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

Holography is the most promising route to true-to-life 3D projections, but the incorporation of complex images with full depth control remains elusive. Digitally synthesised holograms1-7, which do not require real objects to create a hologram, offer the possibility of dynamic projection of 3D video8,9. Extensive efforts aimed 3D holographic projection10-17, however available methods remain limited to creating images on a few planes10-12, over a narrow depth-of-field13,14 or with low resolution15-17. 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 preshaping the wavefronts to locally reduce Fresnel diffraction to Fourier holography, which allows inclusion of random phase for each depth without altering image projection at that particular depth, but eliminates crosstalk due to 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 1000 image planes simultaneously, improving the state-of-the-art12,17 for number of simultaneously created planes by two orders of magnitude. While our proof-of-principle experiments use spatial light modulators, our solution is applicable to all types of holographic media.