Point spread function of hexagonally segmented telescopes by new symmetrical formulation
Point spread function of hexagonally segmented telescopes by new symmetrical formulation
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采用新对称公式的六边形分段望远镜的点扩散函数
DOI：
10.1093/mnras/sty3052
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
T. Sumi
中科院分区：
文献类型：
--
作者：
S. Itoh;T. Matsuo;H. Shibai;T. Sumi
用一种新的对称公式推导了六边形分段望远镜的点扩展函数。通过在瞳孔平面上引入三个变量，通过三维傅里叶变换推导出瞳孔函数的傅里叶变换。三个变量的排列对应于瞳孔平面上正三角形顶点的排列。合成的衍射振幅可以写成三个变量的两个函数的乘积；函数对应于衍射光栅基本理论中使用的sinc函数和狄利克雷核。新的表达式清楚地表明，六边形分段望远镜在数学公式上等同于衍射光栅。
A point spread function of hexagonally segmented telescopes is derived by a new symmetrical formulation. By introducing three variables on a pupil plane, the Fourier transform of pupil functions is derived by a 3D Fourier transform. The permutations of three variables correspond to those of a regular triangle’s vertices on the pupil plane. The resultant diffraction amplitude can be written as a product of two functions of the three variables; the functions correspond to the sinc function and Dirichlet kernel used in the basic theory of diffraction gratings. The new expression makes it clear that hexagonally segmented telescopes are equivalent to diffraction gratings in terms of mathematical formulae.