Optimisation of image reconstruction for phase-contrast x-ray Talbot-Lau imaging with regard to mechanical robustness

X-ray grating-based phase-contrast imaging opens new opportunities, inter alia, in medical imaging and non-destructive testing. Because, information about the attenuation properties and about the refractive properties of an object are gained simultaneously. Talbot-Lau imaging requires the knowledge of a reference or free-field image. The long-term stability of a Talbot-Lau interferometer is related to the time span of the validity of a measured reference image. It would be desirable to keep the validity of the reference image for a day or longer to improve feasibility of Talbot-Lau imaging. However, for example thermal and other long-term external influences result in drifting effects of the phase images. Therefore, phases are shifting over time and the reference image is not valid for long-term measurements. Thus, artifacts occur in differential phase-contrast images. We developed an algorithm to determine the differential phase-contrast image with the help of just one calibration image, which is valid for a long time-period. With the help of this algorithm, called phase-plane-fit method, it is possible to save measurement-time, as it is not necessary to take a reference image for each measurement. Additionally, transferring the interferometer technique from laboratory setups to conventional imaging systems the necessary rigidity of the system is difficult to achieve. Therefore, short-term effects like vibrations or distortions of the system lead to imperfections within the phase-stepping procedure. Consequently, artifacts occur in all three image modalities (differential phase-contrast image, attenuation image and dark-field image) of Talbot-Lau imaging. This is a problem with regard to the intended use of phase-contrast imaging for example in clinical routine or non-destructive testing. In this publication an algorithm of Vargas et al is applied and complemented to correct inaccurate phase-step positions with the help of a principal component analysis (PCA). Thus, it is possible to calculate the artifact free images. Subsequently, the whole algorithm is called PCA minimization algorithm.