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End-to-end optimization of diffractive optical elements (DOEs) profile through a digital differentiable model combined with computational imaging have gained an increasing attention in emerging applications due to the compactness of resultant physical setups. Despite recent works have shown the potential of this methodology to design optics, its performance in physical setups is still limited and affected by manufacturing artifacts of DOE, mismatch between simulated and resultant experimental point spread functions, and calibration errors. Additionally, the computational burden of the digital differentiable model to effectively design the DOE is increasing, thus limiting the size of the DOE that can be designed. To overcome the above mentioned limitations, the broadband imaging system with phase-only spatial light modulator (SLM) as an encoded DOE is proposed and developed in this paper. A co-design of the SLM phase pattern and image reconstruction algorithm is produced following the end-to-end strategy, using for optimization a convolutional neural network equipped with quantitative and qualitative loss functions. The optics of the imaging system is hybrid consisting of SLM as DOE and refractive lens. SLM phase-pattern is optimized by applying the Hardware-in-the-loop technique, which helps to eliminate the mismatch between numerical modeling and physical reality of image formation as light propagation is not numerically modeled but is physically done. In our experiments, the hybrid optics is implemented by the optical projection of the SLM phase-pattern on a lens plane for a depth range 0.4-1.9m. Comparison with compound multi-lens optics such as Sony A7 III and iPhone Xs Max cameras show that the proposed system is advanced in all-in-focus sharp imaging.