Discussion In summary, we have demonstrated that multi-scale x-ray phase contrast tomography can firstly augment pathohistology of the lung to full three dimensions, and secondly provide a link between microscopic and macroscopic scales. For the first time, characteristic morphological changes associated with DAD such as hyaline membranes and pronounced inflammation have been imaged in three dimensions, in particular in Covid-19, the most severe pandemic which mankind has faced for decades. Moreover, we conducted our study in FFPE material, a fixation method established for well over a century and ubiquitously available. The advantage of 3D histology compared to conventional histology relates to the simple fact that features can be visualized and investigated in their full native dimensionality. This enables the accurate determination of cell densities, the quantification of morphological parameters such as the distance metrics shown in Figure 6, and tracing of blood vessels. Standard histology and in particular immunohistochemical staining, on the other hand, can inform us more precisely on the biomolecular origin of the structure, while immunostaining coupled with x-ray contrast agents is not yet within reach. Importantly, since PC-CT is nondestructive, histology can be performed on well-chosen sections after the scan, see Appendix 1. On the side of imaging technology and exploitation, there is still ample room for improvement: higher resolution could be achieved by further geometric zooms, waveguide optics with higher numerical aperture, in combination with pixel detector technology, and further improvements in holographic reconstruction. Equally important to extend the length scales covered to small scales is the further upscaling of the FOV based on stitching different sub-tomograms. At the same time the scales should be extended by including more than two zoom levels, based on different detector and illumination settings. In this way, one could bridge scales to cover the entire lobe of a lung. To this end, optimized recording and data flow is a larger bottleneck than photons and optics, in particular since 4th generation synchrotron radiation sources are about to deliver unprecedented brilliance. Finally, in view of exploitation and information gain, specific labels for different cell types and 3D immunostaining coupled to radiocontrast agents should be developed. Here, lung offers an advantage over other tissue in view of volume accessibility and label diffusivity. Most importantly, efforts have to be directed to exploit the full information contained in the reconstruction volumes based on advanced segmentation. Tracing of capillaries is an obvious important next step, in view of unraveling the role of intussusceptive angiogenesis in Covid-19 (Ackermann et al., 2020). The current data, which are made fully available at https://doi.org/10.5281/zenodo.3892637, are likely to already provide such clues once that more advanced segmentation approaches based on machine learning are applied. More generally, it may advance our understanding of DAD in the particular case of Covid-19, as an intrinsically volumetric phenomenon. Beyond the current data, further studies could shed further light on the differences between moderate and severe progression. Possibly, phase contrast tomography of lung biopsies could in future also help diagnosis and treatment.