  We study the two and three dimensional stochastic Cahn-Hilliard equation in
the sharp interface limit, where the positive parameter $\epsilon$ tends to
zero, which measures the width of transition layers generated during phase
separation. We also couple the noise strength to this parameter. Using formal
asymptotic expansions, we identify the limit. In the right scaling we indicate
that the solutions of stochastic Cahn-Hilliard converge to a solution of a
Hele-Shaw problem with stochastic forcing. In the case when the noise is
sufficiently small, we rigorously prove that the limit is a deterministic
Hele-Shaw problem. Finally, we discuss which estimates are necessary in order
to extend the rigorous result to larger noise strength.
