This invention relates to design and fabrication of broad-band X-ray focussing devices useful in lithographic production of structures of submicron dimension. Such as those employed in integrated electronic circuits. The designs given here exploit the diffractibility of X-radiation by obstacles and apertures (Figure 1), specifically in the Fresnel or nearfield regime. Devices are described that concentrate at least twofold the intensity of white incident X-radiation whose bandwidth may exceed one octave (Figure 6). Their fabrication requires no methods not already in wide use.