Scatter Ptychography

Coherent illumination reflected by a remote target may be secondarily scattered by intermediate objects or materials. Here we show that phase retrieval on remotely observed images of such scattered fields enables imaging of the illuminated object at resolution proportional to $\lambda R_s/A_s$, where $R_s$ is the range between the scatterer and the target and $A_s$ is the diameter of the observed scatter. This resolution may exceed the resolution of directly viewing the target by the factor $R_cA_s/R_sA_c$, where $R_c$ is the range between the observer and the target and $A_c$ is the observing aperture. Here we use this technique to demonstrate $\approx 32\times$ resolution improvement relative to direct imaging.