The use of the diffractive optical element (DOE) can often significantly reduce the size and enhance the performance of the optical system, but it is mostly prevented by low diffraction efficiency and serious speckle noise due to the quantization error. In this paper, an error tracking-control-reduction (ETCR) algorithm is proposed to suppress the quantization error, which adjusts the accumulative action, controls the current state and predicts the trend of the error. The simulation and experiment results verify that the ETCR algorithm has high diffraction efficiency which can be comparable with the Gerchberg-Saxton (GS) and Modified GS algorithms. Furthermore, the root-mean-square error (RMSE) of the proposed algorithm is significantly lower than that of the GS and MGS algorithms. Based on the proposed method, a 2-level DOE has been designed and fabricated to generate several grey images with only 0.05 RMSE.

中文翻译：

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设计具有高图像重建质量的衍射光学元件的误差跟踪控制减少算法

衍射光学元件（DOE）的使用通常可以显着减小尺寸并增强光学系统的性能，但是由于量化误差而导致的低衍射效率和严重的斑点噪声在很大程度上防止了衍射光学元件的使用。本文提出了一种误差跟踪控制减少算法（ETCR）来抑制量化误差，从而调节累加作用，控制当前状态并预测误差趋势。仿真和实验结果验证了ETCR算法具有较高的衍射效率，可以与Gerchberg-Saxton（GS）算法和Modified GS算法相媲美。此外，该算法的均方根误差（RMSE）明显低于GS和MGS算法。根据提出的方法，