# A Stray Light Detection Model for VR Head-Mounted Display Based on Visual Perception
## 3 Results  
The 40 observers completed the experiment according to the above experimental procedure. This study separately recorded the HFOV data and the threshold value of just noticeable stray light when using three VR HMDs. The coefficient of variation (CV) was primarily adopted to estimate the inter-observer variability to investigate the agreement between two data sets. The larger the CV value the poorer the deal. The CV values were formulated as Equation (1) for estimating the inter-observer variability. In the equation, \(\Delta V\) is the estimation of a stimulus from an individual observer, \(\Delta E\) is the geometric mean of \(\Delta V\) from all observers, and \(\overline{\Delta E}\) is the arithmetic mean of all evaluated stimuli \(N\). The scaling factor \(f\) was used to adjust the data between \(\Delta V\) and \(\Delta E\). Fleiss' kappa was also used to analyze the level of agreement in the judges between the observers. Table 2 shows the mean results of the observer variability for each VR HMD. The values of Fleiss' kappa were 0.671, 0.851, and 0.784 for Oculus Quest, Vive Focus Plus, and Vive Focus and showed good levels of inter-rater agreement. The visual response was analyzed by ignoring the data in which the observer's CV value was larger than 20%. Hence, the valid data were 93%, 95%, and 85% sets for Oculus Quest, Vive Focus Plus, and Vive Focus, respectively. \[\text{CV}=100\times\sqrt{\frac{1}{N}\sum\frac{\left(\Delta E-f\times\Delta V \right)^{2}}{\left(\overline{\Delta E}\right)^{2}}},\,f=\frac{\sum\Delta E \times\Delta V}{\sum\left(\Delta V\right)^{2}} \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**VR HMD** & **Oculus Quest** & **Vive Focus Plus** & **Vive Focus** \\ \hline CV(Mean) & 15.22\% & 10.95\% & 16.46\% \\ Fleiss’ kappa & 0.671 & 0.851 & 0.784 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Mean value of inter-observer variability for VR HMDs. Figure 4: Rendering HFOV of VR HMD (Oculus Quest). The max rendering HFOV of three VR HMDs could be found by a free development software called Vysor, where the Oculus Quest was 92\({}^{\circ}\), Vive Focus Plus was 80\({}^{\circ}\), and Vive Focus was 79\({}^{\circ}\), as shown in Figure 5. It could be found that even though the three VR HMDs utilized OLED displays with the same size and resolution, the scales and proportions on the screen were different. There were still apparent differences in design and adjustment between the lens and the display. This phenomenon was also reflected in the subject's actual HFOV size, as shown in Figure 6. Based on the magnitude reported by most observers, the average HFOVs practically experienced by Oculus Quest, Vive Focus Plus, and Vive Focus were 74\({}^{\circ}\), 73\({}^{\circ}\), and 72\({}^{\circ}\), respectively. The Oculus Quest was the furthest from the theoretical value provided, with a difference of up to 18\({}^{\circ}\), and Vive Focus was 7\({}^{\circ}\) between the actual and theoretical values. The phenomenon might have been caused by the distortion of the lens optical design, the matching degree of the eye-box and the user's eye relief, the size of the black area on the edge of the display, and the different adjustments of Frustum. Figure 5: Rendering HFOV of different VR HMDs. Figure 6: Observer’s HFOV of three VR HMDs. The mean threshold of stray light for three kinds of VR HMD devices afterimage with different visual field sizes was analyzed with acceptable visual data, which passed the observer variability exam, as shown in Figure 7. The results indicated that Oculus Quest reached the maximum number of stimuli visual field, whereas the number for Vive Focus Plus and Vive Focus was equivalent. In the experiments regarding Vive Focus Plus and Vive Focus, some image scenes directly exceeded the image display range that most subjects could observe, such as 650, 700, and 750. Therefore, only the data from 0 to 600 were finally retained.