The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

Eyelid pressure on the cornea

The eyelids play an important role in lubricating and protecting the surface of the eye. Each blink serves to spread fresh tears, remove debris and replenish the smooth optical surface of the eye. Yet little is known about how the eyelids contact the ocular surface and what pressure distribution exists between the eyelids and cornea. As the principal refractive component of the eye, the cornea is a major element of the eye’s optics. The optical properties of the cornea are known to be susceptible to the pressure exerted by the eyelids. Abnormal eyelids, due to disease, have altered pressure on the ocular surface due to changes in the shape, thickness or position of the eyelids. Normal eyelids also cause corneal distortions that are most often noticed when they are resting closer to the corneal centre (for example during reading). There were many reports of monocular diplopia after reading due to corneal distortion, but prior to videokeratoscopes these localised changes could not be measured. This thesis has measured the influence of eyelid pressure on the cornea after short-term near tasks and techniques were developed to quantify eyelid pressure and its distribution. The profile of the wave-like eyelid-induced corneal changes and the refractive effects of these distortions were investigated. Corneal topography changes due to both the upper and lower eyelids were measured for four tasks involving two angles of vertical downward gaze (20° and 40°) and two near work tasks (reading and steady fixation). After examining the depth and shape of the corneal changes, conclusions were reached regarding the magnitude and distribution of upper and lower eyelid pressure for these task conditions. The degree of downward gaze appears to alter the upper eyelid pressure on the cornea, with deeper changes occurring after greater angles of downward gaze. Although the lower eyelid was further from the corneal centre in large angles of downward gaze, its effect on the cornea was greater than that of the upper eyelid. Eyelid tilt, curvature, and position were found to be influential in the magnitude of eyelid-induced corneal changes. Refractively these corneal changes are clinically and optically significant with mean spherical and astigmatic changes of about 0.25 D after only 15 minutes of downward gaze (40° reading and steady fixation conditions). Due to the magnitude of these changes, eyelid pressure in downward gaze offers a possible explanation for some of the day-to-day variation observed in refraction. Considering the magnitude of these changes and previous work on their regression, it is recommended that sustained tasks performed in downward gaze should be avoided for at least 30 minutes before corneal and refractive assessment requiring high accuracy. Novel procedures were developed to use a thin (0.17 mm) tactile piezoresistive pressure sensor mounted on a rigid contact lens to measure eyelid pressure. A hydrostatic calibration system was constructed to convert raw digital output of the sensors to actual pressure units. Conditioning the sensor prior to use regulated the measurement response and sensor output was found to stabilise about 10 seconds after loading. The influences of various external factors on sensor output were studied. While the sensor output drifted slightly over several hours, it was not significant over the measurement time of 30 seconds used for eyelid pressure, as long as the length of the calibration and measurement recordings were matched. The error associated with calibrating at room temperature but measuring at ocular surface temperature led to a very small overestimation of pressure. To optimally position the sensor-contact lens combination under the eyelid margin, an in vivo measurement apparatus was constructed. Using this system, eyelid pressure increases were observed when the upper eyelid was placed on the sensor and a significant increase was apparent when the eyelid pressure was increased by pulling the upper eyelid tighter against the eye. For a group of young adult subjects, upper eyelid pressure was measured using this piezoresistive sensor system. Three models of contact between the eyelid and ocular surface were used to calibrate the pressure readings. The first model assumed contact between the eyelid and pressure sensor over more than the pressure cell width of 1.14 mm. Using thin pressure sensitive carbon paper placed under the eyelid, a contact imprint was measured and this width used for the second model of contact. Lastly as Marx’s line has been implicated as the region of contact with the ocular surface, its width was measured and used as the region of contact for the third model. The mean eyelid pressures calculated using these three models for the group of young subjects were 3.8 ± 0.7 mmHg (whole cell), 8.0 ± 3.4 mmHg (imprint width) and 55 ± 26 mmHg (Marx’s line). The carbon imprints using Pressurex-micro confirmed previous suggestions that a band of the eyelid margin has primary contact with the ocular surface and provided the best estimate of the contact region and hence eyelid pressure. Although it is difficult to directly compare the results with previous eyelid pressure measurement attempts, the eyelid pressure calculated using this model was slightly higher than previous manometer measurements but showed good agreement with the eyelid force estimated using an eyelid tensiometer. The work described in this thesis has shown that the eyelids have a significant influence on corneal shape, even after short-term tasks (15 minutes). Instrumentation was developed using piezoresistive sensors to measure eyelid pressure. Measurements for the upper eyelid combined with estimates of the contact region between the cornea and the eyelid enabled quantification of the upper eyelid pressure for a group of young adult subjects. These techniques will allow further investigation of the interaction between the eyelids and the surface of the eye.

Effects of age on peripheral ocular aberrations

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.

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

Axial elongation following prolonged near work in myopes and emmetropes

Background/aims: To investigate the influence of a period of sustained near work upon axial length in groups of emmetropes and myopes. Methods: Forty young adult subjects (20 myopes and 20 emmetropes) were recruited for the study. Myopes were further classified as either early onset (EOM), late onset (LOM), stable (SM) or progressing (PM) subgroups. Axial length was measured with the IOLMaster instrument before, immediately after and then again 10 minutes after a continuous 30 minute near task of 5 D accommodation demand. Measures of distance objective refraction were also collected. Results: Significant changes in axial length were observed immediately following the near task. EOM axial length elongated on average by 0.027 ± 0.021 mm, LOM by 0.014 ± 0.020 mm, EMM by 0.010 ± 0.015 mm, PM by 0.031 ± 0.022 mm, and SM by 0.014 ± 0.018 mm. At the conclusion of the 10 minute regression period, axial length measures were not significantly different from baseline values. Conclusion: Axial elongation was observed following a prolonged near task. Both EOM and PM groups showed increases in axial length that were significantly greater than emmetropes

Axial length charges during accommodation in myopes and emmetropes

Purpose: To investigate the influence of accommodation upon axial length (and a comprehensive range of ocular biometric parameters), in populations of young adult myopic and emmetropic subjects. Methods: Forty young adult subjects had ocular biometry measured utilizing a non-contact optical biometer (Lenstar LS 900) based upon the principle of optical low coherence reflectometry, under three different accommodation demands (0 D, 3 D and 6 D). Subjects were classified as emmetropes (n=19) or myopes (n=21) based upon their spherical equivalent refraction (mean emmetropic refraction -0.05 ± 0.27DS and mean myopic refraction -1.82 ± 0.84 DS). Results: Axial length changed significantly with accommodation, with a mean increase of 11.9 ± 12.3 µm and 24.1 ± 22.7 µm for the 3 D and 6 D accommodation stimuli respectively. A significant axial elongation associated with accommodation was still evident even following correction of the axial length data for potential error due to lens thickness change. The mean ‘corrected’ increase in axial length was 5.2 ± 11.2 µm, and 7.4 ± 18.9 µm for the 3 D and 6 D stimuli respectively. There was no significant difference between the myopic and emmetropic populations in terms of the magnitude of change in axial length with accommodation, regardless of whether the data were corrected or not. A number of other ocular biometric parameters, such as anterior chamber depth, lens thickness and vitreous chamber depth also exhibited significant change with accommodation. The myopic and emmetropic populations also exhibited no significant difference in the magnitude of change in these parameters with accommodation. Conclusions: The eye undergoes a significant axial elongation associated with a brief period of accommodation, and the magnitude of this change in eye length increases for larger accommodation demands, however there is no significant difference in the magnitude of eye elongation in myopic and emmetropic subjects.

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.

Water drinking influences eye length and IOP in young healthy subjects

This study aimed to investigate the influence of water loading upon intraocular pressure (IOP), ocular pulse amplitude (OPA) and axial length. Twenty one young adult subjects who were classified based on their spherical equivalent refraction as either myopes (n=11), or emmetropes (n=10) participated. Measures of IOP, OPA and ocular biometrics were collected before, and then 10, 15, 25 and 30 minutes following the ingestion of 1000 ml of water. Significant increases in both IOP and OPA were found to occur following water loading (p<0.0001), with peaks in both parameters occurring at 10 minutes after water loading (mean ± SEM increase of 2.24 ± 0.31 mmHg in IOP and 0.46 ± 0.06 mmHg in OPA). Axial length was found to reduce significantly following water loading (p=0.0005), with the largest reduction in axial length evident 10 minutes after water drinking (mean decrease 12 ± 3 µm). A significant time by refractive error group interaction (p=0.048) was found in axial length, indicative of a different pattern of change in eye length following water loading between the myopic and emmetropic populations. The largest difference in axial length change was evident at 10 minutes after water loading with a 17 ± 5 µm reduction in axial length evident in the myopes and only a 6 ± 2 µm reduction in the emmetropes. These findings illustrate significant changes in ocular parameters in young adult subjects following water loading.

Thomas Young's contribution to visual optics : the Bakerian lecture "On the mechanism of the eye"

Thomas Young (1773-1829) carried out major pioneering work in many different subjects. In 1800 he gave the Bakerian Lecture of the Royal Society on the topic of the “mechanism of the eye”: this was published in the following year (Young, 1801). Young used his own design of optometer to measure refraction and accommodation, and discovered his own astigmatism. He considered the different possible origins of accommodation and confirmed that it was due to change in shape of the lens rather than to change in shape of the cornea or an increase in axial length. However, the paper also dealt with many other aspects of visual and ophthalmic optics, such as biometric parameters, peripheral refraction, longitudinal chromatic aberration, depth-of-focus and instrument myopia. These aspects of the paper have previously received little attention. We now give detailed consideration to these and other less-familiar features of Young’s work and conclude that his studies remain relevant to many of the topics which currently engage visual scientists.

Immunohistochemical analysis of structural changes in collagen for the assessment of osteoarthritis

Collagen fibrillation within articular cartilage (AC) plays a key role in joint osteoarthritis (OA) progression and, therefore, studying collagen synthesis changes could be an indicator for use in the assessment of OA. Various staining techniques have been developed and used to determine the collagen network transformation under microscopy. However, because collagen and proteoglycan coexist and have the same index of refraction, conventional methods for specific visualization of collagen tissue is difficult. This study aimed to develop an advanced staining technique to distinguish collagen from proteoglycan and to determine its evolution in relation to OA progression using optical and laser scanning confocal microscopy (LSCM). A number of AC samples were obtained from sheep joints, including both healthy and abnormal joints with OA grades 1 to 3. The samples were stained using two different trichrome methods and immunohistochemistry (IHC) to stain both colourimetrically and with fluorescence. Using optical microscopy and LSCM, the present authors demonstrated that the IHC technique stains collagens only, allowing the collagen network to be separated and directly investigated. Fluorescently-stained IHC samples were also subjected to LSCM to obtain three-dimensional images of the collagen fibres. Changes in the collagen fibres were then correlated with the grade of OA in tissue. This study is the first to successfully utilize the IHC staining technique in conjunction with laser scanning confocal microscopy. This is a valuable tool for assessing changes to articular cartilage in OA.

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.

Thomas Young’s contributions to geometrical optics

In addition to his work on physical optics, Thomas Young (1773-1829) made several contributions to geometrical optics, most of which received little recognition in his time or since. We describe and assess some of these contributions: Young’s construction (the basis for much of his geometric work), paraxial refraction equations, oblique astigmatism and field curvature, and gradient-index optics.

Third-order theory of spectacle lenses applied to correction of peripheral refractive errors

Purpose: To demonstrate that relatively simple third-order theory can provide a framework which shows how peripheral refraction can be manipulated by altering the forms of spectacle lenses. Method: Third-order equations were used to yield lens forms that correct peripheral power errors, either for the lenses alone or in combination with typical peripheral refractions of myopic eyes. These results were compared with those of finite ray-tracing. Results: The approximate forms of spherical and conicoidal lenses provided by third-order theory were flatter over a moderate myopic range than the forms obtained by rigorous raytracing. Lenses designed to correct peripheral refractive errors produced large errors when used with foveal vision and a rotating eye. Correcting astigmatism tended to give large errors in mean oblique error and vice versa. When only spherical lens forms are used, correction of the relative hypermetropic peripheral refractions of myopic eyes which are observed experimentally, or the provision of relative myopic peripheral refractions in such eyes, seems impossible in the majority of cases. Conclusion: The third-order spectacle lens design approach can readily be used to show trends in peripheral refraction.