A curated list of resources on holographic displays.

This list is compiled during my paper survey about holographic displays, and is not meant to be exhuastive. The list is organized for me to easily navigate different topics in holography. I would like to thank the authors of the following papers for providing great initial references:

• Neural Holography with Camera-in-the-loop Training (Peng et al. 2020)
• Learned Hardware-in-the-loop Phase Retrieval for Holographic Near-Eye Displays (Chakravarthula et al. 2020)

• Background, Theory, and Survey
• Computer Generated Holography (CGH) Algorithms
  • Traditional Heuristic Methods
  • Iterative Methods
  • Learned Propagation Model Methods
  • Learned Hologram Synthesis Methods
• Topics in Holography Display Systems
  • Speckle Noise Reduction
  • Etendue Expansion
  • Holographic Optical Elements (HOEs)
  • Small Form-factor Displays
  • Compression
  • Zero or Higher Diffraction Orders Optimization
• Labs and Researchers
• Talks, Lectures, and Tutorials

• Introduction to Fourier Optics by Joseph W. Goodman is a great book to learn the basics of wave propagation and holography.
• Numerical simulation of optical wave propagation: With examples in MATLAB by Jason D. Schmidt walks you through the nitty-gritty details of implementing optial wave propagation.

• Toward the next-generation VR/AR optics: a review of holographic near-eye displays from a human-centric perspective (Chang et al. 2020 | Optica, Optica)
• Deep learning in holography and coherent imaging (Rivenson et al. 2019 | Light: Science and Applications, Nature)

This section mainly focuses on the algorithmic aspect of holographic display systems.

• Computer-generated double-phase holograms (Hsueh et al. 1978 | Applied Optics, Optica) proposed to decompose a complex field into two phase-only components to generate holograms using a single phase-only SLM.
• Holographic Near-Eye Displays for Virtual and Augmented Reality (Maimone et al. 2017 | Transactions on Graphics (TOG), ACM) proposed a holographic near-eye display system based on the double phase encoding scheme.
• Monocular 3D see-through head-mounted display via complex amplitude modulation (Gao et al. 2016 | Optics Express, Optica)
• Near-eye Light Field Holographic Rendering with Spherical Waves for Wide Field of View Interactive 3D Computer Graphics (Shi et al. 2017 | Transactions on Graphics (TOG), ACM) uses point-source illumination rather than plane-wave illumination to improve the FOV of holograhic displays.

• Computer-generated holograms of 3-D objects composed of tilted planar segments (Leseberg et al. 1988 | Applied Optics, Optica)
• Computer-generated holograms of tilted planes by a spatial frequency approach (Tommasi et al. 1993 | Journal of the Optical Society of America A, Optica)
• Computer-generated holograms for three-dimensional surface objects with shade and texture (Matsushima 2005 | Applied Optics, Optica)
• Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method (Matsushima et al. 2009 | Applied Optics, Optica)
• Silhouette method for hidden surface removal in computer holography and its acceleration using the switch-back technique (Matsushima et al. 2014 | Optics Express, Optica)
• Computer generated holograms from three dimensional meshes using an analytic light transport model (Ahrenberg et al. 2008 | Applied Optics, Optica)
• Fast and effective occlusion culling for 3D holographic displays by inverse orthographic projection with low angular sampling (Jia et al. 2014 | Applied Optics, Optica)

• Computer-generated hologram with occlusion effect using layer-based processing (Zhang et al. 2017 | Applied Optics, Optica)
• Accurate calculation of computer-generated holograms using angular-spectrum layer-oriented method (Zhao et al. 2015 | Optics Express, Optica)
• Improved layer-based method for rapid hologram generation and real-time interactive holographic display applications (Chen et al. 2015 | Optics Express, Optica)
• Computer generated hologram with geometric occlusion using GPU-accelerated depth buffer rasterization for three-dimensional display (Chen et al. 2009 | Applied Optics, Optica)

• Holographic near-eye displays based on overlap-add stereograms (Padmanaban et al. 2019 | SIGGRAPH Asia, ACM)
• Layered holographic stereogram based on inverse Fresnel diffraction (Zhang et al. 2016 | Applied Optics, Optica)
• Fully computed holographic stereogram based algorithm for computer-generated holograms with accurate depth cues (Zhang et al. 2015 | Optics Express, Optica)

A family of iterative methods is based on the Gerchberg-Saxton (GS) Algorithm where the phase and amplitute patterns at two planes are updated iteratively as the wave propagates back and forth between the two planes:

• A practical algorithm for the determination of phase from image and diffraction plane pictures (Gerchberg et al. 1972 | Optik, Elsevier) proposed the Gerchberg-Saxton (GS) Algorithm
• Mix-and-Match Holography (Peng et al. 2017 | SIGGRAPH Asia, ACM) proposed an interative phase-retrieval method built upon GS
• Fresnel ping-pong algorithm for two-plane computer-generated hologram display (Dorsch et al. 1994 | Applied Optics, Optica)

Other optimization based methods leverage gradient descent or non-convex optimization techniques to optimize the phase pattern of the SLM:

• Accommodative Holography: Improving Accommodation Response for Perceptually Realistic Holographic Displays (Kim et al. 2022 | SIGGRAPH, ACM) analyzed the user accomodation performance when using different CGH methods and proposed a novel constrast ratio-based regularization loss that promotes better accomodation cues.
• Metameric Varifocal Holograms (Walton et al. 2022 | VR, IEEE) proposed a foveated graphics-inspired, gaze-contingent loss function that can be easily integrated into CGH optimization. The loss enforces the defocus image regions to only statistically match the defocus target image regions rather than pixel-wise reconstruction. This increases the degrees of freedom for the hologram to distribute light (compared to fitting a focal stack), thus reducing speckle artifacts.
• Realistic Defocus Blur for Multiplane Computer-Generated Holography (Kavaklı et al. 2021) proposed a novel loss function aimed to synthesize high quality defocus blur, and can be intergated in various iterative (GS, gradient-descent) and non-iterative (double phase encoding) methods.
• Gaze-Contingent Retinal Speckle Suppression for Perceptually-Matched Foveated Holographic Displays (Chakravarthula et al. 2021 | TVCG, IEEE)

• Hogel-free Holography (Chakravarthula et al. 2022 | SIGGRAPH, ACM)
• Optimization of computer-generated holograms featuring phase randomness control (Yoo et al. | Optics Express, Optica) leveraged a learned DPAC encoding optimized using gradinet descent to promote phase randomness, which in turn increases the space-bandwidth product of the display system.
• Multi-depth hologram generation using stochastic gradient descent algorithm with complex loss function (Chen et al. 2021 | Optics Express, Optica)
• Wirtinger Holography for Near-Eye Displays (Chakravarthula et al. 2019 | SIGGRAPH Asia, ACM) optimizes the phase-only SLM pattern using closed-form Wirtinger complex derivatives in gradient descent.
• 3D computer-generated holography by non-convex optimization (Zhang et al. 2017 | Optica, Optica)

Unfortunately, iterative methods are inherently slow and thus not suitble for real-time CGH. See this section for speeding up hologram synthesis using neural networks.

There are often mismatches between a ideal wave propagation model (e.g. ASM) with the actual physical display setup. A major focus in deep learning for CGH is using camera-in-the-loop (CITL) training to learn an accurate free space wave propagation and optical hardware model for holographic displays:

• Neural Holography with Camera-in-the-loop Training (Peng et al. 2020 | SIGGRAPH, ACM) is the first to use camera-in-the-loop training (CITL) to optimize a parameterized wave propagation model, where optical aberrations, SLM non-linearities, and etc are learned from data. A CNN is also proposed to synthesize 2D and 3D holograms in real-time.
• Neural 3D Holography: Learning Accurate Wave Propagation Models for 3D Holographic Virtual and Augmented Reality Displays (Choi et al. 2021 | SIGGRAPH Asia, ACM) uses two CNNs to directly model optical aberrations, SLM non-linearities, and etc, at the input plane and multiple target planes. The usage of two CNNs introduces more degrees of freedom than that of the parameterized propagation model proposed in Peng et al. 2020, such that higher quality 3D holograms can be achieved.
• Time-multiplexed Neural Holography: A Flexible Framework for Holographic Near-eye Displays with Fast Heavily-quantized Spatial Light Modulators (Choi et al. 2022 | SIGGRAPH, ACM) leveraged time-multiplexed quantized SLM patterns to synthesize high quality defocus blur.
• Learned Hardware-in-the-loop Phase Retrieval for Holographic Near-Eye Displays (Chakravarthula et al. 2020 | SIGGGRAPH Asia, ACM) uses CITL to learn an aberration approximator that models the residual between holograms generated from ideal wave propagation (i.e. ASM) and real-world wave propagation models. An adversarial loss is used in addition to reconstruction loss to optimize the synthesized holograms.
• Learned holographic light transport (Kavaklı et al. 2021 | Applied Optics, Optica) learns the wave propagation convolution kernel directly from images captured by a physical holographic display, instead of using the ASM method to propagate fields.

These works often assume a naive wave propagation model (i.e. the angular spectrum method (ASM)), and directly regresses complex holograms using novel CNN architectures:

• End-to-end Learning of 3D Phase-only Holograms for Holographic Display (Liang et al. 2022 | Light: Science and Applications, Nature)
• Towards real-time photorealistic 3D holography with deep neural networks (Liang et al. 2021 | Nature, Nature)
• Diffraction-engineered holography: Beyond the depth representation limit of holographic displays (Yang et al. 2022 | Nature Communications, Nature)
• DeepCGH: 3D computer-generated holography using deep learning (Eybposh et al. 2020 | Optics Express, Optica) uses a CNN to estimate a complex field at a fixed plane from a set of 3D target multiplane inputs; the complex field is then reverse propagated to the SLM plane to generate a phase pattern.
• Deep neural network for multi-depth hologram generation and its training strategy (Lee et al. 2020 | Optics Express, Optica) directly estimates the SLM phase pattern from 3D target multiplane inputs using a CNN.
• Deep-learning-generated holography (Horisaki et al. 2018 | Applied Optics, Optica)
• Phase recovery and holographic image reconstruction using deep learning in neural networks (Rivenson et al. 2018 | Light: Science and Applications, Nature)

• Strategies for reducing speckle noise in digital holography (Bianco et al. 2018 | Light: Sciene and Applications, Nature)

Speckle noise is a result of interference among coherent waves, which is often present in holographic images since holographic displays use coherent laser sources. Methods for reducing speckle noise can roughly be catergorized into the following:

• High‐contrast, speckle‐free, true 3D holography via binary CGH optimization (Lee et al. 2022 | Scientific Reports, Nature) optimized random phase, amplitude only SLMs using gradient descent and time-averaged them to reduce speckle noise.
• DCGH: Dynamic Computer Generated Holography for Speckle-Free, High Fidelity 3D Displays (Curtis et al. 2021 | IEEE, VR) simultaneously optimizes multiple binary, amplitude only SLMs in a modified Gerchberg-Saxton (GS) algorithm and time-averages them to reduce speckle noise.

• Speckle-free holography with partially coherent light sources and camera-in-the-loop calibration (Peng et al. 2021 | Science Advaces, Science) uses partially coherent light sources (i.e. LED) and camera-in-the-loop optimization to reduce speckle noise.
• Light source optimization for partially coherent holographic displays with consideration of speckle contrast, resolution, and depth of field (Lee et al. 2020 | Scientific Reports, Nature)
• Holographic head-mounted display with RGB light emitting diode light source (Moon et al. 2014 | Optics Express, Optica)

• Optimizing image quality for holographic near-eye displays with Michelson Holography (Choi et al. 2021 | Optica, Optica) uses 2 SLMs to correct for the unwanted interference caused by undiffracted light in single-SLM settings. A CITL procedure is also deployed to simultaneously optimize 2 SLM patterns.

The product of the field of view (FoV) and the eyebox size, the etendue, is limited by the number of pixels on the SLM. Hence, there is an inherent tradeoff between these two properties.

• Pupil-aware Holography (Chakravarthula et al. 2022)
• Neural Etendue Expander for Ultra-Wide-Angle High-Fidelity Holographic Display (Baek et al. 2022)
• High Resolution étendue expansion for holographic displays (Kuo et al. 2020 | SIGGRAPH, ACM)
• Holographic Near-eye Display with Expanded Eye-box (Jang et al. 2018 | Transactions on Graphics (TOG), ACM)

• Design and Fabrication of Freeform Holographic Optical Elements (Jang et al. 2020 | SIGGRAPH Asia, ACM)
• Retinal 3D: augmented reality near-eye display via pupil-tracked light field projection on retina (Jang et al. 2017 | SIGGRAPH Asia, ACM)
• Holographic display for see-through augmented reality using mirror-lens holographic optical element (Li et al. 2016 | Optics Letters, Optica)
• 3D holographic head mounted display using holographic optical elements with astigmatism aberration compensation (Yeom et al. 2015 | Optics Express, Optica)

Bulky headsets hamper the development of AR/VR. Reducing the size of holographic displays are important:

• Holographic Glasses for Virtual Reality (Kim et al. 2022 | SIGGRAPH, ACM) presents a holographic display system with eyeglasses-like form factor. An optical stack of 2.5mm is achieved by combining pupil-replicating waveguide, SLMs, and geometric phase lenses.
• Holographic pancake optics for thin and lightweight optical see-through augmented reality (Cakmakci et al. 2021 | Optics Express, Optica)
• Holographic Optics for Thin and Lightweight Virtual Reality (Maimone et al. 2021 | SIGGRAPH, ACM)

CGH compression is also important for deploying holography technology on edge devices:

• Joint Neural Phase Retrieval and Compression for Energy- and Computation-efficient Holography on the Edge (Wang et al. 2022 | SIGGRAPH, ACM)
• Neural compression for hologram images and videos(Shi et al. 2022 | Optics Letters, Optica)

• Unfiltered holography: optimizing high diffraction orders without optical filtering for compact holographic displays g(Gopakumar et al. 2021 | Optics Letters, Optica) incorporated higher diffraction orders into the CGH optimization procedure to remove the 4f filtering system often used in holographic displays, thus reducing the display form factor.
• Elimination of a zero-order beam induced by a pixelated spatial light modulator for holographic projection (Zhang et al. 2009 | Applied Optics, Optica)
• Holographic projection of arbitrary light patterns with a suppressed zero-order beam
• Effect of spurious diffraction orders in arbitrary multifoci patterns produced via phase-only holograms
• Off-axis camera-in-the-loop optimization with noise reduction strategy for high-quality hologram generation (Chen et al. 2022 | Optics Letters, Optica)

• Computational Imaging Lab, Stanford University
• Computational Imaging Lab, Princeton University
• Computational Biophotonics Laboratory, UNC Chapel Hill
• Graphics and Virtual Reality Group, UNC Chapel Hill
• Computational Light Laboratory, University College London
• Computational Imaging Group, KAUST
• Optical Engineering and Quantum Electronics Lab, Seoul National University
• NVIDIA Research
• Meta Research

• Could Deep Learning Improve Visual Quality in Holographic Displays?(Optica, 2022)

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