Introduction Fiber optic Bragg grating (FBG) sensors are functional fiber optic sensors that use FBGs as sensing elements and have a wide range of applications. When these sensors are subjected to external parameters such as temperature and strain, the Bragg wavelength will drift accordingly. Therefore, a key issue in FBG sensor research is how to accurately measure the FBG reflected wavelength drift. Traditionally, spectrometer demodulation systems are used, but these are bulky, difficult to carry, and inconvenient for field use. In recent years, miniature spectrometers have emerged that are small and inexpensive, but their spectral resolution is only on the order of 0.1 nm, far from the pm-level resolution required for FBG demodulation. To improve the measurement accuracy of Bragg wavelength drift, a processing technique based on a FP tunable filter and a wavelength reference, using an interpolation-correlation spectroscopy method, is proposed. This involves first linearly inserting some points between every two adjacent points in the original spectrum, and then using correlation spectroscopy to obtain the Bragg wavelength drift. This method not only effectively suppresses noise but also accurately measures the Bragg wavelength drift, thereby achieving high-precision measurement of external parameters such as temperature and strain. 1. FBG Sensor Principle According to the Bragg diffraction principle, when light emitted from a broadband light source is incident into an FBG, the FBG will reflect the light back within a narrow band of the spectrum centered on the Bragg wavelength. The Bragg wavelength λB is determined by the grating pitch A and the effective refractive index neff of the FBG; therefore, the FBG can be regarded as a narrowband filter, and the center wavelength of the filter is the Bragg wavelength. When the FBG is subjected to factors such as strain and temperature, causing changes in the grating pitch or the effective refractive index neff, the Bragg wavelength λB reflected by the FBG will also change accordingly. From the differential of equation (1), the offset of its Bragg wavelength is obtained as: This achieves wavelength encoding modulation of the reflected signal light to be measured. Therefore, by monitoring the offset of the reflected wavelength in real time, and based on the linear relationship between Δnff, ΔΛ and the measured quantity, the change of the measured physical quantity can be obtained. 2. Interpolation-Correlation Spectrum Method Principle The correlation spectrum method is based on the following characteristic: In many FBG sensing systems, the FBG spectrum only exhibits fluctuations in optical power and an overall spectral drift, while the shape of the spectrum remains constant, resembling a Gaussian distribution. This characteristic suggests the possibility that the Bragg wavelength drift can be obtained by comparing the similarity between the original spectrum and the drifted spectrum. This similarity can be represented by a cross-correlation function. The theoretical analysis of the spectral correlation method is given below. According to the theory of digital signal processing, let two spectra be X(i) and Y(i) after photoelectric conversion sampling (i = 1, 2, 3, ..., N, representing wavelengths), and their cross-correlation operation is defined as: where j is the wavelength drift added to x. Spectra with wavelength subscripts outside the range [1, N] are considered zero. According to the properties of cross-correlation, R(j) reaches its maximum value when x(ij) and Y(i) overlap the most and are most similar. Because the spectrum reflected by each FBG is similar to a Gaussian distribution, by first acquiring a reference spectrum, then performing a cross-correlation operation with the measured spectrum, and finding the j value corresponding to the maximum cross-correlation value, the drift of the measured spectrum can be obtained, which in turn yields the drift of the Bragg wavelength. It is evident that the correlation spectral method is feasible, and importantly, this method offers higher accuracy compared to the traditional peak detection method. The peak detection method calculates the maximum value in the original reflection spectrum, while the spectral correlation method, through correlation calculation, calculates the maximum value among a series of correlation values ​​corresponding to different drift values. When calculating each correlation value, many spectral values ​​are added together, which effectively suppresses noise in the actual original spectrum according to the square root of the sum N, thereby improving the accuracy of wavelength measurement. The following derivation shows that: Before analysis, it is assumed that n1 and n2 are independent noises, both following a Gaussian distribution. The signal-to-noise ratio (SNR) is defined as the root mean square of the signal divided by the root mean square of the noise. Let the SNR of the original signals Xn(i) and Yn(j) both be SNR0. According to the independence of the Gaussian distribution, the SNR of equation (6) is: As can be seen from the above equation, as N increases, the SNR after the correlation spectrum method increases relative to the original signal SNR (theoretically, this is true, and the experiment will show it in practice later). Therefore, the measurement error caused by the noise in the original spectrum can be suppressed. In order to reduce the difficulty of system hardware implementation, ensure demodulation speed, and further improve the wavelength measurement accuracy, this paper also combines the linear interpolation method. The whole process is to first linearly insert some points between every two adjacent points in the original spectrum, and then use the correlation spectrum method to obtain the Bragg wavelength drift. The purpose of using linear interpolation is to make the original spectrum more similar to the drifted spectrum, so that the wavelength drift can be determined more accurately in the correlation spectrum method. [b]3. Experimental Results[/b] The demodulation system setup is shown in Figure 1. It uses a light-emitting diode (LED) with a center wavelength of 1550 nm and a spectral width of 30 nm. The light emitted by the LED enters the FBG after passing through a 3 dB coupler. The light reflected back from the FBG passes through this 3 dB coupler again and enters the FP tunable filter (FOOL2 type). Then, it is converted by photoelectric conversion, amplified, and D/A converter before entering the digital signal processor (DSP) to achieve interpolation-correlation spectrum demodulation (FBG0 is a fixed-wavelength reference FBG. This wavelength reference can eliminate the influence of the cavity length drift of the tunable FP filter on the measurement accuracy). 3.1 Comparison of Interpolation-Correlation Spectrum Method and Peak Method The reflection spectra of FBG1 and FBG2 were continuously measured 10 times. FBG1 and FBG2 were placed freely and the temperature remained constant. Therefore, theoretically, the results of each measurement should be the same, but in practice, there are slight differences. Figure 2 shows the measured values ​​of FBG2 (similar to FBG1) under three different conditions, with 800 sampling points in the 1552–1557 nm range. In Figure 2, a) uses the traditional direct peak finding method, with a standard deviation of 0.04241 nm; b) uses correlation spectroscopy without interpolation, with a standard deviation of 0 nm; c) uses interpolation-spectral correlation (linear interpolation of 8 points between each adjacent point), with a standard deviation of 0.00214 nm. Superficially, b seems to be the best, but this is actually because the interval between each adjacent point is too large, making it impossible to clearly separate them when the Bragg wavelength is in the smallest range, ultimately treating them as the same value. By first interpolating certain data to improve resolution, the original spectrum becomes more similar to the drifted spectrum, and then applying correlation spectroscopy yields the best results. To investigate the optimal number of interpolation points for achieving the highest wavelength resolution under certain conditions in the interpolation-correlation spectroscopy method, the number of interpolation points between adjacent points in the experimental system above was increased from 2 to 17, as shown in Table 1. Table 1 shows that in practice, the wavelength resolution of the interpolation-correlation spectroscopy method for measuring Bragg wavelength drift does not increase significantly with the increase of interpolation points. In this system, the resolution reaches 1 pm when the number of interpolation points between adjacent points increases to 12; further increases do not lead to further improvement. 3.2 Temperature Sensing Experiment: The FBG was gradually heated in 10℃ increments. The relationship between the Bragg wavelength change and temperature measured by the interpolation-correlation spectroscopy method is shown in Figure 3. Figure 3 shows that the error (root mean square error) between the measurement result and the linear fitting is 1.18 pm. 4. Conclusion : Theoretical analysis and experiments demonstrate that measuring Bragg wavelength drift using the correlation spectroscopy method is feasible and can improve the signal-to-noise ratio, thereby improving demodulation accuracy. Building upon this, by combining linear interpolation with a certain number of points inserted between every two adjacent points in the original spectrum, demodulation accuracy can be further improved. Using the interpolation-correlation spectroscopy method, the wavelength resolution of the Bragg grating can reach 1 pm, and the temperature measurement accuracy can reach ±0.2℃.