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We revisit the periodic homogenization of Dirichlet problems for the Laplaceoperator in perforated domains, and establish a unified proof that works fordifferent regimes of hole-cell ratios, that is the ratio between the scalingfactor of the holes and that of the periodic cells. The approach is then madequantitative and it yields correctors and error estimates for vanishinghole-cell ratios. For positive volume fraction of holes, the approach is justthe standard oscillating test function method; for vanishing volume fraction ofholes, we study asymptotic behaviors of a properly rescaled cell problems anduse them to build oscillating test functions. Our method reveals how thedifferent regimes are intrinsically connected through the cell problems and theconnection with periodic layer potentials.

A unified homogenization approach for the Dirichlet problem in Perforated Domains