The present invention is directed to optical element damping systems. In particular, an eddy current damper is disclosed. The eddy current damper includes a rod, a series of conducting plates coupled to the rod, and layers of magnets. The alternating layers have alternating magnetic fields. When an optical element moves, the optical element will exert a force on the rod. The rod causes the conducting plates to move relative to the alternating layers of magnets to generate eddy currents within each of the conducting plates, such that the eddy currents damp the motion of an optical element. In an alternative embodiment, an eddy current damper motion amplifier is used to provide additional mechanical advantage that significantly increases the damping provided by the eddy current damper. Eddy current dampers are provided within conventional scanning lithography devices and optical maskless lithography devices to improve performance by stabilizing optical element motion.