Efficient Decoding of 2D Structured Illumination with Linear Phase Stepping in X-Ray Phase Contrast and Dark-Field Imaging

The ability to map the phase distribution and lateral coherence of an x-ray wavefront offers the potential for imaging the human body through phase contrast, without the need to deposit significant radiation energy. The classic means to achieve this goal is structured illumination, in which a periodic intensity modulation is introduced into the image, and changes in the phase distribution of the wavefront are detected as distortions of the modulation pattern. Two-dimensional periodic patterns are needed to fully characterize a transverse wavefront. Traditionally, the information in a 2D pattern is retrieved at high resolution by acquiring multiple images while shifting the pattern over a 2D matrix of positions. Here we describe a method to decode 2D periodic patterns with single-axis phase stepping, without either a loss of information or increasing the number of sampling steps. The method is created to reduce the instrumentation complexity of high-resolution 2D wavefront sensing in general. It is demonstrated with motionless electromagnetic phase stepping and a flexible processing algorithm in x-ray dark-field and phase contrast imaging.