Diffractive optical elements (DOEs) are promising lens candidates in computational imaging because they candrastically reduce the size and weight of image systems. The inherent strong dispersion hinders the direct useof DOEs in full spectrum imaging, causing an unacceptable loss of color fidelity. State-of-the-art methods ofdesigning diffractive achromats either rely on hand-crafted point spread functions (PSFs) as the intermediatemetric, or frame a differential end-to-end design pipeline that interprets a 2D lens with limited pixels and onlya few wavelengths.In this work, we investigate the joint optimization of achromatic DOE and image processing using a fulldifferentiable optimization model that maps the actual source image to the reconstructed one. This modelincludes wavelength-dependent propagation block, sensor sampling block, and imaging processing block. Wejointly optimize the physical height of DOEs and the parameters of image processing block to minimize theerrors over a hyperspectral image dataset. We simplify the rotational symmetric DOE to 1D profile to reduce thecomputational complexity of 2D propagation. The joint optimization is implemented using auto differentiation ofTensorow to compute parameter gradients. Simulation results show that the proposed joint design outperformsconventional methods in preserving higher image fidelity.
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