  Quantitative phase imaging (QPI) is a label-free computational imaging
technique used in various fields, including biology and medical research.
Modern QPI systems typically rely on digital processing using iterative
algorithms for phase retrieval and image reconstruction. Here, we report a
diffractive optical network trained to convert the phase information of input
objects positioned behind random diffusers into intensity variations at the
output plane, all-optically performing phase recovery and quantitative imaging
of phase objects completely hidden by unknown, random phase diffusers. This QPI
diffractive network is composed of successive diffractive layers, axially
spanning in total ~70 wavelengths; unlike existing digital image reconstruction
and phase retrieval methods, it forms an all-optical processor that does not
require external power beyond the illumination beam to complete its QPI
reconstruction at the speed of light propagation. This all-optical diffractive
processor can provide a low-power, high frame rate and compact alternative for
quantitative imaging of phase objects through random, unknown diffusers and can
operate at different parts of the electromagnetic spectrum for various
applications in biomedical imaging and sensing. The presented QPI diffractive
designs can be integrated onto the active area of standard CCD/CMOS-based image
sensors to convert an existing optical microscope into a diffractive QPI
microscope, performing phase recovery and image reconstruction on a chip
through light diffraction within passive structured layers.
