A novel laser angular-encoder system has been developed based on the principles of radar, the Doppler effect, optical heterodyning and self-aligning multiple-reflection optics. Using this novel three-dimensional multiple-reflection optical path, an increase in resolution of 10 to 20 times has been reached compared with commercially available laser Doppler displacement meters or laser interferometer systems. With the new angular encoder, sub-nrad resolution has been attained in the 8 degrees measuring range in a compact set-up [about 60 (H) x 150 (W) x 370 mm (L)] for high-energy-resolution applications at the Advanced Photon Source undulator beamline 3-ID.