The objective of the research program is to investigate the use of collimating optics with a transition-radiation source to produce a low cost, laboratory scale, intense, focused, soft x- ray source for spectroscopy. As has been seen from the rapid rise in the use of synchrotron radiation, bright, relatively inexpensive x-ray sources are needed for materials studies and other scientific and medical research. An x-ray system will be constructed. This system consists of a transition radiator and collimating optics, which will permit the entire radiation cone to be focused to a 1 - 2 mm2 spot. Flexible capillary tubes will permit the direction of the x-rays to be changed. Phase I research will be used to test the optics and the feasibility of the source for spectroscopy. A computer-driven ray-tracing program has been developed to optimize the design of the x-ray optics. Preliminary experiments at Adelphi have shown that x-rays in the 1 - 3 ke V spectra range can be focused to a 2 mm diameter spot at a distance of 1.35 m from the source. The principal investigator and his colleagues were the first to observe soft x- rays from transition radiators and show focusing of the radiation of large distances from the radiator.