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End-to-end optimization of diffractive optical elements (DOEs) profilethrough a digital differentiable model combined with computational imaging havegained an increasing attention in emerging applications due to the compactnessof resultant physical setups. Despite recent works have shown the potential ofthis methodology to design optics, its performance in physical setups is stilllimited and affected by manufacturing artifacts of DOE, mismatch betweensimulated and resultant experimental point spread functions, and calibrationerrors. Additionally, the computational burden of the digital differentiablemodel to effectively design the DOE is increasing, thus limiting the size ofthe DOE that can be designed. To overcome the above mentioned limitations, thebroadband imaging system with phase-only spatial light modulator (SLM) as anencoded DOE is proposed and developed in this paper. A co-design of the SLMphase pattern and image reconstruction algorithm is produced following theend-to-end strategy, using for optimization a convolutional neural networkequipped with quantitative and qualitative loss functions. The optics of theimaging system is hybrid consisting of SLM as DOE and refractive lens. SLMphase-pattern is optimized by applying the Hardware-in-the-loop technique,which helps to eliminate the mismatch between numerical modeling and physicalreality of image formation as light propagation is not numerically modeled butis physically done. In our experiments, the hybrid optics is implemented by theoptical projection of the SLM phase-pattern on a lens plane for a depth range0.4-1.9m. Comparison with compound multi-lens optics such as Sony A7 III andiPhone Xs Max cameras show that the proposed system is advanced in all-in-focussharp imaging.

Hybrid Diffractive Optics Design via Hardware-in-the-Loop Methodology for Achromatic Extended-Depth-of-Field Imaging