Changes In Vergence Research Articles

Evidence Supporting Open-Loop Control During Early Vergence

Disparity vergence eye movements were analyzed to determine if the early component of this response operates under open-loop, or preprogrammed, control. The analysis compares ratios of peak velocity to response amplitude (i.e., main sequence ratios) for the isolated early component and for the entire disparity vergence response. The stimuli were limited a 4 deg step changes in vergence so that any differences in movement dynamics (i.e., peak velocities) were due only to internal noise. Nine binocularly normal subjects were studied. A significant correlation between peak velocity and amplitude was observed during the early portion of the movement (p < 0.002), but not for the overall vergence response. Results support the widely held, but unproven assumption that the early component of symmetrical vergence is guided by open-loop, or preprogrammed, control processes while the overall response is influenced by internal and/or external feedback.

Hyperstereopsis is attenuated by the addition of secondary visual cues

AbstractPurpose Telestereoscopic (or hyperstereo‐) viewing which increases effective interocular distance has been a subject of interest since Helmholtz’s pioneering work. Increased disparities and vergence alter 3D‐space perception. In particular, apparent egocentric distances decrease, owing to the increased vergence (Priot et al., 2010; Rogers, 2011). This study sought to investigate how the enrichment of stimulus information influences its perceived distance.Methods We assessed distance perception through open‐loop pointing before and during exposure to a telestereoscope in three stimulus viewing conditions: i) a red pinpoint of light (pinhole) providing vergence cue only; ii) a red cross with randomized diameter preventing size cue, providing vergence and some accommodative cues and iii) a real‐size coin slide providing vergence, accommodation, relative‐ and familiar‐size cues.Results Before exposure (normal viewing), we observed an improved perceived‐distance accuracy induced by enriched stimulus information. During exposure (with vergence discrepancy), we found that, on average: i) telestereoscopic viewing altered perceived distance; ii) this effect was modulated by the stimulus viewing condition; iii) the mean slope of the perceived distance of the cross stimulus vs. its physical distance was not different from that predicted by vergence changes according to Helmholtz’s scaling theory; and iv) the hyperstereo effect was attenuated by the enriched stimulus information.Conclusion We ascribe the attenuation of hyperstereopsis by the addition of secondary visual cues to a down‐weighting of vergence contribution relative to those of the other cues.

Evaluation of ocular accommodation, convergence and fusional vergence changes during Ramadan

Introduction: There are a few researches regarding the effects of Islamic fasting on visual system. The aim of this study was to investigate the effects of Ramadan fasting on the amplitude of accommodation (AA), near point of convergence (NPC), positive and negative fusional vergences (PFV and NFV, respectively) in visually healthy fasters. Methods: AA, NPC, PFV and NFV at far (6m) and near (40cm) were measured in 30 male students. Nutritional habits in a week before each examination visit were assessed with the Food Frequency Questionnaire (FFQ). Results: Mean age and fasting average experience were 23.9 and 10 years, respectively. AA and NPC showed significant changes (p<0.05) during Ramadan; but there was no significant difference before and after Ramadan in these parameters. NFV blur, break and recovery points at far significantly reduced in Ramadan than before (p=0.003, p=0.005, p=0.003, respectively) with insignificant compensation after Ramadan. Results showed that there was no significant correlation between changes in diet pattern and AA, NPC and distant NFV variations (p<0.05). Conclusion: Some visual problems may be reported at far and near visual tasks during Ramadan; but most of the problems may be resolved after it. Some visual preparations may be needed for more effective visual activities during Ramadan; essentially for students with intensive visual tasks. Vision therapy may be suggested along with nutrient pattern improvement during Ramadan.

Listing's plane and the 3D-VOR in microgravity – The role of the otolith afferences

The study addresses the question as to what extent the otolith-mediated gravity vector maintains the stability of the coordinate frames of the vestibulo-ocular reflex and the oculomotor system, described by Listing's Plane. Under normal 1 G conditions it has been demonstrated in the monkey that Listing's Plane (LP) and the 3D vestibulo-ocular response (3D-VOR) are close to collinear [10]. In the present study the coordinate frames of the oculomotor system and the three-dimensional vestibulo-ocular reflex (3D-VOR) system were measured under one-g gravity conditions and during a period of prolonged microgravity, on-board the International Space Station (ISS). To this end, the coordinate frame of the oculomotor system is described in Listing's coordinates and that of the 3D-VOR system by the minimal gain vector. The findings demonstrate that under Earthbound, one-g conditions the two coordinate frames diverge by approximately 20° in the human. In the absence of the gravity vector the radical loss in the otolith-mediated contribution to the dynamic VOR leads to a reduction of the torsional VOR component and in turn to a forward tilt of the oculomotor coordinate frame, described by the minimal gain vector. In contrast, the torsional component of LP during horizontal and vertical saccades was found to increase, resulting in a backward tilt of LP. Together with the backward tilt of LP a small but consistent change in LP vergence was observed. The thickness of LP did not appear to change in the absence of gravity. The changes in coordinate frame orientation persisted over the six-month periods spent in zero gravity. The postflight measurements demonstrate that re-adaptation to preflight values proceeds over several days to weeks. The findings demonstrate that the gravity vector represents a common reference for vestibular and oculomotor responses. They also support the idea that the gravity vector provides a central reference for the entire sensorimotor complex.

Developmental Changes in the Balance of Disparity, Blur, and Looming/Proximity Cues to Drive Ocular Alignment and Focus

Accurate coordination of accommodation and convergence is necessary to view near objects and develop fine motor coordination. We used a remote haploscopic videorefraction paradigm to measure longitudinal changes in simultaneous ocular accommodation and vergence to targets at different depths, and to all combinations of blur, binocular disparity, and change-in-size ('proximity') cues. Infants were followed longitudinally and compared with older children and young adults, with the prediction that sensitivity to different cues would change during development. Mean infant responses to the most naturalistic condition were similar to those of adults from 6-7 weeks (accommodation) and 8-9 weeks (vergence). Proximity cues influenced responses most in infants of less than 14 weeks of age, but sensitivity declined thereafter. Between 12 and 28 weeks of age infants were equally responsive to all three cues, while in older children and adults manipulation of disparity resulted in the greatest changes in response. Despite rapid development of visual acuity (thus increasing availability of blur cues), responses to blur were stable throughout development. Our results suggest that, during much of infancy, vergence and accommodation responses are not dependent on the development of specific depth cues, but make use of any cues available to drive appropriate changes in response.

Simulating the Cortical 3D Visuomotor Transformation of Reach Depth

We effortlessly perform reach movements to objects in different directions and depths. However, how networks of cortical neurons compute reach depth from binocular visual inputs remains largely unknown. To bridge the gap between behavior and neurophysiology, we trained a feed-forward artificial neural network to uncover potential mechanisms that might underlie the 3D transformation of reach depth. Our physiologically-inspired 4-layer network receives distributed 3D visual inputs (1st layer) along with eye, head and vergence signals. The desired motor plan was coded in a population (3rd layer) that we read out (4th layer) using an optimal linear estimator. After training, our network was able to reproduce all known single-unit recording evidence on depth coding in the parietal cortex. Network analyses predict the presence of eye/head and vergence changes of depth tuning, pointing towards a gain-modulation mechanism of depth transformation. In addition, reach depth was computed directly from eye-centered (relative) visual distances, without explicit absolute depth coding. We suggest that these effects should be observable in parietal and pre-motor areas.

How perceived egocentric distance varies with changes in tonic vergence

According to the eye muscle potentiation (EMP) hypothesis, sustained vergence leads to changes in egocentric perceived distance. This perceptual effect has been attributed to a change in the resting or tonic state of vergence. The goal of the present study was to test the EMP hypothesis by quantifying the relationship between prism-induced changes in tonic vergence and corresponding changes in perceived distance and by measuring the dynamics of changes in perceived distance. During a 10-min exposure to 5-diopter base-out prisms that increased the vergence demand, thirteen right-handed subjects pointed to visual targets located within reaching space using their left hand, without visual feedback. Pre- and post-exposure tests assessed tonic vergence through phoria measurements and egocentric distance estimate through pointing to visual targets with each hand successively, without visual feedback. Similar distance aftereffects were observed for both hands, although only the left hand was used during exposure, indicating that these aftereffects are mediated by visual processes rather than by visuomotor interactions. The distance aftereffects were significantly correlated with prism-induced changes in phoria, demonstrating a relationship between perceived distance and the level of tonic vergence. Changes in perceived distance increased monotonically across trials during prism exposure and remained stable during the post-test, indicating a long time constant for these perceptual effects, consistent with current models of the vergence control system. Overall, these results support the hypothesis that vergence plays a role in reduced-cue distance perception. They further illustrate that variations in tonic vergence influence perceived distance by altering the sensed vergence effort.

Evidence that convergence rather than accommodation controls intermittent distance exotropia

This study considered whether vergence drives accommodation or accommodation drives vergence during the control of distance exotropia for near fixation. High accommodative convergence to accommodation (AC/A) ratios are often used to explain this control, but the role of convergence to drive accommodation (the CA/C relationship) is rarely considered. Atypical CA/C characteristics could equally, or better, explain common clinical findings. Nineteen distance exotropes, aged 4-11 years, were compared while controlling their deviation with 27 non-exotropic controls aged 5-9 years. Simultaneous vergence and accommodation responses were measured to a range of targets incorporating different combinations of blur, disparity and looming cues at four fixation distances between 2 m and 33 cm. Stimulus and response AC/A and CA/C ratios were calculated. Accommodation responses for near targets (p = 0.017) and response gains (p = 0.026) were greater in the exotropes than in the controls. Despite higher clinical stimulus AC/A ratios, the distance exotropes showed lower laboratory response AC/A ratios (p = 0.02), but significantly higher CA/C ratios (p = 0.02). All the exotropes, whether the angle changed most with lenses ('controlled by accommodation') or on occlusion ('controlled by fusion'), used binocular disparity not blur as their main cue to target distance. Increased vergence demand to control intermittent distance exotropia for near also drives significantly more accommodation. Minus lens therapy is more likely to act by correcting overaccommodation driven by controlling convergence, rather than by inducing blur-driven vergence. The use of convergence as a major drive to accommodation explains many clinical characteristics of distance exotropia, including apparently high near stimulus AC/A ratios.

Speed judgments of three-dimensional motion incorporate extraretinal information

When tracking an object moving in depth, the visual system should take changes of eye vergence into account to judge the object's 3D speed correctly. Previous work has shown that extraretinal information about changes in eye vergence is exploited when judging the sign of 3D motion. Here, we ask whether extraretinal signals also affect judgments of 3D speed. Observers judged the speed of a small target surrounded by a large background. To manipulate extraretinal information, we varied the vergence demand of the entire stimulus sinusoidally over time. At different phases of vergence pursuit, we changed the disparity of the target relative to the background, leading observers to perceive approaching target motion. We determined psychometric functions for the target's approach speed when the eyes were (1) converging, (2) diverging, (3) maximally converged (near), and (4) maximally diverged (far). The target's motion was reported as faster during convergence and slower during divergence but perceived speed was little affected at near or far vergence positions. Thus, 3D speed judgments are affected by extraretinal signals about changes in eye rotation but appear unaffected by the absolute orientation of the eyes. We develop a model that accounts for observers' judgments by taking a weighted average of the retinal and extraretinal signals to target motion.

Ten-Year Changes in Fusional Vergence, Phoria, and Nearpoint of Convergence in Myopic Children

To identify longitudinal changes in fusional vergence ranges and their relationship to other clinical measures in young myopic subjects. Measurements were collected annually for 10 years on 114 subjects from the University of Houston Correction of Myopia Evaluation Trial cohort. Subject age was 7 to 13 years at year 1 of follow-up. Measurements included refractive error, distance and near phoria, interpupillary distance (IPD), prism bar fusional vergence ranges, and nearpoint of convergence (NPC). Multilevel modeling was used to determine baseline and rate of change for fusional vergence ranges and the impact of phoria, IPD, and NPC on these measures. Year 1 mean distance base-out (BO) break was 20 prism diopters (pd) and decreased 5.6 pd over 10 years (p < 0.001). Mean near BO break was 30 pd at year 1 and decreased 9.4 pd over 10 years (p < 0.001). Greater esophoria was significantly related to greater BO break (p < 0.02) and receded NPC was significantly related to lower magnitude BO break at near (p < 0.001). Distance IPD increased 3 mm over 10 years (p < 0.001) but was unrelated to the magnitude of the BO ranges (p > 0.2). Mean distance base-in (BI) break was 7 pd at year 1 and increased 0.5 pd in 10 years (p = 0.04). Mean near BI break was 13 pd at year 1 and did not significantly change. Mean distance phoria was 0.1 pd exophoria at year 1 and did not change, whereas near phoria was 2.4 pd esophoria at year 1 and became more exophoric (4 pd in 10 years, p < 0.001). These results suggest that for myopic children convergence ranges decrease for both distance and near viewing during the school years as near phoria becomes more exophoric. These findings could have clinical implications given that compensating convergence ranges decrease as near phoria becomes more divergent.

Accommodation and convergence during sustained computer work

Purpose With computer usage becoming almost universal in contemporary society, the reported prevalence of computer vision syndrome (CVS) is extremely high. However, the precise physiological mechanisms underlying CVS remain unclear. Although abnormal accommodation and vergence responses have been cited as being responsible for the symptoms produced, there is little objective evidence to support this claim. Accordingly, this study measured both of these oculomotor parameters during a sustained period of computer use. Methods Subjects (N = 20) were required to read text aloud from a laptop computer at a viewing distance of 50 cm for a sustained 30-minute period through their habitual refractive correction. At 2-minute intervals, the accommodative response (AR) to the computer screen was measured objectively using a Grand Seiko WAM 5500 optometer (Grand Seiko, Hiroshima, Japan). Additionally, the vergence response was assessed by measuring the associated phoria (AP), i.e., prism to eliminate fixation disparity, using a customized fixation disparity target that appeared on the computer screen. Subjects were asked to rate the degree of difficulty of the reading task on a scale from 1 to 10. Results Mean accommodation and AP values during the task were 1.07 diopters and 0.74∆ base-in (BI), respectively. The mean discomfort score was 4.9. No significant changes in accommodation or vergence were observed during the course of the 30-minute test period. There was no significant difference in the AR as a function of subjective difficulty. However, the mean AP for the subjects who reported the least and greatest discomfort during the task was 1.55∆ BI and 0, respectively ( P = 0.02). Conclusions CVS, after 30 minutes was worse in subjects exhibiting zero fixation disparity when compared with those subjects having a BI AP but does not appear to be related to differences in accommodation. A slightly reduced vergence response increases subject comfort during the task.

Simultaneous measurement of objective refraction, accommodation response and axial length of the human eye

Accurate measurements of ocular biometry and objective refraction are of vital importance to research laboratories working in the area of refractive error development and oculomotor function. A number of commercially available instruments can provide these measurements, and are used in both their intended modes, and with modifications to increase their research utility. A limitation that exists currently is the inability to conduct simultaneous measurements of refractive error or accommodation response, and the axial length of the same eye. In this technical note we provide details of a method to adapt the Zeiss IOLMaster and the Shin-Nippon SRW-5000 infrared optometer to simultaneously measure refraction and axial length. The optical modification used to combine the measurement paths of the IOLMaster and SRW-5000 instruments consists of a narrow band-pass filter, and optical relay to extend the working distance of the IOLMaster, and an electronic system to provide synchronisation between the IOLMaster and the SRW-5000 continuous accommodation recording system. The optical modification was tested on model eyes, and on a cohort of 20 human eyes. The combined system was then used to measure accommodation response and axial length simultaneously in a single participant. Inclusion of the optical modification in the IOLMaster pathway induced a 0.004 mm shift in the average measurement of a calibration eye, and an average difference of 0.001 mm for a cohort of human eyes. For the SRW-5000, inclusion of the modified optics induced a +0.15 D shift in the spherical component of refraction measurements made on a model eye, and an average shift of +0.12 D in the spherical component of measurements made on a cohort of human eyes. Simultaneous measurement of accommodation response and axial length in a single participant revealed that a change in stimulus vergence from 0 to 5 D caused an average accommodation response of 3.89 D, and an average transient axial length change of 0.059 mm. The system described provides a useful method of achieving simultaneous measurements of axial length, objective refraction and accommodation response in a human eye.

Effect of temporal location of correction of monochromatic aberrations on the dynamic accommodation response

Dynamic correction of monochromatic aberrations of the eye is known to affect the accommodation response to a step change in stimulus vergence. We used an adaptive optics system to determine how the temporal location of the correction affects the response. The system consists of a Shack-Hartmann sensor sampling at 20 Hz and a 37-actuator piezoelectric deformable mirror. An extra sensing channel allows for an independent measure of the accommodation level of the eye. The accommodation response of four subjects was measured during a +/− 0.5 D step change in stimulus vergence whilst aberrations were corrected at various time locations. We found that continued correction of aberrations after the step change decreased the gain for disaccommodation, but increased the gain for accommodation. These results could be explained based on the initial lag of accommodation to the stimulus and changes in the level of aberrations before and after the stimulus step change. Future considerations for investigations of the effect of monochromatic aberrations on the dynamic accommodation response are discussed.

Rotation invariant iris feature extraction using Gaussian Markov random fields with non-separable wavelet

Rotation invariance is important for an iris recognition system since changes of head orientation and binocular vergence may cause eye rotation. The conventional methods of iris recognition cannot achieve true rotation invariance. They only achieve approximate rotation invariance by rotating the feature vector before matching or unwrapping the iris ring at different initial angles. In these methods, the complexity of the method is increased, and when the rotation scale is beyond the certain scope, the error rates of these methods may substantially increase. In order to solve this problem, a new rotation invariant approach for iris feature extraction based on the non-separable wavelet is proposed in this paper. Firstly, a bank of non-separable orthogonal wavelet filters is used to capture characteristics of the iris. Secondly, a method of Markov random fields is used to capture rotation invariant iris feature. Finally, two-class kernel Fisher classifiers are adopted for classification. Experimental results on public iris databases show that the proposed approach has a low error rate and achieves true rotation invariance.

Effect of correction of ocular aberration dynamics on the accommodation response to a sinusoidally moving stimulus

We used an adaptive optics system to correct the aberration dynamics of five subjects while they fixated on a monochromatic stimulus undergoing sinusoidal vergence changes between 1.5 and 2.5 D, at a temporal frequency of 0.2 Hz. The aberrations were measured at 20 Hz using a Shack-Hartmann sensor and corrected using a 37-actuator deformable mirror. The accommodation response (AR) was analyzed in terms of the gain and phase lag. Manipulation of aberrations significantly affected the gain of the AR for only one subject when the odd-order aberrations were corrected. The predictability of the sinusoidal stimulus could account for the lack of an effect in the remaining subjects and conditions.

Validation of a Hartmann-Moiré wavefront sensor with large dynamic range

Our goal was to validate the accuracy, repeatability, sensitivity, and dynamic range of a Hartmann-Moiré (HM) wavefront sensor (PixelOptics, Inc.) designed for ophthalmic applications. Testing apparatus injected a 4 mm diameter monochromatic (532 nm) beam of light into the wavefront sensor for measurement. Controlled amounts of defocus and astigmatism were introduced into the beam with calibrated spherical (-20D to + 18D) and cylindrical (-8D to + 8D) lenses. Repeatability was assessed with three repeated measurements within a 2-minute period. Correlation coefficients between mean wavefront measurements (n = 3) and expected wavefront vergence for both sphere and cylinder lenses were >0.999. For spherical lenses, the sensor was accurate to within 0.1D over the range from -20D to + 18D. For cylindrical lenses, the sensor was accurate to within 0.1D over the range from -8D to + 8D. The primary limitation to demonstrating an even larger dynamic range was the increasingly critical requirements for optical alignment. Sensitivity to small changes of vergence was constant over the instrument's full dynamic range. Repeatability of measurements for fixed condition was within 0.01D. The Hartmann-Moiré wavefront sensor measures defocus and astigmatism accurately and repeatedly with good sensitivity over a large dynamic range required for ophthalmic applications.

Neuromuscular Plasticity and Rehabilitation of the Ocular Near Response

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

Role of ocular aberrations in dynamic accommodation control

Background: Accommodation control is mediated by a number of cues, including blur, chromatic aberration and target proximity. Data from wavefront measurements have shown clear shifts in ocular aberrations during increasing accommodative demand, most notably a negative shift in spherical aberration. Work in adaptive optics, where aberrations have been corrected, has suggested a role for aberrations in the control of accommodation for some individuals. This study aimed to determine the relative effects of aberration correction and inversion on closed‐loop stepwise accommodation responses to small increases and decreases in stimulus vergence.Methods: An adaptive optics system was used to modify ocular aberrations, while five participants viewed a high contrast target stepping 0.5 D in an inward or outward direction. Aberrations were variously unchanged, corrected or inverted following the step change in stimulus vergence. A Shack‐Hartmann wavefront sensor was used to record accommodative responses to the stepwise changes in stimulus vergence. Accommodative response data were analysed using a curve fitting method to calculate the gain, latency and response time.Results: Correction of aberrations failed to have a significant effect on dynamic accommodative responses. Inversion of even‐order aberration terms produced a significant reduction in accommodative response gain for outward steps in stimulus vergence. Additionally, an increase in the number of accommodative responses in the wrong direction was seen following aberration inversion. Inward steps were not altered significantly by aberration inversion.Conclusion: Accommodation in humans appears to derive a cue from the even‐order aberrations of the eye to help guide the initial direction of responses to reductions in stimulus vergence (that is, disaccommodation). With all aberrations and even‐order aberrations inverted, the number of incorrect directional responses to outward moving stimuli increases, suggesting that aberrations are important in determining the initial path of stepwise accommodative responses.

Extra-retinal signals support the estimation of 3D motion

In natural settings, our eyes tend to track approaching objects. To estimate motion, the brain should thus take account of eye movements, perhaps using retinal cues (retinal slip of static objects) or extra-retinal signals (motor commands). Previous work suggests that extra-retinal ocular vergence signals do not support the perceptual judgments. Here, we re-evaluate this conclusion, studying motion judgments based on retinal slip and extra-retinal signals. We find that (1) each cue can be sufficient, and, (2) retinal and extra-retinal signals are combined, when estimating motion-in-depth. This challenges the accepted view that observers are essentially blind to eye vergence changes.

Depth perception during saccades

A number of studies have investigated the localization of briefly flashed targets during saccades to understand how the brain perceptually compensates for changes in gaze direction. Typical version saccades, i.e., saccades between two points of the horopter, are not only associated with changes in gaze direction, but also with large transient changes of ocular vergence. These transient changes in vergence have to be compensated for just as changes in gaze direction. We investigated depth judgments of perisaccadically flashed stimuli relative to continuously present references and report several novel findings. First, disparity thresholds increased around saccade onset. Second, for horizontal saccades, depth judgments were prone to systematic errors: Stimuli flashed around saccade onset were perceived in a closer depth plane than persistently shown references with the same retinal disparity. Briefly before and after this period, flashed stimuli tended to be perceived in a farther depth plane. Third, depth judgments for upward and downward saccades differed substantially: For upward, but not for downward saccades we observed the same pattern of mislocalization as for horizontal saccades. Finally, unlike localization in the fronto-parallel plane, depth judgments did not critically depend on the presence of visual references. Current models fail to account for the observed pattern of mislocalization in depth.