The invention concerns a process for the deposition of an intended dose distribution in a cyclically moved target region moving cyclically (102) by means of multiple irradiations with a beam (105) approaching matrix points of a target matrix in at least two scannings, wherein in each of the scannings, matrix points are approached sequentially. It is characterized through the steps: establishing the maximal tolerance level for local deviation from the intended dose distribution, de-synchronizing the sequence of the irradiation and the cyclical motion of the target region (102), and partitioning the irradiation of the target region (102) in a sufficient number of scannings such that local deviations from the intended dose distribution correspond at most to the maximal tolerance level of deviation from the intended dose distribution. Furthermore, the invention also concerns an irradiation apparatus for executing a process of this type and a process for determining the control parameters for said irradiation apparatus.
