  We consider the Dirichlet problem for elliptic systems with periodically
distributed inclusions whose conduction parameter exhibits a significant
contrast compared to the background media. We develop a unified method to
quantify the convergence rates both as the periodicity of inclusions tends to
zero and as the parameter approaches either zero or infinity. Based on the
obtained convergence rates and a Campanato-type scheme, we also derive the
regularity estimates that are uniform both in the periodicity and the contrast.
