The invention relates to a method and an irradiation installation for irradiating a moving target volume with an ion beam, particularly for the purpose of tumour therapy. Ion radiography measurements are carried out for said target volume, and the irradiation for the deposition and for the radiography are carried out using the same ion beam but in a temporally consecutive manner, with the power of the ion beam being switched between a higher radiography power and a lower deposition power using, for example, a passive power modulator proximal to the patient.