Vergence Angle Research Articles

The geometry of the vergence-accommodation conflict in mixed reality systems

Mixed reality technologies, such as virtual (VR) and augmented (AR) reality, present promising opportunities to advance education and professional training due to their adaptability to diverse contexts. Distortions in the perceived distance in such mediated conditions, however, are well documented and have imposed nontrivial challenges that complicate and limit transferring task performance in a virtual setting to the unmediated reality (UR). One potential source of the distance distortion is the vergence-accommodation conflict—the discrepancy between the depth specified by the eyes’ accommodative state and the angle at which the eyes converge to fixate on a target. The present study involved the use of a manual pointing task in UR, VR, and AR to quantify the magnitude of the potential depth distortion in each modality. Conceptualizing the effect of vergence-accommodation offset as a constant offset to the vergence angle, a model was developed based on the stereoscopic viewing geometry. Different versions of the model were used to fit and predict the behavioral data for all modalities. Results confirmed the validity of the conceptualization of vergence-accommodation as a device-specific vergence offset, which predicted up to 66% of the variance in the data. The fitted parameters indicate that, due to the vergence-accommodation conflict, participants’ vergence angle was driven outwards by approximately 0.2°, which disrupted the stereoscopic viewing geometry and produced distance distortion in VR and AR. The implications of this finding are discussed in the context of developing virtual environments that minimize the effect of depth distortion.

Vergence eye movements in virtual reality

There is increasing interest in incorporating eye tracking in virtual reality (VR) systems to infer gaze in 3 dimensions. Estimation of gaze in depth may be limited by errors of measurement of the small eye vergence angles involved. It may also be limited by true errors of vergence in VR. We found that observers commonly made errors of vergence when viewing in VR, such that the dominant eye was more accurately aligned than the non-dominant eye. Errors of vergence were often larger than Panum’s fusional range. The absence of reported diplopia suggests that some of the visual input from one eye was supressed or the double images escaped attention. Errors of vergence could not be explained by contamination by variations in pupil diameter. Errors of vergence were not reduced when the vergence-accommodation conflict was eliminated by optical correction. These results suggest that the ability to correctly infer gaze distance in VR may be limited by true errors of eye vergence, rather than by measurement errors imposed by limitations of eye tracking.

Interpretation of Regional Geophysical Data Acquired at the Bathurst Mining Camp, Canada

The Bathurst Mining Camp is a major base-metal mining district in New Brunswick, Canada that was a focus area for the Geological Survey of Canada Targeted Geoscience Initiative Phase 3 project. As part of this project, more than 3500 gravimetric observations were acquired in the Bathurst Mining Camp, with an average spacing of 1-2 km, in 2006. The gravimetric data was reduced for an average crustal density value of 2.77 g/cm3 to obtain the Bouguer anomaly, which was analyzed and used to obtain 2.5D gravity models along five transects crossing the Bathurst Mining Camp. As a result of gravity modeling, a model of the general geometry of the main geological groups of the Bathurst Mining Camp (Fournier, California Lake, Tetagouche, and Miramichi) was obtained, which suggests that the Nine Mile Syncline is an open fold, and the Tetagouche Anticline is a gentle fold. Both folds are non-cylindrical and inclined, with their axial planes dipping in the 293° N direction: the angle of vergence of the folds increases towards the northeast of their axes. The structures under the Tetagouche Anticline axis gradually get deeper towards the Northeast reaching a maximum depth of 4 km. The depth of the structures modeled under the axis of the Nine Mile Syncline varies between 2 and 9 km, the deepest part being towards the center of the Bathurst Mining Camp; towards the northeast of its axis, the structures reach an intermediate depth of 4 km while towards the southwest they are 2 km deep on average.

Eye convergence is evoked during larval prey capture (LPC) without visual stimulus and in blind cavefish

In zebrafish larvae, the first response when detecting prey is an oculomotor behavior; eye convergence. Eye convergence increases the overlap between the visual fields of the left and right eyes to prepare for tracking prey. A high vergence angle is maintained throughout the prey-tracking and capture swim phases, enhancing binocular depth. Since the discovery of eye convergence, hundreds of articles reporting on this behavior in zebrafish have been published. In this study, we found that the larvae of blind tetra cavefish, Astyanax mexicanus, despite being adapted to the absence of visual stimuli due to the lack of light in the cave, have retained the oculomotor behavior of eye convergence in their vestigial eyes. In Astyanax, eye convergence responses can be triggered singlehandedly by vibrations elicited with a glass rod at frequencies similar to those generated by its prey (10–35 Hz). The blind cave tetra offers an intriguing combination of regression of the eye structure, while retaining several of the physiological functions and actions performed in the eye, including light-entrained retinomotor rhythms and eye convergence.

Frequency dependence of coordinated pupil and eye movements for binocular disparity tracking.

Coordinated alignment of the eyes during gaze fixation and eye movements are an important component of normal visual function. We have previously described the coordinated behavior of convergence eye movements and pupillary responses using a 0.1 Hz binocular disparity-driven sine profile and a step profile. The goal of this publication is to further characterize ocular vergence-pupil size coordination over a wider range of frequencies of ocular disparity stimulation in normal subjects. Binocular disparity stimulation is generated by presentation of independent targets to each eye on a virtual reality display, while eye movements and pupil size are measured by an embedded video-oculography system. This design allows us to study two complimentary analyses of this motion relationship. First, a macroscale analysis describes the vergence angle of the eyes in response to binocular disparity target movement and pupil area as a function of the observed vergence response. Second, a microscale analysis performs a piecewise linear decomposition of the vergence angle and pupil relationship to permit more nuanced findings. These analyses identified three main features of controlled coupling of pupil and convergence eye movements. First, a near response relationship operates with increasing prevalence during convergence (relative to the "baseline" angle); the coupling is higher with increased convergence in this range. Second, the prevalence of "near response"-type coupling decreases monotonically in the diverging direction; the decrease persists after the targets move (converge back) from maximum divergence toward the baseline positions, with a minimum prevalence of near response segments near the baseline target position. Third, an opposite polarity pupil response is infrequent, but tends to be more prevalent when the vergence angles are at maximum convergence or divergence for a sinusoidal binocular disparity task. We suggest that the latter response is an exploratory "range-validation" when binocular disparity is relatively constant. In a broader sense, these findings describe operating characteristics of the near response in normal subjects and form a basis for quantitative assessments of function in conditions such as convergence insufficiency and mild traumatic brain injury.

The effect of real-world and retinal motion on speed perception for motion in depth.

For motion in depth, even if the target moves at a constant speed in the real-world (physically), it would appear to be moving with acceleration on the retina. Therefore, the purpose of this study was to determine whether real-world and retinal motion affect speed perception in depth and to verify the influence of eye movements on both motion signals in judging speed in depth. We used a two-alternative forced-choice paradigm with two types of tasks. One stimulus moved at a constant speed in the real-world (world constant task) with three conditions: 80-60 cm (far), 60-40 cm (middle), and 40-20 cm (near) from the participant. The other stimulus moved at a constant speed on the retina (retinal constant task) with three conditions: 4-8 deg (far), 8-12 deg (middle), and 12-16 deg (near) as the vergence angle. The results showed that stimulus speed was perceived faster in the near condition than in the middle and far conditions for the world constant task, regardless of whether it was during fixation or convergence eye movements. In contrast, stimulus speed was perceived faster in the order of the far, middle, and near conditions for the retinal constant task. Our results indicate that speed perception of a visual target approaching the observer depends on real-world motion when the target position is relatively far from the observer. In contrast, retinal motion may influence speed perception when the target position is close to the observer. Our results also indicate that the effects of real-world and retinal motion on speed perception for motion in depth are similar with or without convergence eye movements. Therefore, it is suggested that when the visual target moves from far to near, the effects of real-world and retinal motion on speed perception are different depending on the initial target position.

Quotidian Profile of Vergence Angle in Ambulatory Subjects Monitored With Wearable Eye Tracking Glasses.

Wearable eye trackers record gaze position as ambulatory subjects navigate their environment. Tobii Pro Glasses 3 were tested to assess their accuracy and precision in the measurement of vergence angle. Four subjects wore the eye tracking glasses, with their head stabilized, while fixating at a series of distances corresponding to vergence demands of: 0.25, 0.50, 1, 2, 4, 8, 16, and 32°. After these laboratory trials were completed, 10 subjects wore the glasses for a prolonged period while carrying out their customary daily pursuits. A vergence profile was compiled for each subject and compared with interpupillary distance. In the laboratory, the eye tracking glasses were comparable in accuracy to remote video eye trackers, outputting a mean vergence value within 1° of demand at all angles except 32°. In ambulatory subjects, the glasses were less accurate, due to tracking interruptions and measurement errors, partly mitigated by the application of data filters. Nonetheless, a useful record of vergence behavior was obtained in every subject. Vergence profiles often had a bimodal distribution, reflecting a preponderance of activities at near (mobile phone and computer) or far (driving and walking). As expected, vergence angle correlated with interpupillary distance. Wearable eye tracking glasses make it possible to compile a nearly continuous record of vergence angle over hours, which can be correlated with the corresponding visual scene viewed by ambulatory subjects. This technology provides new insight into the diversity of human ocular motor behavior and may become useful for the diagnosis of disorders that affect vergence function such as: convergence insufficiency, Parkinson disease, and strabismus.

Ambulatory Monitoring With Eye Tracking Glasses to Assess the Severity of Intermittent Exotropia

To explore the utility of eye tracking glasses in patients with intermittent exotropia as a means for quantifying the occurrence of exotropia, defined as the percentage of time that the eyes are misaligned. Prospective observational study. Eye tracking glasses were used to obtain 68 recordings in 44 ambulatory patients with a history of intermittent exotropia. Vergence angle was monitored for up to 12 hours to document the occurrence of exotropia. Intermittent exotropia was present in 31 of 44 patients. They had a mean exotropia of 19.3 ± 5.3° and a mean occurrence of 40% (range 3-99%). There was a moderate correlation between the magnitude of exotropia and its occurrence (r=0.59). In 13 patients the occurrence of exotropia was <1%; they were deemed to have an exophoria only. In 35 of 44 cases, families reported an occurrence of intermittent exotropia greater than that measured by the eye tracking glasses. Eye tracking glasses may be a useful tool for quantifying the severity of intermittent exotropia and for defining more precisely its clinical features.

Ultralow Power On-the-Eye Vergence and Distance Sensing Through Differential Magnetometry

We demonstrate the realization of a very low energy, on-the-eye vergence-type distance ranger based on sensing of a locally-uniform vector field, specifically the earth’s magnetic field. This ranging method is passive, only requiring measurement of the magnetic field vector at both eyeballs utilizing magnetometer chips placed on the eye scleral regions. The eye vergence angle and range distance are calculated from these two vector quantities. The method can obtain a range reading with as little as 118 nJ of energy consumed per eye for 3.3V and 50 nJ when operated at 1.9V. This method is thus suitable for applications where energy storage is very limited such as in smart contacts vision correcting microsystems.

Effects of virtual target size, position, and parallax on vergence-accommodation conflict as estimated by actual gaze

Due to the increased utilization of stereoscopic displays, the scope of the vergence–accommodation conflict has been studied extensively to reveal how the human visual system operates. The purpose of this work was to study the phenomenon of vergence–accommodation conflict by comparing the theoretical eye vergence angle (vergence response) and gaze-based eye vergence angle (vergence stimulus) based on eye tracker gaze data. The results indicated that the gaze-based eye vergence angle was largest at the greatest parallax. The result also revealed that the eye vergence angle accuracy was significantly highest at the nearest parallax. Generally, accuracy improves when virtual objects are put in the middle and close to participants' positions. Moreover, the signed error decreases significantly when the virtual object is in the middle. Based on the results of this study, we can gain a greater understanding of the vergence–accommodation conflict in the stereoscopic environment.

How vergence influences the perception of being looked at.

Perceiving other people's direct gaze is important for many areas of everyday activity. For horizontal and vertical eye movements, the area of being looked at, known as the cone of gaze, has been well explored. Previous research has shown a range of eye rotations (up to eccentricities of 4°-9°) that people accept as direct gaze. Vergence is an important cue for perceiving the depth of fixation. This study examines the range of vergence angles that support the perception of being looked at. In two experiments, observers adjusted the degree of vergence of the lookers' eyes until they felt just (not) looked at. The first experiment also asked to adjust the point of being exactly looked at, which was 0° (parallel eyes). The thresholds of being just (not) looked at were around 4.5° of convergence and 2.5° divergence, which results in a depth of 7° of vergence. This depth was replicated in Experiment 2, while the thresholds of convergence (3.5°) and divergence (3.5°) slightly differ from Experiment 1. The results indicate a consistent area of vergences being accepted as direct gaze, yielding first-time evidence for a third dimension-the depth dimension-of direct gaze.

Reduced activity of vertically acting motoneurons during convergence.

Previous studies have revealed unexpected relationships between the firing rates of horizontally acting motoneurons and vergence. During a vergence task, for example, antidromically identified abducens internuclear neurons show a negative correlation between vergence angle and firing rate, which is the opposite of the modulation displayed by the medial rectus motoneurons to which they project. For a given horizontal eye position, medial rectus motoneurons discharge at a higher rate if the eyes are converged than if the same eye position is reached during a task that requires version; paradoxically, however, the horizontal rectus eye muscles show corelaxation during vergence. These complex and unexpected relationships inspired the present author to investigate whether the tonic firing rates of vertically acting motoneurons in oculomotor nucleus are correlated with vergence angle. Monkeys were trained to fixate a single, randomly selected, visual target among an array of 60 red plus-shaped LEDs, arranged at 12 different distances in three-dimensional space. The targets were arranged to permit dissociation of vertical eye position and vergence angle. Here I report, for the first time, that most vertically acting motoneurons in oculomotor nucleus show a significant negative correlation between tonic firing rate and vergence angle. This suggests the possibility that there may be a general corelaxation of extraocular muscles during vergence.NEW & NOTEWORTHY An array of 60 plus-shaped LEDs, positioned at various locations in three-dimensional space, was used to elicit conjugate and disjunctive saccades while single neurons in oculomotor nucleus were recorded from rhesus monkeys. This study demonstrates that most vertically acting motoneurons in oculomotor nucleus discharge at a lower rate when the eyes are converged.

A Novel Tectal/Pretectal Population of Premotor Lens Accommodation Neurons.

PurposeUnder real-world conditions, saccades are often accompanied by changes in vergence angle and lens accommodation that compensate for changes in the distance between the current fixation point and the next target. As the superior colliculus directs saccades, we examined whether it contains premotor neurons that might control lens compensation for target distance.MethodsRabies virus or recombinant rabies virus was injected into the ciliary bodies of Macaca fascicularis monkeys to label circuits controlling lens accommodation via retrograde transsynaptic transport. In addition, conventional anterograde tracers were used to confirm the rabies findings with respect to projections to preganglionic Edinger–Westphal motoneurons.ResultsAt time courses that rabies virus labeled lens-related premotor neurons in the supraoculomotor area and central mesencephalic reticular formation, labeled neurons were not found within the superior colliculus. They were, however, found bilaterally in the medial pretectal nucleus continuing caudally into the tectal longitudinal column, which lies on the midline, between the colliculi. A bilateral projection by this area to the preganglionic Edinger–Westphal nucleus was confirmed by anterograde tracing. Only at longer time courses were cells labeled in the superior colliculus.ConclusionsThe superior colliculus does not provide premotor input to preganglionic Edinger–Westphal nucleus motoneurons, but may provide input to lens-related premotor populations in the supraoculomotor area and central mesencephalic reticular formation. There is, however, a novel third population of lens-related premotor neurons in the tectal longitudinal column and rostrally adjacent medial pretectal nucleus. The specific function of this premotor population remains to be determined.

Measuring the likelihood of VR visual fatigue through ocular biomechanics

Immersion in virtual reality is still linked to symptoms of visual fatigue such as eye strain, dizziness, and overall discomfort. Studies have investigated visual fatigue through pre- and post-immersion tests of the visual function. In this work, we extend on our previous study and derive a visual fatigue likelihood metric using biomechanical analysis. Previously, we have investigated the effect of VR on the vergence system during immersion. The proposed visual fatigue metric exhibited a significant correlation to vergence angle variability which was previously linked to vergence accommodation conflict in VR. We also discuss subjective feedback and its relationship with the proposed visual fatigue metric.

Properties of fast vergence eye movements and horizontal saccades in athletes

Visual information based on eye movements influences sports performance in 3-D space. The purpose of this study was to clarify the properties of fast vergence eye movements and horizontal saccades in athletes. Thirty-four college students were classified into three groups: twelve baseball players (BAS), ten track and field athletes (TRA) and twelve non-athletes (NON). The oculomotor tasks consisted of vergence eye movements (vergence task) including convergence and divergence, and horizontal saccades (saccade task). The participants made a rapid gaze shift toward a visual target. For the vergence task, the target was irradiated at 5 different vergence angles (3, 5, 10, 15, 20°) randomly. For the saccade task, the target was irradiated at 5 different saccade amplitudes (0, ±5, ±10°) randomly. The results showed that the peak eye velocity was higher in order of saccade, convergence, and divergence eye movements. The gain of convergence and saccades was higher than that of divergence. Furthermore, the latency of saccades was shorter than that of convergence and divergence. These results suggest that saccades and convergence are superior compared with divergence, and the dynamic property of convergence is partially analogous to horizontal saccades. The results of the comparison between the three groups showed that the latency of convergence was shorter for BAS than for NON. Therefore, different visual experience and baseball training could influence the gaze-shift dynamics during convergence eye movements.

Is accommodation a confounder in pupillometry research?

Much psychological research uses pupil diameter measurements to investigate the cognitive and emotional effects of visual stimuli. A potential problem is that accommodating at a nearby point causes the pupil to constrict. This study examined to what extent accommodation is a confounder in pupillometry research. Participants solved multiplication problems at different distances (Experiment 1) and looked at line drawings with different monocular depth cues (Experiment 2) while their pupil diameter, refraction, and vergence angle were recorded using a photorefractor. Experiment 1 showed that the pupils dilated while performing the multiplications, for all presentation distances. Pupillary constriction due to accommodation was not strong enough to override pupil dilation due to cognitive load. Experiment 2 showed that monocular depth cues caused a small shift in refraction in the expected direction. We conclude that, for the young student sample we used, pupil diameter measurements are not substantially affected by accommodation.

Eye Vergence Responses During an Attention Task in Adults With ADHD and Clinical Controls

Objective: ADHD patients show poor oculomotor control and recent studies show that attention-related eye vergence is weak in ADHD children. We aimed to assess vergence as a potential diagnostic biomarker for ADHD in adults. Method: We assessed the modulation in the angle of vergence while performing an attention task (N = 144), comparing the results for adults previously diagnosed with ADHD (N = 108) with age-matched clinical controls (N = 36). Results: Significant differences in eye vergence response modulation between clinical controls and ADHD patients were documented. Diagnostic test accuracy was 79%. Conclusion: In combination with an attention task, eye vergence responses could be used as an objective marker to support the clinical diagnosis of adult ADHD.

Effects of aligning prisms on the objective and subjective fixation disparity in far distance.

Fixation disparity (FD) refers to a suboptimal condition of binocular vision. The oculomotor aspect of FD refers to a misadjustment in the vergence angle between the two visual axes that is measured in research with eye trackers (objective fixation disparity, oFD). The sensory aspect is psychophysically tested using dichoptic nonius lines (subjective fixation disparity, sFD). Some optometrists use nonius tests to determine the prisms for constant wear aiming to align the eyes. However, they do not (yet) use eye trackers. We investigate the effect of aligning prisms on oFD and sFD for 60 sec exposure duration of prisms determined with the clinically established Cross test in far distance vision. Without prisms, both types of FD were correlated with the aligning prism, while with prisms the FD was close to zero (these analyses included all base-in and base-out cases). The effect of base-in prisms on oFD was proportional to the amount of the aligning prism for the present 60 sec exposure, similar as for the 2- 5 sec exposure in Schmid et al. (2018). Thus, within 1 minute of prism exposure, no substantial vergence adaptation seems to occur in the present test conditions. Further studies may investigate intra-individual responses to different exposure times of aligning prisms in both prism directions.

Misperception of motion in depth originates from an incomplete transformation of retinal signals.

Depth perception requires the use of an internal model of the eye-head geometry to infer distance from binocular retinal images and extraretinal 3D eye-head information, particularly ocular vergence. Similarly, for motion in depth perception, gaze angle is required to correctly interpret the spatial direction of motion from retinal images; however, it is unknown whether the brain can make adequate use of extraretinal version and vergence information to correctly transform binocular retinal motion into 3D spatial coordinates. Here we tested this hypothesis by asking participants to reconstruct the spatial trajectory of an isolated disparity stimulus moving in depth either peri-foveally or peripherally while participants' gaze was oriented at different vergence and version angles. We found large systematic errors in the perceived motion trajectory that reflected an intermediate reference frame between a purely retinal interpretation of binocular retinal motion (not accounting for veridical vergence and version) and the spatially correct motion. We quantify these errors with a 3D reference frame model accounting for target, eye, and head position upon motion percept encoding. This model could capture the behavior well, revealing that participants tended to underestimate their version by up to 17%, overestimate their vergence by up to 22%, and underestimate the overall change in retinal disparity by up to 64%, and that the use of extraretinal information depended on retinal eccentricity. Since such large perceptual errors are not observed in everyday viewing, we suggest that both monocular retinal cues and binocular extraretinal signals are required for accurate real-world motion in depth perception.

Mice Discriminate Stereoscopic Surfaces Without Fixating in Depth.

Stereopsis is a ubiquitous feature of primate mammalian vision, but little is known about if and how rodents such as mice use stereoscopic vision. We used random dot stereograms to test for stereopsis in male and female mice, and they were able to discriminate near from far surfaces over a range of disparities, with diminishing performance for small and large binocular disparities. Based on two-photon measurements of disparity tuning, the range of disparities represented in the visual cortex aligns with the behavior and covers a broad range of disparities. When we examined their binocular eye movements, we found that, unlike primates, mice did not systematically vary relative eye positions or use vergence eye movements when presented with different disparities. Nonetheless, the representation of disparity tuning was wide enough to capture stereoscopic information over a range of potential vergence angles. Although mice share fundamental characteristics of stereoscopic vision with primates and carnivores, their lack of disparity-dependent vergence eye movements and wide neuronal representation suggests that they may use a distinct strategy for stereopsis.SIGNIFICANCE STATEMENT Binocular vision allows us to derive depth information by comparing right and left eye information. We characterized binocular integration in mice because tools exist in these animals to dissect the underlying neural circuitry for binocular vision. Using random dot stereograms, we find that behavior and disparity tuning in the visual cortex share fundamental characteristics with primates, but we did not observe any evidence of disparity-dependent changes in vergence angle. We propose that mice use a distinct strategy of stereopsis compared with primates by using a broad range of disparities to encode depth over a large field of view and to compensate for nonstereoscopic changes in vergence angle that arise during natural behavior.