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A novel technique to achieve ultrafast and ultra-high-resolution interrogation of a fiber Bragg grating (FBG) sensor based on interferometric temporal spectroscopy is proposed and experimentally demonstrated. In the proposed system, two FBGs with one serving as the sensor grating and the other serving as the reference grating are connected at two arms of an interferometer. An ultrashort optical pulse from a pulsed laser is sent to the interferometer. Two pulses will be obtained due to the reflection of the two FBGs and then both are sent to a dispersive element to map the sensor grating wavelength shift to a temporal spacing change between the two dispersed pulses due to the dispersion-induced wavelength-to-time mapping. A temporal interference pattern is generated between the temporal pulses. The temporal spacing change is further mapped to the interference pattern frequency change, leading to a greatly improved interrogation resolution due to the inherently high sensitivity of a temporal interferometer. The proposed technique overcomes the fundamental tradeoff between the interrogation speed and resolution in a temporal-spectroscopy-based FBG interrogation system and that between the measurement resolution and dynamic range in a dual-wavelength heterodyne-based interrogation system. An ultrafast real-time interrogation of an FBG strain sensor with a sampling rate of 48.6 MHz and an interrogation resolution as high as 0.61 pm are experimentally demonstrated.