Corneal aberrations, monocular diplopia, and ghost images: analysis using corneal topographical data

Catastrophe optics theory unveils the localised wave aberration features that generate ghost images

Monocular polyplopia (ghost or multiple images) is a serious visual impediment for some people who report seeing two (diplopia), three (triplopia) or even more images. Polyplopia is expected to appear if the point spread function (PSF) has multiple intensity cores (a dense concentration of a large portion of the radiant flux contained in the PSF) relatively separated from each other, each of which contributes to a distinct image. We present a theory that assigns these multiple PSF cores to specific features of aberrated wavefronts, thereby accounting optically for the perceptual phenomenon of monocular polyplopia. The theory provides two major conclusions. First, the most likely event giving rise to multiple PSF cores is the presence of hyperbolic, or less probably elliptical, umbilic caustics (using the terminology of catastrophe optics). Second, those umbilic caustics formed on the retinal surface are associated with certain points of the wave aberration function, called cusps of Gauss, where the gradient of a curvature function vanishes. However, not all cusps of Gauss generate those umbilic caustics. We also provide necessary conditions for those cusps of Gauss to be fertile. To show the potential of this theoretical framework for understanding the nature and origin of polyplopia, we provide specific examples of ocular wave aberration functions that induce diplopia and triplopia. The polyplopia effects in these examples are illustrated by depicting the multi-core PSFs and the convolved retinal images for clinical letter charts, both through computer simulations and through experimental recording using an adaptive optics set-up. The number and location of cores in the PSF is thus a potentially useful metric for the existence and severity of polyplopia in spatial vision. These examples also help explain why physiological pupil constriction might reduce the incidence of ghosting and multiple images of daily objects that affect vision with dilated pupils. This mechanistic explanation suggests a possible role for optical phase-masking as a clinical treatment for polyplopia and ghosting.

Ocular surface influences on corneal topography

The shape of a cornea, as measured by corneal topography, can be influenced by a variety of factors. Direct and obvious influences on corneal shape include corneal pathology, corneal surgery, and contact lenses. With the modern and widespread use of computerized videokeratoscopy, subtle topographic changes from other external and systemic influences can now be detailed. The purpose of this review is to examine ocular surface influences and indirect surgical, pathological, and pharmacological factors that affect the corneal shape and acquired topographic maps. The clinical consequences of altered corneal topography will be highlighted throughout.

Wavefront analysis of eyes with cataracts in patients with monocular triplopia1

PURPOSE

To determine whether wavefront analysis using a Hartmann-Shack (H-S) aberrometer can reveal the cause of monocular triplopia in eyes with mild cataracts.

METHODS

Six patients (nine eyes; age range 38-58 years; average 49.8 +/- 6.9 years) who complained of monocular triplopia at the Osaka University Hospital between January and December 2003 were examined. Wavefront analyses of ocular and corneal aberrations of the central 4 mm diameter were performed using a H-S aberrometer equipped with a Placido ring videokeratoscope. The ocular and corneal higher-order wavefronts were fitted with a fourth-order Zernike expansion.

RESULTS

All nine eyes showed mild nuclear cataract and had a mean spherical refractive error of -10.3 +/- 3.5 D. The visual acuity was > or = 20/40 except in one eye with glaucoma. For the Zernike polynomials, the trefoil aberration (C3-3) and the spherical aberration (C40) were significantly higher than those of age-matched normal controls (p < 0.001). The simulated retinal image of a Landolt C showed that the combination of trefoil aberration and the spherical aberration can cause an image with a triple configuration.

CONCLUSIONS

Monocular triplopia was reported by middle-aged patients with mild nuclear cataract and high myopia. Wavefront analyses suggested that the triple configuration was caused by the combined increase of the trefoil and spherical aberration in lenses with mild nuclear cataracts.

Regression of lid-induced corneal topography changes after reading

PURPOSE

The purpose of this article is to investigate the magnitude of lid-induced corneal topography changes as a function of time spent reading and the subsequent time course of regression of these changes.

METHODS

Six young subjects, five myopes and one emmetrope with normal ocular health, participated in the study. Corneal topography of one eye was measured with videokeratoscopy before four reading sessions of 10, 30, 60, and 120 min duration performed on four separate mornings. Corneal topography was again measured at fixed intervals up to 180 min after each reading session. A control trial without reading was also performed on a separate morning.

RESULTS

All six subjects showed significant changes in corneal topography directly after each of the reading sessions. Longer reading periods caused larger corneal changes. Local instantaneous power changes reached up to 5.95 D (+/- 2.80 D), whereas refractive power changes in the superior cornea ranged up to 1.26 D (+/- 0.44) for the 120-min reading trial. The duration of regression of corneal changes showed slower recovery times after longer reading periods. The pattern of regression was similar for all reading times, showing a rapid recovery within the first 10 minutes followed by a slower regression period.

CONCLUSIONS

The length of time spent reading has a cumulative effect on the period over which corneal topography remains altered as a result of lid forces.

Near work induced wavefront aberrations in myopia

We undertook a detailed analysis of the wavefront aberrations of the eyes of 20 young progressing myopes (mean age=22 years; mean spherical equivalent=-3.84 D, range -1.00 to -7.5 D) and twenty young age matched emmetropes (mean age=23 years; mean spherical equivalent=-0.00 D, range +0.25 to -0.25 D). A wavefront sensor was used to measure the ocular wavefront and a videokeratoscope was used to measure corneal topography. The corneal wavefront was subsequently calculated and the difference between the corneal and ocular wavefront was derived to give the internal wavefront component of the eye. Ocular and corneal wavefronts were measured before and after a 2-h reading task. At the baseline measurements, the myopes showed greater levels of some high order ocular wavefronts than the emmetropes. These differences between the groups became larger following 2 h of reading. Ocular higher order wavefront RMS was (baseline RMS: myopes=0.21 microm, emmetropes=0.16 microm, difference p=0.05 and after 2 h reading was RMS: myopes=0.27 microm, emmetropes=0.17 microm, difference p=0.02). The differences between the groups are primarily due to changes in the corneal wavefront associated with a narrower lid aperture during reading for the myopes. These differences are enhanced by longer periods spent reading, larger pupils and consequently low light levels. We suggest lid induced corneal changes caused by reading in downgaze provides a theoretical framework that could explain the known features of myopia development. The inherited characteristics of facial and lid anatomy would provide a mechanism for a genetic component in the genesis of myopia.

Improving Visual Function Diagnostic Metrics With the Use of Higher-order Aberration Information From the Eye

PURPOSE

This paper reviews the currently used visual function diagnostic metrics, acuity, refractive error, and contrast sensitivity, and suggests ways to create new metrics using the information that has recently become available due to advances in measuring the higher-order aberrations of the eye. Particularly, emphasis is placed on finding metrics that address certain aspects of vision rather than on general metrics.

METHODS

Two metrics based on the modulation transfer function are introduced, the Visual Quality Factor (VQF), which is a value based on the modulation transfer function between the spatial frequencies of 3 and 12 cycles per degree (c/deg) giving a measure of the overall degradation of visual quality due to aberrations, and the Subjective Sharpness Factor (SSF), which is a value based on the modulation transfer function between the spatial frequencies of 15 and 40 c/deg, giving a measure of the decrease in perceived image "sharpness" due to aberrations. Two metrics based on the point spread function are suggested, Point Spread Quality (PSQ), which is a measure of the "compactness" of the point spread, and Multiplicity Factor, which is a measure of the multiplicity of perceived images by measuring the number of discrete peaks in the point spread function.

RESULTS

The VQF and SSF values for both monochromatic and polychromatic cases are analyzed with regard to the number of acuity letters lost using data from a published study.

CONCLUSIONS

The SSF is found to be the best overall correlate with acuity performance if the degradation of the letter stimuli is not excessive.

Systematic underablation in laser in situ keratomileusis: ablation pattern identified by advanced topographical analysis

Topographical analysis based on the differential geometry of surfaces-curvature topography-was developed and applied to a patient after laser in situ keratomileusis. The patient had a minimal residual refractive error and normal best corrected visual acuity but had multiple visual aberrations, including ghosting and glare, unless the pupils were maximally constricted. The corneal loci responsible for the aberrations were difficult or impossible to identify on axial topographies but were readily identified with curvature topography. The patient's ablations appeared to be miniature versions of the intended ablation profiles, with small areas of emmetropic central cornea surrounded by annuli of rapidly increasing keratometric power; that is, systematic underablation. This may explain why some patients have visual aberrations with pupil diameters smaller than the programmed optical zones.

Corneal aberrations and reading

PURPOSE

To investigate the effects of eyelid pressure on corneal shape and corneal aberrations during reading.

METHODS

Twenty young subjects with normal ocular health were recruited for the study. The experiment was conducted early in the morning, with subjects instructed not to perform any prolonged reading before the experiment. Corneal topography of one eye was measured with a videokeratoscope before reading and then again after a 60-min reading task. The natural position of the eyelids was photographed in primary gaze and during the reading task.

RESULTS

Twelve of the 20 corneas showed significant changes in central topography immediately after reading. The location of the changes corresponded closely to the position and angle of the subject's eyelids during reading. The change in shape was best described as a wave-like distortion that significantly altered some corneal wavefront Zernike coefficients. There was a significant correlation between the changes in primary vertical coma and trefoil (along 30 degrees). Within the central 6 mm of the cornea, there were significant changes in the root mean square error, overall refractive power, and astigmatism.

CONCLUSIONS

The changes we observed in corneal topography appear to be directly related to the force exerted by the eyelids during reading. Because the cornea is the major light-refracting surface of the eye, the optical characteristics of some eyes can be significantly changed during reading by the force of the eyelids. These findings may have important implications for the definition of refractive status and may also aid in the understanding of the relationship between reading and the development of refractive errors.

Is Abnormal Focal Steepening of the Cornea Related to Persistent Monocular Diplopia?

PURPOSE

Some case reports have shown that abnormal focal steepening of the cornea appears to cause monocular diplopia by prismatic effect. The purpose of this study was to ascertain prospectively if the pattern of corneal distortion was related specifically to persistent monocular diplopia.

METHODS

We selected 16 visually normal eyes (controls) and two groups of volunteers in which abnormal focal steepening of the cornea was expected to be found: 40 eyes of 20 volunteers who wore rigid gas-permeable contact lenses (RGP) for myopia and 10 eyes of seven patients with keratoconus. New charts that consisted of white dials on a black background were prepared for detection and measurement of secondary images. Any secondary image that could not be eliminated by any trial lens correction was defined as a persistent secondary image, using the charts. Corneal topography from all subjects was classified: round or oval, symmetric or asymmetric bowtie, abnormal focal steepening accompanied by contact lens-induced corneal warpage or keratoconus, or amorphous. We analyzed the relationship between the persistent secondary image and the corneal topographical patterns.

RESULTS

A persistent secondary image was detected from seven eyes of RGP wearers and all keratoconus eyes. All corneal topographies of the seven RGP eyes with a persistent secondary image showed abnormal focal steepening related to contact lens-induced corneal warpage. The direction of the persistent secondary image was approximately consistent with the location of the focal steepening as seen on the corneal topography.

CONCLUSION

Abnormal focal steepening of the cornea that appeared to produce a prismatic difference between two parts of the cornea was specifically related to persistent monocular diplopia.

Observations on the optical effects of a cataract

PURPOSE

To describe and measure the optical effects seen by a person with a cataract and to use these observations to deduce physical changes in the crystalline lens caused by the cataract formation.

SETTING

Humphrey Systems, Dublin, California, USA.

METHODS

Caustic patterns created on the retina by a bright point source of white light as that source is viewed at various far-point distances ranging from the anterior focal point of the eye to +15.00 diopters were observed. The subtended retinal angle of a diffractive ring of light created by a small bright source of white light was observed and measured.

RESULTS

Three optical effects were seen and measured: multiple-image formation at certain far-point positions; a diffractive light ring surrounding small bright sources; a radial needle of bright light surrounding a small bright-white source. With a point source of light positioned at the anterior focal point of the eye, the Y sutures of the lens could be visualized. With the point source at other distances, characteristic caustic patterns could be visualized, allowing assessment of the lens' optical character. The subtended retinal angle of the diffractive ring was measured so the periodic lens structure could be evaluated.

CONCLUSIONS

The lens acted refractively as if it were divided into 3 elements with noncoincident optical axes. These 3 segments were associated with areas defined by the Y sutures, causing 3 images to be formed at certain distances. The caustic patterns indicate that each segment is slightly toroidal with axes at about 120 degrees apart combined with overcorrected spherical aberration. The period structure creating the diffractive ring had a period of 10 microns, approximately the width of a cortical lens cell, indicating that fluid between the cells likely creates a diffractive phase grating.

Optical isolation of portions of a wave front

A criterion is established for determining when portions of a wave front can be said to be optically isolated from the rest of the wave front in the sense that they can subsequently be treated separately when one is considering the formation of images. The subarea of the wave front is treated as a separate aperture, and it is said to be isolated if diffraction maxima for the majority of the wave front fall at or beyond the first minima for the subarea. An illustrative example employing two circular unequal-diameter apertures is presented. A method is given for identifying portions of wave front that may be optically isolated; the method uses the technique of fitting a reference surface to the actual wave front and then finding what is defined as the differential deflection of the actual surface with respect to the reference surface at all locations. Subpopulations of locations with similar differential deflection values, sufficient numbers, and sufficient differential deflection are candidates for area of optical isolation.