A novel three-reflector fibre Bragg grating Fabry–Perot interferometer (3R-FPI) based on femtosecond (fs) laser direct writing is proposed and experimentally demonstrated for inclination angle detection. The sensor structure consists of three short Bragg gratings, including one standard core grating and two edge-core gratings inscribed at precise positions along a single-mode fiber. The combination of edge-core and core gratings enables bending-induced asymmetrical electric field distribution to be effectively converted into optical intensity variations. Two 3R-FPI configurations are fabricated with carefully designed cavity lengths to generate distinct, non-overlapping spatial frequency components in the spatial frequency domain, thereby allowing efficient multiplexing through spatial frequency-division multiplexing (sFDM). The sensor’s output is demodulated using selective local Fourier transform, which significantly reduces computational complexity by focusing only on the resonant spatial frequency components of interest. Experimental results show that the proposed 3R-FPI exhibits clear and repeatable spectral responses to inclination changes within a range of − 50° to + 50°, with linear sensitivities of 6 × 10−7a.u./° and 3 × 10−7a.u./° for Configurations I and II, respectively (R2 > 0.98). The developed system further demonstrates biaxial inclination/tilt measurement capability when two 3R-FPI sensors are integrated orthogonally in a single array. The compact design, high sensitivity, and efficient frequency-domain multiplexing make the fs-laser-inscribed 3R-FPI an excellent candidate for distributed and vector inclination sensing in structural monitoring applications.
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