The feasibility of optical systems for short wavelength radiations ranging from the near uv to soft x rays is supported by theoretical and experimental arguments. The major problem of absorption of these radiations by materials has been overcome in the near and middle uv by using the lens properties of a Fresnel zone plate generated on a thin self-supporting film. In typical experiments with narrow field objects, it is shown that the zone plate behaves like a diffraction-limited lens, the gain in resolution is noticeable as the wavelength decreases, the use of the third-order focus improves the resolution of the system, and under certain conditions the depth of field can be increased without loss of resolution. The chromatic aberrations of the zone plate are not restrictive for a large number of applications.