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

Abstract

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.

Keywords: Augmented reality; Depth perception; Manual pointing; Vergence-accommodation conflict; Virtual reality.

Fig. 1

a Images of the pointing tasks performed in UR (left), VR (center), and AR (right) from the participant’s perspective. b A schematic illustration of the experimental setup and timeline for a single trial

Fig. 2

Illustration of the data reduction process. The raw displacement data were smoothed using a low-pass Butterworth filter. Then, a central difference method was used to derive the velocity. Movement initiation (green dashed line) and termination (red dashed line) were determined to be when the velocity exceeds or drops below a threshold of 50 mm/s (Color figure online)

Fig. 3

Mean a constant errors, b variable errors, and c movement time (MT) for each modality as a function of target length. Lines represent constant errors for different modalities whereas error bars represent the 95% confidence intervals

Fig. 4

An illustration of the model 3D environment. The target was plotted on the xz-plane, where the orange dot on the left indicates the home position and the target’s starting point. The red and blue dots indicate the left and right eyes, respectively, whereas the black dot represents the cyclopean eye. The dotted lines start at each eye and end at the fixation point (orange cross), indicating the fixation angle. Similarly, the dashed lines converge at the target endpoint. The cyan right triangle was used to derive the perceived distance, where its hypotenuse was derived based on Eq. (3) (Color figure online)

Fig. 5

Behavioral (solid lines) and model (gray, dashed lines) results for constant errors (cm) as a function of stimulus length for different modalities (columns) and fitting types (top row: training set; bottom row: testing set). Only the optimal version of the model was used for each modality, as indicated in Table 1. Error bars represent 95% confidence intervals

Fig. 6

The model predicted constant errors mapped as a function of distance to the fixation point for different IPD deviations when: a there was no vergence offset and b when the vergence offset was empirically derived from the VR condition (0.22°), as well as for different vergence offsets when c there was no IPD deviation and d the observer’s IPD was the mean empirically derived IPD values from the VR condition (65.38 mm or ΔIPD =  − 3.13 mm). Following the experimental setup, the fixation point was placed 51 cm away from the observers (see 3.1.1 Model environment) and the simulation only used locations in front of the observers (i.e., distance to fixation > 51 cm). The black dotted lines mark a constant error of 0 cm

Fig. 7

a A depiction of how changes in vergence offset, ${\beta }_{\text{IPD}}$, would translate to the equivalent change in IPD, $\mathrm{\Delta }\text{IPD}$, for different fixation distances. b The regression slopes for the relationship between ${\beta }_{\text{IPD}}$ and $\mathrm{\Delta }\text{IPD}$ for different fixation distances