Error tracking-control-reduction algorithm for designing diffractive optical element with high image reconstruction quality

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.