High-pass-filtered diffraction microtomography by coherent hard x rays for cell imaging: theoretical and numerical studies of the imaging and reconstruction principles.

This paper presents theoretical and numerical studies of diffraction tomography using hard x rays, from the viewpoint of imaging and reconstruction methods for cell imaging. The proposed system employs a single-perfect-crystal analyzer in symmetric Laue-case transmission geometry to efficiently detect the higher spatial frequency components of an object's refractive-index distribution, and to effectively suppress interference between the unperturbated wave field and the wave field diffracted by the object. This system features acquisition of a single projection by a single exposure using a simple geometry and aggressive use of diffracted x rays. We present the physical description of the imaging method using the Fourier diffraction theorem derived from the Born approximation. First, we demonstrate that the reconstruction leads to the phase-retrieval problem. We then describe a reconstruction algorithm based on the classical Gerchberg-Saxton-Fienup algorithm. Finally, we show the efficacy of this system by computer simulation. Our simulation demonstrates that the imaging system delineates microstructure 3.5 microm in diameter in a phase object 400 microm in diameter.