Muslimov Eduard, Hugot Emmanuel, Jahn Wilfried, Vives Sebastien, Ferrari Marc, Chambion Bertrand, Henry David, Gaschet Christophe
Opt Express. 2017 Jun 26;25(13):14598-14610. doi: 10.1364/OE.25.014598.
In the recent years a significant progress was achieved in the field of design and fabrication of optical systems based on freeform optical surfaces. They provide a possibility to build fast, wide-angle and high-resolution systems, which are very compact and free of obscuration. However, the field of freeform surfaces design techniques still remains underexplored. In the present paper we use the mathematical apparatus of orthogonal polynomials defined over a square aperture, which was developed before for the tasks of wavefront reconstruction, to describe shape of a mirror surface. Two cases, namely Legendre polynomials and generalization of the Zernike polynomials on a square, are considered. The potential advantages of these polynomials sets are demonstrated on example of a three-mirror unobscured telescope with F/# = 2.5 and FoV = 7.2x7.2°. In addition, we discuss possibility of use of curved detectors in such a design.
近年来，基于自由曲面光学表面的光学系统设计与制造领域取得了重大进展。它们为构建快速、广角和高分辨率系统提供了可能，这些系统非常紧凑且无遮挡。然而，自由曲面设计技术领域仍未得到充分探索。在本文中，我们使用在方形孔径上定义的正交多项式的数学工具（该工具之前是为波前重建任务而开发的）来描述镜面的形状。考虑了两种情况，即勒让德多项式和方形上的泽尼克多项式的推广。在一个F/# = 2.5且视场为7.2×7.2°的三镜无遮挡望远镜的示例中展示了这些多项式集的潜在优势。此外，我们讨论了在这种设计中使用曲面探测器的可能性。
