Abstract：To solve the problem of output demodulation of optical vernier sensors, this paper proposes a spectral data prediction technology based on a bidirectional long short-term memory (Bi-LSTM) network. By utilizing the predictive ability of the Bi-LSTM network for data sequences, a wide spectral range of spectral data prediction has been achieved, thus solving the technical problem of cursor sensors having difficulty achieving output demodulation due to the limited working spectral range of light sources or spectral scanning techniques.By using this method, as long as a limited wavelength range of sensor output spectra is collected, the trained Bi-LSTM model can accurately predict the envelope curve of the sensor output spectra over a wide wavelength range, greatly reducing the technical requirements for the working spectral range of the vernier sensor.The paper introduces the basic principle and implementation process of the Bi-LSTM network for output demodulation of vernier sensors. The experiment proves the accuracy of this method in predicting the spectral data output of vernier sensors. The maximum wavelength error between the predicted curve and the actual spectral envelope at the peak is about 0.02 nm, and the maximum amplitude error is only 0.058%. In addition, the paper also verified the generalization of the Bi-LSTM network for demodulating the output spectra of cursor sensors with different envelope periods. For the output spectra of cursor sensors with different envelope periods, the maximum prediction error was 0.02 nm, and the maximum root mean square error (RMSE) was 9.72×10-5, proving that the trained Bi-LSTM network has accurate “predictability” and “tracking” for the output spectra of cursor sensors with different envelope periods. Comprehensive research papers have shown that in practice, as long as the wavelength range of the working light source can cover half of the spectral envelope period of the vernier sensor (which can be met in most cases), the Bi-LSTM network can accurately predict the output spectrum of the sensor over a wide spectral range, greatly reducing the requirement for the spectral range of the working light source (or other spectral scanning techniques) of the vernier sensor. The paper has solved the problem of the output demodulation spectrum range of the cursor sensor being too wide and has theoretical and practical significance for application.
[1] Li J, Zhang M, Wan M, et al. Optics Express, 2020, 28(3): 4145.
[2] Tian K D, Wang Z C, Wang G C, et al. IEEE Sensors Journal, 2024, 24(15): 23918.
[3] Guo M S, Ding H, Han K C, et al. Journal of Lightwave Technology, 2024, 42(15): 5383.
[4] Cheng A, Wang C Q, Xu J D, et al. IEEE Sensors Journal, 2024, 24(12): 19090.
[5] Yang Y Q, Zhang Y Y, Mu X G, et al. IEEE Sensors Journal, 2024, 24(8): 12419.
[6] GAO Jia-le, YANG Yu-qiang, MOU Xiao-guang, et al（高佳乐, 杨玉强, 牟小光, 等）. Optics and Precision Engineering（光学精密工程）, 2023, 31(24): 3531.
[7] Wang G C, Wang Y G, Wang Z C, et al. IEEE Sensors Journal, 2024, 24(3): 2815.
[8] Zhang T, Han Q, Ma Q Y, et al. IEEE Sensors Journal, 2024, 24(7): 10084.
[9] Li M, Li Y H, Cong A M, et al. IEEE Sensors Journal, 2023, 23(20): 24545.
[10] YANG Yu, ZHANG Lei, WANG Ke-yi（杨 煜, 张 磊, 王克逸）. Optics and Precision Engineering（光学精密工程）, 2022, 30(4): 403.
[11] Leal-Junior A, Frizera-Neto A, Marques C, et al. Sensors, 2018, 18(3): 916.
[12] Zhu C, Alsalman O, Naku W. Optics Letters, 2023, 48(9), 2488.
[13] Zhang T, Han Q, Liang Z Z, et al. Sensors, 2023, 23(5): 2800.
[14] Peng K, Jiang L Z, Zhou W B, et al. Journal of Central South University, 2024, 31(3): 965.
[15] LI Hao, ZHAO Qing, CUI Chen-zhou, et al（李 浩, 赵 青, 崔辰州, 等）. Spectroscopy and Spectral Analysis（光谱学与光谱分析）, 2024, 44(6): 1668.
[16] Tian J B, Zeng G H, Zhao J B, et al. IEEE Transactions on Industrial Informatics, 2024, 20(4): 5428.
[17] Yu S, Tan Z Z, Yang W L, et al. IEEE Sensors Journal, 2024, 20(2): 1502.
[18] Martins G R, da Silve L C B, Segatto M E V, et al. Optical Fiber Technology, 2024, 82: 103636.
[19] Li Y, Zhang H, Li L, et al. Frontiers in Physics, 2023, 11: 1070762.
[20] PAN Xin-liang, YANG Ren-hui, JIANG Tao, et al（潘信亮, 杨仁辉, 江 涛, 等）. Acta Optica Sinica（光学学报）, 2021, 41(10): 142.
