Freeform imaging systems: Fermat’s principle unlocks “first time right” design

Abstract

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.

Review on Panoramic Imaging and Its Applications in Scene Understanding

“…With the continuous development of advanced manufacturing technology and testing technology, freeform optical elements make it possible for compact and high-image-quality imaging optical systems [199]- [202]. Compared with the traditional spherical surface, the freeform surface can provide more degrees of freedom, significantly improve the optical performance of the imaging system, and reduce the size of the system [203] (Fig.…”

Optical design of first time right imaging systems

“…We have developed a web-based user application for the three-mirror design case that allows to experience this unique design method hands-on and in real time. The graphical user interface and the usage of the app are explained in depth in the Supplementary Information document of our recently published article [1].…”

“…As such, it offers a disruptive methodology to design optical imaging systems from scratch. A fully detailed mathematical description can be found in our recently published article [1].…”

Challenges and strategies in high-accuracy manufacture of the world's largest SiC aspheric mirror

“…Aspherical elements used in optical systems can increase the number of independent variables without increasing independent aberrations, which is conducive to improving image quality; meanwhile, the number of optical elements is reduced under the same constraints, thus reducing the size and weight of the optical system. Therefore, aspheric elements are widely used in many fields of optoelectronic instruments, such as aerospace remote sensing, astronomical observation, deep space exploration, photoelectric tracking instruments, lithographic objectives, and high-performance photographic (camera) machines [1][2][3][4][5][6] . As the development of modern science and technology, the performance requirements of optical telescope systems are gradually improved [7][8] .…”