Three different methods are described to determine the 'true' positions of a scintillation event in one- and two-dimensional position-sensitive scintillation detectors from experimental calibration data. Under certain assumptions the methods are shown to yield mathematically exact results. Computer-simulated results are presented to demonstrate the validity of the methods, to estimate the consequences of approximations to be made, and to provide figures for the required accuracy of experimental data. Results concerning spatial resolution and linearity of the response are discussed for the case that scintillation events are stored according to the precalculated and tabulated 'true' positions
