Hexagonal Diffractive Optical Elements and Phase Retrieval Algorithms

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Diffractive Optical Elements (DOEs) play a pivotal role in computational imaging, offering diverse applications across various fields. The traditional use of Cartesian grids in DOE design, however, presents limitations in terms of anisotropy and fabrication precision. To address these challenges, this research introduces a novel approach that integrates hexagonal grids into DOE design, leveraging their superior isotropy and fabrication accuracy. The study establishes a 2D hexagonal arrangement and a specialized hexagonal fast Fourier transform for efficient simulation and design, enabling seamless integration into existing optimization frameworks. The application of the proposed approach is demonstrated in holography, showcasing its effectiveness in simulation accuracy and practical implementations. Rigorous testing of the fabricated DOEs, including comparisons with their Cartesian counterparts, validates the advantages of the hexagonal grid-based design methodology. This work contributes to the advancement of computational imaging techniques, offering a comprehensive approach to harnessing the benefits of hexagonal grids in DOE design.