There are several high-performance adaptive optics systems that deliver diffraction-limited imaging on ground-based telescopes, which has renewed interest in single-mode fiber (SMF) spectroscopy for exoplanet characterization. However, the fundamental mode of a telescope is not well matched to those of conventional SMFs. With the recent progress in asphere manufacturing techniques, it may be possible to reshape the fundamental mode of a SMF into any arbitrary distribution. An optimization problem is set up to investigate what the optimal mode field distribution is and what the fundamental throughput limit is for SMF spectroscopy. Both single-object spectrographs and integral-field spectrographs are investigated. The optimal mode for single-object spectrographs is found to be the aperture function of the exit pupil; for integral-field spectrographs, the optimal mode depends on the spatial sampling of the focal plane. For dense sampling, a uniform mode is optimal; for sparse sampling, the mode of a conventional SMF is near optimal. With the optimal fiber mode, a high throughput (${\gt}{{80}}\%$) can be achieved when the focal plane is (super) Nyquist sampled. For Nyquist sampled cases, the optimal mode has almost 20% more throughput than a conventional SMF.

中文翻译：

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单模积分场光谱的基本极限

有几种高性能自适应光学系统可以在地基望远镜上提供衍射极限成像，这重新引起了人们对用于系外行星表征的单模光纤 (SMF) 光谱学的兴趣。然而，望远镜的基本模式与传统 SMF 的基本模式并不匹配。随着非球面制造技术的最新进展，有可能将 SMF 的基本模式重塑为任意分布。设置了一个优化问题来研究最佳模式场分布是什么以及 SMF 光谱的基本吞吐量限制是什么。研究了单目标光谱仪和积分场光谱仪。发现单物体光谱仪的最佳模式是出瞳的孔径函数；对于积分场光谱仪，最佳模式取决于焦平面的空间采样。对于密集采样，均匀模式是最佳的；对于稀疏采样，传统 SMF 的模式接近最佳。采用最佳光纤模式，高吞吐量（${\gt}{{80}}\%$ ) 可以在焦平面被（超级）奈奎斯特采样时实现。对于奈奎斯特采样情况，最佳模式的吞吐量比传统 SMF 高出近 20%。