The criterion for matching the charged particle bunch with the accelerator beam extraction window, which consists in minimizing the emittance of the accelerated beam extracted through a metal foil, is derived usinуl.g the distribution function for moving particles scattered on foil nuclei. A technique for constructing the phase portrait of the scattered bunch and the criterion for minimizing its area (emittance) are presented. The formula relating the emittances of incident and scattered bunches and the ellipse equation describing the phase portrait of thematched bunch are derived.