  We prove a convergence theorem for a sequence of super-Brownian motions
moving among hard Poissonian obstacles, when the intensity of the obstacles
grows to infinity but their diameters shrink to zero in an appropriate manner.
The superprocesses are shown to converge in probability for the law
$\mathbf{P}$ of the obstacles, and $\mathbf{P}$-almost surely for a
subsequence, towards a superprocess with underlying spatial motion given by
Brownian motion and (inhomogeneous) branching mechanism $\psi(u,x)$ of the form
$\psi(u,x)= u^2+ \kappa(x)u$, where $\kappa(x)$ depends on the density of the
obstacles. This work draws on similar questions for a single Brownian motion.
In the course of the proof, we establish precise estimates for integrals of
functions over the Wiener sausage, which are of independent interest.
