We report on the distributed shape measurement of small deformations produced along the length of an optical fiber. The fiber contains multiple waveguiding cores, each inscribed with weak continuous Bragg gratings. The distributed Bragg-reflectivity data for the fiber cores, obtained from the optical backscatter reflectometry, is used to estimate the local curvature and the position of the fiber. We successfully demonstrate the sensing of periodic micro-deformations—approximately a micrometer or less in amplitude and a few hundred microns in length. Such microbends are known to cause attenuation in optical fibers, and the approach presented here can enable a detailed measurement of the these microbends in applications ranging from telecommunication cable design to, biotechnology, robotics, manufacturing, aerospace and security. © 2020 Optical Society of America

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