We demonstrate a novel method that enables one to measure the structure of highly reflecting fiber Bragg gratings. The method is based on measuring both the transmission and reflection spectra of the grating and applying an inverse-scattering algorithm. The use of the transmission spectrum significantly reduces the sensitivity of the reconstruction to measurement noise, and therefore it significantly decreases the measurement duration. We experimentally demonstrate our method for reconstructing the structure of an apodized grating with a reflectivity of 99.91%.
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