Abstract: A radiation detecting arrangement for measuring or counting an ionizing radiation contains a compensating filter arrangement which safequards a measurement of the radiation dose which is either independent of the energy, or independent of both the energy and the direction thereof. The compensating filter arrangement contains a supporting tube made from a slightly absorbing metal having an ordinal number not higher than about 35, which surrounds a tubular radiation detector and which, on its surface, carries several ring-shaped filter parts. These filter parts are made from one or more metal sleeves of a heavy metal or of a heavy metal alloy slipped onto the supporting tube and soldered or cemented thereto. These filter parts, as regards position and shape, are manufactured by a metal-removing process with only the supporting tube being clamped by the metal-removing machine.