## 7 Limitations  
In this paper, we proposed two methods for representing transparent objects convincingly and confirmed their effects. In this section, we describe the limitations of applying these methods. Pre-computation of caustics: Under our method, the caustics are calculated in advance to avoid the high computational cost of real-time representation. Recently, some research [35] has been conducted on the real-time generation of caustics using generative adversarial networks. It might be possible to represent shadow and caustics in real time by applying such a technique. Figure 13: Experimental results. Shape of transparent object: Our method for displaying shadow and caustics might not be suitable for representing transparent objects with specific shadow patterns. In particular, it is not suitable for transparent objects with holes, such as donut shapes. This is because the luminance gradients of the shadow inducer will overlap within the hole of the shadow, causing the luminance of the hole to become noticeable. Although the width of the gradient is fixed under our current approach, it might be possible to reduce the conspicuousness of this luminance change by dynamically determining the width of the hole by taking the surrounding regions into account. Own depth of image: Our method for reproducing visual effects assumes planar images; in reality, there will be situations in which separate images have different depths. This can be reflected by increasing the number of gazing planes to reproduce the appropriate visual effects, although doing so would require a highly accurate visual-line detector. Use of visual line detectors: Our method for reproducing visual effects is based on the premise that gaze images are determined using a visual-line detector. However, we did not use such a detector in the experiments because the accuracy of the detector varied for each individual participants. For this reason, some participants might have felt uncomfortable with the visual effects. To represent visual effects using our method in a more natural manner to all users, a more accurate visual-line detector will be required. Accuracy of image: To enable real-time representation, our method for reproducing disparity considers only the first refraction. Therefore, the reproduced patterns and parallax of each image differ from those produced by the corresponding real transparent object. We make this tradeoff based on the assumption that the human visual system does not perceive image patterns in a manner that is sufficiently accurate to detect these differences. However, to the best of our knowledge, the effect of image accuracy on the realism of virtual transparent objects has not yet been examined. Transmission of real world light: As mentioned in Section 1, one of the factors that decreases the realism of displaying virtual transparent objects using OST-HMDs is the penetration of the virtual object by light from the real environment. In this study, the problems were not considered; however, recently, research [19] has been carried out on reducing the effects of environmental light penetration on optical see-through displays. If such a method could be adapted to our method, it might be possible to reduce the effects of real environment light penetration, making it possible to represent virtual transparent objects even more convincingly. Capturing Real Environment: Our method is based on the assumption that the real environment can be preliminarily modeled to render user-perspective images or that user-perspective images can be captured by cameras located near the positions of the eyes. However, it is difficult to capture and overlay images in real time with a level of error that will not be noticed by the user.