A novel crystal-analyzer phase retrieval algorithm and its noise property. 
A description of the rocking curve in diffraction enhanced imaging (DEI) is presented in terms of the angular signal response function and a simple multi-information retrieval algorithm based on the cosine function fitting.  A comprehensive analysis of noise properties of DEI is also given considering the noise transfer characteristic of the X-ray source.  The validation has been performed with synchrotron radiation experimental data and Monte Carlo simulations based on the Geant4 toolkit combined with the refractive process of X-rays, which show good agreement with each other.  Moreover, results indicate that the signal-to-noise ratios of the refraction and scattering images are about one order of magnitude better than that of the absorption image at the edges of low-Z samples.  The noise penalty is drastically reduced with the increasing photon flux and visibility.  Finally, this work demonstrates that the analytical method can build an interesting connection between DEI and GDPCI (grating-based differential phase contrast imaging) and is widely suitable for a variety of measurement noise in the angular signal response imaging prototype.  The analysis significantly contributes to the understanding of noise characteristics of DEI images and may allow improvements to the signal-to-noise ratio in biomedical and material science imaging.