Duerr Fabian, Thienpont Hugo
Brussels Photonics, Department of Applied Physics and Photonics (B-PHOT TONA) Vrije Universiteit Brussel, Pleinlaan 2, 1050, Brussels, Belgium.
Light Sci Appl. 2021 May 6;10(1):95. doi: 10.1038/s41377-021-00538-1.
For more than 150 years, scientists have advanced aberration theory to describe, analyze and eliminate imperfections that disturb the imaging quality of optical components and systems. Simultaneously, they have developed optical design methods for and manufacturing techniques of imaging systems with ever-increasing complexity and performance up to the point where they are now including optical elements that are unrestricted in their surface shape. These so-called optical freeform elements offer degrees of freedom that can greatly extend the functionalities and further boost the specifications of state-of-the-art imaging systems. However, the drastically increased number of surface coefficients of these freeform surfaces poses severe challenges for the optical design process, such that the deployment of freeform optics remained limited until today. In this paper, we present a deterministic direct optical design method for freeform imaging systems based on differential equations derived from Fermat's principle and solved using power series. The method allows calculating the optical surface coefficients that ensure minimal image blurring for each individual order of aberrations. We demonstrate the systematic, deterministic, scalable, and holistic character of our method with catoptric and catadioptric design examples. As such we introduce a disruptive methodology to design optical imaging systems from scratch, we largely reduce the "trial-and-error" approach in present-day optical design, and we pave the way to a fast-track uptake of freeform elements to create the next-generation high-end optics. We include a user application that allows users to experience this unique design method hands-on.
150多年来，科学家们不断推进像差理论，以描述、分析和消除影响光学元件及系统成像质量的缺陷。与此同时，他们还开发了适用于成像系统的光学设计方法和制造技术，这些系统的复杂度和性能不断提升，如今已包含表面形状不受限制的光学元件。这些所谓的光学自由曲面元件提供了多种自由度，能够极大地扩展功能，并进一步提升先进成像系统的各项规格。然而，这些自由曲面的表面系数数量急剧增加，给光学设计过程带来了严峻挑战，以至于自由曲面光学的应用至今仍较为有限。在本文中，我们提出了一种针对自由曲面成像系统的确定性直接光学设计方法，该方法基于从费马原理推导并使用幂级数求解的微分方程。该方法能够计算出光学表面系数，确保在每个像差阶次下图像模糊度最小。我们通过反射式和折反射式设计实例展示了该方法的系统性、确定性、可扩展性和整体性。由此，我们引入了一种全新的光学成像系统设计方法，极大地减少了当今光学设计中的“试错”方法，并为快速采用自由曲面元件以打造下一代高端光学器件铺平了道路。我们还提供了一个用户应用程序，让用户能够亲身感受这种独特的设计方法。
