferred directly from wavefront slopes. The result is a wavefront vergence map that is similar to the axial power maps in corneal topography and hence has a potential to be favoured by clinicians. We use our new set of orthogonal Zernike slope polynomials to systematically analyse details of the vergence map analogous to Zernike analysis of wavefront maps. The result is a vector of slope coefficients that describe fundamental aberration components. Three different methods for reducing slope coefficients to a spherocylindrical prescription in power vector forms are compared and contrasted. When the original wavefront contains only second order aberrations, the vergence map is a function of meridian only and the power vectors from all three methods are identical. The differences in the methods begin to appear as we include higher order aberrations, in which case the wavefront vergence map is more complicated. Finally, we discuss the advantages and limitations of vergence map representation of ocular aberrations.

Influence of spherical intraocular lens implantation and conventional laser in situ keratomileusis on peripheral ocular aberrations

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

Peripheral ocular aberrations in mild and moderate keratoconus

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.

Subjective blur limits for higher order aberrations

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.

The role of cardiopulmonary signals in the dynamics of the eye's wavefront aberrations

Abstract—The role of cardiopulmonary signals in the dynamics of wavefront aberrations in the eye has been examined. Synchronous measurement of the eye’s wavefront aberrations, cardiac function, blood pulse, and respiration signals were taken for a group of young, healthy subjects. Two focusing stimuli, three breathing patterns, as well as natural and cycloplegic eye conditions were examined. A set of tools, including time–frequency coherence and its metrics, has been proposed to acquire a detailed picture of the interactions of the cardiopulmonary system with the eye’s wavefront aberrations. The results showed that the coherence of the blood pulse and its harmonics with the eye’s aberrations was, on average, weak (0.4 ± 0.15), while the coherence of the respiration signal with eye’s aberrations was, on average, moderate (0.53 ± 0.14). It was also revealed that there were significant intervals during which high coherence occurred. On average, the coherence was high (>0.75) during 16% of the recorded time, for the blood pulse, and 34% of the time for the respiration signal. A statistically significant decrease in average coherence was noted for the eye’s aberrations with respiration in the case of fast controlled breathing (0.5 Hz). The coherence between the blood pulse and the defocus was significantly larger for the far target than for the near target condition. After cycloplegia, the coherence of defocus with the blood pulse significantly decreased, while this was not the case for the other aberrations. There was also a noticeable, but not statistically significant, increase in the coherence of the comatic term and respiration in that case. By using nonstationary measures of signal coherence, a more detailed picture of interactions between the cardiopulmonary signals and eye’s wavefront aberrations has emerged.

Wavefront aberrations and the depth of focus of the human eye

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.

Myopia and peripheral ocular aberrations

We measured wave aberrations over the central 42° x 32° visual field for a 5 mm pupil for groups of 10 emmetropic (mean spherical equivalent 0.11 ± 0.50 D) and 9 myopic (MSE -3.67 ± 1.91 D) young adults. Relative peripheral refractive errors over the measured field were generally myopic in both groups. Mean values of were almost constant across the measured field and were more positive in emmetropes (+0.023 ± 0.043 microns) than in myopes (-0.007 ± 0.045 microns). Coma varied more rapidly with field angle in myopes: modeling suggested that this difference reflected the differences in mean anterior corneal shape and axial length in the two groups. In general however, overall levels of RMS aberration differed only modestly between the two groups, implying that it is unlikely that high levels of aberration contribute to myopia development.

Effect of accommodation on peripheral ocular aberrations

Changes in peripheral aberrations, particularly higher-order aberrations, as a function of accommodation have received little attention. Wavefront aberrations were measured for the right eyes of 9 young adult emmetropes at 38 field positions in the central 42 x 32 degrees of the visual field. Subjects accommodated monocularly to targets at vergences of either 0.3 or 4.0 D. Wavefront data for a 5 mm diameter pupil were analyzed either in terms of the vector components of refraction or Zernike coefficients and total RMS wavefront aberrations. Relative peripheral refractive error (RPRE) was myopic at both accommodation demands and showed only a slight, not statistically significant, hypermetropic shift in the vertical meridian with the higher accommodation demand. There was little change in the astigmatic components of refraction or the higher-order Zernike coefficients, apart from fourth-order spherical aberration which became more negative (by 0.10 µm) at all field locations. Although it has been suggested that nearwork and the state of peripheral refraction may play some role in myopia development, for most of our adult emmetropes any changes with accommodation in RPRE and aberration were small. Hence it seems unlikely that such changes can be of importance to late-onset myopisation.

Ocular aberrations in the peripheral visual field

We modified a commercial Hartmann-Shack aberrometer and used it to measure ocular aberrations across the central 42º horizontal x 32º vertical visual fields of five young emmetropic subjects. Some Zernike aberration coefficients show coefficient field distributions that were similar to the field dependence predicted by Seidel theory (astigmatism, oblique astigmatism, horizontal coma, vertical coma), but defocus did not demonstrate such similarity.

Specifying peripheral aberrations in visual science

Purpose: Investigations of foveal aberrations assume circular pupils. However, the pupil becomes increasingly elliptical with increase in visual field eccentricity. We address this and other issues concerning peripheral aberration specification. Methods: One approach uses an elliptical pupil similar to the actual pupil shape, stretched along its minor axis to become a circle so that Zernike circular aberration polynomials may be used. Another approach uses a circular pupil whose diameter matches either the larger or smaller dimension of the elliptical pupil. Pictorial presentation of aberrations, influence of wavelength on aberrations, sign differences between aberrations for fellow eyes, and referencing position to either the visual field or the retina are considered. Results: Examples show differences between the two approaches. Each has its advantages and disadvantages, but there are ways to compensate for most disadvantages. Two representations of data are pupil aberration maps at each position in the visual field and maps showing the variation in individual aberration coefficients across the field. Conclusions: Based on simplicity of use, adequacy of approximation, possible departures of off-axis pupils from ellipticity, and ease of understanding by clinicians, the circular pupil approach is preferable to the stretched elliptical approach for studies involving field angles up to 30 deg.