We use the angular Doppler-effect to obtain stable frequency shifts from below one Hertz to hundreds of Hertz in the optical domain, constituting a control of 1 part in 10(14). For the first time, we use these very small frequency shifts to create continuous motion in interference patterns including the scanning of linear fringe patterns and the rotation of the interference pattern formed from a Laguerre- Gaussian beam. This enables controlled lateral and rotational movement of trapped particles. (C) 2002 Optical Society of America.