  We define a map $\mathcal{P}_M$ attached to any polarized Hodge module $M$
such that the restriction of $\mathcal{P}_M$ to a locus on which $M$ is a
variation of Hodge structures induces the usual period integral pairing for
this variation of Hodge structures. In the case that $M$ is the minimal
extension of a simple polarized variation of Hodge structures $V$, we show that
the homotopy image of $\mathcal{P}_M$ is the minimal extension of the graph
morphism of the usual period integral map for $V$.
