Efficient and Reliable Thickness Measurement Method for Multilayer Coatings Based on Terahertz Time-Domain Spectroscopy Technology

Binghua Cao; Dedong Zheng; Mengbao Fan; Fengshan Sun; Lin Liu

doi:10.3788/AOS202242.0112001

Acta Optica Sinica, Volume. 42, Issue 1, 0112001(2022)

Efficient and Reliable Thickness Measurement Method for Multilayer Coatings Based on Terahertz Time-Domain Spectroscopy Technology

Binghua Cao^1、*, Dedong Zheng¹, Mengbao Fan², Fengshan Sun², and Lin Liu³

Author Affiliations

¹School of Information and Control Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221000, China

²School of Mechatronic Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221000, China

³Beijing Institute of Aerospace Metrology and Measurement Technology, Beijing 100076, China

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Figures & Tables(22)

Fig. 1. Schematic of THz wave propagation in a single-layer model

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Fig. 2. Schematic of multi-layer structure deriving equivalent reflection coefficient

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Fig. 3. Comparison of ergodicity between standard Kent chaotic map and improved Kent chaotic map

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Fig. 4. Flow chart of adaptive TLBO algorithm

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Fig. 5. Flow chart of thickness measured by model method

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Fig. 6. THz-TDS diagram

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Fig. 7. Schematic of THz-TDS principle

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Fig. 8. Schematic of multilayer samples. (a) Single-layer paper sheet fixed on the metallic substrate; (b) double-layer paper sheet fixed on the metallic substrate

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Fig. 9. TBC. (a) Surface morphology of top coating; (b) structure diagram; (c) electron microscope image

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Fig. 10. THz measurement signal. (a) Sample 1; (b) sample 2

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Fig. 11. Comparison of fitness between adaptive TLBO algorithm, standard TLBO, and global search in Ref. [20]

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Fig. 12. Comparison of measurement signal and simulation signal. (a) Sample 1; (b) sample 2

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Fig. 13. Signal of TBC sample. (a) THz measurement signal of TBC; (b) comparison of measurement signal and simulation signal of TBC

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Table 1. Adaptive TLBO algorithm functioning statistics table
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Table 1. Adaptive TLBO algorithm functioning statistics table
Sample Number of experiments Number of times which adaptive TLBO algorithm has worked Effectiveness /% Run time /s
Sample 1 50 42 84 48.3
Sample 2 50 45 90 49.7

Table 2. Measurement parameters of sample 1 under the adaptive TLBO algorithm
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Table 2. Measurement parameters of sample 1 under the adaptive TLBO algorithm
Layer Refractive index Extinction coefficient Actual thickness /μm Measured thickness /μm Relative error /%
Layer 1 1.44 0.048 92±1.1 92.5±1.48 0.54
Layer 2 Unknown 116.8

Table 3. Measurement parameters of sample 2 under the adaptive TLBO algorithm

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Table 3. Measurement parameters of sample 2 under the adaptive TLBO algorithm

Layer	Refractive index	Extinction coefficient	Actual thickness /μm	Measured thickness /μm	Relative error /%
Layer 1	1.45	0.048	92±1.1	93.3±1.61	1.41
Layer 2			Unknown	103.8
Layer 3	1.46	0.050	92±1.1	93.3±1.54	1.41
Layer 4			Unknown	129.6

Table 4. Thickness results of sample 1 under the three algorithms

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Table 4. Thickness results of sample 1 under the three algorithms

Layer	Actual thickness /μm	TLBO		Adaptive TLBO		Method in Ref. [20]
Layer	Actual thickness /μm	Measured thickness /μm	Relative error /%	Measured thickness /μm	Relative error /%	Measured thickness /μm	Relative error /%
Layer 1	92±1.1	94.2±1.68	2.39	92.5±1.48	0.54	92.7±1.55	0.76
Layer 2	Unknown	113.1		116.8		118.9

Table 5. Thickness results of sample 2 under the three algorithms

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Table 5. Thickness results of sample 2 under the three algorithms

Layer	Actual thickness /μm	TLBO		Adaptive TLBO		Method in Ref. [20]
Layer	Actual thickness /μm	Measured thickness /μm	Relative error /%	Measured thickness /μm	Relative error /%	Measured thickness /μm	Relative error /%
Layer 1	92±1.1	94.4±1.84	2.61	93.3±1.61	1.41	93.4±1.66	1.52
Layer 2	Unknown	104.5		103.8		103.1
Layer 3	92±1.1	94.8±1.71	3.04	93.3±1.54	1.41	93.3±1.62	1.41
Layer 4	Unknown	128.4		129.6		130.4

Table 6. Time consumption of the three algorithms in a single rununit: s
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Table 6. Time consumption of the three algorithms in a single rununit: s
Sample TLBO Adaptive TLBO Method in Ref. [20]
Sample 1 40.4 48.3 118.3
Sample 2 40.6 49.7 119.1

Table 7. Results of TBC’s thickness under the three algorithms

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Table 7. Results of TBC’s thickness under the three algorithms

Sample	Actual thickness /μm	TLBO		Adaptive TLBO		Method in Ref. [20]
Sample	Actual thickness /μm	Measured thickness /μm	Relative error /%	Measured thickness /μm	Relative error /%	Measured thickness /μm	Relative error /%
TBC	305.3	312.2±1.77	2.26	301.1±1.52	1.38	300.4±1.56	1.60

Table 8. Measurement parameters of TC under the adaptive TLBO algorithm
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Table 8. Measurement parameters of TC under the adaptive TLBO algorithm
Sample Refractive index Extinction coefficient Actual thickness /μm Measured thickness /μm Relative error of thickness /%
TC 4.90 0.072 305.3 301.1±1.52 1.38

Table 9. Single running time of three different algorithms for TBCunit: s
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Table 9. Single running time of three different algorithms for TBCunit: s
Sample TLBO Adaptive TLBO Method in Ref. [20]
TBC 40.1 46.2 114.8

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Binghua Cao, Dedong Zheng, Mengbao Fan, Fengshan Sun, Lin Liu. Efficient and Reliable Thickness Measurement Method for Multilayer Coatings Based on Terahertz Time-Domain Spectroscopy Technology[J]. Acta Optica Sinica, 2022, 42(1): 0112001

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