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


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.


  1. 1.

    Goodman, J. W. Introduction to Fourier Optics (Roberts & Company, 2005).

  2. 2.

    Yu, N. & Capasso, F. Flat optics with designer metasurfaces. Nat. Mater. 13, 139–150 (2014).

    ADS  Article  Google Scholar 

  3. 3.

    Arbabi, A., Horie, Y., Bagheri, M. & Faraon, A. Dielectric metasurfaces for complete control of phase and polarization with subwavelength spatial resolution and high transmission. Nat. Nanotechnol. 10, 937–943 (2015).

    ADS  Article  Google Scholar 

  4. 4.

    Zheng, G. X. et al. Metasurface holograms reaching 80% efficiency. Nat. Nanotechnol. 10, 308–312 (2015).

    ADS  Article  Google Scholar 

  5. 5.

    Li, L. et al. Electromagnetic reprogrammable coding-metasurface holograms. Nat. Commun. 8, 197 (2017).

    ADS  Article  Google Scholar 

  6. 6.

    Tokel, O. et al. In-chip microstructures and photonic devices fabricated by nonlinear laser lithography deep inside silicon. Nat. Photon. 11, 639–645 (2017).

    ADS  Article  Google Scholar 

  7. 7.

    Melde, K., Mark, A. G., Qui, T. & Fisher, P. Holograms for acoustics. Nature 537, 518–522 (2016).

    ADS  Article  Google Scholar 

  8. 8.

    Smalley, D. E., Smithwick, Q. Y. J., Bove, V. M., Barabas, J. & Jolly, S. Anisotropic leaky-mode modulator for holographic video displays. Nature 498, 313–317 (2013).

    ADS  Article  Google Scholar 

  9. 9.

    Sugie, T. et al. High-performance parallel computing for next-generation holographic imaging. Nat. Electron. 1, 254–259 (2018).

    Article  Google Scholar 

  10. 10.

    Dorsch, R. G., Lohmann, A. W. & Sinzinger, S. Fresnel ping-pong algorithm for two-plane computer-generated hologram display. Appl. Opt. 33, 869–875 (1994).

    ADS  Article  Google Scholar 

  11. 11.

    Hernandez, O. et al. Three-dimensional spatiotemporal focusing of holographic patterns. Nat. Commun. 7, 11928 (2016).

    ADS  Article  Google Scholar 

  12. 12.

    Malek, S. C., Ee, H.-S. & Agarwal, R. Strain multiplexed metasurface holograms on a stretchable substrate. Nano Lett. 17, 3641–3645 (2017).

    ADS  Article  Google Scholar 

  13. 13.

    Wakunami, K. et al. Projection-type see-through holographic three-dimensional display. Nat. Commun. 7, 12954 (2016).

    ADS  Article  Google Scholar 

  14. 14.

    Almeida, E., Bitton, O. & Prior, Y. Nonlinear metamaterials for holography. Nat. Commun. 7, 12533 (2016).

    ADS  Article  Google Scholar 

  15. 15.

    Kim, S.-C. & Kim, E.-S. Fast computation of hologram patterns of a 3D object using run-length encoding and novel look-up table methods. Appl. Opt. 48, 1030–1041 (2009).

    ADS  Article  Google Scholar 

  16. 16.

    Huang, L. Three-dimensional optical holography using a plasmonic metasurface. Nat. Commun. 4, 2808 (2013).

    Article  Google Scholar 

  17. 17.

    Yu, H., Lee, K., Park, J. & Park, Y. Ultrahigh-definition dynamic 3D holographic display by active control of volume speckle fields. Nat. Photon. 11, 186–192 (2017).

    ADS  Article  Google Scholar 

  18. 18.

    Li, X. et al. Multicolor 3D meta-holography by broadband plasmonic modulation. Sci. Adv. 2, e1601102 (2016).

    ADS  Article  Google Scholar 

  19. 19.

    Gabor, D. A new microscopic principle. Nature 161, 777–718 (1948).

    ADS  Article  Google Scholar 

  20. 20.

    Gabor, D., Kock, W. E. & Stroke, G. W. Holography. Science 173, 11–23 (1971).

    ADS  Article  Google Scholar 

  21. 21.

    Yaras, F., Kang, H. & Onural, L. State of the art in holographic displays: a survey. J. Disp. Tech. 6, 443–454 (2010).

    Article  Google Scholar 

  22. 22.

    Tsang, P. W. M. & Poon, T. C. Review on the state-of-the-art technologies for acquisition and display of digital holograms. IEEE Trans. Industr. Inform. 12, 886–901 (2016).

    Article  Google Scholar 

  23. 23.

    Khorasaninejad, M., Ambrosio, A., Kanhaiya, P. & Capasso, F. Broadband and chiral binary dielectric meta-holograms. Sci. Adv. 2, e1501258 (2016).

    ADS  Article  Google Scholar 

  24. 24.

    Maimone, A., Georgiou, A. & Kollin, J. S. Holographic near-eye displays for virtual and augmented reality. ACM Trans. Graph. 36, 85 (2017).

    Article  Google Scholar 

  25. 25.

    Li, X. P. et al. Athermally photoreduced graphene oxides for three-dimensional holographic images. Nat. Commun. 6, 6984 (2015).

    Article  Google Scholar 

  26. 26.

    Blanche, P. A. et al. Holographic three-dimensional telepresence using large-area photorefractive polymer. Nature 468, 80–83 (2010).

    ADS  Article  Google Scholar 

  27. 27.

    Lesem, L. B., Hirsch, P. M. & Jordan, J. A. The kinoform: a new wavefront reconstruction device. IBM J. Res. Dev. 13, 150–155 (1969).

    Article  Google Scholar 

  28. 28.

    Makey, G., El-Daher, M. S. & Al-Shufi, K. Utilization of a liquid crystal spatial light modulator in a gray scale detour phase method for Fourier holograms. Appl. Opt. 51, 7877–7882 (2012).

    ADS  Article  Google Scholar 

  29. 29.

    Benton, S. A. & Bove, V. M. Holographic Imaging (Wiley-Interscience, 2008).

  30. 30.

    Jackin, B. J. & Yatagai, T. 360 degrees reconstruction of a 3D object using cylindrical computer generated holography. Appl. Opt. 50, H147–H152 (2011).

    Article  Google Scholar 

  31. 31.

    Gülses, A. A. & Jenkins, B. K. Cascaded diffractive optical elements for improved multiplane image reconstruction. Appl. Opt. 52, 3608–3616 (2013).

    ADS  Article  Google Scholar 

  32. 32.

    Dufresne, E., Spalding, G., Dearing, M., Sheets, S. & Grier, D. Computer generated holographic optical tweezer arrays. Rev. Sci. Instrum. 72, 1810–1816 (2001).

    ADS  Article  Google Scholar 

  33. 33.

    Hsu, C. W. et al. Transparent displays enabled by resonant nanoparticle scattering. Nat. Commun. 5, 3152 (2014).

    Article  Google Scholar 

  34. 34.

    Furuya, M., Sterling, R., Bleha, W. & Inoue, Y. D-ILA full resolution 8K projector. In SMPTE Annu. Tech. Conf. Expo (SMPTE, 2009).

  35. 35.

    Smalley, D. E. et al. A photophoretic-trap volumetric display. Nature 553, 486–490 (2018).

    ADS  Article  Google Scholar 

  36. 36.

    Yue, Z., Xue, G., Liu, J., Wang, Y. & Gu, M. Nanometric holograms based on a topological insulator material. Nat. Commun. 8, 15354 (2017).

    ADS  Article  Google Scholar 

  37. 37.

    Segev, M., Silberberg, Y. & Christodoulides, D. N. Anderson localization of light. Nat. Photon. 7, 197–204 (2013).

    ADS  Article  Google Scholar 

  38. 38.

    Engheta, N. Pursuing near-zero response. Science 340, 286–287 (2013).

    ADS  Article  Google Scholar 

  39. 39.

    Gorban, A. N. & Tyukin, I. Y. Blessing of dimensionality: mathematical foundations of the statistical physics of data. Philos. Trans. A Math. Phys. Eng. Sci. 376, 20170237 (2018).

    ADS  MathSciNet  Article  Google Scholar 

  40. 40.

    Révész, P. The Laws of Large Numbers (Academic Press, 1967).

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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




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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