Monocular diplopia caused by ocular aberrations and hyperopic defocus

Recent advances in measurement of monochromatic aberrations of human eyes

The field of aberrations of the human eye is moving rapidly, being driven by the desire to monitor and optimise vision following refractive surgery. It is important for ophthalmologists and optometrists to have an understanding of the magnitude of various aberrations and how these are likely to be affected by refractive surgery and other corrections. In this paper, I consider methods used to measure aberrations, the magnitude of aberrations in general populations and how these are affected by various factors (for example, age, refractive error, accommodation and refractive surgery) and how aberrations and their correction affect spatial visual performance.

Simulated image doubling and visual acuity: effects of doubling magnitude, orientation, and ghost image intensity

PURPOSE

The effects of image doubling on logarithmic progression chart visual acuity were investigated by simulating diplopia on a computer monitor.

METHODS

Ten participants (6M, 4F) aged 21-28 years (mean 22.4 ± 2.3) were assessed viewing with their left eye while wearing their best correction. Stimuli were eight rows of five Sloan letters, from 0.4 to -0.3 logMAR (6/15 to 6/3) arranged in logarithmic progression format, generated on an HD monitor. Stimuli were generated with different magnitudes of doubling, different directions of doubling, and different intensity ratios between the ghost image and main images.

RESULTS

When the ghost image had the same intensity as the main image, there was a significant effect of doubling magnitude on visual acuity, with the mean acuity being -0.11 logMAR (6/4.7) for no doubling. Acuity thresholds (logMAR) increased when doubling exceeded 1 min of arc, reaching a level of 0.12 logMAR (6/7.9) for doubling of 16 min of arc. There were no significant effects of orientation on acuity, nor were there significant orientation-doubling magnitude interaction effects of visual acuity. Image doubling magnitude level affected visual acuity differently for different ghost image intensities, with the highest acuity elevation occurring when ghost and main images were equal or nearly equal. For faint ghost image intensities (10% and 20%) image doubling did not significantly affect visual acuity.

CONCLUSIONS

Image doubling will degrade visual acuity if doubling is greater than 1 min of arc, and ghost images are sufficiently intense. However, even with very obvious visually-disturbing image doubling, visual acuity remains only slightly reduced.

Monocular Ghost Image Offset Thresholds: Dependent on Target Size and Ghost Image Relative Brightness

SIGNIFICANCE

This is the first report of monocular ghost image offset thresholds measured using O optotypes. Monocular diplopia is a complaint of patients and is the result of a variety of etiologies. Furthermore, monocular image doubling also can be a confounding variable of vectographic stereoacuity tests, warranting an investigation of ghost image offset thresholds.

PURPOSE

To measure ghost image offset thresholds of normal observers and how they are affected by offset orientation, target size, and ghost image relative luminance.

METHODS

Participants were five individuals without ocular abnormalities aged 21 to 32 years. Stimuli were viewed monocularly and consisted of Sloan "O" optotypes generated on a computer monitor with varying levels of image doubling. Ghost image offset thresholds were determined using a spatial 2-alternative forced-choice paradigm and probit analysis of the frequency of seeing data.

RESULTS

Under close-to-optimal conditions, monocular ghost image offset thresholds ranged between 14 and 22 arc seconds, a level that might be considered a hyperacuity. Ghost image offset detection thresholds demonstrated a U-shaped relationship with optotype size, with optimum thresholds occurring for optotypes sizes of approximately -0.15 logarithmic minimum angle of resolution. There was no measurable effect of offset orientation on ghost image offset detection thresholds. Monocular ghost image offset detection thresholds decreased as ghost image relative luminance increased.

CONCLUSIONS

Ghost image offset detection thresholds can be quite low even when viewing under monocular conditions and relatively low ghost image relative luminance. This should be considered when designing and interpreting the results of vectographic stereoacuity tests.

Ophthalmologic manifestations commonly misdiagnosed as demyelinating events in multiple sclerosis patients

PURPOSE OF REVIEW

Multiple sclerosis may affect both afferent and efferent visual pathways, and sometimes physicians err on ordinary ophthalmologic diagnosis due to overlapping symptoms between demyelinating and nondemyelinating visual diseases. The present article highlights nondemyelinating ocular occurrences due to physiologic or other pathologic processes that may appear in some patients.

RECENT FINDINGS

Optic neuritis is representative of the most common and best-studied demyelinating visual occurrence in multiple sclerosis. However, other nondemyelinating visual disturbances also seen in the general population may be erroneously interpreted as being part of the underlying disease. This comparison has not been documented and may be helpful to overcome such difficulties.

SUMMARY

Based on clinical history and some strategies of ophthalmologic examination, physicians can achieve the correct diagnosis. Some clinical situations, however, may be challenging and a multidisciplinary approach in the care of multiple sclerosis is warranted.

Wide-field schematic eye models with gradient-index lens

We propose a wide-field schematic eye model, which provides a more realistic description of the optical system of the eye in relation to its anatomical structure. The wide-field model incorporates a gradient-index (GRIN) lens, which enables it to fulfill properties of two well-known schematic eye models, namely, Navarro's model for off-axis aberrations and Thibos's chromatic on-axis model (the Indiana eye). These two models are based on extensive experimental data, which makes the derived wide-field eye model also consistent with that data. A mathematical method to construct a GRIN lens with its iso-indicial contours following the optical surfaces of given asphericity is presented. The efficiency of the method is demonstrated with three variants related to different age groups. The role of the GRIN structure in relation to the lens paradox is analyzed. The wide-field model with a GRIN lens can be used as a starting design for the eye inverse problem, i.e., reconstructing the optical structure of the eye from off-axis wavefront measurements. Anatomically more accurate age-dependent optical models of the eye could ultimately help an optical designer to improve wide-field retinal imaging.

Visual Acuity and Optical Parameters in Progressive-Power Lenses

PURPOSES

The purposes of this study are to explore the effect of astigmatism and high-order aberrations of progressive-power lenses (PPLs) on visual acuity (VA) and to find a good optical metric for evaluating visual performance of PPLs.

METHODS

A Hartmann-Shack (HS) wavefront sensor was used to measure PPLs and human eyes either independently or in combination. An additional channel permits the measurement of VA under the same optical conditions. Measurements were taken in six relevant locations of a PPL and in three eyes of different normal subjects. In every case, we obtained the wavefront aberration as Zernike polynomials expansions, the root mean square (RMS) error, and two metrics on point spread function (PSF): Strehl ratio and the common logarithm of the volume under the PSF normalized to one (Log_Vol_PSF).

RESULTS

Aberration coupling of the PPL with the eye tends to equalize the retinal image quality between central and peripheral zones of the progressive lenses. In the corridor of the PPL, the combination of small amounts of coma, trefoil, and astigmatism (total RMS 0.1 mum) does not significantly affect VA. The continuous increase of astigmatism from corridor to outside zones reduces moderately the quality of vision. The highest correlations between optical metrics and VA were found for Log_Vol_PSF of the entire system eye plus PPL.

CONCLUSIONS

Ocular aberrations reduce optical quality difference between corridor and peripheral zones of PPLs. In the same way, VA through the corridor is similar to that of eyes without a lens and it decreases slowly toward peripheral locations. VA through PPLs is well predicted by the logarithm of metrics directly related with image spread (Log_Vol_PSF or equivalent) of the complete system of the eye with the lens.

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.

Accommodation stimulus-response function and retinal image quality

Accommodation stimulus-response function (ASRF) and its relationship to retinal image quality were investigated using a modified wavefront sensor. Ten subjects were presented with six vergence stimuli between 0.17 D and 5 D. For each vergence distance, ocular wavefronts and subjective visual acuity were measured. Wavefronts were analysed for a fixed 3-mm pupil diameter and for natural pupil sizes. Visual Strehl ratio computed in the frequency domain (VSOTF) and retinal images were calculated for each condition tested. Subjective visual acuity was significantly improved at intermediate vergence distances (1D and 2D; p < 0.01), and only decreased significantly at 5 D compared with 0.17 D (p < 0.05). VSOTF magnitude was associated with subjective visual acuity and VSOTF peak location correlated with accommodation error. Apparent accommodation errors due to spherical aberration were highly correlated with accommodation lead and lag for natural pupils (R(2) = 0.80) but not for fixed 3-mm pupils (R(2) < 0.00). The combination of higher-order aberrations and accommodation errors improved retinal image quality compared with accommodation errors or higher order aberrations alone. Pupil size and higher order aberrations play an important role in the ASRF.

Homeostasis of eye growth and the question of myopia

As with other organs, the eye's growth is regulated by homeostatic control mechanisms. Unlike other organs, the eye relies on vision as a principal input to guide growth. In this review, we consider several implications of this visual guidance. First, we compare the regulation of eye growth to that of other organs. Second, we ask how the visual system derives signals that distinguish the blur of an eye too large from one too small. Third, we ask what cascade of chemical signals constitutes this growth control system. Finally, if the match between the length and optics of the eye is under homeostatic control, why do children so commonly develop myopia, and why does the myopia not limit itself? Long-neglected studies may provide an answer to this last question.

Further evidence that chick eyes use the sign of blur in spectacle lens compensation

Young animals compensate for defocus imposed by positive or negative spectacle lenses by adjusting the elongation rate of their vitreous chambers, thus matching the length of the eye with the focal length of the eye's optics combined with the spectacle lenses. The ability to compensate for either negative or positive lenses could rely on the ability to distinguish between myopic and hyperopic blur, or it could rely on the fact that positive lenses would bring nearby objects into focus, thereby reducing the amount of blur, whereas negative lenses would not. This study asks whether eyes emmetropize using the magnitude of blur or the sign of blur as a directional cue. We fitted chick eyes with positive lenses while imposing a substantial amount of blur, either (a) by having them wear lenses only when restrained in the center of a cylinder, the walls of which were beyond their far-point or (b) by having them wear mild diffusers over positive lenses. We found good refractive compensation in both situations in a large number of birds. Furthermore, we found that mild diffusers worn on top of positive lenses differentially affected the two ocular components of refractive compensation: there was less choroidal thickening, but more inhibition of ocular elongation, compared to wearing positive lenses alone. These findings argue both that the eye can discern the sign of the blur and that choroidal and ocular-elongation components of the refractive compensation do not respond identically to visual inputs.

Refractive error and monochromatic aberrations in Singaporean children

Higher order optical aberrations were measured in 273 cyclopleged Singaporean school children using a Bausch and Lomb Zywave aberrometer, with 268 of these subjects also undergoing corneal topography measurements (Tomey TMS 2 system). Subjects with low myopia (> -3.00 to -0.50 D) showed slightly, but significantly, less positive levels of spherical aberration than other refractive error groups. Chinese subjects also showed significantly higher amounts of aberrations than Malay subjects, particularly for vertical coma, but also for horizontal coma and spherical aberration. Anterior corneal spherical aberration (calculated from topography) was significantly correlated with whole eye spherical aberration, but did not vary significantly with refractive error or racial background. Residual spherical aberration (i.e. of posterior cornea and crystalline lens) did vary significantly with refractive error and race. Our results do not provide any evidence for aberration-driven form-deprivation as a major mechanism of myopia development.

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.

Correlation between optical and psychophysical parameters as a function of defocus

PURPOSE

To evaluate how ocular optical image quality and psychophysical estimates of visual performance compare to each other as a function of defocus.

METHODS

We measured the optical modulation transfer function using a double-pass apparatus and psychophysical estimates of visual performance: contrast sensitivity function (CSF) and visual acuity. Both sets of data were obtained under the same optical conditions.

RESULTS

We measured optical and psychophysical parameters as a function of defocus. We studied the correlation between optical parameters (Strehl ratio and the logarithm of the volume in the double-pass image [log_Vol D-P]) and psychophysical parameters (the area under the fitted CSF represented in a logarithmic scale with the spatial frequency in linear scale [Area CSF-log_lin] and visual acuity) for different values of defocus.

CONCLUSIONS

Strehl ratio is well correlated with the psychophysical estimates of the visual performance for moderate amount of defocus (within 1 D), whereas the other parameter (log_Vol D-P) is well correlated for larger ranges of defocus (within 2 D) and for different pupil diameters. These results suggest that optical measurements could be used for clinical testing of ophthalmic optics.

Monocular Diplopia Related to Asymmetric Corneal Topography After Laser in situ Keratomileusis

PURPOSE

To show a specific relationship between monocular diplopia and corneal refractive asymmetry after laser in situ keratomileusis (LASIK).

METHODS

One hundred thirty-eight eyes of 98 patients who underwent LASIK for myopia between -2.12 and -17.75 D were examined under room-lighted conditions. We examined 51 eyes at 2 weeks, 46 eyes at 3 months, 32 eyes at 6 months, and 9 eyes at 1 year after LASIK. We attempted to correlate the presence of monocular diplopia with their corneal topographical features.

RESULTS

Eight eyes of five patients (five eyes at 2 weeks, three eyes at 3 months after LASIK) produced symptoms of monocular diplopia. These symptomatic patients had a common corneal topographical feature caused by decentralized or inhomogeneous ablation. Every pupillary area in the patients' topographies contained steeper and flatter areas. The range of refractive power variation in these asymmetric areas was at least 1.50 D. The location of the secondary image correlated with the direction of the steeper area in all eight eyes. Pinhole viewing eliminated or reduced the prominence of secondary images in every case.

CONCLUSION

Monocular diplopia following LASIK appears to correlate with postoperative corneal refractive power variation inside the pupillary area, caused by decentralized or inhomogeneous ablation.

Optics of aberroscopy and super vision

This paper (1) reviews the fundamental limits to visual performance imposed by optical imaging and photoreceptor sampling to determine the limits to the potential gains offered by ideal corrections; (2) examines the predicted losses in vision induced by chromatic aberration, phase shifts, typical ocular aberrations, and the gains possible by correcting the monochromatic aberrations of the eye; (3) discusses the principles of aberration measurement in the eye; and (4) presents methods for measuring and classifying monochromatic aberrations of the eye.

Recognition thresholds for letters with simulated dioptric blur

We examined the effects of simulated dioptric blur on the degradation of visual acuity using digitally filtered letters. Four types of digital filters were applied to 5 letters (C, D, E, O, and S), constructed to the specifications of Sloan optotypes. These filters were: (1) "normal," designed to simulate the positive and negative lobes of the modulation transfer function (MTF) produced by dioptric blur; (2) "truncated," which passed only those spatial frequencies up to the first zero of the MTF; (3) "phase-rectified," which inverted all of the negative lobes of the MTF to positive; and (4) "truncated-plus-negative," which eliminated all positive lobes above the first zero of the MTF. The letter size required to achieve 60%-correct identification was determined for letters that were filtered to simulate +1, +2, and +4 D of blur. Letters subjected to normal, truncated, and truncated-plus-negative filtering had approximately the same acuity threshold, whereas the threshold size for phase-rectified letters was significantly better. Our interpretation of these results is that dioptric blur hinders letter recognition because useful spatial frequency information is limited to that below the first zero of the MTF, and not because of interference from the phase-reversed spatial frequency information above the first zero. Our letter identification thresholds are consistent with recent evidence that the critical information for letter acuity corresponds to approximately 1.5 cycles/letter.

The depth-of-field of the human eye from objective and subjective measurements

The depth-of-field (DOF) measured through psychophysical methods seems to depend on the target's characteristics. We use objective and subjective methods to determine the DOF of the eye for different pupil diameters and wavelengths in three subjects. Variation of image quality with focus is evaluated with a double-pass technique. Objective DOF is defined as the dioptric range for which the image quality does not change appreciably, based on optical criteria. Subjective DOF is based on the accuracy of focusing a point source. Additional DOFs are obtained by simulation from experimental wavefront aberration data from the same subjects. Objective and subjective measurements of DOF are only slightly affected by pupil size, wavelength and spectral composition. Comparison of DOF from double-pass and wavefront aberration data allows us to evaluate the role of ocular aberrations and Stiles-Crawford effect.

Predicting the effects of optical defocus on human contrast sensitivity

We used diffraction modulation transfer functions and model eyes to predict the effect of defocus on the contrast sensitivity function (CSF) and compared these predictions with previously published experimental data. Using the principle that optically induced changes in the modulation transfer function should be paralleled by identical changes in the CSF, we used the modulation transfer function calculations with the best-focus CSF measurements to predict the defocused CSF. An aberration-free model predicted the effects of defocus well when the CSF was measured with small pupils (e.g., 2 mm) but not with larger pupils (6-8 mm). When the model included average aberrations, prediction of the defocused CSF with large pupils was better but remained inaccurate, failing, in particular, to reflect differences between individual subjects. Inclusion of measured aberrations for individual subjects provided accurate predictions in the shape of the monochromatic CSF of two of three subjects with hyperopic defocus and good predictions of the polychromatic CSF of two subjects with hyperopic defocus. Prediction of the effects of myopic defocus by use of measured individual aberrations of one subject were less successful. Hence a diffraction optics model can provide good predictions of the effects of defocus on the human CSF, given that one has knowledge of the individual ocular aberrations. These predictions are dependent on the quality of the aberration measurements.

Measurement of the wave-front aberration of the eye by a fast psychophysical procedure

We used a fast psychophysical procedure to determine the wave-front aberrations of the human eye in vivo. We measured the angular deviation of light rays entering the eye at different pupillary locations by aligning an image of a point source entering the pupil at different locations to the image of a fixation cross entering the pupil at a fixed location. We fitted the data to a Zernike series to reconstruct the wave-front aberrations of the pupil. With this technique the repeatability of the measurement of the individual coefficients was 0.019 micron. The standard deviation of the overall wave-height estimation across the pupil is less than 0.3 micron. Since this technique does not require the administration of pharmacological agents to dilate the pupil, we were able to measure the changes in the aberrations of the eye during accommodation. We found that administration of even a mild dilating agent causes a change in the aberration structure of the eye.

Comparison of the eye's wave-front aberration measured psychophysically and with the Shack-Hartmann wave-front sensor

The Shack-Hartmann wave-front sensor offers many theoretical advantages over other methods for measuring aberrations of the eye; therefore it is essential that its accuracy be thoroughly tested. We assessed the accuracy of a Shack-Hartmann sensor by directly comparing its measured wave-front aberration function with that obtained by the Smirnov psychophysical method for the same eyes. Wave-front profiles measured by the two methods agreed closely in terms of shape and magnitude with rms differences of approximately lambda/2 and approximately lambda/6 (5.6-mm pupil) for two eyes. Primary spherical aberration was dominant in these profiles, and, in one subject, secondary coma was opposite in sign to primary coma, thereby canceling its effect. Discovery of an unusual, subtle wave-front anomaly in one individual further demonstrated the accuracy and sensitivity of the Shack-Hartmann wave-front sensor for measuring the optical quality of the human eye.

Consequences of monocular diplopia for the contrast sensitivity function

Though the human eye generally creates a single image on the retina, the literature contains many examples showing perceptual monocular diplopia. Previously, monocular diplopia resulting from astigmatic defocus has been demonstrated to cause a notch (local minimum) in the contrast sensitivity function (CSF). We examine Verhoeff's (1900) model which explains how monocular diplopia can occur through an interaction between defocus and common ocular aberrations. From the measured ocular transverse aberration function and from the measured monocular diplopia of three cyclopleged subjects we predicted multiple notches in the CSF with hyperopic spherical defocus. Monochromatic and polychromatic CSF were measured for vertical gratings with best refraction and with simulated myopia and hyperopia. Multiple notches in CSF were observed experimentally. Notches in the polychromatic CSF were smaller and broader than those found in the monochromatic CSF. Our aberration model was successful in predicting notches in the CSF with hyperopic spherical defocus. The implications for clinical measurement of CSF are discussed.