This research focuses on optimizing the TIR efficiency of an AR system using holographic optical element with a waveguide glass. Near-eye display AR with wave-guide glass overlays digital content onto the user's real world to enhance the user experience. However, effectively guiding light is a challenging task due to the limitations in reproducing the holographic angle spectrum. We analyzed the recording method of holographic optical element by angle and medium, examining the components that create interference patterns in detail. holographic optical element maximizes TIR efficiency and AR image quality by generating maximum light propagation at specific angles in each medium. Our experimental setup embeds holographic optical element into waveguide structures and creates optimized angles for holographic patterns to precisely control light. Additionally, we investigate the impact of materials and manufacturing processes on HOE performance. The results show significant improvements in TIR efficiency and light utilization when using holographic optical element. Virtual images exhibit enhanced clarity, brightness, and color accuracy, enhancing the display efficiency of AR devices by reducing light loss. In conclusion, the angle analysis of holographic optical element recording demonstrates the potential to enhance optical performance in wave-guide AR displays. This research contributes to advancements in AR technology, benefiting fields such as entertainment, education, healthcare, and industrial training.