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We prove a convergence theorem for a sequence of super-Brownian motionsmoving among hard Poissonian obstacles, when the intensity of the obstaclesgrows 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 asubsequence, towards a superprocess with underlying spatial motion given byBrownian 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 theobstacles. This work draws on similar questions for a single Brownian motion.In the course of the proof, we establish precise estimates for integrals offunctions over the Wiener sausage, which are of independent interest.

Quenched convergence of a sequence of superprocesses in R^d among Poissonian obstacles