In this work, a characterization and optimization of the grating-based x-ray imaging technique is presented. The investigations are introduced by analytical considerations, are underpinned with numerical simulations and validated using exemplary experiments. A detailed examination of the image formation in a grating interferometer is given, highlighting the dependence of the measured signal on the profile of the gratings. Subsequently, it is shown analytically and in experiments that grating-based imaging can be performed using three basic grating arrangements, which differ in their requirements on grating fabrication and experimental implementation. By a characterization of the measurement signal for each arrangement, a dependence of the signal strength on the sample position within the interferometer is identified. The consecutive evaluation of the impact of this position dependence on radiographic and tomographic data leads to the derivation of optimized reconstruction algorithms and to a correction of resulting image artifacts. Additionally, it is shown that the simultaneous measurement of attenuation and phase images allows the determination of the atomic number of the sample, opening new possibilities for material discrimination. Apart from these investigations on the contrast formation, various imperfections of the technique are investigated: The properties of the image noise are examined in a detailed statistical analysis, yielding a fundamental understanding of the signal-to-noise behavior of the three available contrast channels. Additionally, beam-hardening artifacts at polychromatic x-ray sources are investigated and their correction by a linearization approach is resented. By a subsequent analysis of the influence of various different grating imperfections on the image quality, tolerance limits for grating fabrication are specified. Furthermore, analytical considerations show that gratings with a duty cycle of 1/3 are advantageous with respect to the signal-to-noise ratio in comparison to common gratings with a duty cycle of 1/2. In conclusion, the results, concepts and methods developed in this work broaden the understanding of grating-based x-ray imaging and constitute a step forward towards the practical implementations of the technique in imaging applications.

In this work, a characterization and optimization of the grating-based x-ray imaging technique is presented. The investigations are introduced by analytical considerations, are underpinned with numerical simulations and validated using exemplary experiments. A detailed examination of the image formation in a grating interferometer is given, highlighting the dependence of the measured signal on the profile of the gratings. Subsequently, it is shown analytically and in experiments that grating-based imaging can be performed using three basic grating arrangements, which differ in their requirements on grating fabrication and experimental implementation. By a characterization of the measurement signal for each arrangement, a dependence of the signal strength on the sample position within the interferometer is identified. The consecutive evaluation of the impact of this position dependence on radiographic and tomographic data leads to the derivation of optimized reconstruction algorithms and to a correction of resulting image artifacts. Additionally, it is shown that the simultaneous measurement of attenuation and phase images allows the determination of the atomic number of the sample, opening new possibilities for material discrimination. Apart from these investigations on the contrast formation, various imperfections of the technique are investigated: The properties of the image noise are examined in a detailed statistical analysis, yielding a fundamental understanding of the signal-to-noise behavior of the three available contrast channels. Additionally, beam-hardening artifacts at polychromatic x-ray sources are investigated and their correction by a linearization approach is resented. By a subsequent analysis of the influence of various different grating imperfections on the image quality, tolerance limits for grating fabrication are specified. Furthermore, analytical considerations show that gratings with a duty cycle of 1/3 are advantageous with respect to the signal-to-noise ratio in comparison to common gratings with a duty cycle of 1/2. In conclusion, the results, concepts and methods developed in this work broaden the understanding of grating-based x-ray imaging and constitute a step forward towards the practical implementations of the technique in imaging applications.