The significance of super-resolved fluorescence microscopy beyond the diffraction barrier was recognized by the Nobel Prize in Chemistry in 2014. At room temperature, these techniques typically achieve a resolution on the order of twenty nanometers. They already allowed for resolving subcellular structures and organelles, and are starting to enable discoveries in neuroscience, molecular biology and other life sciences. One can dream about increasing the optical resolution by another two orders of magnitude in order to directly resolve sub-molecular structures such as constituents of molecular complexes or even protein structure itself. The aim of the present work is to accomplish exactly that. In this PhD thesis, a novel microscopy technique is presented that exploits cryogenic measurements to push optical resolution to the Angstrom level. The near atomic resolution is made possible by the substantial improvement of the molecular photostability at liquid helium temperature. This method allows one to gain structural information of proteins or other molecular complexes that might not be accessible by existing analytical methods such as X-ray crystallography, cryogenic electron microscopy or magnetic resonance spectroscopy. These results mark record optical resolution and demonstrate that optical resolution can be pushed beyond the diffraction limit by nearly one thousand times.
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