  We report a new coherent imaging technique, termed ptychographic structured
modulation (PSM), for quantitative super-resolution microscopy. In this
technique, we place a thin diffuser (i.e., a scattering lens) in between the
sample and the objective lens to modulate the complex light waves from the
object. The otherwise inaccessible high-resolution object information can thus
be encoded into the captured images. We then employ a ptychographic phase
retrieval process to jointly recover the exit wavefront of the complex object
and the unknown diffuser profile. Unlike the illumination-based
super-resolution approach, the recovered image of our approach depends upon how
the complex wavefront exits the sample - not enters it. Therefore, the sample
thickness becomes irrelevant during reconstruction. After recovery, we can
propagate the super-resolution complex wavefront to any position along the
optical axis. We validate our approach using a resolution target, a
quantitative phase target, a two-layer sample, and a thick PDMS sample. We
demonstrate a 4.5-fold resolution gain over the diffraction limit. We also show
that a 4-fold resolution gain can be achieved with as few as ~30 images. The
reported approach may provide a quantitative super-resolution strategy for
coherent light, X-ray, and electron imaging.
