Theory of aberration fields for general optical systems with freeform surfaces

Abstract

This paper utilizes the framework of nodal aberration theory to describe the aberration field behavior that emerges in optical systems with freeform optical surfaces, particularly φ-polynomial surfaces, including Zernike polynomial surfaces, that lie anywhere in the optical system. If the freeform surface is located at the stop or pupil, the net aberration contribution of the freeform surface is field constant. As the freeform optical surface is displaced longitudinally away from the stop or pupil of the optical system, the net aberration contribution becomes field dependent. It is demonstrated that there are no new aberration types when describing the aberration fields that arise with the introduction of freeform optical surfaces. Significantly it is shown that the aberration fields that emerge with the inclusion of freeform surfaces in an optical system are exactly those that have been described by nodal aberration theory for tilted and decentered optical systems. The key contribution here lies in establishing the field dependence and nodal behavior of each freeform term that is essential knowledge for effective application to optical system design. With this development, the nodes that are distributed throughout the field of view for each aberration type can be anticipated and targeted during optimization for the correction or control of the aberrations in an optical system with freeform surfaces. This work does not place any symmetry constraints on the optical system, which could be packaged in a fully three dimensional geometry, without fold mirrors.

Metasurface Freeform Nanophotonics

“…While manufacturability has often constrained optical elements to have rotational invariance, the emerging field of freeform optics leverages more complex curvatures to enable novel functionalities and simplified compound optical systems 1–4 . These elements have been shown to be capable of correcting aberrations 3 , off-axis imaging 4 , expanding field of view 5 , and increasing depth of field 6 . Recent interest in freeform optics has been driven by potential applications in near-eye displays 7, 8 as well as compact optical systems for medical, aerospace, and mobile devices where there are stringent constraints on the size and weight of the optical package 9 .…”

Prime focus architectures for large space telescopes: reduce surfaces to save cost

“…Further investigations are needed to explore possible other advantages of the prime focus such as: Free form optics -The diffraction limited FOV achievable with the inverse Schwarzschild, in the presence of the radiation-hard apochromatic prime-focus aspheric correctors will be better optimized using modern free-form optimization 14 . Polarization aberration balancing will be needed to optimize the coronagraph contrast.…”

Freeform optics adapted to the design of spatial instrumentation for Earth observation

“…In principle, this theory was limited to optical systems with rotationally symmetric surfaces that were tilted or decentered [1,2]. However, the emergence of freeform optics stimulated the extension of NAT to systems including non-rotationally symmetric components [3,4,5].…”

“…NAT states that non-rotationally symmetric surfaces in an optical system do not originate any new kind of aberrations but a new distribution of the optical aberrations at the image plane in terms of the field, in other words, a new distribution of the field aberrations [3,4,5]. This lack of symmetry produces the appearance of one or more nodes of aberrations (zero or almost zero aberration field points) away from the optical axis.…”

“…Therefore, NAT allows calculating the final contribution to aberrations when a non-rotationally symmetric surface displaced from the stop is introduced in the system. [3,4,5].…”