  Under spatially-coherent light, a diffractive optical network composed of
structured surfaces can be designed to perform any arbitrary complex-valued
linear transformation between its input and output fields-of-view (FOVs) if the
total number (N) of optimizable phase-only diffractive features is greater than
or equal to ~2 Ni x No, where Ni and No refer to the number of useful pixels at
the input and the output FOVs, respectively. Here we report the design of a
spatially-incoherent diffractive optical processor that can approximate any
arbitrary linear transformation in time-averaged intensity between its input
and output FOVs. Under spatially-incoherent monochromatic light, the
spatially-varying intensity point spread functon(H) of a diffractive network,
corresponding to a given, arbitrarily-selected linear intensity transformation,
can be written as H(m,n;m',n')=|h(m,n;m',n')|^2, where h is the
spatially-coherent point-spread function of the same diffractive network, and
(m,n) and (m',n') define the coordinates of the output and input FOVs,
respectively. Using deep learning, supervised through examples of input-output
profiles, we numerically demonstrate that a spatially-incoherent diffractive
network can be trained to all-optically perform any arbitrary linear intensity
transformation between its input and output if N is greater than or equal to ~2
Ni x No. These results constitute the first demonstration of universal linear
intensity transformations performed on an input FOV under spatially-incoherent
illumination and will be useful for designing all-optical visual processors
that can work with incoherent, natural light.
