2.1.

Head-Mounted Display

A Meta Quest 2 HMD was used for perceptual experiments to measure the monocular and binocular CSRs from the participants. The Meta Quest 2 HMD is based on a fast-switching liquid crystal display (LCD) backplane with a pair of Fresnel lenses. The pixel resolution of the display backplane is 1832 (horizontal) × 1920 (vertical) pixels per eye, refreshing at 90 Hz. The Fresnel lenses magnify the virtual images yielding a horizontal FoV of $\sim 90\mathrm{deg}$. It offers three physical IPD settings, i.e., 58 mm (small), 63 mm (nominal), and 68 mm (large), providing users with options to customize the HMD IPD for optimal viewing comfort and visual performance. The Meta Quest 2 HMD was selected to validate the test platform as described in the section below. There are many different optical and display designs for VR HMDs such as using pancake lenses or microdisplays that may vary the perceptual test results. The goal of this paper is to develop the test method instead of comparing the perceptual experimental results across various HMDs and display technologies.

2.2.

WebXR Target Detection Platform

We developed a WebXR platform to perform perceptual experiments by determining the CSR defined as the reciprocal of threshold contrast ($C_{th}$) that a participant can detect on a VR HMD. Note that the CSR measured in this study is different from the contrast sensitivity function (CSF) of the naked human eyes without HMD modulation.³⁴ In other words, CSR measures the CSR that incorporates the HMD optical aberration, whereas CSF describes the human contrast perception capability without the HMD. WebXR is an application programming interface for developing and hosting VR and AR web-based applications on compatible mixed-reality headsets. The WebXR application was built using the A-Frame library and was executed on an Oculus Browser that displayed Gabor stimuli for detection.

The Gabor target is a 2D sinusoidal pattern with predefined contrast ($C_{\mathrm{GL}}$), whose dimension is determined by the standard deviation of a Gaussian bracket ($\sigma$) and spatial frequency ($f$). The Gabor target centered at location $(x_0,y_0)$ can be illustrated as

As shown in Fig. 2(a), the Gabor target was placed at nine locations across the FoV following the IEC 63145-20-20 standards²² at a long distance of 150 m away such that the target aligns with the optical axis of eyepiece lenses when placed at the center ($\alpha$ and $\varphi$ are zero). The target angular dimension is $\sim 1\mathrm{deg}$ in diameter. We admit that the long view distance may cause visual discomfort due to the vergence–accommodation conflict.³⁵ The impact of VR visual distance on contrast sensitivity should be evaluated in future work. Table 1 summarizes the 3D coordinates of the target at various locations. For example, moving from the center to the right, the target was laterally translated by 25 m, i.e., $(x_0,y_0,z)=(25,0,-150)\mathrm{m}$ corresponding to an azimuth angular rotation of $\sim 9\mathrm{deg}$, i.e., $(\alpha ,\varphi )=(9\mathrm{deg},0\mathrm{deg})$. At the top right position, an additional 25-m translation was added on $y_0$, yielding azimuth and elevation rotations of $(\alpha ,\varphi )$ of $(\sim 9\mathrm{deg},-9\mathrm{deg})$, corresponding to an angle of $\sim 13.3\mathrm{deg}$ diagonally. This angle will ensure that the target is within the participant’s FoV for all IPD conditions in the perceptual experiments to be described in Sec. 2.3. At each location, the orientation of the target was modified such that the sinusoidal contrast pattern is always circular (or perpendicular to the radial direction) with respect to the target location. It has been shown that the circular orientation of the pattern is suitable to capture the contrast degradation by optical aberration.¹⁹

Fig. 2

(a) Illustrations of the Gabor target placed at nine locations across the FoV with the orientation of the sinusoidal pattern aligned circularly (graph for illustration only, dimension not scaled). (b) Visual illustration of the perceptual experiments and grouping of participants, namely, group 1: participant $\mathrm{IPD}\approx \mathrm{HMD}$ IPD, group 2: participant $\mathrm{IPD}<\mathrm{HMD}$ IPD, and group 3: participant $\mathrm{IPD}>\mathrm{HMD}$ IPD.

Table 1

Physical parameters of the Gabor target.

2.3.

Perceptual Experiments

The Food and Drug Administration (FDA) Institutional Review Board (IRB) reviewed and approved the study protocol (IRB 2022-CDRH-038) and that all human participant studies were conducted under the approved protocol. We recruited nine human participants (with ages between 21 and 47 years, average age of 27.7, three females, and six males) with normal or corrected to normal vision by wearing refractive glasses in the HMD to participate in the perceptual experiments. Therefore, the potential impacts of visual acuity, astigmatism, and age (presbyopia) on the perceptual experimental results are minimized. In addition, the evaluated spatial frequency range is up to 5.72 cycles per degree, which is primarily limited by the HMD resolution. Such spatial frequencies are much lower than the human visual system capability up to $\sim 60$ cycles per degree. In this case, we ensure that the impact of visual acuity variation among the participants should not substantially affect the test results. The IPD of the participants was recorded. Among the nine participants, three have small IPDs of less than 61 (mean IPD of 58.3 mm) corresponding to the small HMD IPD setting of 58 mm. Three participants with large IPDs beyond 66 mm (mean IPD of 70.3 mm) agree with the 68-mm IPD setting of the HMD. The remaining three participants have IPDs within the range of 61 to 66 mm (mean IPD of 63.3 mm) in alignment with the nominal HMD IPD setting of 63 mm. Perceptual experiments were conducted in three groups on each combination of participant IPD and HMD hardware setting:

Each human observer experiment contains 45 trials (nine target locations × five Gabor spatial frequencies). Prior to the experiment, the physical IPD setting of the HMD was adjusted. During each trial, the participant was instructed to observe the threshold contrast of the target shown on the Quest 2 HMD by adjusting the contrast of the Gabor target using a controller or a Bluetooth keyboard with a minimum adjustable contrast of 0.004. Once the participant determined the threshold contrast ($C_{th}$), the contrast sensitivity, as the reciprocal of the measured threshold contrast, at a specified location and spatial frequency was recorded. For each participant, the above experiment was repeated three times binocularly with both eyes open and monocularly on only the left or right eye by wearing an eye patch on the other eye underneath the headset. The result of each experiment was saved into a JavaScript Object Notation (JSON) file on the headset. We extracted the files and then obtained the HMD-modulated CSR over the spatial frequencies.

Although the user-controlled determination of threshold contrast features fast experiments for the evaluation of multiple spatial frequencies and IPD settings, it introduces potential bias and random error from the participant. In future work, a stair-step procedure with a binary forced choice task (i.e., a yes–no detection task) can be investigated to eliminate potential bias from human participants.³⁶

2.4.

Impact of Display Luminance Response on Contrast Perception

As illustrated in Sec. 2.2, the WebXR engine defines the input contrast ($C_{\mathrm{GL}}$) based on the digital content (i.e., display GLs)

However, it should be clarified that the input contrast for the display differs from the perceptual contrast for an observer. The perceptual contrast ($C_{\mathrm{Lv}}$) is generally determined by the luminance difference of the target, which can be expressed as

Fig. 3

Display luminance response of the evaluated Meta Quest 2 HMD.

The display luminance response can be used to convert the display GLs to luminance. Therefore, by substituting Eqs. (3) and (5) into Eq. (4), the input contrast can be converted to perceptual contrast by

If the detected threshold contrast is small, i.e., for a small $\mathrm{\Delta }$

On the other hand, if the image quality is poor leading to a large threshold contrast, i.e., $C_{\mathrm{GL}}\approx 1$ or $\mathrm{\Delta }\approx I_b$

It is indicated that the nonlinear display luminance response leads to different threshold contrast computed as the GL ($C_{\mathrm{GL}}$) and luminance modulation ($C_{\mathrm{Lv}}$). Therefore, we distinguish CSR computed using input display GL and luminance as ${\mathrm{CSR}}_{\mathrm{GL}}$ and ${\mathrm{CSR}}_{\mathrm{Lv}}$ in the presented results, respectively.

3.1.

Monocular and Binocular Contrast Perception for Participants with Different IPDs

3.1.1.

Monocular contrast perception

Group 1 experiments: First, we focus on monocular contrast sensitivity (see red and yellow lines in Figs. 4Fig. 5–6). For participants using the appropriate IPD configuration on the HMD (group 1 participants), as shown in Fig. 4 (a), ${\mathrm{CSR}}_{\mathrm{GL}}$ is optimized at the center of display FoV, yielding improved contrast perception at spatial frequencies greater than 4 cycles per degree compared with peripheral target locations. It has been reported that optical aberration of the HMD lens degrades the contrast and effective resolution at the periphery of VR display FoV¹⁹ due to the shift of visual point on an eyepiece ($\mathrm{\Delta }d$).

Fig. 4

(a) Monocular (red color, left eye; yellow color, right eye) and binocular (blue color, both eyes) ${\mathrm{CSR}}_{\mathrm{GL}}$ for participants in group 1 with the appropriate IPD setting measured at various locations on the Quest 2 HMD. (b) Ratio between ${\mathrm{CSR}}_{\mathrm{GL}}$ and ${\mathrm{CSR}}_{\mathrm{Lv}}$ for the perceptual data shown in panel (a).

Fig. 5

(a) Monocular (red color, left eye; yellow color, right eye) and binocular (blue color, both eyes) contrast sensitivity functions for participants in group 2 with IPD smaller than that of the HMD measured at various locations on the Quest 2 HMD. (b) Ratio between ${\mathrm{CSR}}_{\mathrm{GL}}$ and ${\mathrm{CSR}}_{\mathrm{Lv}}$ for the perceptual data shown in panel (a).

Fig. 6

(a) Monocular (red color, left eye; yellow color, right eye) and binocular (blue color, both eyes) contrast sensitivity functions for participants in group 3 with IPD greater than that of the HMD measured at various locations on the Quest 2 HMD. (b) Ratio between ${\mathrm{CSR}}_{\mathrm{GL}}$ and ${\mathrm{CSR}}_{\mathrm{Lv}}$ for the perceptual data shown in panel (a).

Group 2 experiments: IPD misalignment, where the IPD of the participant does not match the physical lens displacement of the HMD, negatively affects the monocular image quality. For participants with smaller IPD than that of the HMD (group 2 participants), Fig. 5(a) shows no obvious difference between nasal (e.g., right eye gazing toward left) and temporal (e.g., right eye gazing at the right) ${\mathrm{CSR}}_{\mathrm{GL}}$ nor major interocular contrast perception difference between the left and right eyes. We suspect this is due to the effect of shifts of visual point and visual axis compensating for each other with details and an experimental validation provided in Sec. 3.3.

Group 3 experiments: Fig. 6(a) shows that interocular ${\mathrm{CSR}}_{\mathrm{GL}}$ variation is substantially pronounced for participants with larger IPD than that of the HMD (group 3 participants). ${\mathrm{CSR}}_{\mathrm{GL}}$ drops dramatically if the eye is rotated in the temporal direction (e.g., the right eye rotates toward the right). As illustrated in Sec. 3.3, this is because both the visual point and visual angle shift favor nasal eye rotation.

3.2.

Comparison Between CSR Computed by Input Display Gray Level and Display Luminance

As illustrated in Sec. 2.4, the nonlinear display luminance response results in a difference in threshold contrast computed using display GLs ($C_{\mathrm{GL}}$) and display luminance ($C_{\mathrm{Lv}}$). As shown in Figs. 4Fig. 5–6(b), the ratio of ${\mathrm{CSR}}_{\mathrm{GL}}{/\mathrm{CSR}}_{\mathrm{Lv}}$ equals to ${\mathrm{C}}_{\mathrm{Lv}}{/\mathrm{C}}_{\mathrm{GL}}$, which approaches to $\gamma$ of 2.1 when the threshold contrast is small or for higher CSR values at low spatial frequencies. On the other hand, the ratio drops to 1, indicating ${\mathrm{CSR}}_{\mathrm{GL}}$ approaches ${\mathrm{CSR}}_{\mathrm{Lv}}$ when the threshold contrast is close to 1, i.e., very poor contrast detectability at the high spatial frequencies especially for IPD mismatched conditions. It should be emphasized that the WebXR rendering engine does not involve display luminance calibration. Therefore, the contrast and CSR obtained from the WebXR platform are computed based on the display input GLs. To convert threshold contrast and CSR into the luminance domain, display luminance response as shown in Fig. 3 should be obtained.

3.3.

Impacts of IPD Misalignment and Eye Rotation Geometry

To better understand the perceptual results shown in Figs. 4Fig. 5–6, we investigate the impact of IPD misalignment and eye rotation geometry. Specifically, we believe two geometrical parameters would affect the image quality on the VR HMD: the spatial variation of the lateral shift of the visual point on the HMD eyepiece denoted as $\mathrm{\Delta }d$ and the angle between the optical axes of the eye and HMD lens defined as $\mathrm{\Delta }\beta$.

For group 1 participants, as illustrated in Fig. 7(a), $\mathrm{\Delta }d$ without IPD misalignment ($\mathrm{\Delta }\mathrm{IPD}=0$) is approximately angular symmetric on the right eyepiece but increases radially indicating increased aberration. Comparing monocular CSRs between the left and right eyes with appropriate IPD settings, it shows that contrast detection on the Quest 2 HMD slightly favors nasal eye rotation, i.e., the left eye gazing toward the right or the right eye toward the left (see CSR results in Fig. 4).

Fig. 7

(a) Schematic illustration of the binocular eye rotation geometry with optical axis of the HMD lens (blue color), pupillary axis of the eye (red color), and visual axis (black color) shown. Illustrations of spatial variation of the lateral shift of the visual point on the right eyepiece ($\mathrm{\Delta }d$) for (b) $\mathrm{\Delta }\mathrm{IPD}$ of 0, (d) $-1$ and (e) 1 cm, and (c) the angle between the optical axes of the right eye and the right eyepiece lens of the HMD ($\mathrm{\Delta }\beta$). Angle kappa and $\mathrm{\Delta }\beta$ are highlighted in panel (a).

We suspect that the variation of monocular vision is mainly associated with the angular rotation between the optical axes of the eye (involving angle kappa of the human visual system^39,40) and HMD eyepiece lens (see $\mathrm{\Delta }\beta$ shown in Fig. 7(b) for the right eye). As illustrated in Fig. 7(a), angle kappa is defined as the angle between the pupillary axis (i.e., optical axis of the eye perpendicular to the cornea) and the visual axis (axis that intercepts the fixation point and fovea).³⁹ In other words, angular misalignment between the eye and HMD lenses, as quantified by $\mathrm{\Delta }\beta$, can affect image quality. To validate this hypothesis, we performed optical bench measurements of the modulation transfer function (MTF) on the evaluated Meta Quest 2 HMD using an eye rotation geometry^22,41 with additional rotation equal to an estimated angle kappa of 4 deg. It is shown in Fig. 8(a), on the right eyepiece, that the MTF measured at an azimuth angle of $-9\mathrm{deg}$ (left, nasal rotation) is superior to the result at 9 deg (right, temporal rotation).

Fig. 8

Measured modulation transfer functions on the right eyepiece of the Quest 2 HMD using various IPD settings with $\mathrm{\Delta }\mathrm{IPD}$ of (a) 0, (b) $-1$, and (c) 1 cm, similar to the configurations of groups 1, 2, and 3 in perceptual experiments. The experimental setup enables an eye rotation geometry with an additional 4-deg rotation to emulate the angle kappa with the Gabor target placed at the same location as the perceptual experiments (i.e., left $\alpha =-9\mathrm{deg}$, center and right $\alpha =9\mathrm{deg}$).

For group 2 experiments, Fig. 5 shows that the monocular CSRs of the left and right eyes are not substantially different. This can be illustrated by Figs. 7(c) and 7(d) that $\mathrm{\Delta }d$ and $\mathrm{\Delta }\beta$ individually favor temporal and nasal eye rotation, respectively. Therefore, $\mathrm{\Delta }d$ and $\mathrm{\Delta }\beta$ compensate for the effect of each other. In the MTF measurement shown in Fig. 8(b), with $\mathrm{\Delta }\mathrm{IPD}$ of $-1\mathrm{cm}$ by shifting the camera lateral position by $-5\mathrm{mm}$, the temporal eye rotation (e.g., right eye gazing right, yellow curve) shows slightly higher MTF than the nasal eye rotation. However, the difference may not be substantial to be visualized in the ${\mathrm{CSR}}_{\mathrm{GL}}$ plots in the logarithm scale in Fig. 5, which can be potentially mitigated by increasing the number of group 2 participants in future work. Compared with CSRs measured using the appropriate IPD setting in Fig. 4, participants with smaller IPD than the HMD slightly enhance the contrast sensitivity for temporal eye rotation (e.g., right eye gazing toward right). A similar trend is shown in the MTF measurement in Figs. 8(a) and 8(b).

For group 3 experiments, the perceptual experiment shows much higher ${\mathrm{CSR}}_{\mathrm{GL}}$ for the nasal eye rotation (e.g., the right eye gazing toward left). This is consistent with the MTF measurements shown in Fig. 8(c) with $\mathrm{\Delta }\mathrm{IPD}$ of 1 cm. The interocular discrepancy in CSRs can be explained by Figs. 7(c) and 7(e) with both $\mathrm{\Delta }d$ and $\mathrm{\Delta }\beta$ favor the nasal eye rotation. Smaller values of $\mathrm{\Delta }d$ and $\mathrm{\Delta }\beta$ indicate that (1) IPD misalignment is minimized and (2) the optical axis of the HMD lens aligns with the pupillary axis of the eye, resulting in superior image quality on the HMD for nasal eye rotation.