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Breaking crosstalk limits to dynamic holography using orthogonality of high-dimensional random vectors

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Holography is the most promising route to true-to-life three-dimensional (3D) projections, but the incorporation of complex images with full depth control remains elusive. Digitally synthesized holograms1,2,3,4,5,6,7, which do not require real objects to create a hologram, offer the possibility of dynamic projection of 3D video8,9. Despite extensive efforts aimed at 3D holographic projection10,11,12,13,14,15,16,17, however, the available methods remain limited to creating images on a few planes10,11,12, over a narrow depth of field13,14 or with low resolution15,16,17. Truly 3D holography also requires full depth control and dynamic projection capabilities, which are hampered by high crosstalk9,18. The fundamental difficulty is in storing all the information necessary to depict a complex 3D image in the 2D form of a hologram without letting projections at different depths contaminate each other. Here, we solve this problem by pre-shaping the wavefronts to locally reduce Fresnel diffraction to Fourier holography, which allows the inclusion of random phase for each depth without altering the image projection at that particular depth, but eliminates crosstalk due to the near-orthogonality of large-dimensional random vectors. We demonstrate Fresnel holograms that form on-axis with full depth control without any crosstalk, producing large-volume, high-density, dynamic 3D projections with 1,000 image planes simultaneously, improving the state of the art12,17 for the number of simultaneously created planes by two orders of magnitude. Although our proof-of-principle experiments use spatial light modulators, our solution is applicable to all types of holographic media.

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Fig. 1: Principle of crosstalk suppression in multiplane projection.
Fig. 2: Algorithm and implementation of 3D Fresnel holograms.
Fig. 3: Experimental demonstration of multiplane projection.

Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding authors upon reasonable request.

Change history

  • 02 April 2019

    In the version of this Letter originally published, Supplementary Videos 1–3 were linked to the wrong files; this has now been amended.


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This work was supported partially by the European Research Council (ERC) Consolidator Grant ERC-617521 NLL, TÜBITAK under project 117E823 and the BAGEP Award of the Science Academy. The authors thank J. Toumi and M.S. El-Daher for discussions, L. Onural for critical reading of the manuscript and M. Yaman for inspiration.

Author information

Authors and Affiliations



G.M., O.T. and F.Ö.I. designed the research and interpreted the results with help from S.I. and Ö.Y. Experiments and simulations were performed by G.M., D.K.K., Ö.Y., A.T., O.T. and P.E.

Corresponding authors

Correspondence to Onur Tokel or F. Ömer Ilday.

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The authors declare no competing interests.

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Supplementary information

Supplementary Information

This file contains more information about the work and Supplementary Figures 1–11.

Supplementary Video 1

Simultaneous 1,000-plane projection from a 3D Fresnel hologram.

Supplementary Video 2

Full solid angle projection.

Supplementary Video 3

Simultaneous 21-plane projection from a 3D Fresnel hologram.

Supplementary Video 4

3D dynamic display prototype.

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Makey, G., Yavuz, Ö., Kesim, D.K. et al. Breaking crosstalk limits to dynamic holography using orthogonality of high-dimensional random vectors. Nat. Photonics 13, 251–256 (2019).

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