Dark-field images are formed from x-ray small-angle scattering signals. The small-angle scattering signals are particularly sensitive to structural variation and density fluctuation on a length scale of several tens to hundreds of nanometers, offering a unique contrast mechanism to reveal subtle structural features of an object. In this study, based on the principle of energy conservation, we develop a physical model to describe the relationship between x-ray small-angle scattering coefficients of an object and dark-field intensity images. This model can be used to reconstruct volumetric x-ray small-angle scattering images of an object using classical tomographic algorithms. We also establish a relationship between the small-angle scattering intensity and the visibility function measured with x-ray grating imaging. The numerical simulations and phantom experiments have demonstrated the accuracy and practicability of the proposed model.
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