X-ray coherence evolution in the imaging process plays a key role for x-ray phase-sensitive imaging. In this work we present a phase-space formulation for the phase-sensitive imaging. The theory is reformulated in terms of the cross-spectral density and associated Wigner distribution. The phase-space formulation enables an explicit and quantitative account of partial coherence effects on phase-sensitive imaging. The presented formulas for x-ray spectral density at the detector can be used for performing accurate phase retrieval and optimizing the phase-contrast visibility. The concept of phase-space shearing length derived from this phase-space formulation clarifies the spatial coherence requirement for phase-sensitive imaging with incoherent sources. The theory has been applied to x-ray Talbot interferometric imaging as well. The peak coherence condition derived reveals new insights into three-grating-based Talbot-interferometric imaging and gratings-based x-ray dark-field imaging.
© 2008 Optical Society of America
Coherence and Statistical Optics
Original Manuscript: February 4, 2008
Revised Manuscript: April 24, 2008
Manuscript Accepted: April 25, 2008
Published: May 15, 2008
Xizeng Wu and Hong Liu, "Phase-space evolution of x-ray coherence in phase-sensitive imaging," Appl. Opt. 47, E44-E52 (2008)