We have developed a position response calibration method for a micro-channel plate (MCP) detector with a delay-line anode position readout scheme. Using an {em in situ} calibration mask, an accuracy of 8~$mu$m and a resolution of 85~$mu$m (FWHM) have been achieved for MeV-scale $alpha$ particles and ions with energies of $sim$10~keV. At this level of accuracy, the difference between the MCP position responses to high-energy $alpha$ particles and low-energy ions is significant. The improved performance of the MCP detector can find applications in many fields of AMO and nuclear physics. In our case, it helps reducing systematic uncertainties in a high-precision nuclear $beta$-decay experiment.
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