Mathematical method for designing phase-shifted fiber Bragg gratings for nanoscale strain measurement in high-stability satellite structures

Phase-shifted fiber Bragg gratings (PSFBGs) are promising for in-orbit nanoscale strain monitoring in high-stability satellite structures. However, conventional designs are constrained by a fundamental tradeoff between high strain resolution and compact sensor dimensions, hindering their deployment in space-limited scenarios. To address this issue, this paper proposes what we believe to be a novel parametric design method for PSFBGs that is specifically tailored for in-orbit sensing, enabling the design of a nano-strain sensor with a compact grating length. An experimental system for demodulation and calibration was established, and validation results demonstrate that the designed PSFBG sensor with a 4.5-mm grating length achieves stable measurement of strain as small as 180 n<i>ε</i> peak, exhibiting a mere 1.343% relative error between theoretical and experimental precision. This performance not only fulfills the stringent resolution requirements for satellite structural monitoring but also achieves a highly compact form. Consequently, this work enables precise strain detection in spatially highly constrained scenarios and establishes a robust theoretical foundation for the development of next-generation, high-precision miniaturized strain sensors for advanced satellite platforms.