Under the weak deformation approximation, the motion of rigidly rotating spirals induced by periodic and noisy illuminations are investigated analytically. We derive an approximate but explicit formula of the spiral drift velocity directly from the original reaction-diffusion equation. With this formula we are able to explain the main features in the periodic and noisy illuminations induced spiral drift problems. Numerical computations of the Oregonator model are carried out as well, and they agree with the main qualitative conclusions of our analytical results. (C) 2004 American Institute of Physics.