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The size of the smallest detectable sample feature in an x-ray imaging systemis usually restricted by the spatial resolution of the system. This limitationcan now be overcome using the diffusive dark-field signal, which is generatedby unresolved phase effects or the ultra-small-angle x-ray scattering fromunresolved sample microstructures. A quantitative measure of this dark-fieldsignal can be useful in revealing the microstructure size or material formedical diagnosis, security screening and materials science. Recently, wederived a new method to quantify the diffusive dark-field signal in terms of ascattering angle using a single-exposure grid-based approach. In thismanuscript, we look at the problem of quantifying the sample microstructuresize from this single-exposure dark-field signal. We do this by quantifying thediffusive dark-field signal produced by 5 different sizes of polystyrenemicrospheres, ranging from 1.0 $\mu$m to 10.8 $\mu$m, to investigate how thestrength of the dark-field signal changes with the sample microstructure size,$S$. We also explore the feasibility of performing single-exposure dark-fieldimaging with a simple equation for the optimal propagation distance givenmicrostructure with a specific size and thickness, and successfully verify thisequation with experimental data. Our theoretical model predicts that thedark-field scattering angle is inversely proportional to $\sqrt{S}$, which isconsistent with our experimental data.

Single-exposure x-ray dark-field imaging: quantifying sample microstructure using a single-grid setup