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 holograms 1 , 2 , 3 , 4 , 5 , 6 , 7 , which do not require real objects to create a hologram, offer the possibility of dynamic projection of 3D video 8 , 9 . Despite extensive efforts aimed at 3D holographic projection 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , however, the available methods remain limited to creating images on a few planes 10 , 11 , 12 , over a narrow depth of field 13 , 14 or with low resolution 15 , 16 , 17 . Truly 3D holography also requires full depth control and dynamic projection capabilities, which are hampered by high crosstalk 9 , 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 art 12 , 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.