In recent years, fiber shape measurement technology has advanced rapidly. However, shape measurement technology based on fiber Bragg grating (FBG) cannot achieve completely distributed shape measurement due to limitation in the number and spacing of FBGs. The traditional single-mode fiber Brillouin optical time-domain analysis system, which suffers from low spatial resolution, limited communication capacity, and high bending loss, can no longer meet the current research requirements. Multi-core fibers (MCFs) have shown promising potential in bending strain measurement, especially due to the off-core fibers that are not located on the neutral axis of the fiber. In this paper, we employ a differential pulse Brillouin optical time-domain analysis system, with a spatial resolution of several centimeters, to measure the bending of seven-core fibers. In addition, recognizing that the temperature characteristics of each core in seven-core fibers may vary due to differences in production and processing, we calibrate the temperature coefficients of each core. A novel temperature compensation method is proposed to address the cross-sensitivity issue between temperature and strain in multi-core fibers during bending measurements. We hope that the proposed temperature method can more accurately determine the bending curvature of the fiber.

In this study, a differential pulse Brillouin optical time-domain analysis system with a spatial resolution of 20 cm is used. Seven intermediate cores and three asymmetric cores are selected for experimental measurement. First, we conduct temperature calibration experiments on four selected fiber cores over a temperature range of 20?70 ℃ (with 10 ℃ increments), and the temperature coefficients for each of these four cores are determined. Then, we apply both temperature and bending strain at the 17.5?18.5 m position on the fiber to measure temperature-compensated curvature. The proposed temperature compensation method involves extracting the Brillouin frequency shift from the intermediate core, calculating the fiber temperature using the previously measured temperature coefficients, and subtracting the Brillouin frequency shift caused by temperature from the actual measured shift. This allows the bending strain information of the core to isolated. From the resulting Brillouin frequency shift, the curvature of the bending section of the fiber can be reconstructed.

Cores 1, 3, 5, and 7 of the seven-core fiber are selected for experiments, yielding temperature coefficients of 1.103, 0.962, 1.277, and 0.937 MHz/℃ respectively, which are comparable to those of single-mode fiber. Using these temperature coefficients, the fiber is wrapped around a disc with a bending radius of 4.9 cm and heated in a water bath to simultaneously induce temperature and strain effects. The curvature of the bending section is calculated using a parallel transmission frame algorithm. The results show that the maximum curvature obtained is 20.593 m^-1, while the average curvature is 19.910 m^-1. To reduce experimental error, we repeat the experiment for three times, and the final measurement used is the average of these three trials. The actual curvature of the bending section is 20.408 m^-1. The error between the maximum measured curvature and the actual curvature is 0.91%, while the error between the average curvature and the actual curvature is 0.24%.

Analysis of the experimental results demonstrate that the proposed temperature compensation method for bending measurement can more accurately separate temperature and bending strain effects, and more precisely reconstruct the curvature information of the fiber. The main sources of error in curvature reconstruction are the limited spatial resolution and sampling rate of the system, which leads to a sparse dataset, and the artificial control of bending and strain application in the experiment, which introduces minor deviations. These issues will be the focus of future work to improve the accuracy of curvature measurement.