A topology optimization implementation for depth-of-focus extension of binary phase filters
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INDUSTRIAL APPLICATION PAPER
A topology optimization implementation for depth-of-focus extension of binary phase filters Stephen W. K. Roper 1
&
Suho Ryu 2 & Baekcheon Seong 2 & Chulmin Joo 2
&
Il Yong Kim 1
Received: 29 October 2019 / Revised: 7 April 2020 / Accepted: 15 April 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
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 TObased 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. Keywords Topology optimization . Binary phase filter . Depth-of-focus . Applied optics
1 Introduction Binary phase filters (BPFs) are a specialized class of optical element (Sheppard 2011; Sheppard and Hegedus 1988) used for improving three-dimensional focus in diverse applications including microscopy (Botcherby et al. 2006; Leitgeb et al. 2006; Liu et al. 2008), tomography (Kim et al. 2017),
Responsible editor: Ji-Hong Zhu * Chulmin Joo [email protected] * Il Yong Kim [email protected] 1
Queen’s University, Kingston, Ontario K7L 3N6, Canada
2
Yonsei Univer
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