Fiber optic magnetic sensors have gained significant interest due to their advantages of miniature size, resistance to electromagnetic interference, and the ability to operate under harsh conditions. Optical fiber-based sensors are usually demodulated using an optical spectrum analyzer to monitor wavelength shifts or power variations. However, the demodulation speed and resolution are limited by the capabilities of the measurement equipment. Recently, optical carrier-based microwave interferometry (OCMI) has gained attention for its advantages in sensing applications, including insensitivity to polarization variation, high signal-to-noise ratio, and clear interference fringes. These features make OCMI ideal for interrogating FBG sensors. However, fiber optic sensors are typically sensitive to multiple parameters. For instance, fiber optic magnetic field sensors combining giant magnetostrictive material (GMM) with fiber Bragg grating (FBG) are sensitive to both temperature and magnetic field. Therefore, although the OCMI demodulation technique enhanced by the vernier effect increases sensitivity to the target parameter, it also amplifies errors caused by interfering factors, limiting the application of such FBG magnetic field sensors. The proposed sensing system features high sensitivity, a simple setup, and low temperature cross-sensitivity, and holds potential value in magnetic field sensing applications.

The sensing unit is composed of GMM-FBG and FBG. The system mainly consists of the sensing unit, a three-arm Mach-Zehnder interferometer, and dispersion-compensated fiber, forming a six-tap incoherent microwave photonic filter (MPF). A vector network analysis (VNA) is used to collect the system’s frequency response, and an inverse Fourier transform (IFT) is applied to obtain the MPF’s time-domain response. This response consists of a series of pulses with different delays. By applying a gate function to any two pulses and then performing a Fourier transform (FT), the microwave interferogram of a specific RF Fabry-Perot interferometer (FPI) can be reconstructed. The vernier effect is achieved by superimposing two reconstructed FPI microwave interference spectra. Magnetic field and temperature changes can then be demodulated by tracking the frequency drift of the dip in the envelope signal of the superimposed spectrum. In temperature sensing, the sensitivity of the vernier envelope is minimized, while an enhanced vernier effect is applied in magnetic field sensing. This allows for high-sensitivity magnetic field sensing with low temperature cross-sensitivity. In the experiment, the sensor unit is placed in a coil for magnetic field detection and in a temperature control box for temperature measurement. To evaluate sensing performance, the magnetic field is increased in 10 mT steps from 20 to 50 mT, which is the optimal operating range of the probe, by adjusting the power supply current.

The frequency response of the sensing system is collected by the VNA. By applying IFT to the microwave spectrum, a time-domain response of the sensing system is obtained. Using the gate function, a selected time-domain signal is used to reconstruct the microwave interference spectrum via FT. After applying the vernier effect, the free spectral range of the envelope signals required for magnetic field and temperature demodulation are 350 MHz and 99 MHz, respectively (Fig. 4). When the magnetic field increases from 0 to 50 mT, the dip frequency of the envelope signal shifts from 3.259 to 3.5946 GHz [Fig. 5(c)]. Fitting results show a magnetic field sensitivity of 6.792 MHz/mT, with a correlation coefficient (R²) of 99.9% [Fig. 5(f)]. This sensitivity is 43 times higher than that achieved by tracking the frequency drift of a single interference spectrum [Fig. 5(e)]. When the temperature increases from 35.0 ℃ to 39.5 ℃, fitting results show that temperature sensitivity decreases to 0.040 MHz/℃, with an R² of 90% [Fig. 6(f)]. This reduces the magnetic field demodulation error caused by temperature crosstalk to 5.9 μT in the range of 35.0?39.5 ℃.

We propose a magnetic field sensor with low temperature cross-sensitivity based on the vernier effect and OCMI. The sensor system converts the wavelength shift in the FBG, caused by magnetic field and temperature changes, into dip frequency shifts of the reconstructed interference spectrum. When the magnetic field changes, the reconstructed interference spectra of FPI 1 and FPI 2 shift in opposite directions, resulting in amplified magnetic sensitivity in the superimposed spectrum. When temperature changes, the interference spectra of FPI 3 and FPI 4 move in the same direction, thus minimizing the sensitivity of the vernier envelope to temperature. Experimental results demonstrate a magnetic field sensitivity of 6.792 MHz/mT within the range of 0?50 mT, and a temperature-induced magnetic field demodulation error reduced to 5.9 μT in the range of 35.0?39.5 ℃. In summary, the proposed OCMI demodulation scheme combined with the vernier effect offers a simple system configuration and low temperature cross-sensitivity, providing an effective solution for fiber optic magnetic field sensing in applications such as resource exploration and aerospace.