Direct mapping of fiber diffraction patterns into reciprocal space

On the basis of the concept of Polanyi [Z. Phys. (1921), 7, 149-180], the mapping of fiber diffraction patterns into reciprocal space is revisited. The result is a set of concise mapping relations that does not contain any approximations. This set permits the design of a direct method that, in principle, does not require refinement of mapping parameters even for patterns of tilted fibers. The method is unsuitable for diffuse scattering patterns. If inaccuracies of two pixels can be tolerated, a pattern is automatically mapped into reciprocal space in real time. The method is proposed for the processing of the extensive sets of patterns that are recorded in time-resolved wide-angle X-ray diffraction investigations of polymer materials.