A comprehensive two-step approach to design staircase-type multilevel diffractive phase elements (DPEs) that generate arbitrary desired diffraction patterns with the highest possible accuracy is presented. First a preliminary periodic grating with an unconstrained phase delay and an optimized nonuniform amplitude profile is designed by means of a customized iterative Fourier-transform algorithm. Then this preliminary grating is subjected to a phase quantization in which strict periodicity is forgone in favour of the best possible preservation of the shape of the power spectrum yielding a final phase only DPE with only rudimentary periodicity. An arbitrarily high similarity between the diffraction patterns of the final DPE and the preliminary grating can be achieved independently of the number D of discrete phase delay levels as long as D ≥ 3. The signal-to-noise ratio of the final DPE is close to the theoretical upper limit. These properties are confirmed in computer simulations and demonstrated in optical experiments. Pseudoperiodic DPEs may have applications in optical computing, optical communication and networking, optical authentication, or coherent laser coupling.
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