Respiratory diseases are one of the most common causes of death, and their early detection is crucial for prompt treatment. X-ray dark-field radiography (XDFR) is a promising tool to image objects with unresolved micro-structures such as lungs. Using Talbot-Lau XDFR, we imaged inflated porcine lungs together with Polymethylmethacrylat (PMMA) microspheres (in air) of diameter sizes between 20 and 500 [Formula: see text] over an autocorrelation range of 0.8-5.2 [Formula: see text]. The results indicate that the dark-field extinction coefficient of porcine lungs is similar to that of densely-packed PMMA spheres with diameter of [Formula: see text], which is approximately the mean alveolar structure size. We evaluated that, in our case, the autocorrelation length would have to be limited to [Formula: see text] in order to image [Formula: see text]-thick lung tissue without critical visibility reduction (signal saturation). We identify the autocorrelation length to be the critical parameter of an interferometer that allows to avoid signal saturation in clinical lung dark-field imaging
