  We propose and demonstrate a new phase retrieval method for imaging through
random media. Although methods to recover the Fourier amplitude through random
distortions are well established, recovery of the Fourier phase has been a more
difficult problem and is still a very active research area. Here, we show that
by simply ensemble averaging shift-corrected images, the Fourier phase of an
object obscured by random distortions can be accurately retrieved up to the
diffraction limit. The method is simple, fast, does not have any optimization
parameters, and does not require prior knowledge or assumptions about the
sample. We demonstrate the feasibility and robustness of our method by
realizing all computational diffraction-limited imaging through atmospheric
turbulence as well as imaging through multiple scattering media.
