David A. Atchison

Optics of the human eye

The first stage in the process of vision is the formation of images of the outside world on the retina at the back of the eye. This article describes the optical structure and optical properties of the human eye, how the retinal image is formed and the factors affecting its quality. Brief mention is given to neural factors that combine with the optics to determine how well we see. The article concentrates on the optics of healthy eyes.

Measurement of monochromatic ocular aberrations of human eyes as a function of accommodation by the howland aberroscope technique

Further development of the objective version of the Howland and Howland [(1976) Science, 193, 580-582; (1977) Journal of the Optical Society of America, 67, 1508-1518] aberroscope technique for measuring ocular aberrations is described. Compensation for refractive corrections and calibration is discussed. The technique was used to investigate the effect of accommodation upon the monochromatic aberrations of the right eyes of 15 subjects. Coma and coma-like aberrations were the dominant aberrations for most people at different accommodation levels, thus confirming previous findings. Variations in aberrations were considerable between subjects. About half the subjects showed the classical trend towards negative spherical aberration with accommodation. Changes in spherical aberration with accommodation in this study were less than found in previous studies where all monochromatic aberration was considered to be spherical aberration.

Refractive index distribution and optical properties of the isolated human lens measured using magnetic resonance imaging (MRI).

Using a non-invasive MRI technique for measuring the refractive index distribution through the crystalline lens, refractive index maps were obtained through 20 intact isolated human lenses (7-82years). Focal length measurements, obtained by simulated light ray propagation through each index map were found to be in agreement with direct measurements performed on a scanning laser apparatus. With increasing age, the refractive index profiles became flatter in the central region, accompanied by steepening of the profile in the periphery. This appears to be an important mechanism underlying the observed changes in power and longitudinal aberration of the human lens.

Age-related changes in optical and biometric characteristics of emmetropic eyes

We measured optical and biometric parameters of emmetropic eyes as a function of age. There were approximately 20 subjects each in age groups 18-29, 30-39, 40-49, 50-59, and 60-69 years with similar male and female numbers. One eye was tested for each subject, having spherical equivalent in the range -0.88 D to +0.75 D and <or=0.50 D astigmatism. Despite considerable data scatter, we found significant age changes: anterior chamber depth decreased 0.011 mm/year, lens central thickness increased 0.024 mm/year, anterior segment depth increased 0.013 mm/year, eye length increased 0.011 mm/year, anterior lens radius of curvature decreased 0.044 mm/year, and lens equivalent refractive index decreased 0.0003/year. Males had higher anterior corneal radii of curvature (0.16 mm), lower lens equivalent refractive index (0.006), longer vitreous lengths (0.51 mm), and longer axial lengths (0.62 mm) than females. Superficially, the results suggest that eyes get bigger as they age. However, results can be related to refraction patterns in which refraction is stable in 20s to 40s and then moves in the hypermetropic direction. It is likely that several young subjects will become hypermetropic as they age, and it is possible that some of the older subjects were myopic when younger.

Monochromatic aberrations and myopia.

The monochromatic aberrations present in the eyes of a group of 21 young myopic subjects and 16 young emmetropic subjects were measured along the visual axis at three levels of accommodation. The aberrations were measured using a modified aberroscope technique which makes use of a retinal camera to photograph the shadow image of the aberroscope grid on the retina, while accommodation levels of 0, 1.5 and 3.0 D were induced consensually. Fourth-order aberrations were significantly different between the emmetropic and myopic groups, with the myopes showing lower fourth-order terms. A high proportion of the aberroscope grids photographed in the myopic eyes were too highly aberrated to permit analysis.

Modeling the power of the aging human eye

A hypothesis is presented that may explain why the aging eye does not become myopic with age. The power of the eye lens is predicted with a modeling approach to determine how the form of the refractive-index gradient within the lens can change to maintain a constant power in spite of age-related curvature increase. Methods used include published age-dependent data on the optical parameters of the eye, a mathematical model of the lens based on elliptical isoindicial contours, and a refractive-index profile that can be expressed as a power series in the distance from the lens center. The kinds of change in profile required to prevent the eye from becoming myopic as its lens grows are shown.

Subjective depth-of-focus of the eye.

An experiment is described in which the subjective depth-of-focus (DOF) of the eye, defined as the range of focusing errors for which the image of the target appears to have the same clarity, contrast, and form as the optimal in-focus image, was measured as a function of the size of high contrast (99%) Snellen Es for 5 trained subjects under cycloplegia. Mean DOF increased by approximately 60% as the size of the letter detail increased from −0.2 to 0.87 log min arc (Snellen equivalent: 6/3.8 to 6/45), although there were considerable intersubject variations. DOF declined with increasing pupil diameter, the mean total DOFs being 0.86, 0.59, and 0.55 D for 2-, 4-, and 6-mm pupils, respectively. In a second experiment, use of low (21%) contrast letters with a 4-mm pupil and 4 subjects marginally increased the DOF (by 0.08 ± 0.05 D); refraction also shifted in a myopic direction by a mean of 0.15 ± 0.06 D compared with the high contrast letters. A third experiment with four less-experienced subjects demonstrated the importance of instruction and training in any measurement involving judgment of just-perceptible defocus blur. The clinical implications of the results for measurements of refraction and amplitude of accommodation are discussed.

Optical models for human myopic eyes.

Data from the authors investigations and other studies are used to construct refractive dependent models. These models include a gradient index lens and aspheric corneal, lens and retinal surfaces. Elements that alter with refraction are anterior corneal radius, vitreous length and retinal shape (vertex radius of curvature and asphericity) and decentration. Two versions of the models are produced, one with centred and symmetrical optical elements, and one with tilts of the lens and decentrations and tilts of the retina. The centred model predicts increase in spherical aberration in myopia. It predicts the relative change in mean sphere in the periphery between the horizontal and vertical meridians that has been observed in a recent experimental study. It overestimates peripheral astigmatism by about 50%. The decentred version has limited success in predicting changes in peripheral refraction of average eyes.

Peripheral refraction in orthokeratology patients.

Purpose. The purpose of this study is to measure refraction across the horizontal central visual field in orthokeratology patients before and during treatment. Methods. Refractions were measured out to 34° eccentricity in both temporal and nasal visual fields using a free-space autorefractor (Shin-Nippon SRW5000) for the right eyes of four consecutively presenting myopic adult patients. Measurements were made before orthokeratology treatment and during the course of treatment (usually 1 week and 2 weeks into treatment). Refractions were converted into mean sphere (M), 90° to 180° astigmatism (J180), and 45° to 135° astigmatism (J45) components. Results. Before treatment, subjects had either a relatively constant mean sphere refraction across the field or a relative hypermetropia in the periphery as compared with the central refraction. As a result of treatment, myopia decreased but at reduced rate out into the periphery. Most patients had little change in mean sphere at 30° to 34°. In all patients, the refraction pattern altered little after the first week. Conclusion. Orthokeratology can correct myopia over the central ± 10° of the visual field but produces only minor changes at field angles larger than 30°. If converting relative peripheral hypermetropia to relative peripheral myopia is a good way of limiting the axial elongation that leads to myopia, orthokeratology is an excellent option for achieving this.

In vivo study of changes in refractive index distribution in the human crystalline lens with age and accommodation.

PURPOSE Magnetic resonance imaging (MRI) was used to map the refractive index distribution in human eye lenses in vivo and to investigate changes with age and accommodation. METHODS Whole-eye MR images were obtained for sagittal and transverse axial planes in one eye each of 15 young (19-29 years) and 15 older (60-70 years) subjects when viewing a far ( approximately 6 m) target and at individual near points in the young subjects. Refractive index maps of the crystalline lens were calculated by using a procedure previously validated in vitro. RESULTS A central high refractive index plateau region and sharp decline in refractive index at the periphery were seen in all three groups. The peripheral decline was steepest in the older lenses and least steep in the young accommodated lenses. Average lens thickness increased (+0.27 mm; P < 0.05) and equatorial diameter decreased (-0.35 mm; P < 0.05) with accommodation. Axial thickness (+0.96 mm; P < 0.05) and equatorial diameter (+0.28 mm; P < 0.05) increased with age. The central index (1.409 +/- 0.008) did not differ between groups. The axial thickness of the central plateau increased with age (+0.83 mm; P < 0.05) but not significantly with accommodation. The equatorial diameter of the central plateau increased with age (+0.56 mm; P < 0.01) and decreased with accommodation (-0.43 mm; P < 0.05). CONCLUSIONS The refractive index of the central plateau region does not change significantly with accommodation or ageing, but its size increases with age and the peripheral decline in refractive index becomes steeper in older lenses.