  The diffraction contrast modalities accessible by X-ray grating
interferometers are not imaged directly but have to be inferred from sine like
signal variations occurring in a series of images acquired at varying relative
positions of the interferometer's gratings. The absolute spatial translations
involved in the acquisition of these phase stepping series usually lie in the
range of only a few hundred nanometers, wherefore positioning errors as small
as 10nm will already translate into signal uncertainties of one to ten percent
in the final images if not accounted for.
  Classically, the relative grating positions in the phase stepping series are
considered input parameters to the analysis and are, for the Fast Fourier
Transform that is typically employed, required to be equidistantly distributed
over multiples of the gratings' period. More general optimization based
approaches with relaxed requirements on the sampling positions are often deemed
too time consuming in contrast.
  In the following, a fast converging optimization scheme is presented
simultaneously determining the phase stepping curves' parameters as well as the
actually performed motions of the stepped grating, including also erroneous
rotational motions which are commonly neglected. While the correction of solely
the translational errors along the stepping direction is found to be sufficient
with regard to the reduction of image artifacts, the possibility to also detect
minute rotations about all axes proves to be a valuable tool for system
calibration and monitoring. The simplicity of the provided algorithm, in
particular when only considering translational errors, makes it well suitable
as a standard evaluation procedure also for large image series.
