  X-ray grating interferometry allows for the simultaneous acquisition of
attenuation, differential-phase contrast, and dark-field images, resulting from
X-ray attenuation, refraction, and small-angle scattering, respectively. The
modulated phase grating (MPG) interferometer is a recently developed grating
interferometry system capable of generating a directly resolvable interference
pattern using a relatively large period grating envelope function that is
sampled at a pitch that allows for X-ray spatial coherence using a microfocus
X-ray source or by use of a source G0 grating that follows the Lau condition.
We present the theory of the MPG interferometry system for a 2-dimensional
staggered grating, derived using Fourier optics, and we compare the theoretical
predictions with experiments we have performed with a microfocus X-ray system
at Pennington Biomedical Research Center, LSU. The theoretical and experimental
fringe visibility is evaluated as a function of grating-to-detector distance.
Quantitative experiments are performed with porous carbon and alumina samples,
and qualitative analysis of attenuation and dark-field images of a dried
anchovy are shown.
