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Computer-generated holography

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Computer-generated holography (CGH) is the calculation of holographic interference or diffraction patterns by computer, instead of recording them optically with a laser and a photosensitive plate. The result, a computer-generated hologram, is either fabricated as a fixed element or loaded onto a spatial light modulator (SLM); when the pattern is illuminated with coherent light, it diffracts that light into the wavefront of the intended scene.[1] Because the recording step is simulated, CGH can produce holograms of objects that exist only as mathematical descriptions or 3D models, and with a refreshable SLM it can produce dynamic holographic 3D images.[1][2]

CGH is the computational side of a holographic display. In virtual reality (VR) and augmented reality (AR) research it matters because a hologram can place each part of an image at its own focal distance, which conventional stereoscopic headsets cannot do; a 2020 review in Optica names natural depth cues and the correction of eye aberrations as the unique advantages of holographic displays over other 3D displays.[3] The main obstacles are computation time, image quality (in particular speckle) and the limited space-bandwidth product of available SLMs.[1][3] Holographic near-eye displays driven by CGH have so far been shown as research prototypes; press coverage of a 2025 Meta and Stanford prototype described commercial products as still many years away.[4][5]

Reviewed 6 October 2026. Bibliographic details of all cited papers checked against Crossref/OpenAlex; history, algorithm, encoding, speckle and SLM-limit statements checked against the Pi et al. 2022 and Chang et al. 2020 reviews, the cited paper abstracts and texts; prototype figures checked against the papers, Microsoft Research pages, UploadVR and Road to VR; VividQ and Swave claims checked against their sites. About review dates.

Definition and scope

In optical holography, an object beam and a reference beam interfere on a recording medium, and the recorded fringe pattern later reconstructs the object wave when it is illuminated again. In computer-generated holography the recording process is simulated numerically, and the reconstruction is done physically by displaying the computed hologram on an SLM under coherent illumination.[1] The Optica review describes the same process for near-eye displays: the wavefront from a 3D object is encoded into a digital diffractive pattern, the CGH, which is then shown on an SLM and illuminated with a coherent source.[3]

CGH is distinct from digital holography, which records holograms of real objects with an image sensor and reconstructs the wavefront numerically; that technique is used mainly for quantitative phase imaging and optical metrology.[1]

Computed holograms have uses well beyond displays. A 2020 benchmarking preprint by Peter Christopher and Timothy Wilkinson of the University of Cambridge and George Gordon of the University of Nottingham lists augmented reality, medical imaging, additive manufacturing, lithography, optical tweezers and telecommunications among the fields that use SLM-based holography.[6]

History

Early computed holograms

According to the 2022 review by Pi, Liu and Wang, work in the 1960s by Kozma and Kelly on designing matched spatial filters with a computer laid the foundation for the field.[1] In 1966 B. R. Brown and Adolf W. Lohmann, of IBM's research division in San Jose, California, published "Complex spatial filtering with binary masks" in Applied Optics. Instead of producing a hologram through an interference experiment, they had a computer-guided plotter draw it; the plot was then reduced and recorded on film. The drawing contained only binary transmittance values, no grey levels, and the authors reported reconstructed images of a quality equal to those from conventional holograms of comparable size.[7] Their encoding is known as the detour-phase method.[1]

In 1967 Lohmann and D. P. Paris, also at IBM in San Jose, published a theory of binary Fraunhofer holograms generated by computer, for objects "known in mathematical terms" that do not exist physically; again an automatic plotter made a large drawing that was reduced photographically.[2] Pi and colleagues credit this work with applying the fast Fourier transform to the calculation of Fourier-transform CGHs, which greatly shortened computation time.[1]

In March 1969 L. B. Lesem, P. M. Hirsch and J. A. Jordan described the kinoform in the IBM Journal of Research and Development. A kinoform is a computer-generated optical element that acts only on the phase of the incident wave and forms a single image without the extra diffraction orders of ordinary holograms; the authors reported that it used reconstruction energy more efficiently and could be computed in considerably less time than a digital hologram.[8]

In 1972 R. W. Gerchberg and W. O. Saxton published an iterative phase-retrieval method in the journal Optik. It was designed for phase retrieval rather than holography, but it soon became a common way to generate holograms.[1][6] In 1978 C. K. Hsueh and A. A. Sawchuk described computer-generated double-phase holograms, in which a complex value is decomposed into two phase quantities that are then encoded with the detour-phase technique.[9]

Interactive and video-rate CGH

Real-time display required much faster computation. In a 1993 paper, Mark E. Lucente of the Massachusetts Institute of Technology presented methods for computing off-axis transmission holograms for real-time holographic display. A precomputed look-up table of elemental interference patterns, one for each possible point position in image space, gave an order-of-magnitude speed increase. On a data-parallel supercomputer, a horizontal-parallax-only pattern of six megasamples showing an image of 10,000 points could be computed in under one second, and on a common workstation the look-up table approach increased computation speed by a factor of 43.[10]

Polygon-based methods describe an object with surfaces instead of points. Kyoji Matsushima of Kansai University described CGHs of surface objects with shade and texture in 2005, computing the field from each planar surface with one fast Fourier transform per surface.[11] In 2009 Matsushima and Sumio Nakahara created a full-parallax CGH with four billion (216 x 216) pixels, fabricated by laser lithography, that reconstructed an occluded 3D scene.[12]

Near-eye displays and learned methods

In 2017 Andrew Maimone, Andreas Georgiou and Joel S. Kollin of Microsoft Research published "Holographic near-eye displays for virtual and augmented reality" in ACM Transactions on Graphics.[13] Microsoft's project page reports real-time hologram generation at 90-260 Hz on a desktop GPU (an NVIDIA GeForce GTX 980 Ti), per-pixel focus control, correction of optical aberrations in software, and a prototype with an 80 degree horizontal field of view.[14] The accompanying Microsoft Research blog post said holographic displays can correct vision problems such as astigmatism entirely in software by pre-distorting the emitted light waves.[15]

Later work applied numerical optimization and machine learning to hologram synthesis. At SIGGRAPH Asia 2020, Yifan Peng, Suyeon Choi, Nitish Padmanaban and Gordon Wetzstein of Stanford University presented "Neural holography with camera-in-the-loop training". It optimized holograms with stochastic gradient descent, used a camera to feed the real display output back into the optimization or into a learned model of the optics, and introduced a network called HoloNet, which the authors described as the first CGH algorithm able to generate full-color, high-quality 1080p holographic images in real time.[16][17]

In March 2021 Liang Shi, Beichen Li, Changil Kim, Petr Kellnhofer and Wojciech Matusik of MIT published "Towards real-time photorealistic 3D holography with deep neural networks" in Nature. Their convolutional neural network computes a color 3D hologram from a single RGB-depth image; it is under 620 kilobytes and runs at 60 Hz at 1,920 x 1,080 pixels on one consumer graphics card, at 1.1 Hz on an iPhone 11 Pro and at 2.0 Hz on a Google Edge TPU. It was trained on MIT-CGH-4K, a dataset of 4,000 RGB-depth images paired with 3D holograms.[18] The researchers named the approach "tensor holography".[18] MIT News noted that physics-based simulation on a clustered supercomputer "could take seconds or minutes for a single holographic image".[19]

How it works

Computing the object field

A CGH algorithm first describes the scene as a set of primitives and computes the complex light field (amplitude and phase) that the scene would produce at the hologram plane. Pi and colleagues group the methods by primitive into point-based, polygon-based and layer-based methods;[1] holographic stereograms, which convert a light field into a hologram, are a further ray-based approach.[3]

Method Scene representation Characteristics
Point-based Millions of self-luminous points, each emitting a spherical wave Simple and widely used; the fringe patterns of all points are summed. Look-up tables (Lucente) and later variants trade memory for speed, and wavefront recording planes (Shimobaba et al., 2009) restrict each point's calculation to a small region.[1][20]
Polygon-based Thousands of polygons, each treated as a polygonal aperture Far fewer primitives than points; works with computer graphics rendering to add texture and shading. The core problem is diffraction between tilted polygons and the hologram plane.[1]
Layer-based Several depth layers parallel to the hologram plane Each layer is propagated with Fresnel diffraction or the angular-spectrum method and the sub-holograms are summed; the 2D FFT is the main cost.[1] Efficient, but has difficulty with occlusion, shading, reflection and transparency.[3]
Holographic stereogram A light field of the scene computed with ray-based methods The hologram is divided into small elements ("hogels") that send plane waves in different directions; this provides accommodation cues and view-dependent effects.[3]

Peng and colleagues note that most point-based methods do not model occlusion, depth discontinuities or view-dependent lighting and shading, and that polygon, light-ray and layer primitives, as well as holographic stereograms, have been used to address this.[16] Shi and colleagues wrote in 2021 that existing physically based methods could not produce holograms with both per-pixel focal control and accurate occlusion.[18]

Encoding for a spatial light modulator

Most commercial SLMs cannot modulate amplitude and phase simultaneously and independently, so the computed complex field must be encoded into what the device can display, and information is lost in the process.[1] Conventional holographic displays use phase-only SLMs; amplitude-only devices such as LCDs and digital micromirror devices (DMDs) are cheaper in large formats, and the Optica review notes that complex wavefronts can also be encoded into amplitude-only holograms.[3]

Peng and colleagues divide phase-only encoding into two families. Direct methods use phase coding, such as the double-phase approach of Hsueh and Sawchuk or the encoding used by Maimone et al., to approximate the complex field in one pass. Iterative methods use optimization based on phase retrieval, such as the Gerchberg-Saxton algorithm, Fienup's method and Wirtinger holography; they are typically slower but give higher image quality or brightness.[16] In the double-phase hologram, the target complex amplitude is split into two phase-only holograms that are interleaved with complementary checkerboard patterns.[1]

The Gerchberg-Saxton algorithm starts from the target image with a random phase and repeatedly transforms the field between the image plane and the hologram plane. At the hologram plane the amplitude is discarded so that only phase remains; at the image plane the reconstructed amplitude is replaced by the target amplitude while the computed phase is kept. Error falls quickly in the first few iterations, then convergence slows or stagnates; variants such as the Fienup algorithm were developed to speed it up.[1] Christopher, Gordon and Wilkinson found in 2020 that the algorithm fails to converge for binary SLMs.[6]

Color is usually produced by computing separate red, green and blue holograms. They can be shown on three SLMs at once (spatial multiplexing), which is bulky, or one after another on a single fast SLM synchronized with red, green and blue lasers (time multiplexing).[1]

Image quality and speckle

Holographic displays usually use lasers because the technique needs coherent light, and the coherence produces speckle, a grainy intensity pattern on the image.[3] Random phase, which is widely added to diffuse object information across the hologram plane, causes unwanted interference between adjacent pixels, which Pi and colleagues identify as speckle noise.[1] The Optica review groups suppression methods into superposition (showing several holograms with statistically independent random phases within the eye's response time), spatial coherence construction and temporal coherence destruction, the last using partially coherent sources such as superluminescent LEDs.[3] In 2021 Peng, Choi, Jonghyun Kim and Wetzstein modeled partially coherent light-emitting diodes and superluminescent LEDs in a CGH algorithm with camera-in-the-loop calibration. They reported better speckle characteristics than with coherent lasers and described superluminescent LEDs as promising because they can produce bright, eye-safe images that are almost free of speckle.[21]

Another source of error is the mismatch between the simulated light propagation and the real optics. Peng and colleagues reported in 2020 that, in simulation, introducing a slight mismatch of this kind made image quality significantly worse for all algorithms they tested, which motivated their camera-in-the-loop calibration.[16] Choi and colleagues extended the idea in 2021 with a neural-network model of plane-to-multiplane propagation, trained from camera feedback, for 3D holograms on VR and optical see-through AR prototypes.[22]

Hardware limits that affect computation

The SLM's pixel pitch sets the maximum diffraction angle and therefore the field of view. Under plane-wave illumination the maximum angle is sin-1(wavelength / 2p), where p is the pixel size; with typical SLM pixels of 3 to 12 micrometres, this angle is generally under 5 degrees, so displays use relay optics or spherical-wave illumination to widen the view.[3] The product of field of view and eye box is proportional to the space-bandwidth product of the SLM, so increasing one reduces the other unless the SLM has more pixels.[3]

Applications in VR and AR

The case for CGH in head-mounted displays is that a hologram reproduces the wavefront of the scene, so the eye can focus on virtual content at its intended depth. This addresses the vergence-accommodation conflict of stereoscopic headsets, the mismatch between where the eyes converge and where they focus.[3] The same wavefront control allows a user's eyeglass prescription or the display's own optical aberrations to be corrected in software.[3][15]

Notable research prototypes that depend on CGH algorithms include:

Year Prototype Organization Reported characteristics
2017 Holographic near-eye displays Microsoft Research 80 degree horizontal field of view; 90-260 Hz hologram generation on a desktop GPU; sunglasses-like prototype[14]
2022 Holographic Glasses for Virtual Reality NVIDIA and Stanford University Pupil-replicating waveguide, SLM and geometric phase lens; 2.5 mm optical stack; 22.8 degree diagonal field of view; 2.3 mm static eye box; 60 g excluding the driving board[23]
2023 Multisource holography Reality Labs Research, Meta Array of light sources and two SLMs to suppress speckle in a single frame; up to 10 dB higher peak signal-to-noise ratio than an equivalent single-source system (benchtop)[24]
2024 Waveguide holography Reality Labs Research, Meta, with Seoul National University SLM at the input coupler of an exit-pupil-expanding waveguide combiner; software-steerable eye box[25]
2024 Full-color 3D holographic AR with metasurface waveguides Stanford University, with co-authors at NVIDIA and the University of Hong Kong Inverse-designed metasurface gratings and a waveguide, with an image formation model whose learned parts are calibrated from camera feedback[26]
2025 Synthetic aperture waveguide holography Stanford University and Meta Optical stack under 3 mm; 38 degree diagonal field of view; 9 x 8 mm static eye box; AI-based models of the waveguide and of partially coherent light[27][4]

The 2025 paper by Choi, Changwon Jang, Douglas Lanman and Wetzstein combined a custom waveguide with an algorithmic framework that includes a large-etendue waveguide model, a wave propagation model for partially coherent light and a CGH framework.[27] UploadVR's David Heaney wrote that its 38 degree field of view is far narrower than the roughly 115 degrees of the Meta Quest 3, and that no commercial-scale supply chain yet exists for the SLMs, fiber-coupled lasers and volume Bragg grating waveguides it uses.[4] Road to VR wrote that a commercial product "may still be years away".[5]

Some companies are developing CGH or holographic display hardware for products. VividQ develops hologram-generation algorithms and has product lines named CoReality AR, CoReality VR and CoReality HUD, for headsets and head-up displays; it states that its algorithms generate holograms in real time at 100 FPS.[28] Swave Photonics develops the Holographic Extended Reality (HXR) chip, a CMOS-based spatial light modulator that the company says uses pixels smaller than 300 nm, aimed at AR glasses.[29]

See also

References

  1. ↑ 1.00 1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 Dapu Pi, Juan Liu, Yongtian Wang (2022-07-26). "Review of computer-generated hologram algorithms for color dynamic holographic three-dimensional display". Light: Science & Applications, vol. 11, article 231. https://doi.org/10.1038/s41377-022-00916-3. Retrieved 2026-10-06.
  2. ↑ 2.0 2.1 Adolf W. Lohmann, D. P. Paris (1967). "Binary Fraunhofer holograms, generated by computer". Applied Optics, vol. 6, no. 10, pp. 1739-1748. https://doi.org/10.1364/AO.6.001739. Retrieved 2026-10-06.
  3. ↑ 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 3.10 3.11 3.12 Chenliang Chang, Kiseung Bang, Gordon Wetzstein, Byoungho Lee, Liang Gao (2020-11). "Toward the next-generation VR/AR optics: a review of holographic near-eye displays from a human-centric perspective". Optica, vol. 7, no. 11, pp. 1563-1578. https://doi.org/10.1364/OPTICA.406004. Retrieved 2026-10-06.
  4. ↑ 4.0 4.1 4.2 David Heaney (2025-07-28). "Meta & Stanford's Thin Holographic Display Brings "VR Glasses" Closer To Reality". UploadVR. https://www.uploadvr.com/meta-stanford-synthetic-aperture-waveguide-holography-vr-glasses-research/. Retrieved 2026-10-06.
  5. ↑ 5.0 5.1 Scott Hayden (2025-07-30). "Meta & Stanford Reveal Ultra-Thin Holographic XR Display the Size of Glasses". Road to VR. https://roadtovr.com/meta-stanford-xr-holographic-display-glasses/. Retrieved 2026-10-06.
  6. ↑ 6.0 6.1 6.2 Peter J. Christopher, George S. D. Gordon, Timothy D. Wilkinson (2020-05-18). "Benchmarking the Gerchberg-Saxton Algorithm". arXiv preprint 2005.08623. https://arxiv.org/abs/2005.08623. Retrieved 2026-10-06.
  7. ↑ B. R. Brown, Adolf W. Lohmann (1966). "Complex spatial filtering with binary masks". Applied Optics, vol. 5, no. 6, pp. 967-969. https://doi.org/10.1364/AO.5.000967. Retrieved 2026-10-06.
  8. ↑ L. B. Lesem, P. M. Hirsch, J. A. Jordan (1969-03). "The Kinoform: A New Wavefront Reconstruction Device". IBM Journal of Research and Development, vol. 13, no. 2, pp. 150-155. https://doi.org/10.1147/rd.132.0150. Retrieved 2026-10-06.
  9. ↑ C. K. Hsueh, A. A. Sawchuk (1978-12-15). "Computer-generated double-phase holograms". Applied Optics, vol. 17, no. 24, pp. 3874-3883. https://doi.org/10.1364/AO.17.003874. Retrieved 2026-10-06.
  10. ↑ Mark E. Lucente (1993). "Interactive computation of holograms using a look-up table". Journal of Electronic Imaging, vol. 2, no. 1, pp. 28-34. https://doi.org/10.1117/12.133376. Retrieved 2026-10-06.
  11. ↑ Kyoji Matsushima (2005-08-01). "Computer-generated holograms for three-dimensional surface objects with shade and texture". Applied Optics, vol. 44, no. 22, pp. 4607-4614. https://doi.org/10.1364/AO.44.004607. Retrieved 2026-10-06.
  12. ↑ Kyoji Matsushima, Sumio Nakahara (2009-12-01). "Extremely high-definition full-parallax computer-generated hologram created by the polygon-based method". Applied Optics, vol. 48, no. 34, pp. H54-H63. https://doi.org/10.1364/AO.48.000H54. Retrieved 2026-10-06.
  13. ↑ Andrew Maimone, Andreas Georgiou, Joel S. Kollin (2017-07-20). "Holographic near-eye displays for virtual and augmented reality". ACM Transactions on Graphics, vol. 36, no. 4. https://doi.org/10.1145/3072959.3073624. Retrieved 2026-10-06.
  14. ↑ 14.0 14.1 "Holographic Near-Eye Displays for Virtual and Augmented Reality". Microsoft Research. https://www.microsoft.com/en-us/research/project/holographic-near-eye-displays-virtual-augmented-reality/. Retrieved 2026-10-06.
  15. ↑ 15.0 15.1 Andrew Maimone, Andreas Georgiou, Joel Kollin (2017-05-19). "Holograms: The future of near-eye display?". Microsoft Research Blog. https://www.microsoft.com/en-us/research/blog/holograms-future-near-eye-display/. Retrieved 2026-10-06.
  16. ↑ 16.0 16.1 16.2 16.3 Yifan Peng, Suyeon Choi, Nitish Padmanaban, Gordon Wetzstein (2020-11-27). "Neural holography with camera-in-the-loop training". ACM Transactions on Graphics, vol. 39, no. 6. https://doi.org/10.1145/3414685.3417802. Retrieved 2026-10-06.
  17. ↑ "Neural Holography". Stanford Computational Imaging Lab. https://www.computationalimaging.org/publications/neuralholography/. Retrieved 2026-10-06.
  18. ↑ 18.0 18.1 18.2 Liang Shi, Beichen Li, Changil Kim, Petr Kellnhofer, Wojciech Matusik (2021-03-10). "Towards real-time photorealistic 3D holography with deep neural networks". Nature, vol. 591, pp. 234-239. https://doi.org/10.1038/s41586-020-03152-0. Retrieved 2026-10-06.
  19. ↑ Daniel Ackerman (2021-03-10). "Using artificial intelligence to generate 3D holograms in real-time". MIT News. https://news.mit.edu/2021/3d-holograms-vr-0310. Retrieved 2026-10-06.
  20. ↑ Tomoyoshi Shimobaba, Nobuyuki Masuda, Tomoyoshi Ito (2009-10). "Simple and fast calculation algorithm for computer-generated hologram with wavefront recording plane". Optics Letters, vol. 34, no. 20, p. 3133. https://doi.org/10.1364/OL.34.003133. Retrieved 2026-10-06.
  21. ↑ Yifan Peng, Suyeon Choi, Jonghyun Kim, Gordon Wetzstein (2021-11-12). "Speckle-free holography with partially coherent light sources and camera-in-the-loop calibration". Science Advances, vol. 7, no. 46, eabg5040. https://doi.org/10.1126/sciadv.abg5040. Retrieved 2026-10-06.
  22. ↑ Suyeon Choi, Manu Gopakumar, Yifan Peng, Jonghyun Kim, Gordon Wetzstein (2021-12). "Neural 3D holography". ACM Transactions on Graphics, vol. 40, no. 6. https://doi.org/10.1145/3478513.3480542. Retrieved 2026-10-06.
  23. ↑ Jonghyun Kim, Manu Gopakumar, Suyeon Choi, Yifan Peng, Ward Lopes, Gordon Wetzstein (2022). "Holographic Glasses for Virtual Reality". ACM SIGGRAPH 2022 Conference Proceedings. https://doi.org/10.1145/3528233.3530739. Retrieved 2026-10-06.
  24. ↑ Grace Kuo, Florian Schiffers, Douglas Lanman, Oliver Cossairt, Nathan Matsuda (2023-12-05). "Multisource Holography". ACM Transactions on Graphics, vol. 42, no. 6 (SIGGRAPH Asia 2023). https://doi.org/10.1145/3618380. Retrieved 2026-10-06.
  25. ↑ Changwon Jang, Kiseung Bang, Minseok Chae, Byoungho Lee, Douglas Lanman (2024-01-02). "Waveguide holography for 3D augmented reality glasses". Nature Communications, vol. 15, article 66. https://doi.org/10.1038/s41467-023-44032-1. Retrieved 2026-10-06.
  26. ↑ Manu Gopakumar, Gun-Yeal Lee, Suyeon Choi, Brian Chao, Yifan Peng, Jonghyun Kim, Gordon Wetzstein (2024-05-08). "Full-colour 3D holographic augmented-reality displays with metasurface waveguides". Nature, vol. 629, pp. 791-797. https://doi.org/10.1038/s41586-024-07386-0. Retrieved 2026-10-06.
  27. ↑ 27.0 27.1 Suyeon Choi, Changwon Jang, Douglas Lanman, Gordon Wetzstein (2025-07-28). "Synthetic aperture waveguide holography for compact mixed-reality displays with large etendue". Nature Photonics, vol. 19, no. 8, pp. 854-863. https://doi.org/10.1038/s41566-025-01718-w. Retrieved 2026-10-06.
  28. ↑ "Technology". VividQ. https://www.vividq.com/technology. Retrieved 2026-10-06.
  29. ↑ "Home". Swave Photonics. https://swave.io/. Retrieved 2026-10-06.
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