Optical fibers play a key role in many different fields of science and technology. In particular, fibers with a diameter of several micrometers are intensively used in photonics. For these applications, it is often important to precisely know and control the fiber radius. Here, we demonstrate a novel technique to determine the local radius variation of a 30-micrometer diameter silica fiber with sub-AA ngstrom precision with axial resolution of several tens of micrometers over a fiber length of more than half a millimeter. Our method relies on taking an image of the fibers whispering-gallery modes (WGMs). In these WGMs, the speed of light propagating along the fiber axis is strongly reduced. This enables us to determine the fiber radius with a significantly enhanced precision, far beyond the diffraction limit. By exciting different axial modes, we verify the precision and reproducibility of our method and demonstrate that we can achieve a precision better than 0.3 AA. The method can be generalized to other experimental situations where slow light occurs and, thus, has a large range of potential applications in the realm of precision metrology and optical sensing.
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