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Light sheets for continuous-depth holography and three-dimensional volumetric displays

Nature Photonics volume 17, pages 427–434 (2023)Cite this article

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Abstract

Projecting high-quality three-dimensional (3D) scenes via computer-generated holography is a sought-after goal for virtual and augmented reality, human–computer interaction and interactive learning. Three-dimensional objects are usually constructed from a single hologram by cascading a stack of two-dimensional (2D) scenes along the optical path and perpendicular to it. The spatial separation between those scenes, however, is fundamentally constrained by the numerical aperture of the hologram, limiting the axial resolution and depth perception of the generated 3D image. Here we propose a new class of hologram that instead projects a desired scene onto 2D sheets oriented perpendicular to the plane of the display screen, thus enabling continuous reconstruction of the object along the optical path. To achieve this, we decompose the target scene into threads of light—arrays of non-diffracting pencil-like beams whose envelopes can be locally structured along the propagation direction at will. Using a spatial light modulator, we project 2D scenes onto the plane normal to the hologram and by stacking multiple 2D sheets in parallel we construct 3D objects with high fidelity and low crosstalk. Computer-generated holography of this kind opens new routes to realistic 3D holography and can be deployed in wearable smart glasses, portable devices and wide-angle volumetric displays.

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Fig. 1: Different approaches to holographic projection.
Fig. 2: Concept of holographic light sheets.
Fig. 3: Generation of 2D holographic light sheets.
Fig. 4: Assembling 2D holographic light sheets to construct volumetric (3D) scenes.

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Data availability

All key data that support the findings of this study are included in the article and its Supplementary Information. Additional datasets and raw measurements are available from the corresponding authors upon reasonable request.

Code availability

The codes and simulation files that support Figs. 1–4, Extended Data Figs. 1 and 2 and the data analysis are available from the corresponding authors upon reasonable request.

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Acknowledgements

We thank A. Zaidi, A. Palmieri and M. Greiner, all of Harvard University, as well as M. Ritsche-Marte of the Medical University of Innsbruck for insightful discussions. A.H.D. acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC) under award no. PDF-533013-2019. F.C. acknowledges financial support from the Office of Naval Research (ONR) under the MURI programme, grant no. N00014-20-1-2450, and from the Air Force Office of Scientific Research (AFOSR) under grant nos FA9550-21-1-0312 and FA9550-22-1-0243. V.S.d.A. acknowledges financial support from the National Council for Scientific and Technological Development (CNPq) under grant no. 140270/2022-1. M.Z.-R. acknowledges financial support from CNPq under grant no. 306689/2019-7 and from São Paulo Research Foundation (FAPESP) under grant no 2021/15027-8. L.A.A. acknowledges financial support from CNPq under grant no. 309201/2021-7 and from FAPESP under grant nos 2020/05280-5 and 2021/06121-0.

Author information

Authors and Affiliations

  1. Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA

    Ahmed H. Dorrah, Priyanuj Bordoloi & Federico Capasso

  2. Department of Electrical and Computer Engineering, São Carlos School of Engineering, University of São Paulo, São Paulo, Brazil

    Vinicius S. de Angelis, Jhonas O. de Sarro & Leonardo A. Ambrosio

  3. School of Electrical and Computer Engineering, University of Campinas, São Paulo, Brazil

    Michel Zamboni-Rached

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Contributions

A.H.D. designed and built the experiment, created the CGHs with input from P.B. and analysed and processed the data. P.B. performed the measurements and acquired and processed the data. V.S.d.A. and J.O.d.S developed the MATLAB simulations of surface frozen waves. M.Z.-R. conceived the frozen wave theory. L.A.A. developed the mathematical formulation of surface frozen waves. F.C. supervised the project. A.H.D., P.B. and F.C. wrote the paper with input from all co-authors.

Corresponding authors

Correspondence to Ahmed H. Dorrah or Federico Capasso.

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Nature Photonics thanks Fatih Ilday, YongKeun Park and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 Projecting 2D images with Fresnel holography.

Four digits ‘1 2 3 4’ are axially projected along the propagation direction. The longitudinal separation between the image planes is (a) 5 cm, (b) 2.5 cm, (c) 1 cm, and (d) 0.5 cm. The scale bars in (a-d) are 2 mm, 1.5 mm, 1 mm and 0.8 mm, respectively. While cross-talk can be reduced by placing the images further apart (a), the size of the displayed images vary significantly (becoming larger) at longer propagation distances. This magnification can be mitigated by reducing the separation between the images, however, at the expense of more significant cross-talk (d). Here, ϵ depicts the reconstruction error as detailed in Supplementary Note 4.

Extended Data Fig. 2 Projecting 2D images with holographic light sheets.

Four digits ‘1 2 3 4’ are projected in the lateral direction perpendicular to the display. The lateral separation between the images is (a) 3.042 mm, (b) 1.872 mm, (c) 0.936 mm, and (d) 0.468 mm. The horizontal and vertical scale bars are 10 mm and 0.5 mm, respectively. Here, cross-talk (signified by ϵ) can be reduced by placing the images further apart in the lateral direction without affecting the size of the projected images. Furthermore, given their non-diffracting behavior, our holographic light sheets exhibit a relatively smooth profile (with less grainy features) compared to Fresnel-based multi-plane techniques.

Supplementary information

Supplementary Information

Supplementary Figs. 1–14, Notes 1–5 and refs. 1–23.

Animated visualization of volumetric digit (1) projected onto eight holographic sheets and viewed over the full 4π solid angle.

Animated visualization of a hollow sphere composed of eight stacked rings and viewed over the entire 4π solid angle.

Animated visualization of a hollow sphere composed of eight stacked rings while including two planes between the rings, as viewed over the full 4π solid angle.

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Dorrah, A.H., Bordoloi, P., de Angelis, V.S. et al. Light sheets for continuous-depth holography and three-dimensional volumetric displays. Nat. Photon. 17, 427–434 (2023). https://doi.org/10.1038/s41566-023-01188-y

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