Signal-to-noise and spatial resolution in in-line imaging. 3. Optimization using a simple model

The problem of optimization of propagation-based phase-contrast imaging setups is considered in the case of projection X-ray imaging and three-dimensional tomography with phase retrieval. For two-dimensional imaging, a simple model for a homogeneous edge feature embedded in a bulk sample is used to obtain analytical expressions for the image intensity. This model allows for explicit optimization of the geometrical parameters of the imaging setup and the choice of X-ray energy that maximizes the image contrast or the contrast-to-noise ratio. We also consider the question of optimization of the biomedical X-ray imaging quality characteristic which balances the contrast-to-noise against the spatial resolution and the radiation dose. In the three-dimensional case corresponding to propagation-based phase-contrast tomography with phase retrieval according to Paganin's method, the optimization of the imaging setup is studied with respect to the source size, the detector resolution, the geometrical magnification and the X-ray energy. The optimization is performed explicitly only for monochromatic X-ray beams. However, it is shown that the optimizations with respect to magnification and the X-ray energy can be performed independently of each other, and, in particular, the optimal magnification remains the same for all X-ray energies within the validity range of the used approximations.