  In this paper, we study the diffusion approximation for singularly perturbed
stochastic reaction-diffusion equation with a fast oscillating term. The
asymptotic limit for the original system is obtained, where an extra Gaussian
term appears. Such a term is explicitly given in terms of the solution of
Poisson equation in Hilbert space. Moreover, we also obtain the optimal rate of
convergence, and the convergence rate is shown not to depend on the regularity
of the coefficients of the original system with respect to the fast variable,
which coincides with the intuition since the fast component has been totally
homogenized out in the limit equation.
