Random-phase Gaussian Wave Splatting
for Computer-generated Holography

Brian Chao* Jackie Yang* Suyeon Choi Manu Gopakumar Ryota Koiso Gordon Wetzstein

*equal contribution

Stanford University
Paper arXiv

Related Work: Please visit our Gaussian Wave Splatting (GWS) project website to learn about our prior work on converting Gaussians to smooth-phase holograms.

Experimentally captured 3D focal stacks of generated holograms on a holographic display prototype.
(hover over the video to pause)

Gaussian splatting techniques take a few casually captured photographs as input and output a Gaussian scene representation. Random-phase Gaussian Wave Splatting (GWS-RP) turns these types of representations into holograms that reconstructs natural, physically-accurate defocus blur and light field parallax that can be directly displayed on emerging holographic displays.


We experimentally captured 3D focal stacks of generated holograms on a holographic display prototype.

Abstract

Holographic near-eye displays offer ultra-compact form factors for virtual and augmented reality systems, but rely on advanced computer-generated holography (CGH) algorithms to convert 3D scenes into interference patterns that can be displayed on spatial light modulators (SLMs). Gaussian Wave Splatting (GWS) has recently emerged as a powerful CGH paradigm that allows for the conversion of Gaussians, a state-of-the-art neural 3D representation, into holograms. However, GWS assumes smooth-phase distributions over the Gaussian primitives, limiting their ability to model view-dependent effects and reconstruct accurate defocus blur, and severely under-utilizing the space--bandwidth product of the SLM.

In this work, we propose random-phase GWS (GWS-RP) to improve bandwidth utilization, which has the effect of increasing eyebox size, reconstructing accurate defocus blur and parallax, and supporting time-multiplexed rendering to suppress speckle artifacts. At the core of GWS-RP are

  1. a fundamentally new wavefront compositing procedure and
  2. an alpha-blending scheme specifically designed for random-phase Gaussian primitives, ensuring physically correct color reconstruction and robust occlusion handling.
Additionally, we present the first formally derived algorithm for applying random phase to Gaussian primitives, grounded in rigorous statistical optics analysis and validated through practical near-eye display applications. Through extensive simulations and experimental validations, we demonstrate that these advancements, collectively with time-multiplexing, uniquely enables full-bandwith light field CGH that supports accurate accurate parallax and defocus, yielding state-of-the-art image quality and perceptually faithful 3D holograms for next-generation near-eye displays.

Overview

Random-phase Gaussian Wave Splatting (GWS-RP) takes a set of optimized 2D Gaussians as input and outputs a hologram that can be directly displayed on emerging holographic displays. Unlike Gaussian Wave Splatting (GWS), which assumes smooth-phase distributions over the Gaussian primitives, GWS-RP applies random phases to the Gaussians, which increases the eyebox size, reconstructs accurate defocus blur and parallax, and supports time-multiplexed rendering to suppress speckle artifacts. At the core of GWS-RP is

  1. a novel wavefront compositing and alpha-blending scheme (Random-phase Alpha Blending), and
  2. a principled way of applying random phases to Gaussian primitives (Structured Random Phase).
These advancements collectively lead to high image quality and perceptually realistic 3D holograms for next-generation near-eye displays, as we demonstrate through extensive simulated and experimental results.

1. Random-phase Alpha Blending

We propose a novel wavefront compositing scheme that performs back-to-front compositing of Gaussian primitives, inspired by the silhouette method from prior polygon-based computer-generated holography (CGH) research. Furthermore, we introduce a completely new alpha-blending formulation compatible with arbitrary random-phase primitives, based on the observation that alpha blending of wavefronts is linear in the intensity domain for random-phase wavefronts, instead of the amplitude domain for smooth-phase wavefronts.

Together, these two algorithmic advancements reproduce accurate color and reconstructs exact defocus blur and occlusion of random-phase Gaussian wavefronts, while fully eliminating the dark halo artifacts commonly observed in previous alpha-blending approaches.

2. Structured Random Phase

We discuss a principled way of applying random phases to Gaussian primitives, which allows for the correct modeling of any angular emission profile, or Fourier spectrum, of the Gaussian primitive while maintaining its amplitude distribution in the spatial domain. This is different from prior random-phase CGH methods where only fully diffuse surfaces can be reconstructed. This allows for the correct reconstruction of view-dependent effects such as specular colors using spherical harmonics, and introduces new capabilities for GWS-RP such as programmatical control of the depth of field of the hologram. For the first time, we provide rigorous and extensive proofs grounded in statistical optics that validate the mathematical correctness of the heuristic outlined in the GWS supplemental materials.

Interactive Comparisons

3D Focal Stack Comparison

Select different scenes and GWS variants to compare the 3D focal stack reconstruction quality between smooth-phase and random-phase GWS approaches. Random-phase GWS shows improved bandwidth utilization and more accurate defocus blur while smooth-phase GWS exhibits unnatural defocus blur with ringing artifacts.

Far Near

4D Light Field Comparison

Select different scenes and GWS variants to compare the 4D light field horizontal parallax effects between smooth-phase and random-phase GWS approaches. Random-phase GWS demonstrates natural view-dependent effects and improved parallax, while smooth-phase GWS suffer from severe image quality degradation as the pupil moves away from the center of the eyebox.

Left Right

Extended 4D Light Field Results

Select different scenes to view extended 4D light field results with full 2D parallax using random phase GWS. These results demonstrate the full range of view-dependent effects and natural parallax across various scenes.

4D Light Field Parallax from Random Phase GWS