  As an optical processor, a Diffractive Deep Neural Network (D2NN) utilizes
engineered diffractive surfaces designed through machine learning to perform
all-optical information processing, completing its tasks at the speed of light
propagation through thin optical layers. With sufficient degrees-of-freedom,
D2NNs can perform arbitrary complex-valued linear transformations using
spatially coherent light. Similarly, D2NNs can also perform arbitrary linear
intensity transformations with spatially incoherent illumination; however,
under spatially incoherent light, these transformations are non-negative,
acting on diffraction-limited optical intensity patterns at the input
field-of-view (FOV). Here, we expand the use of spatially incoherent D2NNs to
complex-valued information processing for executing arbitrary complex-valued
linear transformations using spatially incoherent light. Through simulations,
we show that as the number of optimized diffractive features increases beyond a
threshold dictated by the multiplication of the input and output
space-bandwidth products, a spatially incoherent diffractive visual processor
can approximate any complex-valued linear transformation and be used for
all-optical image encryption using incoherent illumination. The findings are
important for the all-optical processing of information under natural light
using various forms of diffractive surface-based optical processors.
