  We introduce a single-frame diffractive imaging method called randomized
probe imaging (RPI). In RPI, a sample is illuminated by a structured probe
field containing speckles smaller than the sample's typical feature size.
Quantitative amplitude and phase images are then reconstructed from the
resulting far-field diffraction pattern. The experimental geometry of RPI is
straightforward to implement, requires no near-field optics, and is applicable
to extended samples. When the resulting data are analyzed with a complimentary
algorithm, reliable reconstructions which are robust to missing data are
achieved. To realize these benefits, a resolution limit associated with the
numerical aperture of the probe-forming optics is imposed. RPI therefore offers
an attractive modality for quantitative X-ray phase imaging when temporal
resolution and reliability are critical but spatial resolution in the tens of
nanometers is sufficient. We discuss the method, introduce a reconstruction
algorithm, and present two proof-of-concept experiments: one using visible
light, and one using soft X-rays.
