X ray radiography and tomography are important tools in medicine as well as in life science and materials science. Not long ago an approach called in-line holography based on simple propagation became possible using partially coherent synchrotron beams like the ones available at the European Synchrotron Radiation Facility (ESRF). Theoretical and experimental work by Cloetens et al. [Appl. Phys. Lett 75, 2912 (1999)] have shown that quantitative retrieval of the optical phase, from a set of radiographs taken at different sample-to-detector distances, is feasible. Mathematically speaking we are dealing with a direct method based on linearization in order to solve an inverse nonlinear problem. The phase retrieval can be combined with classical tomography in order to obtain a three-dimensional representation of the object’s electron density (holotomography). In order to optimize the image contrast for the numerical phase retrieval process, we have carried out calculations resulting in an optimized choice of value and number of the sample-to-detector distances as well as of the photon energy. These results were then confirmed by experiments on the ESRF long beamline ID19.

$\mathrm{Zn}–\mathrm{Mn}{\mathrm{O}}_2$ alkaline batteries were investigated in situ at different stages of electric discharge by synchrotron tomography with monochromatic x rays and by neutron tomography. The spatial distribution and the changes in the morphology of different components of a battery caused by the reduction of $\mathrm{Mn}{\mathrm{O}}_2$ , the dissolution of Zn, and the nucleation and growth of ZnO are investigated with high spatial resolution around several micrometers with x rays. Neutron tomography is used to monitor the changes in the spatial distribution of hydrogen in the $\mathrm{Mn}{\mathrm{O}}_2$ matrix and provides complementary information about the process.