Understanding accommodative control in the clinic: Modeling latency and amplitude for uncorrected refractive error, presbyopia and cycloplegia.

Accommodation is the process of adjusting the eye's optical power so as to focus at different distances. Uncorrected refractive error and/or functional presbyopia mean that sharp focus may not be achievable for some distances, so observers experience sustained defocus. Here, we identify a problem with current models of accommodative control: They predict excessive internal responses to stimuli outside accommodative range, leading to unrealistic adaptation effects. Specifically, after prolonged exposure to stimuli outside range, current models predict long latencies in the accommodative response to stimuli within range, as well as unrealistic dynamics and amplitudes of accommodative vergence innervation driven by the accommodative neural controller. These behaviors are not observed empirically. To solve this issue, we propose that the input to blur-driven accommodation is not retinal defocus, but correctable defocus. Predictive models of accommodative control already estimate demand from sensed defocus, using a realistic "virtual plant" to estimate accommodation. Correctable defocus can be obtained by restricting this demand to values physically attainable by the eye. If we further postulate that correctable defocus is computed using an idealized virtual plant that retains a young accommodative range, we can explain why accommodative-convergence responses are observed for stimuli that are too near-but not too far-to focus on. We model cycloplegia as a change in gain, and postulate a form of neural myopia to explain the additional relaxation of accommodation often seen with cycloplegia. This model produces plausible predictions for the accommodative response and accommodative convergence signal in a wide range of clinically relevant situations.

Seeing the future: Predictive control in neural models of ocular accommodation.

Ocular accommodation is the process of adjusting the eye's crystalline lens so as to bring the retinal image into sharp focus. The major stimulus to accommodation is therefore retinal defocus, and in essence, the job of accommodative control is to send a signal to the ciliary muscle which will minimize the magnitude of defocus. In this article, we first provide a tutorial introduction to control theory to aid vision scientists without this background. We then present a unified model of accommodative control that explains properties of the accommodative response for a wide range of accommodative stimuli. Following previous work, we conclude that most aspects of accommodation are well explained by dual integral control, with a "fast" or "phasic" integrator enabling response to rapid changes in demand, which hands over control to a "slow" or "tonic" integrator which maintains the response to steady demand. Control is complicated by the sensorimotor latencies within the system, which delay both information about defocus and the accommodation changes made in response, and by the sluggish response of the motor plant. These can be overcome by incorporating a Smith predictor, whereby the system predicts the delayed sensory consequences of its own motor actions. For the first time, we show that critically-damped dual integral control with a Smith predictor accounts for adaptation effects as well as for the gain and phase for sinusoidal oscillations in demand. In addition, we propose a novel proportional-control signal to account for the power spectrum of accommodative microfluctuations during steady fixation, which may be important in hunting for optimal focus, and for the nonlinear resonance observed for low-amplitude, high-frequency input. Complete Matlab/Simulink code implementing the model is provided at https://doi.org/10.25405/data.ncl.14945550.

Binocular cross-correlation analyses of the effects of high-order aberrations on the stereoacuity of eyes with keratoconus.

Stereoacuity losses are induced by increased magnitudes and interocular differences in high-order aberrations (HOAs). This study used keratoconus as a model to investigate the impact of HOAs on disparity processing and stereoacuity. HOAs and stereoacuity were quantified in subjects with keratoconus (n = 21) with HOAs uncorrected (wearing spectacles) or minimized (wearing rigid gas-permeable contact lenses) and in control subjects without keratoconus (n = 5) for 6-mm pupil diameters. Disparity signal quality was estimated using metrics derived from binocular cross-correlation functions of stereo pairs convolved with point-spread functions from these HOAs. Metrics computed for all subjects were compared with stereoacuities. The effects of contrast losses and phase shifts on disparity signal quality were studied independently by manipulating the amplitude and phase components of optical transfer functions. The magnitudes, orientations, interocular relationships in magnitude, and shape of the point-spread function affected the cross-correlation metrics that determine disparity signal quality. Stereoacuity covaries strongly with cross-correlation metrics and moderately with image-quality metrics. Both phase distortions and contrast losses due to HOAs significantly influence computations of binocular disparity. HOA-induced stereoacuity reductions are attributable to disparity blur and noise from image properties that reduce the height and kurtosis of the peak stimulus disparity match of the cross-correlation. Phase distortions and contrast losses due to HOAs are both partly responsible for the greater stereoacuity losses seen with spectacles compared to rigid gas-permeable contact lenses in keratoconus.

LogMAR and Stereoacuity in Keratoconus Corrected with Spectacles and Rigid Gas-permeable Contact Lenses.

SIGNIFICANCE: This study showed an improvement in three-dimensional depth perception of subjects with bilateral and unilateral keratoconus with rigid gas-permeable (RGP) contact lens wear, relative to spectacles. This novel information will aid clinicians to consider RGP contact lenses as a management modality in keratoconic patients complaining of depth-related difficulties with their spectacles. PURPOSE: The aim of this study was to systematically compare changes in logMAR acuity and stereoacuity from best-corrected spherocylindrical spectacles to RGP contact lenses in bilateral and unilateral keratoconus vis-à-vis age-matched control subjects. METHODS: Monocular and binocular logMAR acuity and random-dot stereoacuity were determined in subjects with bilateral (n = 30; 18 to 24 years) and unilateral (n = 10; 18 to 24 years) keratoconus and 20 control subjects using standard psychophysical protocols. RESULTS: Median (25th to 75th interquartile range) monocular (right eye) and binocular logMAR acuity and stereoacuity improved significantly from spectacles to RGP contact lenses in the bilateral keratoconus cohort (P < .001). Only monocular logMAR acuity of affected eye and stereoacuity improved from spectacles to RGP contact lenses in the unilateral keratoconus cohort (P < .001). There was no significant change in the binocular logMAR acuity from spectacles to RGP contact lenses in the unilateral keratoconus cohort. The magnitude of improvement in binocular logMAR acuity and stereoacuity was also greater for the bilateral compared with the unilateral keratoconus cohort. All outcome measures of cases with RGP contact lenses remained poorer than control subjects (P < .001). CONCLUSIONS: Binocular resolution and stereoacuity improve from spectacles to RGP contact lenses in bilateral keratoconus, whereas only stereoacuity improves from spectacles to RGP contact lenses in unilateral keratoconus. The magnitude of improvement in visual performance is greater for the binocular compared with the unilateral keratoconus cohort.

Envisioning Eye Care From a Rural Perspective: A Photovoice Project From India.

Background To understand barriers and promoters for accessing eye care by rural communities, we used a modified approach to Photovoice, a community-based participatory action research approach Methods Community members took photographs and wrote or spoke stories based upon a series of questions intended to facilitate deeper thinking. Fifteen rural paramedical team members who were affiliated with the rural network of L V Prasad Eye Institute, and 60 people from four villages reported barriers and promoters for eye care access for 20 villages Results Important barriers for accessing eye care included the following: no caretaker at home for grandchildren except for the grandparent(s), alcoholism, uncontrolled blood pressure, inadequate diabetes management, lack of escort for blind people and elders, affordability, and inadequate clinic staffing during summer season when farming villagers were available. Important promoters for seeking eye care included having a neighbor who had a good surgical outcome in one eye which resulted in the ability to resume work. The Photovoice project offered specific suggestions to hospital management for improving eye care access, including providing evening transportation, providing additional surgical staffing during busy summer season, and the creation of tool spectacle repair kits to be kept at the primary vision centers Conclusions This Photovoice project facilitated a deeper understanding of the important barriers and promoters for accessing eye care by villagers, and by the rural eye care team, offering specific suggestions to hospital management for improving eye care access and to communicate without any inhibiting factors like fear of hierarchy within the hospital administration.

Saccadic latency in amblyopia.

We measured saccadic latencies in a large sample (total n = 459) of individuals with amblyopia or risk factors for amblyopia, e.g., strabismus or anisometropia, and normal control subjects. We presented an easily visible target randomly to the left or right, 3.5° from fixation. The interocular difference in saccadic latency is highly correlated with the interocular difference in LogMAR (Snellen) acuity-as the acuity difference increases, so does the latency difference. Strabismic and strabismic-anisometropic amblyopes have, on average, a larger difference between their eyes in LogMAR acuity than anisometropic amblyopes and thus their interocular latency difference is, on average, significantly larger than anisometropic amblyopes. Despite its relation to LogMAR acuity, the longer latency in strabismic amblyopes cannot be attributed either to poor resolution or to reduced contrast sensitivity, because their interocular differences in grating acuity and in contrast sensitivity are roughly the same as for anisometropic amblyopes. The correlation between LogMAR acuity and saccadic latency arises because of the confluence of two separable effects in the strabismic amblyopic eye-poor letter recognition impairs LogMAR acuity while an intrinsic sluggishness delays reaction time. We speculate that the frequent microsaccades and the accompanying attentional shifts, made while strabismic amblyopes struggle to maintain fixation with their amblyopic eyes, result in all types of reactions being irreducibly delayed.

Potential role for microfluctuations as a temporal directional cue to accommodation.

The goal was to revisit an important, yet unproven notion that accommodative microfluctuations facilitate the determination of direction (sign) of abrupt focus changes in the stimulus to accommodation. We contaminated the potential temporal cues from natural accommodative microfluctuations by presenting uncorrelated external (screen) temporal defocus noise that combined with the retinal image effects of natural microfluctuations. A polychromatic Maltese spoke pattern thus either modulated defocus at a combination of two temporal frequencies (on-screen noise condition) or was static (control condition). The on-screen conditions were combined with step changes in optical vergence that were randomized in direction and magnitude. Five subjects monocularly viewed stimuli through a Badal optical system in a Maxwellian view. An artificial 4-mm aperture was imaged at the entrance pupil of the eye. Wavefront aberrations were measured dynamically at 50 Hz using a custom Shack-Hartmann aberrometer. Dynamic changes in the Zernike defocus term with step changes in optical vergence were analyzed. We calculated the percentage of correct directional responses for 1, 2, and 3 D accommodative and disaccommodative step stimuli using preset criteria for latency, velocity, and persistence of the response. The on-screen noise condition reduced the percent-correct responses compared to the static stimulus, suggesting that this manipulation affected the detectability of the sign of the accommodative stimulus. Several possible reasons and implications of this result are discussed.

The impact of higher-order aberrations on the strength of directional signals produced by accommodative microfluctuations.

It has been proposed that the accommodation system could perform contrast discrimination between the two dioptric extremes of accommodative microfluctuations to extract directional signals for reflex accommodation. Higher-order aberrations (HOAs) may have a significant influence on the strength of these contrast signals. Our goal was to compute the effect HOAs may have on contrast signals for stimuli within the upper defocus limit by comparing computed microcontrast fluctuations with psychophysical contrast increment thresholds (Bradley & Ohzawa, 1986). Wavefront aberrations were measured while subjects viewed a Maltese spoke stimulus monocularly. Computations were performed for accommodation or disaccommodation stimuli from a 3 Diopter (D) baseline. Microfluctuations were estimated from the standard deviation of the wavefronts over time at baseline. Through-focus Modulation Transfer, optical contrast increments (ΔC), and Weber fractions (ΔC/C) were derived from point spread functions computed from the wavefronts at baseline for 2 and 4 cycles per degree (cpd) components, with and without HOAs. The ΔCs thus computed from the wavefronts were compared with psychophysical contrast increment threshold data. Microfluctuations are potentially useful for extracting directional information for defocus values within 3 D, where contrast increments for the 2 or 4 cpd components exceed psychophysical thresholds. HOAs largely reduce contrast signals produced by microfluctuations, depending on the mean focus error, and their magnitude in individual subjects, and they may shrink the effective stimulus range for reflex accommodation. The upper defocus limit could therefore be constrained by discrimination of microcontrast fluctuations.

Success rates, near-response patterns, and learning trends with free-fusion stereograms.

Free-fusion stereograms are routinely used for demonstrating various stereoscopic effects. Yet, untrained observers find it challenging to perform this task. This study showed that only less than 1/3rd of sixty-one pre-presbyopic adults with normal binocular vision could successfully free-fuse random-dot image pairs and identify the stereoscopic shapes embedded in these patterns. Another one-third of participants performed the task with poor success rates, while the remaining could not perform the task. There was a clear dissociation of vergence and accommodative responses in participants who were successful with free-fusion, as recorded using a dynamic infrared eye tracker and photorefractor. Those in the unsuccessful cluster either showed strong vergence and accommodation or weak vergence and strong accommodation during the task. These response patterns, however, were specific to the free-fusion task because all these participants generated good convergence/accommodation to real-world targets and to conflicting vergence and accommodative demands stimulated with prisms or lenses. Task performance of the unsuccessful cluster also improved significantly following pharmacological paralysis of accommodation and reached the performance levels of the successful cluster. A minority of participants also appeared to progressively learn to dissociate one of the two directions of their vergence and accommodation crosslinks with repeated free-fusion trials. These results suggest that successful free-fusion might depend upon how well participants generate a combination of volitional and reflex vergence responses to large differences in disparity with conflicting static accommodative demands. Such responses would require that only one direction of the vergence-accommodation crosslinks be active at any given time. The sequence of near-responses could also be learnt through repeated trials to optimize task performance.

Does ethnicity influence the short-term adaptation to first reading correction?

PURPOSE: Ethnic variations in accommodative amplitude (AA) are not uncommon. Accommodation can become reduced in response to short-term wear of first near spectacles. Whether ethnicity has an influence on the magnitude of this adaptation is not well understood. We investigated the impact of first near spectacles on changes in AA and on convergence cross-link interactions in incipient presbyopes of Chinese and Caucasian ethnicities. METHODS: Forty-one subjects (22 Caucasians and 19 Chinese) aged 36 to 44 years completed the study. Accommodative stimulus response function, AA, and AC/A and CA/C ratios were measured before and after single vision reading spectacles were used for near tasks over a 2-month period and then again 2 months after discontinuing near spectacle wear. RESULTS: After wearing reading spectacles for 2 months, the accommodative stimulus response slopes and AC/A and CA/C ratios remained invariant irrespective of ethnicity. The accommodative, but not vergence, bias decreased (p < 0.05). The nearpoint of accommodation shifted distally producing an average decrease in AA of 0.52 D from baseline (p < 0.05). Recovery to near baseline values occurred after discontinuing the reading glasses for 2 months. Differences based on ethnicity were not significant. The baseline AA vs. age plots showed steeper slopes for Chinese than the Caucasian subjects in the sample. CONCLUSIONS: The pattern of adaptation by accommodation and cross-link interactions to short-term first reading spectacles is not influenced by ethnicity.

The effect of perceptual grouping on perisaccadic spatial distortions.

Perisaccadic spatial distortion (PSD) occurs when a target is flashed immediately before the onset of a saccade and it appears displaced in the direction of the saccade. In previous studies, the magnitude of PSD of a single target was affected by multiple experimental parameters, such as the target's luminance and its position relative to the central fixation target. Here we describe a contextual effect in which the magnitude of the PSD for a target was influenced by the synchronous presentation of another target: PSD for simultaneously presented targets was more uniform than when each was presented individually. Perisaccadic compression was ruled out as a causal factor, and the results suggest that both low- and high-level perceptual grouping mechanisms may account for the change in PSD magnitude. We speculate that perceptual grouping could play a key role in preserving shape constancy during saccadic eye movements.

Effects of accommodation training on accommodation and depth of focus in an eye implanted with a crystalens intraocular lens.

PURPOSE: To investigate objective measures of the effects of accommodative training of a pseudophakic eye implanted with a Crystalens AT-52SE (eyeonics Inc) intraocular lens (IOL) on reading performance, accommodation, and depth of focus. METHODS: Objective dynamic measures of accommodation, pupil size, and depth of focus were quantified from wavefront measures before and after 1 week of accommodative training that began 29 months after implantation of an accommodating IOL in one patient. Depth of focus was estimated from 50% cut-off of peak performance levels for defocus curves that were computed from the image quality metric VSOTF based on ocular wavefront aberrations. RESULTS: The patient reported improved near vision reading performance after completing the training procedure. After training, there was a shift in conjugate focus in the hyperopic direction, yet the depth of focus increased significantly for near objects. Simulated retinal images and the calculated modulation transfer function of the eye both demonstrated improved quality for near vision after training. CONCLUSIONS: The subjective report of improved near vision after training was correlated with improvement of objective measures. Depth of focus increased for near objects with attempts to accommodate after training. This change was linked to increases in aberrations and pupil size and occurred despite the conjugate focus shifting in the hyperopic direction. These results demonstrate that accommodative training may be useful in improving near vision in patients with accommodating IOLs.

A computational analysis of retinal image quality in eyes with keratoconus.

Higher-order aberrations (HOA's) are exaggerated in eyes with keratoconus but little is known about their impact on the retinal image quality (IQ) of these eyes. This computational study determined changes in IQ [peak IQ, best focus and depth of focus (DOF)] of 12 subjects with manifest keratoconus in both eyes (KCE cohort), 9 subjects with very asymmetric ectasia (VAE cohort) with and without their Rigid Gas Permeable contact lenses (RGP CL's) and 20 age-matched controls, using a HOA-based through-focus analysis performed on the logNS IQ metric over 5 mm pupil diameter following cycloplegia. All IQ parameters were significantly worse in the KCE cohort with their native HOA's, relative to controls and in the ectatic eye of the VAE cohort, relative to the fellow non-ectatic eye (p ≤ 0.008 for all). Reduction in HOA's of these eyes with RGP CL's resulted in a significant improvement in all IQ parameters but they all remained significantly poorer than controls (p ≤ 0.02 for all). The inter-subject variability of best focus and the DOF range were inversely related to peak IQ in these eyes (r = 0.85; p < 0.001). These results provide the optical basis for two clinical observations on keratoconus: (1) optical performance of keratoconic eyes are significantly better with RGP CL's than with spectacles or unaided conditions and (2) the endpoint of subjective refraction is elusive in keratoconic eyes, relative to healthy controls or to the non-ectatic eye in bilaterally asymmetric ectasia.

Neuromuscular plasticity and rehabilitation of the ocular near response.

The near response is composed of cross-coupled interactions between convergence and other distance-related oculomotor responses including accommodation, vertical vergence, and cyclovergence. The cross-coupling interactions are analogous to the body postural reflexes that maintain balance. Near-response couplings guide involuntary motor responses during voluntary shifts of distance and direction of gaze without feedback from defocus or retinal-image disparity. They optimize the disparity stimulus for stereoscopic depth perception and can be modified by optically induced sensory demands placed on binocular vision. In natural viewing conditions, the near response is determined by passive orbital mechanics and active-adaptable tonic components. For example, the normal coupling of vertical vergence with convergence in tertiary gaze is partly a byproduct of passive orbital mechanics. Both, adapted changes of vertical vergence in response to anisophoria, produced by unequal ocular magnification (aniseikonia), and adapted changes in the orientation of Listing's plane in response to torsional disparities can be achieved by a combination of passive orbital mechanics and neural adjustments for the control of the vertical vergence and cyclovergence. Adaptive adjustments are coupled with gaze direction, convergence angle, and head tilt. Several adaptation studies suggest that it is possible to achieve non-linear changes in the coupling of both vertical vergence and cyclovergence with gaze direction. This coupling can be achieved with changes in neural control signals of ocular elevator muscles that are cross-coupled with both convergence and direction of tertiary gaze. These linear and non-linear coupling interactions can be adapted to compensate for (1) anisophoria induced by spectacle corrections for anisometropia, (2) accommodative esotropia, (3) convergence excess and insufficiency, and (4) non-concomitant deviations with ocular torticollis associated with trochlear palsy. The adaptable near-response couplings form the basis of an area of orthoptics that optimizes visual performance by facilitating our natural ability to calibrate neural pathways underlying binocular postural reflexes.

Charles F. Prentice award lecture 2008: surgical correction of presbyopia with intraocular lenses designed to accommodate.

Surgical restoration of accommodation with accommodating intra-ocular lenses (A-IOLs) presents a complex set of problems involving the design of the prosthetic mechanism. A variety of designs are currently employed that either translate the A-IOL toward the cornea along the sagittal axis, shear two lens components laterally, or deform lens shape to change dioptric power of the eye during attempts to accommodate. Effective biomechanical properties (elasticity and viscosity) of these lenses depend on both material properties and structural design of the A-IOL. Inevitable mismatches between the neuromuscular control of accommodation and the effective biomechanical properties of the prosthetic lens could lead to either unstable oscillations or sluggishness of dynamic accommodation; however, optimal dynamic responses may possibly be restored by neural recalibration. A model of dynamic accommodation is used to predict the consequences of these mismatches on dynamic accommodation, and reverse engineering is used to test the feasibility of neuromuscular recalibration. Empirical measures verify that neuromuscular adaptation of dynamic accommodation is possible in response to optically simulated increases and decreases of ocular-lens stiffness. Other design issues for A-IOLs include stability of optical properties, aberrations and image quality, and interactions of restored accommodation with binocular eye alignment (the near response).

Adaptive calibration of dynamic accommodation--implications for accommodating intraocular lenses.

PURPOSE: When the aging lens is replaced with prosthetic accommodating intraocular lenses (IOLs), with effective viscoelasticities different from those of the natural lens, mismatches could arise between the neural control of accommodation and the biomechanical properties of the new lens. These mismatches could lead to either unstable oscillations or sluggishness of dynamic accommodation. Using computer simulations, we investigated whether optimal accommodative responses could be restored through recalibration of the neural control of accommodation. Using human experiments, we also investigated whether the accommodative system has the capacity for adaptive recalibration in response to changes in lens biomechanics. METHODS: Dynamic performance of two accommodating IOL prototypes was simulated for a 45-year-old accommodative system, before and after neural recalibration, using a dynamic model of accommodation. Accommodating IOL I, a prototype for an injectable accommodating IOL, was less stiff and less viscous than the natural 45-year-old lens. Accommodating IOL II, a prototype for a translating accommodating IOL, was less stiff and more viscous than the natural 45-year-old lens. Short-term adaptive recalibration of dynamic accommodation was stimulated using a double-step adaptation paradigm that optically induced changes in neuromuscular effort mimicking responses to changes in lens biomechanics. RESULTS: Model simulations indicate that the unstable oscillations or sluggishness of dynamic accommodation resulting from mismatches between neural control and lens biomechanics might be restored through neural recalibration. CONCLUSIONS: Empirical measures reveal that the accommodative system is capable of adaptive recalibration in response to optical loads that simulate effects of changing lens biomechanics.

Effects of luminance and saccadic suppression on perisaccadic spatial distortions.

Visual directions of foveal targets flashed just prior to the onset of a saccade are misperceived as shifted in the direction of the eye movement. We examined the effects of luminance level and temporal interactions on the amplitude of these perisaccadic spatial distortions (PSDs). PSDs were larger for both single and sequentially double-flashed stimuli with low than high luminance levels, and there was a reduction of PSDs for low luminance targets flashed immediately before the saccade. Significant temporal interactions were suggested by PSDs for a pair of sequentially presented flashes (ISI = 50 ms) that could not be predicted from the single-flash distortions: PSD increased for the first flash and decreased for the second compared to the single-flash distortions. We also found that when the flash pair was presented near saccade onset, the perceived distortion of the earlier flash overtook that of the later flash, even though the late flash occurred closer in time to the saccade. To explain these effects, we propose that stimulus-dependent nonlinearities (contrast gain control and saccadic suppression) influence the duration of the temporal impulse response of both single- and double-flashed stimuli.

How does saccade adaptation affect visual perception?

Three signals are used to visually localize targets and stimulate saccades: (1) retinal location signals for intended saccade amplitude, (2) sensory-motor transform (SMT) of retinal signals to extra-ocular muscle innervation, and (3) estimates of eye position from extra-retinal signals. We investigated effects of adapting saccade amplitude to a double-step change in target location on perceived direction. In a flashed-pointing task, subjects pointed an unseen hand at a briefly displayed eccentric target without making a saccade. In a sustained-pointing task, subjects made a horizontal saccade to a double-step target. One second after the second step, they pointed an unseen hand at the final target position. After saccade-shortening adaptation, there was little change in hand-pointing azimuth toward the flashed target suggesting that most saccade adaptation was caused by changes in the SMT. After saccade-lengthening adaptation, there were small changes in hand-pointing azimuth to flashed targets, indicating that 1/3 of saccade adaptation was caused by changes in estimated retinal location signals and 2/3 by changes in the SMT. The sustained hand-pointing task indicated that estimates of eye position adapted inversely with changes of the SMT. Changes in perceived direction resulting from saccade adaptation are mainly influenced by extra-retinal factors with a small retinal component in the lengthening condition.

The surface of the empirical horopter.

The distribution of empirical corresponding points in the two retinas has been well studied along the horizontal and the vertical meridians, but not in other parts of the visual field. Using an apparent-motion paradigm, we measured the positions of those points across the central portion of the visual field. We found that the Hering-Hillebrand deviation (a deviation from the Vieth-Müller circle) and the Helmholtz shear of horizontal disparity (backward slant of the vertical horopter) exist throughout the visual field. We also found no evidence for non-zero vertical disparities in empirical corresponding points. We used the data to find the combination of points in space and binocular eye position that minimizes the disparity between stimulated points on the retinas and the empirical corresponding points. The optimum surface is a top-back slanted surface at medium to far distance depending on the observer. The line in the middle of the surface extending away from the observer comes very close to lying in the plane of the ground as the observer fixates various positions in the ground, a speculation Helmholtz made that has since been misunderstood.

Variation of binocular-vertical fusion amplitude with convergence.

PURPOSE: The maximum binocular vertical disparity that can be fused with disparity vergence (vertical-fusion amplitude or VFA), varies with convergence angle. VFA is larger for convergence responses to near than to far viewing distances; however, the clinical norms for changes in VFA with convergence have not been established. VFA at several convergence angles was measured to obtain a quantitative description of the changes in VFA with convergence. METHODS: Fifty-six adults took part in the study. Horizontal and vertical disparity stimuli were presented on a computer monitor by using the red-green anaglyphic technique. Stimulus to convergence was altered either by changing horizontal disparity on the computer monitor (experiment I: nine horizontal disparities: 1.2-22.5 PD [Delta]) or by changing the binocular viewing distance (experiment II: five viewing distances: 25-300 cm). Convergence was held constant during an experimental session, while vertical disparity was incremented in steps of 0.05 Delta after a subjective report of fusion, until the subject reported diplopia. The maximum vertical disparity that could be fused was defined as the VFA. RESULTS: VFA increased linearly over the range of convergence stimuli (y = 0.10x + 1.62) and intersubject variability of VFA increased marginally with the amount of convergence. Linear regression equations with similar slopes and y-intercepts were observed in experiments I and II. CONCLUSIONS: The results of the experiments provide a quantitative description of a linear relationship between VFA and convergence. The linear regression equation could be used in a clinical setting to establish norms and to screen for vertical vergence abnormalities.