Abstract: Spectrally resolved detection of ionizing radiation in a detector comprising a chamber (13) filled with an ionizable substance, a radiation entrance (33), an electron avalanche amplification means, and a read-out arrangement (29), comprises introducing a broadband radiation beam (1) into the chamber between and in parallel first and second electrode arrangements for ionization of the ionizable substance and avalanche amplifying said electrons. By means of the read-out arrangement (29) electron avalanches (SX1, SX2, . . . SXN), derivable mainly from ionization in sections (X1, H2, . . . , XN) of the chamber that are separated in the direction of the introduced radiation beam, are separately detected. From spectrally resolved absorption data, weighting factors (W11, W21, . . . , WM1, W12, W22, . . . , WM2, . . . , W1N, W2N, . . . , WMN) for different spectral components (E1, E2, . . . , EM) of the radiation (1) and for different sections (X1, X2, . . .