Point Spread Function of Hexagonally Segmented Telescopes by New Symmetrical Formulation. (arXiv:1811.02762v1 [astro-ph.IM])

Point Spread Function of Hexagonally Segmented Telescopes by New Symmetrical Formulation. (arXiv:1811.02762v1 [astro-ph.IM])
<a href="http://arxiv.org/find/astro-ph/1/au:+Itoh_S/0/1/0/all/0/1">Satoshi Itoh</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Matsuo_T/0/1/0/all/0/1">Taro Matsuo</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Hiroshi_S/0/1/0/all/0/1">Shibai Hiroshi</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Sumi_T/0/1/0/all/0/1">Takahiro Sumi</a>

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 three-dimensional
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.

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 three-dimensional
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.

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