For several centuries, far-field optical microscopy has remained a key instrument in many scientific disciplines, including physical, chemical, and biomedical research. Nonetheless, far-field imaging has many limitations: the spatial resolution is controlled by the diffraction of light, and the imaging speed follows the Nyquist-Shannon sampling theorem. The recent development of super-resolution techniques has pushed the limits of spatial resolution. However, these methods typically require complicated setups and long acquisition times and are still not applicable to deep-tissue bioimaging. Here, we report imaging through an ultra-thin fibre probe with a spatial resolution beyond the Abbe limit and a temporal resolution beyond the Nyquist limit simultaneously in a simple and compact setup. We use the random nature of mode coupling in a multimode fibre, the sparsity constraint and compressive sensing reconstruction. The new approach of super-resolution endo-microscopy does not use any specific properties of the fluorescent label, such as depletion or stochastic activation of the molecular fluorescent state, and therefore can be used for label-free imaging. We demonstrate a spatial resolution more than 2 times better than the diffraction limit and an imaging speed 20 times faster than the Nyquist limit. The proposed approach can significantly expand the realm of the application of nanoscopy for bioimaging.

中文翻译：

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内窥镜检查超出了阿贝和奈奎斯特极限。

几个世纪以来，远场光学显微镜一直是许多科学学科（包括物理，化学和生物医学研究）中的重要仪器。但是，远场成像有很多局限性：空间分辨率受光的衍射控制，成像速度遵循Nyquist-Shannon采样定理。超分辨率技术的最新发展推动了空间分辨率的极限。但是，这些方法通常需要复杂的设置和较长的采集时间，并且仍然不适用于深组织生物成像。在这里，我们报告了通过一种超薄光纤探头进行成像的过程，该探头的空间分辨率超出了Abbe限制，而时间分辨率超出了Nyquist限制，同时以简单紧凑的方式进行设置。我们在多模光纤，稀疏约束和压缩感测重建中使用模式耦合的随机性。超高分辨率内窥镜检查的新方法不使用荧光标记的任何特定属性，例如分子荧光状态的耗竭或随机激活，因此可以用于无标记的成像。我们证明了空间分辨率比衍射极限好2倍以上，成像速度比奈奎斯特极限快20倍。所提出的方法可以大大扩展纳米技术在生物成像中的应用领域。例如分子荧光状态的耗竭或随机激活，因此可用于无标记成像。我们证明了空间分辨率比衍射极限好2倍以上，成像速度比奈奎斯特极限快20倍。所提出的方法可以大大扩展纳米技术在生物成像中的应用领域。例如分子荧光状态的耗竭或随机激活，因此可用于无标记成像。我们证明了空间分辨率比衍射极限好2倍以上，成像速度比奈奎斯特极限快20倍。所提出的方法可以大大扩展纳米技术在生物成像中的应用领域。