Volumetric additive manufacturing has emerged as a promising technique for the flexible production of complex structures, with diverse applications in engineering, photonics and biology1,2. However, present methods still face a trade-off between resolution and volumetric build rate, restricting efficient and flexible production of high-resolution 3D structures. Here we propose a method, called digital incoherent synthesis of holographic light fields (DISH), to generate high-resolution 3D light distributions through continuous multi-angle projections with a high-speed rotating periscope without the requirement of sample rotation. The iterative optimization of the holograms for different angles in DISH maintains 19-μm printing resolution across the 1-cm range that is far beyond the depth of field of the objective and enables high-resolution in situ 3D printing of millimetre-scale objects within only 0.6 s. Acrylate materials in a range of viscosities are used to demonstrate the general compatibility of DISH. Integrating DISH with a fluid channel, we achieved mass production of complex and diverse 3D structures within low-viscosity materials, demonstrating its potential for broad applications in diverse fields.