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MULTILAYER REFLECTORS FOR SOFT X-RAYS.Current technology has made possible the fabrication of multilayered optical elements for soft x-ray radiation. These structures find a variety of important applications. Difficulties in the design and fabrication of multilayers for soft x-rays are related to the lack of information about the properties of materials in the very thin layers (~5-100 Å) required. Imperfections cause the measured optical properties of the multilayers to deviate strongly from ideal behavior. Realistic calculations of reflectance must take these imperfections into account. We review the pertinent theory, with attention to the problem of including non-ideal properties. We also review characterization techniques suitable for the measurement of relevant structural and stoichiometric parameters of the multilayer. A detailed characterization procedure is presented. This procedure is capable of accurately determining the layer thicknesses, material densities, interfacial rms roughness or diffusion values, crystalline structure, concentration of contaminants, and extent of surface oxidation. The techniques used included low-angle x-ray θ-2θ diffraction with parallel-beam and Bragg-Brentano geometries, wide-film Debye-Scherrer ("Read") camera and Seemann-Bohlin diffractometer, Rutherford backscattering spectroscopy, and transmission electron microscopy. Si/W multilayer mirrors were designed for normal-incidence 210 Å radiation. Samples were fabricated using a magnetically-confined-plasma dc-triode sputtering technique. Our characterization procedure was applied to these samples. To our knowledge, this is the first time such a comprehensive set of characterization techniques has been applied to a multilayer x-ray optical element. The same samples were tested with synchrotron radiation over a wide spectral range, and for several incidence angles. The measured reflectance is in excellent agreement with curves calculated using the information obtained from the characterization results, with no adjustable parameters. The Si/W combination is shown to have good layering characteristics. The near-normal reflectance of the multilayers was 20 to 30 times better than the reflectivity of the best single-surface mirrors at the same wavelengths.