X-ray computed tomography is an important tool for evaluating the three dimensional microstructure of modern materials non-destructively. To resolve material structures in the micrometre range and below high brilliance synchrotron radiation has to be taken. But materials of low absorption or mixed phases show a weak absorption contrast at there interfaces. A Contrast enhancement can be achieved by exploiting the refraction of X-rays at interfaces. This technique was developed and applied at the NDT department of the Federal Institute for Materials Research and Testing (BAM) during the last decade. It meets the actual demand for improved non-destructive characterisation of high performance composites, ceramics and other low density materials and components. The technique is based on Ultra Small Angle Scattering (USAXS) by micro structural elements causing phase related effects like refraction and total reflection at a few minutes of arc as the refractive index of X-rays is nearly unity. The extraordinary refraction contrast of inner surfaces is far beyond absorption effects and hence especially useful for materials of low absorption or mixed phases, showing similar X-ray absorption properties. Crack orientation and fibre-matrix debonding in plastics, polymers, ceramics and metal-matrix-composites after cyclic loading and hydro thermal aging can be visualized. By combining the refraction technique with the computed tomography technique the three dimensional imaging of the micro structure of the materials is obtained. In most cases the investigated inner surface and interface structures correlate to mechanical properties. Recent results with a sub-micrometer resolution will be presented.