An improved radiation window comprises a film permeable to radiation disposed on a support structure. The support structure comprises a primary transmissive area comprising a plurality of support members defining a plurality of apertures for radiation to pass through; a flange disposed around the periphery of the primary transmissive area having generally greater mechanical rigidity than the primary transmissive area; and a transition region disposed between, and contiguous with, the primary transmissive area and the flange; the transition region having generally greater mechanical rigidity than the primary transmissive area and generally lesser mechanical rigidity than the flange, thereby providing an intermediate rigidity transition between the dissimilar rigidities of the primary transmissive area and the flange. A radiation detection system comprises a sensor configured to detect radiation, disposed behind such an improved radiation window.