A target structure (T) made by lithography or used in lithography is inspected by irradiating the structure at least a first time with EUV radiation (304) generated by inverse Compton scattering. Radiation (308) scattered by the target structure in reflection or transmission is detected (312) and properties of the target structure are calculated by a processor (340) based on the detected scattered radiation. The radiation may have a first wavelength in the EUV range of 0.1 nm to 125 nm. Using the same source and controlling an electron energy, the structure may be irradiated multiple times with different wavelengths within the EUV range, and/or with shorter (x-ray) wavelengths and/or with longer (UV, visible) wavelengths. By rapid switching of electron energy in the inverse Compton scattering source, irradiation at different wavelengths can be performed several times per second.