  The power-balanced hybrid optical imaging system is a special design of a
diffractive computational camera, introduced in this paper, with image
formation by a refractive lens and Multilevel Phase Mask (MPM). This system
provides a long focal depth with low chromatic aberrations thanks to MPM and a
high energy light concentration due to the refractive lens. We introduce the
concept of optical power balance between the lens and MPM which controls the
contribution of each element to modulate the incoming light. Additional unique
features of our MPM design are the inclusion of quantization of the MPM's shape
on the number of levels and the Fresnel order (thickness) using a smoothing
function. To optimize optical power-balance as well as the MPM, we build a
fully-differentiable image formation model for joint optimization of optical
and imaging parameters for the proposed camera using Neural Network techniques.
Additionally, we optimize a single Wiener-like optical transfer function (OTF)
invariant to depth to reconstruct a sharp image. We numerically and
experimentally compare the designed system with its counterparts, lensless and
just-lens optical systems, for the visible wavelength interval (400-700)nm and
the depth-of-field range (0.5-$\infty$m for numerical and 0.5-2m for
experimental). The attained results demonstrate that the proposed system
equipped with the optimal OTF overcomes its counterparts (even when they are
used with optimized OTF) in terms of reconstruction quality for off-focus
distances. The simulation results also reveal that optimizing the optical
power-balance, Fresnel order, and the number of levels parameters are essential
for system performance attaining an improvement of up to 5dB of PSNR using the
optimized OTF compared with its counterpart lensless setup.
