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.

二进制相位滤波器（BPF）形成一类特殊的光学结构，其特征是它们具有交替的0-π相的不同同心环。一旦放置在聚焦透镜的光瞳平面中，BPF就会产生清晰的细长聚焦，可用于从光学陷印到聚焦扫描显微镜的各种应用。随着对BPF需求的不断增长，需要新的设计技术来调整和优化滤波器性能。在本文中，提出了一种拓扑优化方法，可在保持清晰的横向分辨率的同时扩展BPF的焦深。通常，二进制相位滤波器可以通过三个可设计的特征来完全描述：每个环的径向位置，每个环的宽度以及环的总数。传统的BPF设计方法通常仅考虑这些关键设计特征中的两个，通常具有预定义的环数，并随后对径向位置和宽度进行尺寸优化。此外，这些方法通常依赖于效率低下的不确定性优化器，例如粒子群和模拟退火。这些实现最终限制了设计自由度，并且通常需要以多种方式进行手动研究，而这会浪费计算时间和解决方案质量。取而代之的是，本文引入拓扑优化（TO）作为BPF生成的第一个也是唯一方法，该方法能够同时考虑所有三个设计特征而无需任何预定义的假设。在这里，基于TO的方法首先用一系列同心环初始化，以覆盖整个设计领域。然后，类似于经典的材料分布问题，每个同心环的相位值使用基于梯度的算法直接优化，以满足目标函数和约束函数。本文介绍了基于TO的新方法，并演示了基本功能和设计优势。数值结果经过实验验证，并与现有方法进行了比较，重点是定量性能，非直观结构生成和计算效率。