Deep learning assisted real-time and portable refractometer using a <inline-formula><math display="inline" id="m1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mi>π</mi></mrow></math></inline-formula>-phase-shifted tilted fiber Bragg grating sensor

Ziqi Liu; Chang Liu; Tuan Guo; Zhaohui Li; Zhengyong Liu

doi:10.1364/PRJ.561101

Photonics Research, Volume. 13, Issue 8, 2202(2025)

Deep learning assisted real-time and portable refractometer using a $π$ -phase-shifted tilted fiber Bragg grating sensor

Ziqi Liu¹, Chang Liu¹, Tuan Guo^2,3, Zhaohui Li^1,3, and Zhengyong Liu^1,3、*

Author Affiliations

¹School of Electronics and Information Technology, Guangdong Provincial Key Laboratory of Optoelectronic Information Processing Chips and Systems, Sun Yat-sen University, Guangzhou 510006, China

²Guangdong Key Laboratory of Optical Fiber Sensing and Communications, Institute of Photonics Technology, Jinan University, Guangzhou 511443, China

³Southern Marine Science and Engineering Guangdong Laboratory (Zhuhai), Zhuhai 519082, China

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Figures & Tables(13)

Fig. 1. (a) Structure of the TFBG and (b) transmission spectrum and local amplification of TFBG with a tilted angle of 16°; (c) structure of the $π$ -PSTFBG and (d) transmission spectrum and local amplification of PSTFBG with a tilted angle of 16°; (e) schematic illustration of the fiber grating inscription setup based on two-beam interferometry; (f) introduction of $π$ -phase shift during grating inscription based on two-beam interferometry method.

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Fig. 2. Experimentally measured transmission spectrum of $π$ -PSTFBG with tilted angles of (a) 6°, (b) 8°, (c) 10°, and (d) 16°.

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Fig. 3. (a) Schematic setup to acquire transmission spectral data of 16° $π$ -PSTFBG under the conditions of various SRIs, while a conventional 16°-TFBG is employed as control group for comparison; transmission spectra collected under different RIs of (b) TFBG and (c) $π$ -PSTFBG.

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Fig. 4. (a) Schematic diagram of the proposed demodulation algorithm based on deep learning for analyzing the full spectrum of the $π$ -PSTFBG sensor; two-dimensional distribution of the intermediate features via t-SNE visualization for (b) the input data and (c) the output data after the DenseBlock_2 layer.

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Fig. 5. Prediction results of $π$ -PSTFBG RI sensor based on the well-trained models of (a) convolutional neural network (CNN) and (b) densely connected CNN (D-CNN) in comparison with labeled truth values.

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Fig. 6. Histogram of the mean absolute error of prediction results based on machine learning model in three noise scenarios.

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Fig. 7. Predicted RI results by the well-trained D-CNN model with respect to the labeled truth values: (a) TFBG, (b) SPR-TFBG. (c) Measured transmission spectra at different RIs using SPR-TFBG.

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Fig. 8. The compositions of (a) the real-time demodulation system and (b) the spectrometer unit; (c) the prototype of the real-time demodulation system for $π$ -PSTFBG-based RI sensor.

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Fig. 9. (a) Measured transmission spectra of $π$ -PSTFBG collected by a low-resolution spectrometer at different RIs; (b) predicted RI results by well-trained D-CNN model based on the original spectral data of $π$ -PSTFBG obtained via low-resolution interrogator.

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Fig. 10. (a)–(g) 7-day continuous measurement using the developed prototype of real-time demodulation assisted by D-CNN model for the NaCl solutions with RIs of 1.3480, 1.3562, 1.3647, and 1.3730. (h) Predicted RIs in a longer duration individually for each solution of 1.3462, 1.3579, 1.3679, and 1.3717. (i) Average predicted RIs with respect to the labeled truth values. (j) Predicted value change curve of real-time demodulation system when a NaCl solution with high RI drops into a NaCl solution with low RI.

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Table 1. Configured Parameters in Each Layer of CNN and D-CNN Models

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Table 1. Configured Parameters in Each Layer of CNN and D-CNN Models

CNN		D-CNN
Layer Name	Parameters	Layer Name	Parameters
Input	–	Input	–
Conv1D	96	Conv1D	128
Batch normalization	32	Batch normalization	64
MaxPool1D	0	MaxPool1D	0
Conv1D	3616	Conv1D	5152
MaxPool1D	0	MaxPool1D	0
Conv1D	14,400	DenseBlock1	1380
MaxPool1D	0	DenseBlock2	1780
Conv1D	20,544	Conv1D	2628
MaxPool1D	0	AvgPool1D	0
Conv1D	20,544	DenseBlock3	1460
MaxPool1D	0	AvgPool1D	0
Conv1D	12,352	Flatten	0
AvgPool1D	0	Linear	18,593
Flatten	0	–	–
Linear	5185	–	–

Table 2. Spectral Demodulation Results of $π$ -PSTFBG Based on Machine Learning Algorithm

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Table 2. Spectral Demodulation Results of $π$ -PSTFBG Based on Machine Learning Algorithm

ML Algorithm	$R^{2}$	MSE	MAE
DTR	84.77%	$2.261 \times 10^{- 5}$	$2.24 \times 10^{- 3}$
RFR	98.84%	$1.633 \times 10^{- 6}$	$8.94 \times 10^{- 4}$
GBR	98.21%	$2.522 \times 10^{- 6}$	$1.08 \times 10^{- 3}$
LR	99.13%	$1.253 \times 10^{- 6}$	$5.29 \times 10^{- 4}$
MLP	99.14%	$1.442 \times 10^{- 6}$	$6.64 \times 10^{- 4}$
CNN	98.36%	$2.742 \times 10^{- 6}$	$1.02 \times 10^{- 3}$
D-CNN	99.67%	$5.083 \times 10^{- 7}$	$5.99 \times 10^{- 4}$

Table 3. Comparison of the Test Results Using the Same Well-Trained D-CNN Model for TFBG-, SPR-TFBG-, and $π$ -PSTFBG-Based Sensors
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Table 3. Comparison of the Test Results Using the Same Well-Trained D-CNN Model for TFBG-, SPR-TFBG-, and $π$ -PSTFBG-Based Sensors
Sensor $R^{2}$ MSE MAE
TFBG 99.17% $1.2902 \times 10^{- 6}$ $8.796 \times 10^{- 4}$
SPR-TFBG 99.26% $1.1340 \times 10^{- 6}$ $8.15 \times 10^{- 4}$
$π$ -PSTFBG 99.67% $5.0829 \times 10^{- 7}$ $5.99 \times 10^{- 4}$

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Ziqi Liu, Chang Liu, Tuan Guo, Zhaohui Li, Zhengyong Liu, "Deep learning assisted real-time and portable refractometer using a $π$ -phase-shifted tilted fiber Bragg grating sensor," Photonics Res. 13, 2202 (2025)

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Paper Information

Category: Optical Devices

Received: Mar. 4, 2025

Accepted: May. 9, 2025

Published Online: Jul. 25, 2025

The Author Email: Zhengyong Liu (liuzhengy@mail.sysu.edu.cn)

DOI:10.1364/PRJ.561101

CSTR:32188.14.PRJ.561101

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Configured Parameters in Each Layer of CNN and D-CNN Models

Table 1. Configured Parameters in Each Layer of CNN and D-CNN Models

Table 2. Spectral Demodulation Results of π-PSTFBG Based on Machine Learning Algorithm

Table 2. Spectral Demodulation Results of π-PSTFBG Based on Machine Learning Algorithm

Table 3. Comparison of the Test Results Using the Same Well-Trained D-CNN Model for TFBG-, SPR-TFBG-, and π-PSTFBG-Based Sensors

Table 3. Comparison of the Test Results Using the Same Well-Trained D-CNN Model for TFBG-, SPR-TFBG-, and π-PSTFBG-Based Sensors

Table 2. Spectral Demodulation Results of $π$ -PSTFBG Based on Machine Learning Algorithm

Table 2. Spectral Demodulation Results of $π$ -PSTFBG Based on Machine Learning Algorithm

Table 3. Comparison of the Test Results Using the Same Well-Trained D-CNN Model for TFBG-, SPR-TFBG-, and $π$ -PSTFBG-Based Sensors

Table 3. Comparison of the Test Results Using the Same Well-Trained D-CNN Model for TFBG-, SPR-TFBG-, and $π$ -PSTFBG-Based Sensors