The sampling rate and angular resolution of diffraction-based beam steering employing a digital micromirror device (DMD) can be simultaneously enhanced by at least an order of magnitude by synchronizing multiple nanosecond laser sources and pulses during each DMD actuation. A time-of-flight single-chip DMD lidar with three sources measures a range at a 3.34 kHz sampling rate and a 3.4° angular resolution across a 48° field of view. Employing multiple diffraction orders of the DMD improves the sampling rate at least by a factor of 2 and up to the number of diffraction orders supported by the DMD. An improved sampling rate of 6.68 kHz with a 9.6° angular resolution is experimentally demonstrated by illuminating micromirrors multiple times within a single transition period of the micromirrors.