Stereoscopic Viewing Can Induce Changes in the CA/C Ratio

Abstract

Purpose: Stereoscopic displays challenge the neural cross-coupling between accommodation and vergence by inducing a constant accommodative demand and a varying vergence demand. Stereoscopic viewing calls for a decrease in the gain of vergence accommodation, which is the accommodation caused by vergence, quantified by using the convergence-accommodation to convergence (CA/C) ratio. However, its adaptability is still a subject of debate.

Methods: Cross-coupling (CA/C and AC/A ratios) and tonic components of vergence and accommodation were assessed in 12 participants (27.5 ± 5 years, stereoacuity better than 60 arc seconds, 6/6 acuity with corrected refractive error) before and after a 20-minute exposure to stereoscopic viewing. During stimulation, vergence demand oscillated from 1 to 3 meter angles along a virtual sagittal line in sinusoidal movements, while accommodative demand was fixed at 1.5 diopters.

Results: Results showed a decreased CA/C ratio (−10.36%, df = 10, t = 2.835, P = 0.018), with no change in the AC/A ratio (P = 0.090), tonic vergence (P = 0.708), and tonic accommodation (P = 0.493).

Conclusions: These findings demonstrated that the CA/C ratio can exhibit adaptive adjustments. The observed nature and amount of the oculomotor modification failed to compensate for the stereoscopic constraint.

Accommodation and vergence are neurologically cross-coupled and interact dynamically, so that an accommodative stimulus induces both accommodative and vergence responses—and vice versa for a vergence stimulus. The vergence evoked by accommodation, known as accommodative vergence, can be quantified by using the AC/A ratio, which assesses the amount of vergence per unit change in accommodation. The accommodation induced by vergence, known as vergence accommodation, can be quantified by using the CA/C ratio, which measures the amount of accommodation per unit change in vergence. Different static and dynamic models of the accommodative and vergence systems have been proposed to provide an understanding of the organization and the interaction between the two systems.^1–8 Although models do not include adaptive components to the cross-coupling, several studies^9–13 have suggested that it is subject to adaptive regulation. 

Changes in AC/A and CA/C ratios have been obtained with a telestereoscope, which increases the interocular separation.¹⁰ Telestereoscopic viewing challenges the cross-coupling, as it increases required vergence by a multiplicative factor, while leaving accommodation almost unchanged.¹⁰ Miles et al.¹⁰ have observed an increase of the accommodative vergence gain (AC/A ratio) associated to a decrease of the vergence accommodation gain (CA/C ratio). This can be considered as an adaptive response to the constraint. The study of Miles et al.¹⁰ is the only one to address the CA/C ratio. Several other studies^9,11,13 have found an increase of the AC/A ratio following telestereoscopic exposure. 

Stereoscopic displays differ from telestereoscopes by dissociating the accommodation and vergence demands. These devices induce a constant accommodative demand but a varying vergence demand.¹² An adaptive response would be a decrease of the CA/C ratio, helping the accommodative system to remain in focus by reducing vergence accommodation.¹⁴ This hypothesis has been investigated by a pioneer study limited to two participants, with an observed decrease in CA/C ratio.¹² Predicting an appropriate response of the AC/A ratio during stereoscopic viewing is more difficult.^15–17 Eadie et al.¹² have suggested that the cross-coupling has to be ignored (i.e., decrease of the CA/C and AC/A ratios). However, the literature also mentions an inverse relationship between AC/A and CA/C ratios,¹⁸ suggesting that any decrease in CA/C ratio should be associated with an increase in the AC/A ratio. 

The present study sought to investigate adaptive changes in the cross-coupling following exposure to 20 minutes of stereoscopic viewing. Building upon preliminary earlier findings, we hypothesized that adaptation to sustained stereoscopic viewing must entail at least a decrease of the CA/C ratio. Based on existing models, the different oculomotor components are interdependent. Especially, tonic adaptation is known to reduce cross-coupling interaction.¹⁹ Therefore, tonic vergence and accommodation were assessed in addition to CA/C and AC/A ratios. 

Methods

Participants

Twelve participants (three males and nine females aged between 24 and 36 years, mean 27.5 ± 5 years) were enrolled in the experiment. All participants gave written informed consent and were naïve to the goals of the study, which was conducted in accordance with the Declaration of Helsinki and under the terms of the local legislation. Inclusion criteria were as follows: 

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  Monocular visual acuity (evaluated with a decimal-scale chart) better than 6/6;
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  Stereoacuity better than 60 arc seconds using TNO;
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  No history of functional or organic ocular pathology;
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  No use of medication that might interfere with oculomotor performance;
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  No visual complaint (such as headache, eyestrain, or reddening of the eyes) before the experiment.

One subject needed correction for myopia (limited to −3 diopters [D]) using contact lenses. To prevent any effect of ametropia, we checked the Z-score for this participant, for all accommodation-related parameters. The Z-score was lower than 2 and the participant was included in the study. The other participants had a refraction between −0.50 and +0.50 with a cylinder limited to 0.75 D and were not corrected. 

Assessment Apparatus

The oculomotor assessments were obtained by using a haploscope (Fig. 1).²⁰ This apparatus is composed of a right arm for accommodative stimulation, and of a left arm for vergence stimulation and measurement. Accommodative measurements were performed by using an optometer (PowerRef II [PR II]; Plusoptix, Nürnberg, Germany). This optometer was located 1 m away from the participant's eyes such that both eyes were visible in the instrument screen (as specified in the manufactured instructions). It was calibrated for each participant at the beginning of the experiment.^21–26 To perform the calibration, the right eye was occluded with a Wratten filter while the left eye fixated a Maltese cross at infinity (viewed through the haploscope device); during fixation with the left eye, trial lenses (+4 D to −4 D in 1-D step) were placed in front of the right occluded eye; measured refraction was compared to the refraction expected from the trial lenses considering a distance of 12 mm between the lens and the eye. A correction factor was obtained from the linear regression between PR II refraction and expected refraction. This correction factor was incorporated into any PR II measurement. The optometer used an infrared light source (870 nm), did not interfere with the visual stimulation, and allowed a 25-Hz measurement of refraction. The accommodative stimulus was varied by displacing a motorized target (on the right arm of the haploscope) along the participant's line of sight. The left-arm servomotor induced calibrated vergence disparities. For each arm, a Badal system maintained the angular size of the target constant, independently of the target position,^27,28 in order to prevent changes in nearness perception, which are known to evoke proximal oculomotor responses.³,²⁹,³⁰ The background luminance of the targets in the device was fixed at 50 cd/m². Assessments were performed in an otherwise dark room. A Maxwellian view was used to open the accommodative loop.^31–33 Using two lenses of equal power, this method projected a 0.50-mm pinhole pupil into the plane of the participant's entrance pupil in order to increase the depth of focus by 5 D. The vergence loop was opened by removing any fusible stimulus. 

Figure 1

 

Haploscope-optometer. The device features two arms: the right for accommodative stimulation (on the dominant eye), and the left for vergence stimulation and measurement. A motor located on the right arm moved the target along the subject's line of sight to stimulate accommodation. The left-arm servomotor induced calibrated vergence disparities. The optometer is located 1 m in front of the subject's eyes.

Assessment Procedure

The order of the tests (tonic vergence, tonic accommodation, CA/C, and AC/A ratios) was randomized across participants. Oculomotor assessments were performed four times each, and the results of the four measurements were averaged. All accommodative responses were assessed with the PowerRef II and all vergence responses were obtained by using the haploscope. The oculomotor assessment procedure and targets are described in detail in Neveu et al.²⁶ 

Tonic Components.

Several methods are available to assess tonic components (for review see Refs. 34 and 35). As it is the variation of the parameters that was our interest in the present study, we used a haploscopic method, which gives a subjective estimation for the tonic vergence.^10,36 The targets were similar to those used by Fisher et al.³⁶ Accommodative and vergence loops were opened as described above. Participants were instructed to fixate the upper point of the target, using their right eye. For tonic vergence measurements, a lower pinpoint was seen by the left eye and was horizontally movable by using a joystick. Participants were instructed to align the two monocular targets by using the joystick and to validate their response by pushing a button. The tonic vergence measure corresponded to the disparity value induced on the left arm when alignment was obtained. 

For tonic accommodation measurements, only the right eye point of light was used. The target was presented for 300 ms, which is under the magnitude of the accommodative latency.³⁷ Participants were instructed to fixate the point of light as soon as it appeared. Tonic accommodation was quantified by averaging the 10 optometer measurements of the accommodative responses obtained before the onset of the light. 

Cross-Coupling Components.

The targets used for the measurements of the CA/C ratio were two fusible black crosses with two nonfusible monocular cues (point) to check for the absence of monocular suppression. The high spatial frequency targets reduced the size of the Panum area and prevented inaccurate vergence responses, inducing some variability in the CA/C ratio as observed by Sweeney et al.³⁸ The accommodative loop was opened. Participants were instructed to indicate when the two crosses were fused while the monocular points were simultaneously viewed. Vergence accommodation was determined for 11 vergence stimuli, ranging from 0 to 5 meter angles (MA) in 0.50-MA increments. Stimuli were randomized (within the limits of a 1-D range) between consecutive presentations. The CA/C ratio was computed as the slope of the regression line through the accommodative responses plotted as a function of the vergence stimulus. 

The nonfusible targets used for the measurements of the AC/A ratio were a black Maltese cross presented to the right eye and a luminous broken line presented to the left eye. The accommodative loop was opened for the left eye, not to interfere with the accommodative stimulus on the right eye. Participants were instructed to fixate the Maltese cross and to keep it clear (accommodative stimulus), while aligning the two monocular targets by using the joystick. Accommodation was quantified by averaging the 10 measurements of the accommodative responses obtained preceding target-alignment completion. Accommodative vergence was determined for six accommodation stimuli ranging from 0 to 5 D in 1-D increments. Stimuli were randomized (within the limits of a 2-D range) between consecutive presentations. The vergence angle was measured as the value recorded at target-alignment completion. The AC/A ratio was computed as the slope of the regression line through the vergence responses plotted as a function of the accommodative responses. 

Exposure

Stereoscopic Viewing Apparatus.

The device used for the stereoscopic viewing exposure was a Wheatstone modified stereoscope consisting of two 22″ LCD screens and two pairs of mirrors at 45° angle relative to the participant's mid-sagittal plane (Fig. 2). The screens were optically placed at 0.67 m from the participant, which corresponded to 1.5 MA. The participant's head was stabilized by using a bite bar. For details on the stereoscopic device, see Neveu et al.³⁹ 

Figure 2

 

Schema of the stereoscope. The target was displayed on each of two screens. Owing to binocular fusion, the participant perceived a single virtual target.

Stereoscopic Stimuli.

The visual target was a white orthogonal cross, 10-by-10 pixels (14.5 arc minutes) with a 2-pixel (3 arc minutes) thickness and a luminance of 230 cd/m². It was displayed on a gray background with a luminance of 30 cd/m². A single target was displayed on each screen. The range of the vergence demand was comparable to that used by Eadie et al.¹² However, considering the divergence/convergence asymmetry of the human zone of clear and single binocular vision,^40,41 the target was moved from 1 to 3 MA to limit the divergence constraint. The vergence stimulus oscillated along a virtual sagittal line in sinusoidal movements of 0.3 Hz.¹² For details on the stereoscopic stimuli, see Neveu et al.³⁹ 

General Procedures

Participants had the oculomotor assessment before and after the stereoscopic exposure. Each participant was exposed to stereoscopic viewing during 20 minutes. During exposure, subjects had to fuse the white orthogonal cross moved from 1 to 3 MA. 

Statistical Analysis

Pre–post data were analyzed by using a two-tailed Student's paired t-test. Test results with P < 0.05 were considered statistically significant. 

Results

One of the participants was excluded from the analysis of the CA/C ratio owing to missing data from the optometer. All the participants reported diplopia during stereoscopic viewing (between 10%–90% of the time of exposure; mean = 55% ± 26.80%). Group oculomotor parameters values before and after exposure are given in Table 1. The only statistically significant change was a decrease in the CA/C ratio of 0.049 ± 0.058 D/MA (df = 10; t = 2.835, P = 0.018). Individual data are shown in Table 2. We performed a nonlinear regression between individual change in tonic vergence and CA/C ratio. No correlation was observed (ρ = −0.555; P = 0.080). Figure 3 shows examples of individual regression lines for the cross-coupling. 

Table 1

 

Group Aftereffects of the Stereoscopic Viewing

 

Table 2

 

Individual Data

 

Figure 3

 

Representative individual examples of vergence-induced accommodation (left) and accommodation-induced vergence (right).

Discussion

The aim of this study was to investigate adaptive changes in the cross-coupling following exposure to 20 minutes of stereoscopic viewing. Results showed changes in the CA/C ratio. These findings are consistent with the results obtained by Miles et al.¹⁰ and Eadie et al.¹² Thus, stereoscopic viewing induces a decrease of the CA/C ratio, helping the accommodative system to remain in focus by a decrease of the vergence accommodation. It is known that the amount of the phasic element is inversely related to the level of tonic adaptation.^5,42 As we did not observe an increase in tonic vergence, the decrease of the CA/C ratio cannot be explained by a decrease in phasic vergence. Hence, this result is likely due to a change in the gain of vergence accommodation.¹⁹ However, we cannot definitively rule out any effect of a reduced tonic accommodation adaptability.¹⁹ 

The decrease of the CA/C ratio in response to stereoscopic viewing observed in the present study is qualitatively consistent with the results of Eadie et al.¹² However, the magnitude of the effect was smaller in the present study than in that of Eadie et al.¹² These authors have observed declines of 0.20 and 0.42 D/MA in one participant, for a vergence demand oscillating from 0 to 6 MA and from 0 to 3 MA, respectively, during 60 minutes. In our study, the largest and mean changes in CA/C ratio were −0.16 and −0.05 D/MA, respectively. The smaller effects in our study may be due to the shorter duration of exposure—three times as short as in study of Eadie et al.¹²—and to the range of vergence demand being 1.5 to 3 times as small. Thus, the exposure time and the range of vergence demand appear to be important parameters in the CA/C ratio changes. Moreover, the different number of participants is likely to account for quantitative differences in outcomes across the two studies owing to large interindividual variations in adaptability. All of the participants in our study reported diplopia during stereoscopic viewing, consistent with the findings of Eadie et al.¹² The initial loss of binocular fusion reduces the effective stimulation of accommodation and vergence and the resulting adaptive process. 

We observed a mean CA/C ratio of 0.47 D/MA, which is consistent with the data from Schor and Narayan,⁴³ who have observed a CA/C ratio between 0.25 and 0.68 D/MA. During exposure, vergence demand oscillated between 1 and 3 MA. Except during diplopia, when taking into account a 30-arcmin Panum area, the minimal vergence required to match the stimulus was from 1.27 to 2.73 MA. Owing to the initial CA/C ratio, vergence accommodation relative to the screen oscillated between −0.11 and 0.58 D. The minimum estimate for depth of field obtained under optimum conditions is ±0.3 D at a pupil diameter of 3 mm.⁴⁴ Thus, owing to vergence demand, vergence accommodation may induce blurred vision. The decrease of the CA/C ratio from 0.47 to 0.42 D/MA leads to a relative vergence accommodation between −0.10 and 0.52 D. Thus, the decrease is not large enough for accommodative demand to stay within the depth of focus, especially for convergence demand. To compensate for the blurred vision, a reflex accommodative response is necessary. 

Any change in the AC/A ratio is not predictable and remains unclear. We observed, on average, a tendency for the AC/A ratio to increase. This increase was obtained in eight participants. This trend is opposite to that observed in the study of Eadie et al.¹² These authors have observed AC/A ratio declines of 0.53 MA/D and 0.62 MA/D in one participant for vergence demands oscillating between 0 and 6 MA and between 0 and 3 MA, respectively. However, several other studies^15–17 have found no significant change in the AC/A ratio. Based on a previous study,²⁶ the coefficient of repeatability is 0.277 MA/D for the AC/A ratio. This variability may have masked any effect for the AC/A ratio. More participants and longer exposure durations are needed to establish the existence of AC/A ratio changes in response to stereoscopic viewing, and the direction of the change. 

No change in the tonic components was observed. Mean tonic vergence and accommodation were 0.956 MA and 0.855 D, while mean vergence and accommodation demands were 2 MA and 1.5 D, respectively. The lack of significant tonic changes implies that reflex responses are necessary throughout the exposure.^1,6 Since vergence accommodation decreased while tonic accommodation remained stable, reflex accommodation had to increase during the exposure. Thus, the change in CA/C ratio reduces the conflict but increases the reflex response. Based on existing models, we expected to see a decline of the CA/C ratio accompanied by an increase of the tonic accommodation to ensure clear vision with no or reduced reflex accommodation. The decrease of reflex accommodation would reduce the accommodative vergence during exposure unless the AC/A ratio increased. Vergence response can be adjusted through an increase of the tonic vergence. Thus, a fully adaptive response would imply a decrease of the CA/C ratio associated to an increase of the tonic components to prevent large reflex demand. 

The observation of a change in CA/C ratio without a change in tonic components suggests that the cross-coupling conflict is a more challenging issue than the reflex demand during stereoscopic viewing. The too small decline of CA/C ratio, without a change in the tonic components, suggests an incomplete adaptive process. Longer or repeated exposure is likely necessary to obtain a consistent change in the oculomotor parameters with a nonphysiological demand. 

To our knowledge, this is the first study to demonstrate that stereoscopic displays can induce a change in the CA/C ratio. Such findings have important implications in stereoscopic environments, where the accommodation vergence conflict is a source of discomfort and fatigue.^45–52 

Acknowledgments

The authors thank Yannick Vincensini for help with the experimental software, Loïc Bonnevie for help with designing the haploscope, and Véronique Chastres for help with the statistical analysis. 

Supported by Grants No. 10CO804 and PDH1-SMO3-0807 from Direction Générale pour l'Armement. This research was a part of a PhD degree. 

Disclosure: P. Neveu, None; C. Roumes, None; M. Philippe, None; P. Fuchs, None; A.-E. Priot, None