## 1 Introduction
Conventional methods do not sufficiently reproduce these visual effects because of problems arising from computational cost and the mechanical properties of OST-HMDs. Reproducing the disparities between the transparent object images requires rendering for  
Figure 1: Results of representing a glass sphere as a virtual transparent object on different displays. (**a**) Real-world environment. (**b**) Result obtained using an ordinary display (capable of overwriting the real environment pixel-by-pixel). (**c**) Result obtained using a transmissive display (capable only of light transmission) such as an optical see-through head-mounted display (OST-HMD). both eyes through the use of ray tracing methods. This incurs very high computational cost and cannot ensure the real-time representation required for AR. Furthermore, the vergence point for OST-HMD users is adjusted to the exact 3-D position of the virtual object but with the accommodation point fixed at the display focal plane (see Section 2 for details). This means that defocus between virtual objects with different depths does not occur naturally on such systems. The purpose of this study was to improve the realism of the virtual transparent objects produced on OST-HMDs by taking the characteristics of human vision into account. We developed two display methods. The first method represents shadow and caustics using illusions that utilize the human characteristics of brightness perception. Specifically, shadow is pseudo-represented without decreasing the luminance of the real environment using a previously proposed method [4]. The caustics of transparent objects are calculated with the floor of the real environment taken into account and added to the shadow. The second method reproduces the visual effects caused by vergence and accommodation that occur when observing real transparent objects. In this method, the disparity caused by vergence and the defocus caused by accommodation are reproduced separately. Specifically, the disparity is reproduced by calculating the parallax of each image for both eyes in real time using a polygon-based calculation for representing the refraction. Simultaneously, the defocus is reproduced by applying blur processing to each image based on the gaze image in a process that takes the amount of blur in the human crystalline lens into account. We experimentally confirmed that both methods could contribute to improving the realism of virtual transparent objects. In a preliminary experiment on shadow and caustics, we examined the perception of these features using an illusory image. Using this method, participants observed the shadow and caustics produced by two types of transparent objects with different shapes--a simple shape comprising a glass sphere and a more complex diamond shape. The results of the preliminary experiment suggested that, even if the shadow and caustics were represented using illusion, humans would perceive them in nearly the same manner as the phenomenon caused by physical effects. In the main experiment, participants evaluated the realism of virtual transparent objects directly. Specifically, they evaluated three types of virtual transparent objects based on different representations of shadow and caustics in two different environments. The experimental results indicated that both methods could represent virtual transparent objects more convincingly than the other types of representation. Additionally, we conducted an experiment on the reproduction of visual effects, wherein the participants evaluated the inherent realism of virtual transparent objects. They observed five types of virtual transparent objects produced using different visual effects while focusing alternately on different images. The experimental results indicated that the virtual transparent objects produced using the proposed method reproduced visual effects more convincingly than the images produced by using no visual effects.