Initial phase pre-encoded design of cascaded diffractive optical elements with enhanced azimuthal robustness for multi-channel reconfigurable holography

Multi-channel reconfigurable holography based on cascaded diffractive optical elements (DOEs) with channel multiplexing achieved by rotating one DOE to pre-defined azimuthal angles benefits from the degrees of freedom in design, but its performance can be significantly affected by even slight azimuthal angle deviation. So far, cascaded DOEs are usually designed using computer algorithms combined with diffraction model to calculate the target phase distributions, with a random initial phase distribution. Currently, the best reported rotated azimuthal angle deviation is up to 0.5° [1]. Deviation beyond this will prevent the achievement of designed performance. Such small azimuthal angle rotation tolerance limits their application in practical scenario. In this work, we proposed for the first time a new strategy on phase initialization for cascaded DOEs design to achieve enhanced azimuthal robustness, addressing the aforementioned issue. Unlike random initial phase given in the algorithm-based design process, our approach employs a per-encoded initialized phase, which is embedded with the structural information of all target patterns. The obtained results show that cascaded DOE designed using the iterative Fourier transform algorithm (IFTA) with pre-encoded phase initialization enables an enlarged rotational angle misalignment tolerance of 1.79°. This is 3.6 times broader than the reported best result (approximately 0.5°) in literature and demonstrates a significant enhancement of azimuthal robustness. In addition, this cascaded DOEs have a root mean square error (RMSE) of 0.0542 ± 0.0001, diffraction efficiency of 9.64% ± 0.13%, and correlation coefficient of 0.4672 ± 0.0096. It exhibits a reduced RMSE and a comparable diffraction efficiency and correlation coefficient, but with less deviations, compared to the cascaded DOEs designed using the same algorithm but with random initial phase, which yields a RMSE, diffraction efficiency and correlation coefficient of 0.0563 ± 0.0002, 10.07% ± 0.25%, and 0.4677 ± 0.0173, respectively. This demonstrates a suppressed background noise (indicated by decreased RMSE) and an improved consistency among the reconstructed images (indicated by the deviation decrease in diffraction efficiency and correlation coefficient across different channels). The enhancement in both the imaging performance and the azimuthal robustness of cascaded DOEs demonstrate the capabilities of our approach enabling a generalizable framework of cascaded DOEs design for multi-channel reconfigurable holography.