Reconstruction of complex-valued electron density with x-ray in-line holograms

A reconstruction algorithm is proposed to analyze the complex-valued electron-density distribution in an object with x-ray in-line holograms. The real and imaginary parts of the electron density correspond to local variations of x-ray phase shift and absorption, respectively. In the algorithm, the least-squares error of the holograms is iteratively minimized under sign constraints on the real and imaginary parts. The constraints, which are derived from the physical conditions in the interaction between x rays and materials, facilitate robust reconstruction. The reconstruction was applied to holograms of a biological specimen that caused both phase shift and absorption.