Active sub-Rayleigh alignment of parallel or antiparallel laser beams

We measure and stabilize the relative angle of (anti-)parallel laser beams to 5 nanoradian per root Hertz resolution by comparing the phases of radio frequency beat notes on a quadrant photodetector. The absolute accuracy is 5.1 microradian and 2.1 microradian for antiparallel and parallel beams, respectively, which is more than 6 and 16 times below the Rayleigh criterion.