# Focus-Adjustable Head Mounted Display with Off-Axis System  
[PERSON]  
1 BRYTN Co., #303, KETI Incubation Center 25, Saenari-ro, Bundang-gu, Seongnam 13509, Korea; [EMAIL_ADDRESS]  
[PERSON]  
2 Department of Optical Engineering, Kumoh National Institute of Technology, 350-27 Gumi-daero, Gumi 39253, Korea 2*  
Figure 1 displays the optical layout of both optical systems on the same scale. The off-axis system depicted in Figure 1b is thinner than the on-axis system presented in Figure 1a. In Figure 1, the blue, red, and green lines represent rays for +1.0-field, 0.0-field, and \(-\)0.1-field, respectively. There is a reduction in the assembly time and cost reduction becomes possible when an asymmetric aspheric prism is used instead of multiple lenses [11, 12, 13]. The asymmetric aspherical surface is made of a light plastic material and the size of the optical system can be made short and small, primarily by using a reflective surface [14, 15]. In particular, it is impossible to superimpose an image of an external landscape and a micro-display with a rotationally symmetric optical system [4]. Moreover, the off-axis system can suppress stray light, has a wider angle of view than a rotationally symmetric system, and can prevent ghost images [16]. In the past, these off-axis optical systems have been applied to astronomical telescopes. Recently, they have been predominantly used for HMDs or head-up displays [17]. In an astronomical telescope with an off-axis system, focusing is not required, so there is no need to calculate the first orders. However, since the HMD optical system in this study requires focusing, the first orders should be calculated. Two types of HMDs are depicted in Figure 2.  
Figure 1: Eyepiece optics with the same specifications. (**a**) Examples of rotationally symmetric (on-axis) optical systems, (**b**) examples of asymmetric (off-axis) optical systems. Figure 2a displays an HMD that visually removes the external world and presents a virtual reality (VR) and Figure 2b depicts an HMD that presents an augmented reality (AR), allowing simultaneous observation of a virtual object and an external scene [19; 20]. The optical system applied to the see-through type HMD in Figure 2b must be designed with asymmetry about the optical axis for AR. The size of the global AR/VR market in 2022 is estimated to be USD 105 billion, and the augmented reality market is expected to grow more than six times than that of VR [21; 22; 23]. It is expected that the demand for see-through AR HMDs will increase. An afocal optical system, such as an HMD, serves to enlarge the image of a small display into a virtual image [17; 24]. Because the virtual image distance is very large compared to the size of the optical system, it is represented by the reciprocal of the distance (in meters); this is referred to as the dipper (D) [22; 25; 26]. HMDs require focus adjustment because the uncorrected vision of a person varies among individuals [27]. The focus adjustment of the off-axis optical system used in the see-through type HMD is performed by moving the micro-display [28]. In the optical system with the infrared region, 2D materials or metasurfaces are about to be commercialized and many studies are being conducted in the visible region. However, since the main purpose of this study is to propose a method to calculate the first order of an off-axis system, the correlation can be applied irrespective of whether 2D materials or metasurfaces are utilized. The amount of micro-display movement of the off-axis optical system used for a see-through type HMD was obtained by rotating the axial rays passing through the center of the stop in a straight line and using the system matrix to calculate the first order [29]. The calculation results were verified by gradually lowering the height of the axial ray and the angle of the chief ray to confirm whether the EFL converged to a constant value.