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Reconstruction method for grating-based x-ray phase-contrast images without knowledge of the grating positions

To retrieve the phase information of x-rays using a Talbot-Lau interferometer, the knowledge of the grating positions is mandatory. Transferring the interferometer technique from the laboratory to a conventional x-ray imaging system, this requirement is no longer guaranteed. This is due to distortions and vibrations which are coupled into the interferometer. Therefore, we applied a principal-component analysis to Talbot-Lau x-ray phase-contrast data. In experiments we compared this alternative approach for image reconstruction to the conventional procedure. As a result, a superior robustness of the principal-component analysis against imperfect phase-stepping data was found. Furthermore, using the proposed method, the reconstruction of x-ray phase-contrast images from randomly distributed phase-step positions is possible.