Due to their exceptional properties, such as high coherence, brightness, monochromaticity, and directivity, lasers find extensive use in various fields, including material processing, communication, medical treatment, and semiconductor heat treatment. However, the typical output of a laser cavity emits a Gaussian distributed beam, which is mostly unsuitable for practical use. Therefore, it is necessary to shape the output Gaussian beam to fulfill specific requirements regarding shape and energy distribution. Herein, a novel algorithm is proposed, building upon the mixed-region amplitude freedom (MRAF) algorithm. The objective is to achieve a highly uniform and efficiently diffracted spot. Unlike the static mode of amplitude limitation seen in traditional Gerchberg-Saxton(GS) and MRAF algorithms, the proposed algorithm employs a dynamic amplitude limitation mode. This dynamic mode effectively preserves the initial phase matching with the target spot while effectively utilizing the dead zone of the diffractive optical element (DOE) edge. As a result, a high diffraction efficiency and high uniformity spots are obtained, and the speckle noise in the non-signal area is well suppressed.

The traditional GS algorithm has proven effective in obtaining satisfactory results for circular/annular and rectangular flat-top beams. However, when applied to the triangular light spot proposed in this paper, it does no yield ideal outcomes. The reason behind this discrepancy is that the triangular light spot and spherical initial phase do not align perfectly, resulting in residual dead zones at the edge of the DOE. Consequently, remarkable errors are observed. On the other hand, using only the MRAF algorithm would severely damage the alignment between the initial phase and the target light spot, resulting in low efficiency. To overcome these limitations, this paper introduces a dynamic amplitude limiting mode that enables iterative optimization of the target light spot. To initiate the optimization process, the phase coefficient Z is optimized through amplitude limiting across the entire region. This optimization helps determine an optimal initial Zvalue within a certain range, thereby obtaining an optimal initial phase form (Fig. 4). Subsequently, segmented iterative optimization is performed using the hill-climbing neighborhood algorithm (Fig. 7). The traditional GS algorithm, the MRAF algorithm, and the improved algorithm proposed in this paper are compared to analyze the difference in effects.

After conducting simulations to compare the effects of the traditional GS algorithm, the MRAF algorithm, and the improved algorithm proposed in this paper, it was found that the traditional GS algorithm failed to meet the constraint condition with an error level of 32.78%, far from the desired constraint of RMSE≤0.1%. Both the MRAF algorithm and the improved algorithm displayed a light spot error of 0.09%. At this time, the uniformity inside the triangular light spot constructed by the two was consistent. However, the diffraction efficiency of the improved algorithm proposed in this paper is 97.77%, which is higher than the diffraction efficiency of the MRAF algorithm (87.48%). Moreover, the peak background ratio (PBR) of the improved algorithm is 2.0357, a value larger than that of the MRAF algorithm (0.0079). As shown in Fig. 13, the improved algorithm exhibits a strong suppression effect on speckles in non-signal areas, demonstrating that the improved algorithm incorporates desirable aspects from both the GS and MRAF algorithms to a certain extent.

By using the improved MRAF algorithm to shape the triangular light spot and obtain the DOE phase distribution, the paper demonstrated its effectiveness through simulation and experimental analysis. The light spot obtained by the improved algorithm exhibited enhanced diffraction efficiency and better control of speckles in non-signal areas compared with the MRAF algorithm, while ensuring low errors. The experimental results confirmed the validity of the improved algorithm, aligning well with the simulation results. This substantiated the reliability of the simulation analysis methods used in this paper. In subsequent research work, this paper aims to improve the convergence speed of the algorithm and explore the incorporation of other methods to further enhance the final results. The method proposed in this paper provides a reference for designing DOE for complex flat-top beams with high diffraction efficiency and low error.