Holographic parallax enhances 3D perceptual realism. This study investigates the impact of different computer-generated holography (CGH) formats on 3D realism using a full-color, high-quality holographic near-eye display. The results show that light field holograms outperform other formats in terms of 3D realism, especially under natural viewing conditions. CGH algorithms designed for specific targets lag in perceptual realism, while light field holograms consistently deliver better results. The study also highlights the importance of parallax cues in enhancing the overall quality of the holographic experience. The findings suggest that incorporating parallax cues in CGH rendering is crucial for achieving a perceptually realistic 3D experience with holographic near-eye displays. The study provides guidelines for creating perceptually realistic 3D holographic scenes and represents an initial step towards delivering a realistic 3D experience with holographic near-eye displays. The results indicate that 4D-supervised CGHs significantly improve 3D realism compared to other formats, especially in scenarios involving head movement. The study also demonstrates that the number of light field views required for 3D realism depends on the scene's depth range and spatial bandwidth. The findings have implications for the development of future holographic displays and the evaluation of 3D perceptual realism. The study underscores the importance of considering natural viewing conditions and the impact of eye movements on the perceived 3D experience. The results suggest that the inclusion of parallax cues in CGH rendering is essential for achieving a realistic 3D experience with holographic near-eye displays. The study provides insights into the effectiveness of CGH algorithms and their potential to pass the visual Turing test for displays using future holographic light field near-eye displays.Holographic parallax enhances 3D perceptual realism. This study investigates the impact of different computer-generated holography (CGH) formats on 3D realism using a full-color, high-quality holographic near-eye display. The results show that light field holograms outperform other formats in terms of 3D realism, especially under natural viewing conditions. CGH algorithms designed for specific targets lag in perceptual realism, while light field holograms consistently deliver better results. The study also highlights the importance of parallax cues in enhancing the overall quality of the holographic experience. The findings suggest that incorporating parallax cues in CGH rendering is crucial for achieving a perceptually realistic 3D experience with holographic near-eye displays. The study provides guidelines for creating perceptually realistic 3D holographic scenes and represents an initial step towards delivering a realistic 3D experience with holographic near-eye displays. The results indicate that 4D-supervised CGHs significantly improve 3D realism compared to other formats, especially in scenarios involving head movement. The study also demonstrates that the number of light field views required for 3D realism depends on the scene's depth range and spatial bandwidth. The findings have implications for the development of future holographic displays and the evaluation of 3D perceptual realism. The study underscores the importance of considering natural viewing conditions and the impact of eye movements on the perceived 3D experience. The results suggest that the inclusion of parallax cues in CGH rendering is essential for achieving a realistic 3D experience with holographic near-eye displays. The study provides insights into the effectiveness of CGH algorithms and their potential to pass the visual Turing test for displays using future holographic light field near-eye displays.