A topology optimization implementation for depth-of-focus extension of binary phase filters

Abstract

Binary phase filters (BPFs) form a special class of optical structure characterized by their distinct concentric rings of alternating 0-π phases. Once placed in the pupil plane of a focusing lens, a BPF generates a sharp elongated focus, which can be utilized for diverse applications ranging from optical trapping to focus scanning microscopy. As demand for BPFs continues to expand, new design techniques are required to tune and optimize filter performance; in this paper, a topology optimization method is presented to extend BPF’s depth-of-focus while maintaining a sharp lateral resolution. In general, binary phase filters can be completely described by three designable characteristics: the radial location of each ring, the width of each ring, and the total number of rings. Conventional BPF design methods typically only consider two of these key design characteristics, often with a predefined number of rings and subsequent sizing optimization of radial locations and widths. Furthermore, these methods often rely on inefficient non-deterministic optimizers like particle swarm and simulated annealing. These implementations ultimately limit design freedom and often require manual investigation of multiple configurations at the expense of computational time and solution quality. Instead, this paper introduces topology optimization (TO) as the first and only method for BPF generation capable of considering all three design characteristics simultaneously and without any predefined assumptions. Here, the TO-based approach is first initialized with a series of concentric rings to cover the entire design domain. Then, similar to classical material distribution problems, the phase value of each concentric ring is optimized directly to satisfy the objective and constraint functions using gradient-based algorithms. This paper describes the new TO-based approach and demonstrates fundamental capabilities and design advantages. Numerical results are validated experimentally and compared with existing approaches with an emphasis on quantitative performance, non-intuitive structure generation, and computational efficiency.

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Funding

This work was supported by the National Research Foundation of Korea (NRF) (NRF-2015R1A1A1A05001548) and the Mitacs Globalink Research Award.

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Correspondence to Chulmin Joo or Il Yong Kim.

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Replication of results

The final TO-BPF configurations are provided in Table 1, showing a general sizing diagram and radial position vectors of each design for distribution and replication purposes. Simulation and optimization parameters are discussed throughout this report to provide sufficient means of numerical replication (optimization tolerances, algorithm, etc.), along with the pseudocode provided in Appendix A. Lastly, the experimental setup and measurement procedure are described in section 4.2, with equipment details and corresponding assumptions. Any additional data will be made available upon request to the corresponding authors.

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Appendix A: Pseudocode

Appendix A: Pseudocode

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Roper, S.W.K., Ryu, S., Seong, B. et al. A topology optimization implementation for depth-of-focus extension of binary phase filters. Struct Multidisc Optim (2020). https://doi.org/10.1007/s00158-020-02611-6

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Keywords

  • Topology optimization
  • Binary phase filter
  • Depth-of-focus
  • Applied optics