Random-phase Wave Splatting of Translucent Primitives for Computer-generated Holography

TL;DR

Random-phase Wave Splatting (RPWS) introduces a unified CGH framework that converts translucent 2D primitives into random-phase holograms. By coupling a novel back-to-front wavefront compositing method with a probabilistic intensity-domain alpha blending and time multiplexing, RPWS achieves accurate defocus, robust parallax, and wide eyebox across Gaussians and soft-edged triangles. The approach addresses the limitations of Gaussian Wave Splatting (GWS) and enables scalable holography for modern 3D representations, validated through extensive simulations and experimental focal stacks and light fields. RPWS thus bridges primitive-based scene representations with next-generation near-eye holographic displays, promising perceptually realistic VR/AR experiences.

Abstract

Holographic near-eye displays offer ultra-compact form factors for VR/AR systems but rely on advanced computer-generated holography (CGH) algorithms to convert 3D scenes into interference patterns on spatial light modulators (SLMs). Conventional CGH typically generates smooth-phase holograms, limiting view-dependent effects and realistic defocus blur, while severely under-utilizing the SLM space-bandwidth product. We propose Random-phase Wave Splatting (RPWS), a unified wave optics rendering framework that converts arbitrary 3D representations based on 2D translucent primitives into random-phase holograms. RPWS is fully compatible with modern 3D representations such as Gaussians and triangles, improves bandwidth utilization which effectively enlarges eyebox size, reconstructs accurate defocus blur and parallax, and leverages time-multiplexed rendering not as a heuristic for speckle suppression, but as a mathematically exact alpha-blending mechanism derived from first principles in statistics. At the core of RPWS are (1) a new wavefront compositing procedure and (2) an alpha-blending scheme for random-phase geometric primitives, ensuring correct color reconstruction and robust occlusion when compositing millions of primitives. RPWS departs substantially from the recent primitive-based CGH algorithm, Gaussian Wave Splatting (GWS). Because GWS uses smooth-phase primitives, it struggles to capture view-dependent effects and realistic defocus blur and under-utilizes the SLM space-bandwidth product; moreover, naively extending GWS to random-phase primitives fails to reconstruct accurate colors. In contrast, RPWS is designed from the ground up for arbitrary random-phase translucent primitives, and through simulations and experimental validations we demonstrate state-of-the-art image quality and perceptually faithful 3D holograms for next-generation near-eye displays.

Figures (5)

• Figure 1: Effectiveness of RPWS sqrt-blending of random-phase wavefronts. We show the effectiveness of our sqrt-blending procedure using the toy example described in Section \ref{['sec:awb_random']} with two random-phase Gaussians, where the orange Gaussian is in front of the blue Gaussian and alpha blended. The straightforward extension of GWS amplitude-based blending with random phase (GWS-NRP) fails to reconstruct the correct appearance with significant errors near occlusion borders --- which is exactly the cross term in Eq. \ref{['eq:awb_random']}. RPWS sqrt-blending achieves perfect alpha blending results.
• Figure 2: Ablation study on random-phase CGH rendering algorithms. We compare our RPWS algorithm with three other alpha blending methods on random-phase primitives. (a) Naïvely applying random phase to GWS fails to reconstruct accurate appearance. (b) GWS with our square root alpha blending formulation generates somewhat accurate appearance. However, incorrect occlusion handling at depth discontinuities manifests as light leakage and halo artifacts in focal stacks and black holes near occlusion borders. This is an artifact frequently observed in conventional multifocal displays narain2015multimercier2017fastchang2020toward. (c) RPWS without square root-based blending also fails to reconstruct accurate colors. (d) Our full RPWS model reconstructs accurate color, natural defocus blur, and physically-correct parallax. Please refer to the supplementary materials for equations and pseudocodes of all alpha-blending formulations.
• Figure 3: Simulated 3D focal stacks and 4D light fields reconstructed from various baseline CGH algorithms. The image quality of random-phase polygons-based CGH (Polygons-RP) is inherently limited by the coarse per-face textured mesh representation, resulting in poor image quality even in in-focus regions. GWS choi2025gaussian reconstructs sharp details at in-focus regions, but suffers from large depth of field and unnatural ringing artifacts. Our method (RPWS) generates sharp content at focused regions and the resulting hologram has shallow depth of field, reconstructing natural defocus blur across different depths. With additional time-multiplexing, the image quality of RPWS significantly improves.
• Figure 4: Simulated 3D focal stacks and 4D light fields reconstructed from RPWS of triangle splats Held2025Triangle. We run our RPWS algorithm on Triangle splats proposed by Held2025Triangle. RPWS with triangle splats accurately reconstructs natural defocus blur and parallax on a wide variety of scenes, validating the robustness of our method to different translucent primitive types.
• Figure 5: Experimentally captured 3D focal stacks and 4D light fields of holograms generated using different CGH algorithms. Polygon-based CGH (Polygons-RP) matsushima2005computermatsushima2009extremelymatsushima2014silhouette achieves low image quality due to the low quality of the underlying textured mesh 3D representation. GWS choi2025gaussian generates smooth-phase holograms, resulting in limited defocus blur with unnatural ringing artifacts and little-to-no parallax. Our method, RPWS with Gaussian (-GS) and triangle splatting ($-\Delta$) variants, achieves good image quality in in-focus regions, reconstructs natural incoherent blur in defocus regions, and shows significantly more parallax than GWS. With 24 frames time-multiplexing, RPWS (both -GS and $-\Delta$ variants) achieves near speckle-free results.