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.
© 2006 Optical Society of America
Original Manuscript: April 28, 2006
Revised Manuscript: June 11, 2006
Manuscript Accepted: June 16, 2006
Vol. 2, Iss. 1 Virtual Journal for Biomedical Optics
Hiroshi Yamazaki, Yoshiki Kohmura, Tatsuyuki Sakurai, and Tetsuya Ishikawa, "Reconstruction of complex-valued electron density with x-ray in-line holograms," J. Opt. Soc. Am. A 23, 3171-3176 (2006)