Quantification of the dark-field signal and its linear decomposition approximation of packed spheres

Grating based X-ray dark-field chest imaging using a Talbot-Lau interferometer is a promising technique for the early detection of emphysema and fibrosis. In this study, we focus on the densely packed spheres because the dark-field signals generated by different sizes are similar to those of real lung tissue and we introduce a theoretical model for calculating the dark-field signal of monodisperse packed spheres and use our model to fit experimental data. Then, we examine the dark-field signal of a polydisperse system composed of two different sizes of spheres mixed with equal mass, and explore the theoretical model in the context of polydispersion.