An interrogation scheme based on wavelength-to-time mapping to achieve ultrafast, high-precision, and large dynamic range interrogation of fiber Bragg grating (FBG) sensors is proposed and experimentally demonstrated. The wavelength-to-time mapping, also called temporal self-imaging effect, is realized in the optical domain, using a dispersive element that has a large group velocity dispersion. For a practical dispersive element, higher order dispersions exist, which makes the wavelength-to-time mapping nonlinear. Thus, an interrogation system based on wavelength-to-time mapping without considering the high-order dispersion would reduce the interrogation accuracy. In this paper, for the first time to the best of our knowledge, a mathematical model that incorporates higher order dispersion to achieve an accurate wavelength-to-time mapping is developed, which is then verified by a numerical simulation. An FBG-based strain sensor interrogated based on the developed wavelength-to-time mapping scheme is experimentally investigated. The system has a sampling speed of 48.6 MHz, a dynamic range as large as 20nm, and a sensing accuracy as high as 0.87 $\mu \varepsilon$ for a single-shot measurement.
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