Soft x-ray projection lithography and microscopy require a high throughput and diffraction-limited performance of a multielement imaging system. To meet these requirements for a specific design it is necessary to (1) achieve high normal incidence reflectivity on each optical element while optimizing the d-spacing variation across the surface of the optical element and (2) match the rf-spacing on each optical element to that of the others according to the ray-tracing design. A technique used to achieve normal incidence reflectivity greater than 60% at 13 nm for Mo/Si and greater than 2.7% at the "water window" region for W/B4C coatings is discussed. In addition, methods to obtain a rf-spacing uniformity of ±0.4% and to match the d-spacing between imaging mirrors with an accuracy of ±0.5% are considered. A method for characterizing multilayer coatings on curved surfaces, using cylindrical witness optics with precalculated shape and radius of curvature to simulate final optics, and a manufacturing method for witness optics are also presented.