We introduce field synthesis, a theorem and method that can be used to synthesize any scanned or dithered light sheet, including those used in lattice light-sheet microscopy (LLSM), from an incoherent superposition of one-dimensional intensity distributions. Compared to LLSM, this user-friendly and modular approach offers a simplified optical design, higher light throughput and simultaneous multicolor illumination. Further, field synthesis achieves lower rates of photobleaching than light sheets generated by lateral beam scanning.