Since 2015, various commercial virtual-reality (VR) and augmented-reality (AR) devices have been released, and the number and types of products continue to increase. These devices have attracted growing attention due to their versatile applications including education, medical care, industry, the military. Recently VR devices have become more popular as tools for distance education have proliferated, due to the COVID-19 pandemic. Even though manufacturers advertise their products with an emphasis on specifications such as display resolution, frame rate, and nominal field of view (FOV), they still do not show the measured results for optical properties based on international standards (ISs). For example, when one searches the Internet for the FOV of the HP Reverb G2 (HP Co., CA, USA), the description of the FOV of the device varies on different websites [1–3]. To identify the actual optical performance of VR/AR devices and perform a comparative evaluation between different devices, ISs for measuring methods and conditions for optical performance should be established. To this end, a great deal of research has been conducted to accurately measure the optical performance of VR/AR devices considering the human-eye condition. As a result, the methods and conditions for measuring fundamental factors such as the eye point (the designed location where the entrance pupil of the eye is placed to achieve optimal performance when using a VR/AR device [4]), FOV, and the eye box (qualified viewing space), and the optical requirements of light-measuring devices (LMDs), such as the entrance pupil size and viewing angle, have been determined [4–9]. Moreover, based on the research and ISs, two international-standards documents have been published by the International Electrotechnical Commission (IEC) [4, 10], so that the optical properties and image qualities of VR and AR devices can be correctly measured. Following the development of the standard documents, several measurement instruments for VR and AR devices have been released in the market. Nevertheless, it is still difficult to fully measure the optical properties of VR devices with a wide FOV because of the shape of these VR devices. Specifically, the goggles in a VR device have a shape that blocks ambient light and the real view from the sides of the VR device, which restricts the rotation of the LMD’s probe.

In this paper we propose an LMD design with a novel probe that is able to measure the optical properties of VR devices having a wide FOV, and we propose a pivot-point correction method as well. To show the feasibility of the probe, seven VR devices with different wide FOVs are tested. The results show that up to 160° of nominal FOV can be measured well with the new light-measuring device.

The probe in a typical LMD for VR/AR devices using an image sensor and a spectrometer has the structure illustrated in Fig. 1.

Figure 1. The structure of a typical light-measuring devices (LMD) for virtual-reality/augmented-reality (VR/AR) devices.

In Fig. 1, the transmitted beam from the display of a VR/AR device passes through a beam splitter and travels to the spectroradiometer via an optical fiber, and then photometric and colorimetric measurements can be performed. By using the reflected beam from the beam splitter that travels to the image sensor, monitoring the measuring area is possible, and image qualities such as Michelson contrast and distortion can be measured. Requirements [4, 10] based on human-eye conditions have been applied to the probe: The diameter of the aperture stop should be less than 5 mm [7], and the viewing angle should be less than 2°, considering the human eye [6]. Based on the structure in Fig. 1, a previous version of the proposed probe was manufactured, as shown in Fig. 2.

Figure 2. Previous version of the probe.

For an LMD to have enough travel space to measure VR devices with a wide FOV, the front part of the probe should be small and slender. However, because our previous version of the probe and the probes of other research groups are bulky, they are not suitable for measuring VR devices with a wide FOV, as shown in Fig. 3.

Figure 3. Probes of light-measuring devices (LMDs) for measuring near-eye displays: (a) GS-E10 (Gamma Scientific, CA, USA), (b) Lumitop (Instrument Systems GmbH, München, Germany) [11, 12].

If the front part of a probe of an LMD is too bulky, the probe cannot scan over the full FOV of VR devices with a wide FOV. This is because of the shape of the VR goggles, as shown in Fig. 4. The goggles of VR devices on the market usually cover the user’s face, to block ambient light and the real view from the side of the device (red dashed boxes in Fig. 4). This restricts the movement of the probe when it rotates at the eye point to measure the optical properties of a VR device at various measuring angles, since the pivot point should be at the center of the entrance pupil of the device being tested, or at the eye’s rotation center (10 mm behind the entrance pupil) [4]. In addition, the eye point [4] of a VR device is usually located 10–30 mm behind the last surface of the lens of the VR device. Inevitably, some parts of a VR device should be cut to be measured, resulting in deteriorated optical performance and precluding use of the device after finishing the test.

Figure 4. Conflict problem between the probe and the virtual-reality (VR) device being tested.

Bearing in mind the above considerations, we propose a new probe concept to overcome this problem, as illustrated in Fig. 5.

Figure 5. New design of the probe: (a) camera part, (b) fiber part.

In addition, we provide information about the distortion of the camera part and a full-field spot diagram of the fiber part, as illustrated in Fig. 6. In the case of the camera part, the FOV is 8°. In the case of the fiber part, the FOV is 2° and the full-field spot diagram shows that the beam is focused well within the fiber core, which has a diameter of 800 μm.

Figure 6. Detailed specifications of the new probe design: (a) distortion of camera part, (b) full-field spot diagram of the fiber part.

The most important factor to be considered for the probe design is avoiding movement restriction between the probe and VR device during measurements. For this, a relay lens system with a periscope shape is added in the proposed concept. Moreover, we measure the physical dimensions of most VR devices on the market and design the probe considering those dimensions, so that the probe can cover most of the VR devices on the market. The newly fabricated probe, as presented in Fig. 7, satisfies all the conditions required in the IS documents.

Figure 7. Pictures of the new probe: (a) side view of the new probe, (b) the new probe mounted on a biaxial goniometer plus a three-axis translation stage.

Figure 7 shows the new probe mounted on a biaxial goniometer (rotating about the x and y axes) plus an orthogonal three-axis translation stage. As mentioned, the pivot point of the goniometer and the translation stage should be located either at the center of the entrance pupil or 10 mm behind the entrance pupil, according to IEC 63145-20-10 [4]. Here we choose the center of the entrance pupil as the pivot point.

To adjust the pivot point to the correct position, we calibrate the pivot point using the following method. Figure 8 shows that the pivot point is located α mm away from the center of the entrance pupil in the z direction, and β mm away from the center of the entrance pupil in the y direction. We first correct the distance α and then the distance β, as shown in Fig. 8.

Figure 8. The pivot-point correction method. (a) The pivot is located α mm away from the entrance pupil in the z direction. (b) The pivot is located β mm away from the entrance pupil in the y direction.

In Fig. 8(a), θ represents the rotation angle of the probe about the y axis. a and a′ are the distances between the center of the entrance pupil and the last surface of the lens in the VR device at θ = 0 and θ = θ respectively. When the probe rotates by an angle θ about the y axis,

(1)$$a-\alpha +\alpha \text{cos}\theta =a^{\prime },\alpha =\frac{a-a^{\prime }}{1-\text{cos}\theta }$$

Therefore, if a, a′, and θ are given, we can calculate the distance α and correct it using the x-position adjuster shown in Fig. 7. We can then calculate the distance β, as illustrated in Fig. 8(b). In Fig. 8(b) φ represents the rotation angle of the probe about the x axis, while b and b′ denote the distances between the center of the entrance pupil and the last surface of a lens in the VR device at φ = 0 and φ = φ respectively. When the probe rotates by an angle φ about the x axis,

(2)$$b-\beta \text{sin}\phi =b^{\prime },\beta =\frac{b-b^{\prime }}{\text{sin}\phi }$$

Therefore, if b, b′, and φ are given, we can calculate the distance β and correct it using the y-position adjuster shown in Fig. 7.

For example, assume that the eye relief is set to 20 mm. Thus a = b = 20 mm. θ, φ are the angles rotated by the two-axis goniometer, as determined by the user. After rotating both θ and φ by 30°, the distances between the entrance pupil and the VR lens a′ and b′ are measured to be 15 mm and 25 mm respectively. By substituting the values for a, b, a′, b′, θ, and φ in Eqs. 1 and 2, α and β can be calculated as 37.3 mm and −10 mm respectively. Therefore, we can calibrate the pivot point by pulling the position of the entrance pupil 37.3 mm in the x direction and pushing it 10 mm in the y direction, using the position adjusters.

In the next section, the FOV measurements of seven cutting-edge VR devices on the market are presented, to show the feasibility of the new probe.

Before measuring the VR devices, we calibrate our new light-measuring device using an LED source calibrated in advance by the Korea Research Institute of Standards and Science (KRISS) as a reference. As a result, the uncertainty of our light measuring device is determined to be 1.95% (k = 2).

We next perform FOV measurements of various VR devices: device 1 (smartphone VR), devices 2, 3, and 7 (stand-alone VR), and devices 4, 5, and 6 (tethered VR). The FOV-measurement procedure follows the method in IEC 63145-20-10 [4], which measures a monocular FOV. Since there is no information on the eye points of the VR devices except for device 1 (eye point = 10 mm), we measure FOVs with 20 mm of eye relief. Table 1 shows the eye relief, measured FOVs, and nominal FOVs. Here only monocular FOVs are measured.

TABLE 1. Comparison of the measured and nominal FOVs of seven VR devices.

Device	Eye Relief	Display Resolution	Rendered (or visible) Diagonal FOV	Measured Diagonal FOV
Device 1	10 [17]	1,480 × 1,440	110° [13]	112.2°
Device 2	20	1,832 × 1,920	113.5° [2]	100.5°
Device 3		1,920 × 2,160	100° [14]	98.6°
Device 4		2,160 × 2,160	107.5° [2]	102.7°
Device 5		2,560 × 1,440	159.2° [2]	121.4°
Device 6		1,280 × 1,440	102° [15]	103.7°
Device 7		1,920 × 2,160	101° [16]	100.2°

According to Table 1, devices 1, 3, 6, and 7 have measured FOVs similar to the nominal values, but the measured FOVs of devices 2, 4, and 5 are smaller than their nominal FOVs. The VR device with the widest FOV is device 5, which has a nominal 159.2° diagonal FOV and a measured diagonal FOV of 121.4°.

The experimental results can be classified into two cases:

Case 1. The rendered FOVs have small differences from the measured FOVs (devices 1, 3, 6, and 7).

Case 2. There are large differences between the rendered and measured FOVs (devices 2, 4, and 6).

In Case 1, the eye relief used in the experiment may be different from the eye point of the VR device, which could cause the small difference between the rendered FOVs and the measured values. Eye relief is defined as the distance between the last surface of the lens of a VR device and the eye point of the device. The rendered FOV is the maximum achievable FOV when a user’s eye is at the eye point [4]. However, since there is no information about the exact eye relief of the VR devices except for device 1 (10 mm), 20 mm of eye relief is used for the measurements, which results in the measured FOVs being lower than the rendered FOVs. In addition, the fact that the rendered FOVs do not consider the loss caused by the lens of the VR device may be another factor causing the difference between rendered and measured FOVs. In reality, the rendered image is predistorted to compensate for the distortion produced by passing through the lens. As the predistorted image passes through the lens, the outer region of the image is dimmer, which makes the FOV narrower.

In Case 2, there appears to be a large difference between the rendered FOV and the measured value. However, this is due to the difference in measurement methods, where one considers binocular FOV and the other monocular FOV; it is expected that there would be no difference if the same method were employed. Reducing binocular overlap is one of the methods that manufacturers generally use to obtain a wider FOV, which creates large differences between binocular and monocular FOVs. According to the information provided in [2], the binocular overlaps of the three VR devices 2, 4, and 5 are far less than 100%. Therefore, the measured monocular FOVs based on IEC 63145-20-10 considering only monocular vision must be narrower than the rendered FOVs (binocular FOVs) of the three VR devices presented in [2]. To compare the results to reference values with the same criteria, we converted the rendered binocular FOVs into monocular horizontal FOVs and monocular vertical FOVs, using the information about the binocular FOVs and binocular overlaps given in [2]. The comparison results are given in Table 2.

TABLE 2. Comparison of the monocular field of views (FOVs) and binocular FOVs of three VR devices.

Device	Binocular FOV [2]			Monocular FOV
	HFOV	VFOV	DFOV	HFOV	VFOV	MDFOV
Device 2	104.0°	98.0°	113.5°	97.0°	98.0°	100.5°
Device 4	98.9°	90.9°	107.5°	91.7°	90.8°	102.7°
Device 5	160.3°	102.7°	158.0°	123.5°	102.7°	121.4°

Figure 9 shows how the binocular FOVs of device 4 listed in [2] are calculated. The red points correspond to the measurement points for calculating the horizontal, vertical, and diagonal FOVs. The sum of the two pink triangles and the one orange triangle in the left and the right images correspond to the binocular horizontal FOV, since the orange triangles correspond to the horizontal overlapping region. The top and bottom yellow triangles correspond to the monocular vertical FOVs. The sum of the cyan triangles in the left and right images corresponds to the binocular diagonal FOV. From the information about the triangles given in [2], we calculate the monocular horizontal FOV and the monocular vertical FOV, as shown in Table 2. However, since there is no information about the red triangle (diagonal overlapping region) in Fig. 9, we cannot calculate the monocular diagonal FOV. Fortunately, we can see that the monocular diagonal FOV would be much smaller than the binocular diagonal FOV, by comparing the sizes of the cyan triangle and the red triangle. In conclusion, it can be expected that there are not large differences between the rendered monocular diagonal FOVs and the measured ones.

Figure 9. The rendered image for device 4 [2].

The new probe of an LMD for measuring the optical properties of VR devices with wide FOV has been proposed in this study. This probe was designed to solve the problem of physical conflict between the probe and the covering goggles of a VR device during rotation for measurements. To verify that the new probe could cover most VR devices with a wide FOV that are on the market, seven VR devices were measured using the probe. As a result, we confirmed that there was no physical conflict between the VR devices and the probe while measuring their FOVs. In addition, some of the VR devices had measured FOVs similar to the nominal values, whereas the measured FOVs of the others were narrower than the nominal FOVs. This is because the experimental parameters such as eye relief did not agree with the designed parameters. Moreover, the nominal FOVs were larger than the measured FOVs since the lens distortions of VR devices are not considered in the nominal FOV calculations. Furthermore, since the measured FOVs were monocular FOVs while the nominal FOVs were binocular FOVs, the difference between the nominal and measured values would increase as the binocular overlaps of the devices decrease. Considering that the FOV-measurement method in IEC 63145-20-10 [4] deals with a monocular FOV, we expect that the actual monocular FOVs of the VR devices would not show a large difference from the measured FOVs.

The authors declare no conflicts of interest.

Data underlying the results presented in this paper are not publicly available at the time of publication, but may be obtained from the authors upon reasonable request.

Smart Healthcare VR Infrastructure Construction project (P0001940).