Acta Photonica Sinica, Volume. 54, Issue 4, 0426001(2025)

Fast On-line Optimization for Multifocal Modulation with Controllable Position and Intensity Ratio

Xiaonan WANG and Jian LIN*
Author Affiliations
  • School of Artificial Intelligence Science and Technology,University of Shanghai for Science and Technology,Shanghai 200093,China
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    Precise control of multi-focal intensity is crucial for enhancing the performance of optical systems in various optical applications. However, existing multifocal modulation techniques often exhibit discrepancies between theoretical calculations and experimental outcomes, making it challenging to achieve the desired uniformity of focal intensity and relative diffraction efficiency. This discrepancy may stem from system errors, non-ideal factors in the optical path, and algorithmic limitations. Therefore, it is essential to account for the actual parameters of the experimental system in calculations to ensure consistency between theoretical and experimental results, thereby enhancing the accuracy and reliability of the system.To address this issue, this paper proposes a fast online optimization method that enables effective control over the number, position, and intensity ratio of multiple focal points through iterative phase modulation optimization. The optimization process of this method is as follows. First, the modulation phase map corresponding to the target focal distribution is obtained through theoretical calculations and loaded onto a Spatial Light Modulator (SLM). Then, focal plane imaging is performed using a camera to analyze the intensity distribution of the focal points. Based on the analysis results, the phase modulation pattern is optimized and reloaded onto the SLM. By iteratively refining the modulation pattern multiple times, precise control of multi-focal intensity is achieved. The optimization algorithm adopts an intensity coefficient-based update strategy, gradually adjusting the intensity weighting of each focal point to ensure a more uniform intensity distribution among them. The primary advantage of the online optimization method is its ability to dynamically adjust and optimize phase patterns in real time, ensuring that the expected target is achieved promptly during the optimization process. However, when the same optimized phase pattern is reloaded for testing, slight degradation in uniformity may occur.To verify the effectiveness of this method, experiments were conducted using a collimated Gaussian beam with a wavelength of 638 nm, modulated by an SLM (Thorlabs EXULUS-HD2, 1 200×1 920 pixels) and focused through a high numerical aperture (NA=0.70) objective lens. The intensity distribution at the focal plane was recorded using a CMOS camera. The method's effectiveness was validated by generating focal spot arrays in 3×3, 4×4, and 5×5 matrix configurations, as well as in irregular distributions. Experimental results demonstrated that after optimization, the uniformity of the 3×3, 4×4, and 5×5 focal spot arrays increased to 97.12%, 94.51%, and 88.47%, respectively, compared to pre-optimization values of only 35.65%, 17.15%, and 14.10%. Simultaneously, the relative diffraction efficiency improved to 83.86%, 64.17%, and 57.95%, respectively, confirming the method's effectiveness in energy utilization. Compared with the traditional Gerchberg-Saxton (GS) iterative algorithm, the proposed method exhibits a significantly faster optimization convergence rate. For instance, when constructing a 3×3 focal spot array, the GS algorithm typically requires over 100 iterations to achieve uniformity between 20% and 60%, whereas the proposed method achieves 97.12% uniformity with only 31 iterations. Furthermore, this method allows flexible control over the intensity ratio between focal points. In the experiments, a "W"-shaped multi-focal pattern was generated, successfully achieving an intensity ratio of 3∶1∶2, demonstrating the feasibility of the proposed method in controlled multi-focal intensity modulation.The proposed online optimization method enables real-time control over the number, position, and intensity ratio of multiple focal points while significantly improving focal array uniformity and diffraction efficiency, thereby reducing the computational burden associated with traditional iterative algorithms. This method provides a highly efficient and reliable solution for multi-focal modulation and has broad application potential in optical manipulation, parallel direct laser writing, optogenetics, and super-resolution imaging. By achieving precise control over the number, position, and intensity ratio of multiple focal points, the proposed method significantly enhances the performance of optical systems.

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    Xiaonan WANG, Jian LIN. Fast On-line Optimization for Multifocal Modulation with Controllable Position and Intensity Ratio[J]. Acta Photonica Sinica, 2025, 54(4): 0426001

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    Paper Information

    Category: Physical Optics

    Received: Jan. 15, 2025

    Accepted: Mar. 4, 2025

    Published Online: May. 15, 2025

    The Author Email: Jian LIN (jianlin@usst.edu.cn)

    DOI:10.3788/gzxb20255404.0426001

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