  In homogenization theory and multiscale modeling, typical functions satisfy
the scaling law $f^{\epsilon}(x) = f(x,x/\epsilon)$, where $f$ is periodic in
the second variable and $\epsilon$ is the smallest relevant wavelength,
$0<\epsilon\ll1$. Our main result is a new $L^{2}$-stability estimate for the
reconstruction of such bandlimited multiscale functions $f^{\epsilon}$ from
periodic nonuniform samples. The goal of this paper is to demonstrate the close
relation between and sampling strategies developed in information theory and
computational grids in multiscale modeling. This connection is of much interest
because numerical simulations often involve discretizations by means of
sampling, and meshes are routinely designed using tools from information
theory. The proposed sampling sets are of optimal rate according to the minimal
sampling requirements of Landau \cite{Landau}.
