Virtual reality head-mounted displays (VR-HMDs) are crucial to Metaverse which appears to be one of the most popular terms to have been adopted over the internet recently. It provides basic infrastructure and entrance to cater for the next evolution of social interaction, and it has already been widely used in many fields. The VR-HMDs with traditional aspherical or Fresnel optics are not suitable for long-term usage because of the image quality, system size, and weight. In this study, we designed and developed a large exit pupil diameter (EPD), compact, and lightweight VR-HMD with catadioptric optics. The mathematical formula for designing the catadioptric VR optics is derived. The reason why this kind of immersive VR optics could achieve a compact size and large EPD simultaneously is answered. Various catadioptric forms are systematically proposed and compared. The design can achieve a diagonal field of view (FOV) of 96° at -1 diopter, with an EPD of 10 mm at 11 mm eye relief (ERF). The overall length (OAL) of the system was less than 20 mm. A prototype of a compact catadioptric VR-HMD system was successfully developed.
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