The present disclosure relates to a method and to an irradiation system for irradiating a moving target volume with an ion beam, in particular for tumor therapy, wherein ion radiography measurements of the target volume are performed and the irradiation for deposition purposes and for radiography purposes is performed with the same ion beam but consecutively in time by alternating the energy of the ion beam between a higher radiography energy and a lower deposition energy using, for example, a passive energy modulator proximal with respect to the patient.