In this paper, we demonstrate two image reconstruction schemes for continuously self-imaging gratings (CSIGs). CSIGs are diffractive optical elements that generate a depth-invariant propagation pattern and sample objects with a sparse spatial frequency spectrum. To compensate for the sparse sampling, we apply two methods with different regularizations for CSIG imaging. The first method employs continuity of the spatial frequency spectrum, and the second one uses sparsity of the intensity pattern. The two methods are demonstrated with simulations and experiments.
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