Objective measurement of wave aberrations of the human eye with the use of a Hartmann-Shack wave-front sensor

Monocular diplopia caused by ocular aberrations and hyperopic defocus

As a single aperture, approximately monofocal optical system, the human eye generally creates a single image on the retina. However, the literature contains many reports of perceptual monocular diplopia. While it is easy to understand how distortion may produce monocular diplopia, its reported high incidence in normal eyes is less easily understood. We examine a model which ascribes monocular diplopia to an interaction between defocus and ocular spherical aberration. Using a psychophysical hyperacuity-based alignment procedure we measured the transverse aberration function in 0.5 mm steps horizontally across the pupil in the eyes of three cyclopleged subjects. Ocular transverse aberration functions were derived with best refraction and with simulated myopia and hyperopia. Monocular diplopia was also measured under the same conditions. All three subjects showed significant, but different, degrees of positive spherical aberration. The measured ocular transverse aberration functions were predictably modified by the hyperopic and myopic defocus. Hyperopic defocus combined with positive (myopic) spherical aberration changes a monotonic transverse aberration function with a single inflection point into a biphasic function with two inflection points. The locations of the inflections predict the presence and magnitude of the perceived diplopia. These experimental results confirm Verhoeff's (1900) hypothesis for the ocular cause of monocular diplopia.

Off-axis optical quality and retinal sampling in the human eye

Using the double pass procedure, Navarro et al. (1993; Journal of the Optical Society of America A, 10, 201-212) measured the monochromatic modulation transfer function (MTF) of the human eye as a function of retinal eccentricity. They chose conditions as similar as possible to those encountered in natural viewing. We report new measurements obtained with conditions chosen instead to optimize retinal image quality: we paralyzed accommodation, used a 3 mm pupil, and corrected defocus and oblique astigmatism at each retinal location. MTFs were estimated at the tangential focus, circle of least confusion, and sagittal focus produced by oblique astigmatism. Though optical blur is well-known to have little effect on peripheral visual acuity, it can nonetheless substantially reduce aliasing by receptoral and post-receptoral spatial sampling.

Images of cone photoreceptors in the living human eye

Though the photoreceptor mosaic has been imaged through the intact optics of the eyes of several species, it has not been clear whether individual photoreceptors can be resolved in the living human eye. We have constructed a high-resolution fundus camera and have resolved cones with a spacing as small as 3.5 microns in single images of the fundus. The high contrast of these images implies that almost all the light returning from the retina at this wavelength (555 nm) has passed through the apertures of foveal cones. The average power spectra of our retinal images show that it is possible to recover spatial frequencies as high as 150 c/deg in eyes with normal optical quality, a conclusion that was confirmed with estimates of the optical quality of these eyes obtained with a Hartmann-Shack wavefront sensor. These results emphasize the superiority of the eye's optics over the spatial sampling limits of the retina when the eye's optical quality is optimized. They also show that it would be possible to routinely resolve retinal structures as small as photoreceptors in the normal living eye if its aberrations could be corrected.

Geometrical technique to determine the influence of monochromatic aberrations on retinoscopy

A geometrical-optical analysis is developed to predict the reflex observed in retinoscopy. The analysis can be expanded to explain the reflex for an eye with aberrations. The succession of reflexes across the pupil for each position of the retinoscope is represented in a contour plot. The plots demonstrate that retinoscopy can be considered a measure of the transverse ray aberration of the eye. For an eye with simple defocus this causes the typical with and against motions observed with hyperopic and myopic refractive errors. For an eye with aberrations we predict more-complex retinoscopic reflexes. This theory is confirmed by actual measurements on a human eye with known aberrations.

Phase transfer and point-spread function of the human eye determined by a new asymmetric double-pass method

A recent study has shown that the double-pass method provides a good estimate of the ocular modulation transfer function (MTF) but that it does not yield the phase transfer function (PTF) [J. Opt. Soc. Am. A 12, 195 (1995)]. Therefore, one cannot recover the true retinal point-spread function (PSF). We present a modification of the double-pass method to overcome this problem. The key is to break the symmetry between the two passes. By using an unexpanded Gaussian input beam, we produce a diffraction-limited PSF for the first passes. Then, by using a large exit pupil, we get an aberrated PSF for the second pass. The double-pass aerial image is the cross correlation of both PSF's, so that the Fourier transform of such an aerial image directly provides the true retinal PTF, up to the cutoff frequency of the effective (small), diffraction-limited entrance pupil. The resulting double-pass aerial image is a blurred version of the true retinal PSF. Thus it shows the effect not only of even symmetric aberrations but also of odd and irregular aberrations such as coma. We have explored two different ways to retrieve the true retinal PSF: (a) deblurring of the aerial image and (b) PSF reconstruction combining PTF data with conventional double-pass MTF. We present promising initial results with both artificial and real eyes.

Odd aberrations and double-pass measurements of retinal image quality

We investigated the formation of the aerial image in the double-pass method to measure the optical quality of the human eye. We show theoretically and empirically that the double pass through the eye's optics forces the light distribution in the aerial image to be an even-symmetric function even if the single-pass point-spread function is asymmetric as a result of odd aberrations in the eye. The reason for this is that the double-pass imaging process is described by the autocorrelation rather than the autoconvolution of the single-pass point-spread functions, as has been previously assumed. This implies that although the modulation transfer function can be computed from the double-pass aerial image, the phase transfer function cannot. We also show that the lateral chromatic aberration of the eye cannot be measured with the double-pass procedure because it is canceled by the second pass through the eye's optics.

Double-pass and interferometric measures of the optical quality of the eye

We compare two methods for measuring the modulation transfer function (MTF) of the human eye: an interferometric method similar to that of Campbell and Green [J. Physiol. (London) 181, 576 (1965)] and a double-pass procedure similar to that of Santamaria et al. [J. Opt. Soc. Am. A 4, 1109 (1987)]. We implemented various improvements in both techniques to reduce error in the estimates of the MTF. We used the same observers, refractive state, pupil size (3 mm), and wavelength (632.8 nm) for both methods. In the double-pass method we found close agreement between the plane of subjective best focus for the observer and the plane of objective best focus, suggesting that much of the reflected light is confined within individual cones throughout its double pass through the receptor layer. The double-pass method produced MTF's that were similar to but slightly lower than those of the interferometric method. This additional loss in modulation transfer is probably attributable to light reflected from the choroid, because green light, which reduces the contribution of the choroid to the fundus reflection, produces somewhat higher MTF's that are consistent with the interferometric results. When either method is used, the MTF's lie well below those obtained with the aberroscope method [Vision Res. 28, 659 (1988)]. On the basis of the interferometric method, we propose a new estimate of the monochromatic MTF of the eye.