Ultrafast laser direct writing processing technology with a single focus has a small processing area and low energy utilization and is not suitable for applications in large-area processing, volume processing, and the single forming of structures. To solve these problems, researchers generally adopt multibeam parallel processing method. The most important aspect of parallel processing technology is to realize three-dimensional (3D) multibeams and form 3D multi-focus with the same energy. Therefore, a method for generating 3D multi-focus is urgently required. In industrial applications, laser focusing requires precise control to obtain high quality results. Moreover, in the actual optical path, setup and manufacturing errors exist in the optical elements and have a significant impact on the final machining results; however, the existing iterative algorithms rarely compensate for such errors. Therefore, a 3D multi-focus control method based on a feedback-weighted 3D-GS algorithm is proposed in this study.

A spatial light modulator (SLM) can adjust optical parameters such as amplitude, phase, and polarization of a laser beam by loading computer-generated holograms. With the help of SLM, the light intensity distribution in the target region can be easily controlled. The key to obtaining uniform 3D multiple beams with SLM is to obtain the corresponding computer-generated holograms, which can then be used to flexibly control the number, position, and focus energy distribution of the outgoing laser beam. In this study, to improve the uniformity of the energy distribution of multiple beams, a feedback method was used to improve the traditional 3D-GS algorithm. Each beam was set using a weight coefficient. The feedback-weighted 3D-GS algorithm collected the energy and position information of multiple foci through a CCD camera in real time and fed the information back to the controlling terminal to dynamically adjust the weight coefficient of each beam. After a couple of iterations, 3D multi-focus with high uniformity were obtained.

The coordinate parameters related to the desired 3D structures in different Z-axis planes are set, and the energy uniformity of the 3D multi-focus is calculated using the feedback-weighted 3D-GS algorithm and traditional 3D-GS algorithm. For the expected 3D structure of “HBUT,” the feedback-weighted 3D-GS algorithm improved the uniformity of 47 diffraction points on four different planes from 47% to more than 96% after 20 iterative feedback calculations. Using the feedback-weighted 3D-GS algorithm, the homogeneity of the 3D multi-focus energy distribution is significantly improved, as shown in Table 1. Another experiment was performed for the 3D spiral structure, and the feedback-weighted 3D-GS algorithm improved the uniformity of 15 diffraction points on 15 different planes from 47% to 94% after five iterative feedback calculations. The spots at the corresponding positions were filled according to the 3D model of the spiral structure (Fig.9). From a comparison of spot energy distribution calculated by different algorithms, it can be found that the presented feedback-weighted 3D-GS method can effectively improve the uniformity of 3D multi foci.

Based on the feedback-weighted 3D-GS algorithm and programmable SLM, this study proposes a method to generate 3D multi-focus with high uniformity to compensate for the fabrication and setup errors of devices in real optical paths. The designed pattern of “HBUT” and helical structures are used to prove the validity of the method. Through the analysis and calculation of feedback parameters in iterative feedback calculations, the uniformity of the 3D multibeam obtained by this method is verified to be 95%. The number of multifocal points in the 3D structure has a greater influence on the stability of the reconstructed 3D multi-focus light field than the number of Z-planes in the 3D structure during the feedback iterative calculation. Additionally, the laser high-uniformity 3D multi-focus optical field reconstruction technique proposed in this study can be used for 3D structure machining.