Quantitative diffraction-enhanced x-ray imaging of weak objects

Theoretical aspects of quantitative diffraction-enhanced imaging of weak objects are considered using the Fourier optics approach. The amplitude and phase transfer functions are introduced by analogy with the well-known case of in-line (holographic) imaging. The inverse problem of the reconstruction of the phase and amplitude of the incident wave from recorded images is solved in the case of non-absorbing objects and objects consisting of a single material and in the general case of objects with uncorrelated refraction and absorption characteristics. A comparison is given between the solutions to the inverse problem obtained using the new formalism and the geometric-optics approximation.