Terahertz Time-Domain Spectral Hierarchical Detection Algorithm Based on Sparse Representation

Meng Liu; Teng Li; Xudong Liu; Yiwen Sun

doi:10.3788/LOP231372

Laser & Optoelectronics Progress, Volume. 60, Issue 18, 1811014(2023)

Terahertz Time-Domain Spectral Hierarchical Detection Algorithm Based on Sparse Representation

Meng Liu, Teng Li, Xudong Liu, and Yiwen Sun^*

Author Affiliations

School of Biomedical Engineering, Health Science Center, Shenzhen University, Shenzhen 518000, Guangdong , China

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Figures & Tables(23)

Fig. 1. Sparse representation method based on LASSO

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Fig. 2. Schematic of some atoms in the dictionary. (a) Some atoms in non-dispersive dictionary A; (b) some atoms in dispersion dictionary D

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Fig. 3. Terahertz wave reflection model

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Fig. 4. THz reference signal generated by DGMM for 3000 data points with a sampling period of 0.0333 ps

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Fig. 5. L-curve diagrams and their values for regularization problems under different noise levels. (a) LASSO; (b) BPDN

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Fig. 6. Reconstruction results of pulse response function for non overlapping echo signals using three methods. (a) Absence of noise; (b) R_SN=40 dB; (c) R_SN=20 dB; (d) R_SN=10 dB

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Fig. 7. Reconstruction results of pulse response function for overlapping echo signals using three methods. (a) Absence of noise; (b) R_SN=40 dB; (c) R_SN=20 dB; (d) R_SN=10 dB

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Fig. 8. Variation of the minimum TOF with noise level distinguishable by different algorithms

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Fig. 9. Effect of dispersion on the reflected THz echo signal

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Fig. 10. Comparison between the reconstruction results of three methods and the preset value. (a) Absence of noise; (b) R_SN=40 dB; (c) R_SN=20 dB; (d) R_SN=10 dB

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Fig. 11. THz-TDS system. (a) Physical image of the THz system and sample placement window; (b) switch for displacement table; (c) display interface of the software program for controlling data collection, display, and storage written through LabVIEW, the first part includes control buttons related to system initialization, start/stop operation, and data storage, the second part is about setting and displaying the spectral range, the third part is to control the displacement table for displacement or imaging scanning, the fourth part is the display of scanning results

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Fig. 12. Experimental spectrograms and pulse response functions reconstructed using three algorithms. (a) THz time-domain spectra of PTFE films with different thicknesses; (b) PTFE200; (c) PTFE100; (d) PTFE50

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Fig. 13. Physical diagram of GFRP model and schematic of THz detection principle. (a) Physical image; (b) schematic of detection principle

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Fig. 14. Experimental spectrograms and pulse response functions reconstructed using three algorithms. (a) THz time-domain spectrograms of three sets of models; (b) GFRP1; (c) GFRP2; (d) GFRP3

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Fig. 15. Physical image of composite material model, schematic of imaging area, and diagram of terahertz detection principle. (a) Physical image; (b) schematic of the imaging area, triangulation dots represent random sampling points in defect‑free areas, round dots represent random sampling points in the defect area; (c) schematic of terahertz detection

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Fig. 16. Original data graph and B-scan imaging graph of the model before and after processing for two groups of sampling points. (a) Terahertz time-domain spectrogram before processing; (b) terahertz time-domain spectrogram after processing; (c) B-scan imaging image before processing; (d) B-scan imaging image after processing

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Fig. 17. Imaging pseudo color images of GFRP samples with mixed defects before and after processing. (a) Original imaging result; (b) imaging result without amplitude correction; (c) terahertz time-domain spectrogram before and after correcting the amplitude of sampling points in the defect area; (d) imaging result after amplitude correction

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Table 1. DGMM preset values for different echoes in THz signals
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Table 1. DGMM preset values for different echoes in THz signals
Signal $β_{1}$ $t_{1}$ $α_{1}$ $β_{2}$ $t_{2}$ $α_{2}$
Echo1 1.5 10.45 0.2 -0.5 10 0.7
Echo2 0.9 13.7 0.3 -0.375 13.1 0.9
Echo3 0.6 15.55 0.5 -0.25 14.9 1.1
Echo4 0.3 18.2 0.8 -0.125 17.2 1.4

Table 2. Localization of TOF of PTFE films with different thicknesses by three algorithms

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Table 2. Localization of TOF of PTFE films with different thicknesses by three algorithms

Method	PTFE200			PTFE100			PTFE50
Method	$t_{1}$	$t_{2}$	$Δ t$	$t_{1}$	$t_{2}$	$Δ t$	$t_{1}$	$t_{2}$	$Δ t$
FWDD	62.5333	64.3667	1.8333	61.8667	62.6667	0.8	61.5	61.9667	0.4667
BPDN	62.5333	64.3667	1.8333	61.8667	62.6667	0.8	61.5	61.9	0.4
LASSO	62.5333	64.3667	1.8333	61.8667	62.6667	0.8	61.5	61.9333	0.4333

Table 3. Actual thickness of three sets of PTFE films and detected thicknesses obtained by different algorithms respectively
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Table 3. Actual thickness of three sets of PTFE films and detected thicknesses obtained by different algorithms respectively
Method PTFE200 Error PTFE100 Error PTFE50 Error
Actual value 200 100 50
FWDD 208.4 4.2% 94.8 5.2% 53.1 6.2%
BPDN 208.4 4.2% 94.8 5.2% 45.5 9.0%
LASSO 208.4 4.2% 94.8 5.2% 49.3 1.4%

Table 4. Localization of TOF of PTFE thin film in detection layer by three algorithms
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Table 4. Localization of TOF of PTFE thin film in detection layer by three algorithms
Method GFRP1 GFRP2 GFRP3
$t_{1}$ $t_{2}$ $Δ t$ $t_{1}$ $t_{2}$ $Δ t$ $t_{1}$ $t_{2}$ $Δ t$
FWDD 74.5333 77.1 2.5667 74.7333 76.2333 1.5 74.3667 75.6667 1.3
BPDN 74.8667 76.7 1.8333 74.9 75.9 1.0 74.6 75.2 0.6
LASSO 74.7667 76.6 1.8333 74.9667 75.8667 0.9 74.7333 75.2 0.4667

Table 5. Actual thickness of three sets of GFRP models and detected thicknesses obtained by different algorithms respectively
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Table 5. Actual thickness of three sets of GFRP models and detected thicknesses obtained by different algorithms respectively
Method GFRP1 Error GFRP2 Error GFRP3 Error
Actual value 200 100 50
FWDD 291.8 45.9% 170.5 70.5% 147.8 195.6%
BPDN 208.4 4.2% 113.7 13.7% 68.2 60.4%
LASSO 208.4 4.2% 102.3 2.3% 53.1 6.2%

Table 6. Weber contrast of images
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Table 6. Weber contrast of images
Parameter Fig.16（a） Fig.16（b） Fig.16（d）
$C_{w}$ 0.1021 0.6756 0.8985

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Meng Liu, Teng Li, Xudong Liu, Yiwen Sun. Terahertz Time-Domain Spectral Hierarchical Detection Algorithm Based on Sparse Representation[J]. Laser & Optoelectronics Progress, 2023, 60(18): 1811014

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Paper Information

Category: Imaging Systems

Received: May. 24, 2023

Accepted: Aug. 1, 2023

Published Online: Sep. 19, 2023

The Author Email: Yiwen Sun (ywsun@szu.edu.cn)

DOI:10.3788/LOP231372

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. DGMM preset values for different echoes in THz signals

Table 1. DGMM preset values for different echoes in THz signals

Table 2. Localization of TOF of PTFE films with different thicknesses by three algorithms

Table 2. Localization of TOF of PTFE films with different thicknesses by three algorithms

Table 3. Actual thickness of three sets of PTFE films and detected thicknesses obtained by different algorithms respectively

Table 3. Actual thickness of three sets of PTFE films and detected thicknesses obtained by different algorithms respectively

Table 4. Localization of TOF of PTFE thin film in detection layer by three algorithms

Table 4. Localization of TOF of PTFE thin film in detection layer by three algorithms

Table 5. Actual thickness of three sets of GFRP models and detected thicknesses obtained by different algorithms respectively

Table 5. Actual thickness of three sets of GFRP models and detected thicknesses obtained by different algorithms respectively

Table 6. Weber contrast of images

Table 6. Weber contrast of images