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.

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.

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.

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.

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.

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.

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.

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.

Perisaccadic stereo depth with zero retinal disparity

When an object is viewed binocularly, unequal perspective projections of the two eyes' half images (binocular disparity) provide a cue for the sensation of stereo depth. For almost 200 years, binocular disparity has remained synonymous with retinal disparity, which is computed by subtracting the distance of each half image from its respective fovea. However, binocular disparity could also be coded in headcentric instead of retinal coordinates, by combining eye position and retinal image position in each eye and representing disparity as differences between visual directions of half images relative to the head. Although these two disparity-coding schemes suggest very different neural mechanisms, both offer identical predictions for stereopsis in almost every viewing condition, making it difficult to empirically distinguish between them. We designed a novel stimulus that uses perisaccadic spatial distortion to generate inconsistency between headcentric and retinal disparity. Foveal half images flashed asynchronously just before a horizontal saccade have zero retinal disparity, yet they produce a sensation of depth consistent with a nonzero headcentric disparity. Furthermore, this headcentric disparity can cancel and reverse the perceived depth stimulated with nonzero retinal disparity. This is the first demonstration that a coding scheme other than retinal disparity has a role in human stereopsis.

The first and second order dynamics of accommodative convergence and disparity convergence

Main sequences, the function describing the relationship between eye movement amplitude and velocity, have been used extensively in oculomotor research as an indicator of first-order dynamics yet it is difficult to find main sequence analyses for accommodative vergence or for disparity vergence in isolation when all mitigating factors have been well controlled and there are no studies in which accommodative vergence and disparity vergence main sequences have been generated for the same group of subjects. The present study measured main sequences in: (1) accommodative vergence with disparity vergence open loop, (2) disparity vergence with accommodation open loop, and (3) combinations of accommodative and disparity vergence. A dynamic AC/A ratio was defined and was found to be similar to the traditional static AC/A ratio. Vergence acceleration was measured for all conditions. A pulse-step model of accommodation and convergence was constructed to interpret the dynamics of the crosslinked interactions between the two systems. The model supports cross-coupling of both the pulse and step components and simulates the primary empirical findings that: (1) disparity vergence has a higher main sequence slope than accommodative vergence, (2) both accommodative and disparity vergence acceleration increase with response amplitude whereas accommodation acceleration does not.

The influence of first near-spectacle reading correction on accommodation and its interaction with convergence

PURPOSE

Accommodation and convergence can adapt to blur and disparity stimuli and to age-related changes in accommodative amplitude. Does this ability decline with age? The authors investigated short-term adaptation to first near-spectacle reading correction on the accommodative-stimulus response (ASR) function, accommodative amplitude (AA), AC/A, and CA/C ratios in a pre-presbyopic and an incipient presbyopic population and determined whether changes in these functions recovered after discontinuation of the use of near spectacles.

METHODS

Thirty subjects with normal vision participated; their ages ranged from 21 to 30 years (n = 15) and 38 to 44 years (n = 15). Oculomotor functions were measured before and after single-vision reading spectacles were worn for near tasks over a 2-month period and then 2 months after the use of near spectacles was discontinued.

RESULTS

The slope of the ASR function and the AC/A and CA/C ratios did not change significantly after near spectacles were worn. There was a hyperopic shift of the ASR function that significantly reduced the near point of accommodation (NPA) and lowered the far-point refraction. These changes were age invariant and did not recover after 2 months of discontinuation of near spectacle wear.

CONCLUSIONS

These results imply that the NPA may be enhanced normally by tonic bias of accommodation that elevates the entire ASR function and produces myopic refraction bias. When this bias relaxes after reading spectacles are worn, there is a hyperopic shift of the refractive state and a reduction of the NPA, specified from optical infinity.

Short-term adaptive modification of dynamic ocular accommodation

PURPOSE

Indirect observations suggest that the neural control of accommodation may undergo adaptive recalibration in response to age-related biomechanical changes in the accommodative system. However, there has been no direct demonstration of such an adaptive capability. This investigation was conducted to demonstrate short-term adaptation of accommodative step response dynamics to optically induced changes in neuromuscular demands.

METHODS

Repetitive changes in accommodative effort were induced in 15 subjects (18-34 years) with a double-step adaptation paradigm wherein an initial 2-D step change in blur was followed 350 ms later by either a 2-D step increase in blur (increasing-step paradigm) or a 1.75-D step decrease in blur (decreasing-step paradigm). Peak velocity, peak acceleration, and latency of 2-D single-step test responses were assessed before and after 1.5 hours of training with these paradigms.

RESULTS

Peak velocity and peak acceleration of 2-D step responses increased after adaptation to the increasing-step paradigm (9/12 subjects), and they decreased after adaptation to the decreasing-step paradigm (4/9 subjects). Adaptive changes in peak velocity and peak acceleration generalized to responses that were smaller (1 D) and larger (3 D) than the 2-D adaptation stimulus. The magnitude of adaptation correlated poorly with the subject's age, but it was significantly negatively correlated with the preadaptation dynamics. Response latency decreased after adaptation, irrespective of the direction of adaptation.

CONCLUSIONS

Short-term adaptive changes in accommodative step response dynamics could be induced, at least in some of our subjects between 18 and 34 years, with a directional bias toward increasing rather than decreasing the dynamics.

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.

Stimulus dependence of the flash-lag effect

When two moving objects are presented in perfect alignment, but are not visible for the same amount of time, the briefer object will often be perceived as "lagging" the object of greater duration. Most investigations of this flash-lag effect (FLE) employ high velocity broadband stimuli, such as lines or dots with sharp boundaries and flashes with rapid onset and offset. We introduce a stimulus paradigm with narrow-band stimuli and measure the stimulus dependence of the FLE when basic stimulus parameters of spatio-temporal frequency and temporal duration are varied. We suggest that this dependence is consistent with the involvement of early visual mechanisms and interpret our results in the context of existing theories of the FLE.

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.

A pulse-step model of accommodation dynamics

Abrupt step changes in human ocular accommodation have been traditionally modeled using a continuous feedback control system supplied by a step-position control signal. However, recent behavioral data show that, while the velocity of the step response increases proportionally with response magnitude, the peak acceleration remains constant. This argues against a step input control signal and suggests the existence of a dual-mode control of accommodation: an initial fixed innervation component related to the constant acceleration followed by an innervation component that increases with response amplitude. Specifically, we proposed a pulse-step that provides a velocity-coded input to the system that is integrated to form two position-input signals, that when combined produce high velocity responses. The pulse height controls the acceleration; the pulse width controls the velocity and the step height controls the position of the accommodation response. The pulse-step model simulations were similar to empirical observations and illustrated an enhancement of the peak velocity of accommodation when compared to when the pulse component was removed from the model. The main functional advantage of the pulse is to overcome the high viscosity of the crystalline lens and achieve rapid step responses.

The coordination of binocular eye movements: vertical and torsional alignment

Precise binocular alignment of the visual axes is of utmost importance for good vision. The fact that so few of us ever experience diplopia is evidence of how well the oculomotor system performs this function in the face of changes due to development, disease and injury. The capacity of the oculomotor system to adapt to visual stimuli that mimic alignment deficits has been extensively explored in laboratory experiments. While the present paper reviews many of those studies, the primary focus is on issues involved in maintaining good vertical and torsional alignment in everyday viewing situations where the parsing of muscle forces may vary for the same horizontal and vertical eye positions due to changes in horizontal vergence and head posture.

Dynamic performance of accommodating intraocular lenses in a negative feedback control system: a simulation-based study

A dynamic model of ocular accommodation is used to simulate the stability and dynamic performance of accommodating intraocular lenses (A-IOLs) that replace the hardened natural ocular lens that is unable to change focus. Accommodation simulations of an older eye with A-IOL materials having biomechanical properties of a younger eye illustrate overshoots and oscillations resulting from decreased visco-elasticity of the A-IOL. Stable dynamics of an A-IOL are restored by adaptation of phasic and tonic neural-control properties of accommodation. Simulations indicate that neural control must be recalibrated to avoid unstable dynamic accommodation with A-IOLs. An interactive web-model of A-IOL illustrating these properties is available at http://schorlab.berkeley.edu.

Dynamic control of ocular disaccommodation: first and second-order dynamics

Velocity and acceleration characteristics provide valuable information about dynamic control of accommodation. We investigated velocity and acceleration of disaccommodation (near-far focusing) from three starting positions. Peak velocity and peak acceleration of disaccommodation increased with the proximity of starting position however for a given starting position they were invariant of response magnitude. These results suggest that all disaccommodation responses are initiated towards a constant primary destination and are switched mid-flight to attain the desired final position. Large discrepancies between the primary destination and desired final position appear to produce overshoots and oscillations of small responses from proximal starting positions.

The extended horopter: Quantifying retinal correspondence across changes of 3D eye position

The theoretical horopter is an interesting qualitative tool for conceptualizing binocular correspondence, but its quantitative applications have been limited because they have ignored ocular kinematics and vertical binocular sensory fusion. Here we extend the mathematical definition of the horopter to a full surface over visual space, and we use this extended horopter to quantify binocular alignment and visualize its dependence on eye position. We reproduce the deformation of the theoretical horopter into a spiral shape in tertiary gaze as first described by Helmholtz (1867). We also describe a new effect of ocular torsion, where the Vieth-Müller circle rotates out of the visual plane for symmetric vergence conditions in elevated or depressed gaze. We demonstrate how these deformations are reduced or abolished when the eyes follow the modification of Listing's law during convergence called L2, which enlarges the extended horopter and keeps its location and shape constant across gaze directions.

Initial destination of the disaccommodation step response

Peak velocity and peak acceleration of disaccommodation step responses remain invariant of response magnitude for a constant starting position and they increase linearly with proximity of starting position. This suggests that disaccommodation response is initiated towards an initial (default) destination and is switched mid-flight to attain the desired final destination. The dioptric location of initial destination was estimated from the x-intercept of regression of peak velocity on response starting position. The x-intercept correlated well with subject's cycloplegic refractive state and poorly with their dark focus of accommodation. Altering the dark focus by inducing fatigue in the accommodative system did not alter the x-intercept. These observations suggest that cycloplegic refractive state is a good behavioral correlate of initial destination of disaccommodation step responses.

Pulse-step models of control strategies for dynamic ocular accommodation and disaccommodation

Dynamic properties and control strategies of step responses by accommodation and disaccommodation differ from one another. Peak velocity of accommodation increases with response magnitude, while peak velocity and peak acceleration of disaccommodation increase with starting position. These dynamic properties can be modeled as control strategies that use independent acceleration-pulse and velocity-step components that are integrated respectively into phasic-velocity signals that control movement and tonic-position signals that control magnitude. Accommodation is initiated toward its final destination by an acceleration-pulse whose width increases with response magnitude to increase peak velocity. Disaccommodation is initiated toward a default destination (the far point) by an acceleration-pulse whose height increases with dioptric distance of the starting position to increase peak velocity and peak acceleration. Both responses are completed and maintained by tonic-position signals whose amplitudes are proportional to the final destination. Mismatched amplitudes of phasic-velocity and tonic-position signals in disaccommodation produce unstable step responses.

Effects of partial occlusion on perceived slant difference

When two slanted surfaces are placed in proximity, the perceived slant difference between them is exaggerated. This effect has been called slant contrast. When a partial occluder is presented in front of the gap between them, the perceived slant difference between the surfaces is reduced. We refer to this reduction in perceived slant difference as stereo-slant assimilation. We investigated two properties of the occluder that might affect perceived stereo-slant difference. Three vertically aligned random-dot patterns were presented either with a partial occluder over the gaps between them or without it. Observers judged the perceived slant difference between the center pattern and two surround random-dot patterns that had the same slant. The perceived slant difference was reduced when the partial occluder was present. We varied stereo-depth and slant of the occluder and found that the decreased perceived slant difference was not due to either of these. Note that the surfaces were all simulated and presented on a computer screen and the results may not apply to real surfaces. The effect of the occluder on perceived slant differences could have resulted from either a reduction of slant contrast or an increase of slant assimilation.

Adaptation to the induced effect stimulus normalizes surface slant perception and recalibrates eye position signals for azimuth

A frontoparallel plane viewed with unequal vertical magnification of the two ocular images appears rotated about a vertical axis (i.e., induced effect; Ogle, 1938). Several experiments were conducted to investigate changes in the visual system that occurred after adapting to the induced effect. Adaptation at 57 cm was tested using tall stimuli at various viewing distances to test for the adaptation of vertical size ratio (VSR) information and normalization of the slant percept. When aftereffects were expressed in units of slant, they were larger at 57 cm than other test distances and were not significantly different from each other at other distances. Short stimuli were used to test adaptation of eye position signals for azimuth. The aftereffects were in the opposite direction to those measured with tall stimuli. The combined results suggest that the visual system normalizes slant percepts based on the surface slant of the adaptation stimulus and when there is a conflict between VSR signals and eye position cues for azimuth that the primary eye position signal for azimuth is recalibrated toward the direction indicated by the binocular differential vertical magnification in the adaptation stimulus.

Stereo-slant adaptation is high level and does not involve disparity coding

We have investigated the potential stages of visual processing at which adaptation may occur to a slanted surface produced by horizontal magnification. Predictions of three hypotheses were tested utilizing a property of depth from binocular disparity, namely that slant scales with distance. If adaptation occurs at the disparity level, then the after-effect expressed in units of horizontal magnification will be independent of the test distance. If adaptation occurs at either a perceived slant or mapping level, then the after-effect, expressed in units of slant, will be independent of the test distance. If adaptation is contingent on distance, then the after-effect will not transfer over distance. Subjects adapted to a stereo-defined slanted surface at a distance of 57 cm. The after-effect was measured with a test stimulus at a distance of 28, 57, 85, or 114 cm by means of a nulling method. When the after-effect was expressed in units of slant, we found that it was larger at the adapting distance than other test distances, and that the after-effect was constant at test distances different from the adaptation distance. These results suggest that two types of adaptation occurred, namely adaptation on a mapping/perception level and adaptation contingent on distance.

Acceleration characteristics of human ocular accommodation

Position and velocity of accommodation are known to increase with stimulus magnitude, however, little is known about acceleration properties. We investigated three acceleration properties: peak acceleration, time-to-peak acceleration and total duration of acceleration to step changes in defocus. Peak velocity and total duration of acceleration increased with response magnitude. Peak acceleration and time-to-peak acceleration remained independent of response magnitude. Independent first-order and second-order dynamic components of accommodation demonstrate that neural control of accommodation has an initial open-loop component that is independent of response magnitude and a closed-loop component that increases with response magnitude.

A pulse-step model of accommodation dynamics in the aging eye

We have developed a dynamic model of accommodation that combines independent phasic-velocity and tonic-position neural signals to control position, velocity and acceleration properties of accommodative step responses. Phasic and tonic signals were obtained from neural integration of a fixed-height acceleration-pulse and variable-height velocity-step respectively to control independent acceleration and velocity properties of the step response. Duration and amplitude of the acceleration-pulse are increased with age to compensate for age-related increases of visco-elastic properties of the lens to maintain youthful velocity. The model illustrates a neural control strategy that is similar to the classical neural control model of step changes by the saccadic and vergence systems.

Temporal aspects of spatial interactions affecting stereo-matching solutions

Stereo-matching solutions minimize disparity relative to the horopter (minimum-absolute-disparity or MAD), and differences in disparity between adjacent features (minimum-relative-disparity or MRD). When placed in conflict, spatial proximity promotes MRD over MAD solutions. How does temporal proximity of neighboring features affect strength of these spatial interactions? We quantified the inter-stimulus interval (ISI) over which an unambiguous disparity pattern influenced stereo-matches for patterns with several possible solutions. Likelihood of MRD decreased as ISI increased (48.9 ms time constant) and increased as contrast was reduced for short ISIs, suggesting that monocular persistence (temporal impulse response) underlies the temporal interaction.

Symmetrical horizontal vergence contributes to the asymmetrical pursuit of targets in depth

When a target travels slowly and smoothly along the line of sight of one eye, the eye that is aligned with the target remains stationary while the other eye adducts. The mechanism that is commonly invoked is that commands signaling conjugate pursuit and symmetrical vergence are combined. The two signals are in the same direction in the adducting eye but are in the opposite direction in the stationary eye and, so, cancel. Recent data have challenged this view and the idea that the two eyes are controlled independently has been resurrected. Pursuit and vergence movements are difficult to separate when they occur together because they have similar latencies and dynamics. We have developed a method where horizontal vergence is "tagged" by training it to have a vertical vergence component that can then be identified in combined pursuit-vergence movements. Four subjects trained eye movements to have a vertical vergence component by fusing vertical disparities that varied in association with horizontal convergence. Following training, the vertical vergence aftereffect was found whenever horizontal vergence was stimulated regardless of whether the horizontal vergence resulted from movement of the target in the midsagittal plane (symmetrical vergence) or from movement of the target along the line of sight of one eye (asymmetrical vergence). The vertical vergence aftereffect was never observed in association with conjugate movements indicating that asymmetrical slow eye movements are not controlled monocularly but contain a vergence component along with symmetrical smooth pursuit.

Eye movements facilitate stereo-slant discrimination when horizontal disparity is noisy

Conditions in which saccadic gaze shifts within planar surfaces facilitate stereo-slant discrimination for slant about the horizontal and vertical axis were investigated. When horizontal disparity noise was added, large gaze shifts in the direction of the slant lowered stereo-slant discrimination thresholds compared to thresholds measured with steady central fixation, whereas eye movements orthogonal to the slant orientation did not lower slant-discrimination thresholds. When no horizontal noise was added, performance was the same with and without gaze shifts. These results suggest that slant is recovered from depth differences between target edges when horizontal disparity signals are variable and that foveal fixation improves the measures of disparity. Eye movements did not lower slant thresholds by providing multiple foveal samples of slant at different target locations that were averaged to reduce disparity noise levels, because eye movements only lowered the thresholds when there was a depth difference between the fixation points. To study which signals for azimuth are used when slant is recovered from the difference in depth between target edges, vertical disparity noise was added and stimulus height was reduced. Both methods elevated slant-discrimination thresholds when horizontal disparity noise was present, suggesting that vertical disparity is used as a cue for azimuth.

Thresholds for stereo-slant discrimination between spatially separated targets are influenced mainly by visual and memory factors but not oculomotor instability

Surface-slant variations can be sensed either simultaneously with steady fixation or sequentially with saccadic gaze shifts. Stereo-slant discrimination thresholds are affected by visual, oculomotor, and memory factors. We have investigated the effects of fixation strategy, target separation, and exposure duration on stereo-slant discrimination. With long exposure durations (734 ms), stereo-slant discrimination thresholds measured with simultaneous presentation of test and reference stimuli were lower with gaze shifts than without them when target separations exceeded 4 deg. Above 4-deg target separations, the benefits of improved disparity resolution with foveal gaze shifts outweighed the costs of oculomotor variability associated with saccades. With short exposure durations (167 ms), as target separation increased, stereo-slant discrimination thresholds measured without gaze shifts increased with both sequential and simultaneous stimulus presentations, whereas thresholds with gaze shifts remained constant. This indicates that oculomotor errors are not an important factor in stereo-slant discrimination. In contrast to stereo-slant thresholds, sequential stereo-depth thresholds between two dots, measured with gaze shifts, increased with target separation. Thus, oculomotor error increases with target separation, and it is an important factor in stereo-depth discrimination.

Comparison of the time courses of concomitant and nonconcomitant vertical phoria adaptation

Vertical phoria adaptation was measured before, during, and after 1 h of training with either a prism or magnifying lens. With the prism (concomitant adaptation) a single vertical disparity was presented at primary position. With the magnifier (nonconcomitant adaptation) two vertical disparities of opposite sign were presented along the vertical meridian. Following adaptation, binocular vision was prevented with an eye patch, and vertical phorias were measured periodically along the primary vertical meridian over the course of 8 h. Despite individual variation, adaptation followed approximately exponential time courses. The average time constants for the decay of concomitant and nonconcomitant adaptation were 31 and 83 min, respectively. There was no consistent relationship between the rates of acquisition and decay nor was there a strong relationship between the gains of the adaptive responses and the rates of decay although there was a general trend for the gains of the nonconcomitant responses to be higher and the rate of decay slower than the concomitant responses. The results support the notion that concomitant and nonconcomitant phoria adaptation involve different mechanisms but not the contention that adaptation to prisms is easier or more robust than adaptation to lenses.

Changes in cyclotorsion and vertical eye alignment during prolonged monocular occlusion

When binocular vision is prevented with monocular occlusion, the two eyes assume a position of rest related to the combination of underlying tonic innervation of the oculomotor system, cross-coupled accommodative-vergence input and vergence responses to perceptual cues for spatial location relative to the head. When the latter two are controlled, the covered eye has been shown in the majority of subjects to turn outward (exophoria) and upward (hyperphoria) after prolonged monocular occlusion. The present study investigates the change in torsional eye alignment and its relation to vertical eye alignment after eight hours of monocular occlusion. The results revealed an excyclophoria during occlusion in four out of five subjects. The patched eye also became elevated in two subjects and depressed in two others. Thus, during prolonged monocular occlusion, the relative directions of cyclophoria and vertical phoria appear to be independent. In addition, there were non-concomitant changes in vertical phoria with horizontal gaze, toward a state where the adducted eye was elevated relative to the abducted eye. Simulations with Orbit(TM) suggest that these non-concomitant changes in vertical phoria with a concomitant excyclophoria may be based upon orbital mechanics. Excyclophoria appears to be the baseline state of binocular alignment.

Adaptive control of vergence in humans

Vergence eye alignment minimizes horizontal, vertical, and cyclodisparities to optimize stereo-depth perception. Only the horizontal component of vergence is under voluntary control. Couplings with voluntary version and horizontal vergence guide vertical vergence and cyclovergence. Can these couplings be modified in response to sensory demands on binocular vision? We have modified vertical vergence and cyclovergence in response to optical changes in disparity. Vertical vergence was stimulated with aniseikonic lenses that exaggerated vertical disparity in tertiary gaze. Vertical vergence adapted in an hour to produce nonconcomitant changes in vertical phoria that varied with vertical eye position in tertiary gaze. Cyclovergence was stimulated with cyclodisparities that varied with gaze elevation and convergence angle. Cyclovergence adapted within 2 hours to produce nonconcomitant changes in cyclophoria that varied with gaze elevation and convergence. The adaptive couplings for vertical vergence and cyclovergence are modeled as a combination of passive orbital mechanics and active gain control of the vertical recti and obliques. Vergence adaptation is a calibration process that adjusts the innervation for horizontal, vertical, and torsion components of vergence to the physical constraints set by the extraocular muscles and orbital connective tissues. Passive orbital mechanics simplify the neural control for precise vertical vergence and cyclovergence that are needed to achieve binocular alignment under open-loop conditions in response to perceived spatial location.

Plasticity of convergence-dependent variations of cyclovergence with vertical gaze

Binocular alignment of foveal images is facilitated by cross-couplings of vergence eye movements with distance and direction of gaze. These couplings reduce horizontal, vertical and cyclodisparities at the fovea without using feedback from retinal image disparity. Horizontal vergence is coupled with accommodation. Vertical vergence that aligns tertiary targets in asymmetric convergence is thought to be coupled with convergence and horizontal gaze. Cyclovergence aligns the horizontal retinal meridians during gaze elevation in symmetrical convergence and is coupled with convergence and vertical gaze. The latter vergence-dependent changes of cyclovergence have been described in terms of the orientation of Listing's plane and have been referred to as the binocular extension of Listing's law. Can these couplings be modified? Plasticity has been demonstrated previously for two of the three dimensions of vergence (horizontal and vertical). The current study demonstrates that convergence-dependent changes of the orientation of Listing's plane can be adapted to either exaggerate or to reduce the cyclovergence that normally facilitates alignment of the horizontal meridians of the retinas with one another during gaze elevation in symmetrical convergence. The adaptability of cyclovergence demonstrates a neural mechanism that, in conjunction with the passive forces determined by biomechanical properties of the orbit, could play an active role in implementing Listing's extended law and provide a means for calibrating binocular eye alignment in three dimensions.

Adaptation of torsional eye alignment in relation to smooth pursuit and saccades

The long-term fusion of vertical or horizontal disparities by vergence eye movements is known to evoke persistent changes in vertical and horizontal eye alignment. Adaptive changes in response to torsional disparities have not been well studied. Torsional eye position was measured binocularly with a video system before and after 90 min training periods in which subjects attempted to fuse cyclodisparities. Subjects trained with either a single cyclodisparity presented at a single vertical eye position or with cyclodisparities that varied smoothly from an incyclodisparity to an excyclodisparity as a function of either vertical or horizontal eye position. All five subjects showed persistent changes in binocular torsional eye alignment following both types of training. Incyclodisparities were more easily fused during training and the training aftereffect was greater in that direction. The training aftereffect was observed in relation to both saccades and smooth pursuit under both open-loop and closed-loop viewing conditions. During saccades, the dynamics of the cyclovergence training aftereffect more closely resembled the dynamics of cyclofusional movements than the dynamics of the saccades with which they were associated.

Age changes in the interactions between the accommodation and vergence systems

Experiments are described in which static and dynamic accommodation (Ar), accommodative convergence (AC), vergence (C) and convergence accommodation (CA) responses to small stimuli were measured dynamically in 13 subjects with ages in the range 16 to 48 years. Analysis showed that the amplitudes of both blur and disparity-driven accommodation declined significantly with age, whereas the two types of vergence response did not. As a result, the AC/Ar ratio rose significantly with age, whereas the CA/C ratio fell. No significant change with age was found in response latencies and durations.

Spatial interactions minimize relative disparity between adjacent surfaces

Computational models of stereopsis employ a number of algorithms that constrain stereo matches to produce the smallest absolute disparity and to minimize the relative disparity between nearby features. In some natural scenes, such as large slanted textured surfaces, these two constraints lead to different matching solutions. The current study utilized a stimulus in which there was a large discrepancy in both the magnitude and direction of matches that solved for minimum absolute and minimum relative disparity. This discrepancy revealed a dominance for the minimum relative disparity over the minimum absolute disparity matching solution that increased with spatial proximity, spatial frequency and width of adjacent features. The likelihood of a minimum-relative-disparity matching solution also increased when the difference between the amplitudes of the alternative relative disparities was large. When alternative relative disparity matching solutions had similar amplitudes but opposite signs (crossed vs. uncrossed), an idiosyncratic depth bias served as a tie-breaker. The present results show that absolute disparity matches are constrained to minimize relative disparity between adjacent features.

Envelope size tuning for stereo-depth perception of small and large disparities

Stereopsis is the sense of depth derived from binocular disparities that are formed between targets that are matched between the two retinal images. Binocular matches for sustained stereopsis are based on similarity of orientation, spatial frequency and contrast of the two retinal images whereas matches for transient stereopsis depend on these parameters to a very limited extent. In this investigation we have tested the possibility that transient stereopsis forms matches between objects of similar overall size. The tuning of sustained and transient stereopsis to contrast-envelope size was investigated by presenting narrow-band Gabor targets of unequal size to the two eyes. Bandwidth for envelope-size tuning was estimated from the range of dichoptic size-differences over which stereo performance remained above chance level. An equal bandwidth of 2 octaves was found for the sustained and transient stereo systems when stimulated with parallel orientation Gabors that subtended a small disparity. Sustained-stereo performance with orthogonal carriers was reduced with large envelope sizes. Bandwidth of the transient stereo system increased to 3 octaves when tested with a larger disparity stimulus and it was independent of carrier orientation. Reducing the contrast of the larger-size Gabor improved transient-stereo performance from near chance (48-58%) to 85-95%. Thus the bandwidth for envelope-size tuning is much broader than indicated with equal physical contrast stimuli. The observed tuning to envelope size, while broad, is tighter than that observed for carrier spatial-frequency [Vis. Res. 38 (1998) 3057], carrier orientation [Vis. Res. 39 (1999) 2717] and contrast polarity [Vis. Res. 39 (1999) 4010] of the stimulus. Thus it would appear that envelope size and, to a greater extent, temporal synchrony of the dichoptic stimuli [Perception 24 (1995) 33] are the primary means for selecting matched binocular inputs for transient stereopsis.

Envelope size-tuning for transient disparity vergence

Our prior studies have demonstrated that the transient-vergence system responds preferably to dichoptic stimulus pairs that contain the highest combined energy, regardless of dichoptic differences in spatial frequency, contrast, orientation, or luminance polarity (Edwards, M., Pope, D. R., & Schor, C. M. (1998), Vision Research 38, 705; Pope, D. R., Edwards, M., & Schor, C. M. (1999) Vision Research 39, 575). This broadband tuning for spatial frequency, orientation and contrast is indicative of a second order (non-linear) extraction system. The current study examined the potential size-tuning of binocular channels to the contrast envelope that is extracted by a non-linear process. Stimuli were size-scaled Gabor patches with parallel and orthogonal carrier orientations that subtended a large (3.8 degrees ) disparity. Results indicate that the transient-vergence system exhibits broad band-pass tuning to overall size of dichoptic targets, independent of interocular differences in carrier orientation, spatial frequency or contrast. Equal sizes elicited a higher proportion of vergence responses than unequal sizes, however responses to unequal size still occurred over a 2-octave range, illustrating broad band-pass tuning. Size tuning was found to be broader for small than large envelope sizes. The broad tuning for envelope size is likely to result from the overlapping extracted low-pass frequency spectra of the contrast envelopes. However, the transient-vergence system also responds to monocular, hemi-retinal stimuli over a larger (3-octave) range. Thus some of the observed "binocular tuning" may be due to these monocular responses.

Fatigue reduces tonic accommodation

Ocular accommodation adopts a mean baseline response level of approximately 1.0 D in the absence of blur feedback (open-loop state). This baseline or tonic accommodation (TA) can be elevated following a sustained monocular accommodative response to a dioptric stimulus (lens adaptation) that exceeds the baseline open-loop level of TA. The accommodative response to the lens persists in the open-loop state (accommodative hysteresis), and eventually decays to a stable end-point. Interestingly, if the baseline TA is high, the monocularly adapted accommodative state can decay to an end-point that is below the initial pre-adapted baseline level of the TA (counter-adaptive response) (McBrien, N.A. and Millodot, M., (1988). Differences in adaptation of TA with refractive state. Invest. Ophthalmol. Vis. Sci., 29, 460-469). We have investigated the possible contribution of accommodation fatigue to the counter-adaptive change in baseline TA following sustained accommodation. Two fatigue procedures were used while viewing a target at 66 or 33 cm. In a monocular condition, accommodation was stimulated for 3 min with lens values alternating from -1.5 to +1.5 D at a rate of 0.25 Hz. In the binocular condition, convergence was stimulated with alternating prism values from 9 prism diopters (PD) base-out to 9 PD base-in. Both monocular and binocular tasks resulted in a significant reduction of TA. These results suggest that previously reported reductions of baseline TA following sustained monocular accommodation or binocular convergence could have resulted from fatigue of the accommodative system. Accommodative fatigue could be responsible for the lower values of TA observed in counter-adaptive responses to sustained accommodative or convergence effort.

Adaptation of torsional eye alignment in relation to head roll

The coordination of head tilt, ocular counter-roll and vertical vergence is maintained by adaptive mechanisms; the desired outcome being clear single vision. A disruption or imbalance in otolith-ocular pathways may result in diplopia which stimulates these adaptive processes. In the present experiment, dove prisms were used to create cyclodisparities that varied with head tilt about a naso-occipital axis (roll). A stimulus for incyclovergence was presented with the head rolled 45 degrees to one side and a stimulus for an excyclovergence was presented with the head rolled 45 degrees to the other side. At the end of 1 h of training, all subjects demonstrated a change in open-loop cyclovergence that would help to correct for the cyclodisparities experienced during the closed-loop training period. The change appeared to be a simple gain change in the ocular counter-roll of one or both eyes.

First- and second-order processing in transient stereopsis

Large-field stimuli were used to investigate the interaction of first- and second-order pathways in transient-stereo processing. Stimuli consisted of sinewave modulations in either the mean luminance (first-order stimulus) or the contrast (second-order stimulus) of a dynamic-random-dot field. The main results of the present study are that: (1) Depth could be extracted with both the first-order and second-order stimuli; (2) Depth could be extracted from dichoptically mixed first- and second-order stimuli, however, the same stimuli, when presented as a motion sequence, did not result in a motion percept. Based upon these findings we conclude that the transient-stereo system processes both first- and second-order signals, and that these two signals are pooled prior to the extraction of transient depth. This finding of interaction between first- and second-order stereoscopic processing is different from the independence that has been found with the motion system.

Unconstrained stereoscopic matching of lines

The computation of horizontal binocular disparities used in stereoscopic depth perception depends upon the identification of corresponding features in the two retinal images. In principle, binocular matching is a two-dimensional problem that considers matches in all possible meridians. Normally, constraints such as end points or crossing points limit the direction and magnitude of matches. If matching is unconstrained, such as is the case with long lines, it is completely ambiguous. Under these conditions the default match will be determined by the operating range, or upper disparity limit, of matchable vertical and horizontal disparities. We computed the operating range of vertical matches for stereoscopic depth as a function of line orientation. Our results suggest that the two-dimensional operating range is anisotropic for vertical and horizontal disparity and that unconstrained matches are not based upon either epipolar geometry or nearest neighbor constraints, but rather the mean of disparity estimates within the operating range for binocular matches. This operating range can be extended vertically when matches are constrained by image primitives.