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Proceedings Paper • Open Access

Low-order aberration coefficients applied to design of telescopes with freeform surfaces

Paper Abstract

As the number of smallsats and cubesats continues to increase [1], so does the interest in the space optics community to miniaturize reflective optical instrumentation for these smaller platforms. Applications of smallsats are typically for the Earth observing community, but recently opportunities for them are being made available for planetary science, heliophysics and astrophysics concepts [2]. With the smaller satellite platforms come reduced instrument sizes that they accommodate, but the specifications such as field of view and working f/# imposed on the smaller optical systems are often the same, or even more challenging. To meet them, and to “fit in the box”, it is necessary to employ additional degrees of freedom to the optical design. An effective strategy to reduce package size is to remove rotational symmetry constraints on the system layout, allowing it to minimize the unused volume by applying rigid body tilts and decenters to mirrors. Requirements for faster systems and wider fields of view can be addressed by allowing optical surfaces to become “freeform” in shape, essentially removing rotational symmetry constraints on the mirrors themselves. This dual approach not only can reduce package size, but also can allow for increased fields of view with improved image quality. Tools were developed in the 1990s to compute low-order coefficients of the imaging properties of asymmetric tilted and decentered systems [3][4]. That approach was then applied to reflective systems with plane symmetry, where the coefficients were used to create closed-form constraints to reduce the number of degrees of freedom of the design space confronting the designer [5][6]. In this paper we describe the geometric interpretation of these coefficients for systems with a plane of symmetry, and discuss some insights that follow for the design of systems without closed-form constraints. We use a common three-mirror design form example to help illustrate these concepts, and incorporate freeform surfaces for each mirror shape. In section II, we evoke the typical form of the wave aberration function taught in most texts on geometrical optics, and then recast it into a general form that no longer assumes rotational symmetry. A freeform surface definition for mirrors is then defined, and the example three-mirror system used throughout this paper is introduced. In section III, the first-order coefficients of the plane symmetric system are discussed, and then the second-order in section IV. In both of these discussions, the example system is perturbed to present the explicit form of the aberration coefficient laid out in section II, and plots are presented using optical design software. Finally, some concluding remarks are given in section V.

Paper Details

Date Published: 25 September 2017
PDF: 9 pages
Proc. SPIE 10562, International Conference on Space Optics — ICSO 2016, 1056229 (25 September 2017); doi: 10.1117/12.2296163
Show Author Affiliations
Bryan D. Stone, Synopsys, Inc. (United States)
Joseph M. Howard, NASA Goddard Space Flight Ctr. (United States)


Published in SPIE Proceedings Vol. 10562:
International Conference on Space Optics — ICSO 2016
Bruno Cugny; Nikos Karafolas; Zoran Sodnik, Editor(s)

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