We have developed a robust method for the unprecedentedly accurate angstrom-scale detection of local variations of the fiber radius based on the idea suggested by Birks et al. [IEEE Photon. Technol. Lett. IPTLEL1041-1135 12, 182 (2000)]. The method uses an optical microfiber (MF) translated at a small distance along the tested fiber and periodically touching it at measurement points. At these points, the MF transmission spectrum exhibits whispering-gallery-mode (WGM) resonances shifting with the tested fiber radius. A simple and comprehensive optimization scheme, which determines the radius variation without visual recognition of resonances and treats their shifts simultaneously, is developed. The optics of WGM propagation is discussed, and the condition for the validity of the developed method is established.
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