  Reconstruction of in-line holograms of unknown objects in general suffers
from twin-image artifacts due to the appearance of an out-of-focus image
overlapping with the desired image to be reconstructed. Computer-based
iterative phase retrieval algorithms and learning-based methods have been used
for the suppression of such image artifacts in digital holography. Here we
report an all-optical hologram reconstruction method that can instantly
retrieve the image of an unknown object from its in-line hologram and eliminate
twin-image artifacts without using a digital processor or a computer. Multiple
transmissive diffractive layers are trained using deep learning so that the
diffracted light from an arbitrary input hologram is processed all-optically,
through light-matter interaction, to reconstruct the image of an unknown object
at the speed of light propagation and without the need for any external power.
This passive all-optical processor composed of spatially-engineered
transmissive layers forms a diffractive network, which successfully generalizes
to reconstruct in-line holograms of unknown, new objects and exhibits improved
diffraction efficiency as well as extended depth-of-field at the hologram
recording distance. This all-optical hologram processor and the underlying
design framework can find numerous applications in coherent imaging and
holographic display-related applications owing to its major advantages in terms
of image reconstruction speed and computer-free operation.
