## 4 Evaluation Experiment: Shadow and Caustics
### Main Experiment
#### 4.2.2 Results and Discussion  
The results of the experiment are shown in Figure 6, in which (A) and (B) indicate the results of the glass sphere and diamond, respectively. We mapped the comparison results to a unified scale using [PERSON]'s paired comparison method (Case-V) and performed [PERSON]'s \(\chi^{2}\) test [30] with a significance level of 5%. In the figure, the horizontal axis indicates the extent to which each virtual object appeared to be real on a psychological scale.  
The significance of results (A) and (B) were confirmed as (\(\chi^{2}(1)=4.10\times 10^{-6}\), \(p\)=.00 and (\(\chi^{2}(1)=4.10\times 10^{-6}\), \(p\)=.00), respectively. The results demonstrated that:  
1. each virtual transparent object with caustics was more convincing than the same object without shadow effects;
2. the virtual objects with shadow and caustics were more convincing than the others.  
For the glass sphere, we obtained comments from 16 out of the 23 participants. Thirteen of these comments indicated that the object with both shadow and caustics appeared most convincing. Two of the 16 responses noted that the shadow appeared to be unnaturally bright and did not appear to be the shadow of a transparent object. One noted that the shadow and caustics did not resemble those produced by a transparent object. For the glass sphere, we obtained comments from 18 out of 23 participants. Fourteen of the comments noted that the objects with both shadow and caustics appeared most convincing and that the virtual diamond with both shadow and caustics appeared more convincing of the two. Two respondents noted that the shadow was too conspicuous and did not look like a real shadow. One comment mentioned that the participant did not know how a diamond shadow on the ground should appear. One respondent selected the virtual object without a shadow as the most convincing each time because none of the virtual shadows looked like shadows to the respondent.  
These results confirm that the shadow and caustics representations produced by our method have the effect of improving the realism of transparent virtual objects. It is likely that, as we did not intentionally create unconvincing or rarely occurring experimental conditions, the same effects can be achieved in more diverse environments and conditions. Additionally, the results agree with the finding by [PERSON] [31] that the presence of shadow and caustics improves the reality of transparent objects. In a demonstration of our system at the IEEE VR 2019 international conference [32], at least 90 out of approximately 130 participants noted that the realism of the system was higher than expected.  
On the other hand, in the experiment, some participants commented that did they not experience the intended effect of our method. Although the specific causes of these responses need to be further explored, there are some possible explanations. The most prominent of these is the positional shift of the shadow and caustics. The accuracy of tracking was insufficient, which may have caused the shadow and caustics overlaid onto the floor surface to have shifted in some cases. Here, we used the tracking function of  
Figure 6: Results of the main experiment.  
HoloLens. Empirically, registration errors of approximately 1.0 cm frequently occurred. When this type of mis-registration was identified by us or a participant, we reset and adjusted the world coordinate system using keyboard input. However, we cannot ignore the possibility that some participants observed virtual objects without noticing the small misalignments. Overall, our experimental results indicate that the proposed method for representing shadow and caustics has the effect of improving the realism of virtual transparent objects displayed on OST-HMDs. Further investigation will be necessary to determine the effective range and conditions of our approach.