  The x-ray near-field speckle-scanning concept is an approach recently
introduced to obtain absorption, phase, and dark-field images of a sample. In
this paper, we present ways of recovering from a sample its ultrasmall-angle
x-ray scattering distribution using numerical deconvolution. We also show how
to access the 2D phase gradient signal from random step scans, the latter
having the potential to elude the flat-field correction error. Each feature is
explained theoretically and demonstrated experimentally at a synchrotron x-ray
facility.
