  Depth of field is an important factor of imaging systems that highly affects
the quality of the acquired spatial information. Extended depth of field (EDoF)
imaging is a challenging ill-posed problem and has been extensively addressed
in the literature. We propose a computational imaging approach for EDoF, where
we employ wavefront coding via a diffractive optical element (DOE) and we
achieve deblurring through a convolutional neural network. Thanks to the
end-to-end differentiable modeling of optical image formation and computational
post-processing, we jointly optimize the optical design, i.e., DOE, and the
deblurring through standard gradient descent methods. Based on the properties
of the underlying refractive lens and the desired EDoF range, we provide an
analytical expression for the search space of the DOE, which is instrumental in
the convergence of the end-to-end network. We achieve superior EDoF imaging
performance compared to the state of the art, where we demonstrate results with
minimal artifacts in various scenarios, including deep 3D scenes and broadband
imaging.
