Multilayer coating thickness measuring method based on terahertz time-domain spectroscopy

Abstract

The invention discloses a multilayer coating thickness measurement method based on terahertz time-domain spectroscopy, and belongs to the technical field of coating thickness measurement, and the method comprises the steps: employing a reflection-type terahertz time-domain spectroscopy system to measure a signal with a coating and a signal without the coating on a metal plate, and enabling the signals to serve as a measurement signal and a reference signal; establishing a coating thickness inversion model, and fitting a multi-layer coating signal; inputting the measurement signal and the reference signal into a coating thickness inversion model, and solving through an evolutionary optimization algorithm to obtain an optimal solution of an inversion parameter; and inverting the thickness of each coating according to the optimal solution. According to the method, based on the terahertz time-domain spectroscopy, self-consistent and nondestructive measurement of the thicknesses of the multiple layers of coatings is achieved through the coating thickness inversion model and the hybrid optimization algorithm, and errors are small.

Description

Technical Field

[0001] This invention relates to the field of coating thickness measurement technology, and in particular to a method for measuring the thickness of multilayer coatings based on terahertz time-domain spectroscopy. Background Technology

[0002] Coating thickness measurement is a critical process for ensuring coating performance and service life, directly affecting the product's corrosion resistance, wear resistance, and insulation properties. Accurate thickness measurement effectively avoids insufficient protection due to excessively thin coatings or performance defects caused by excessively thick coatings, making it an essential means of quality control and ensuring product reliability. Currently, there are many methods for measuring coating thickness in industry, such as eddy current measurement, ultrasonic measurement, and magnetic induction measurement. However, these methods are limited by certain application scenarios, such as contact damage to the coating surface, low measurement accuracy, and sensitivity to metal substrates, making it difficult to meet the requirements of accurate measurement and non-destructive testing. Summary of the Invention

[0003] The purpose of this invention is to provide a method for measuring the thickness of multilayer coatings based on terahertz time-domain spectroscopy, in order to solve the problems mentioned in the background art.

[0004] To achieve the above objectives, the present invention provides a method for measuring the thickness of multilayer coatings based on terahertz time-domain spectroscopy, comprising the following steps: S1. Measure the signals on the metal plate with and without coating using a reflective terahertz time-domain spectroscopy system, and use them as the measurement signal and reference signal, respectively. S2. Establish a coating thickness inversion model and fit the multilayer coating signal; S3. Input the measured signal and reference signal into the coating thickness inversion model, and solve it through an evolutionary optimization algorithm to obtain the optimal solution of the inversion parameters; S4. Calculate the thickness of each coating layer based on the optimal solution.

[0005] Preferably, step S2, establishing the coating thickness inversion model, includes: S21. Establish a multivariate reflection signal regression sub-model and calculate the time-of-flight difference and refractive index between the reflection echo signal and the reference signal in each layer. S22. Considering multiple reflections of the signal between layers, establish a multi-reflection correction sub-model. S23. Establish a dispersion correction sub-model to correct the dispersion effect when terahertz waves propagate in the coating. S24. Combining the three sub-models, we obtain the total fitted signal; S25. Based on the total fitted signal and the measurement signal, the fitting error is defined as the objective function of the coating thickness inversion model.

[0006] Preferably, the multivariate reflection signal regression sub-model in step S21 includes: ; In the formula, express The fitted signal of the reflected echo signal, Indicates the first One reflected echo signal, For the first The reflected echo signal and the reference signal The time difference between the flights, Indicates the number of reflected echoes. Given the coefficients of each reflected pulse, the refractive index of each layer is calculated using Fresnel's law based on these coefficients. .

[0007] Preferably, the multiple reflection correction sub-model in step S22 includes: ; In the formula, This represents the time delay between multiple reflected signals, where the multiple reflected signals have the same time delay. Indicates the total signal from multiple reflections. The multi-reflection amplitude attenuation coefficient represents the loss of terahertz waves due to multiple reflections within the coating. For multiple reflection pulse coefficients, This represents the time delay between the reflected echo signal from the metal substrate and the reference signal. Indicates the first Multiple reflections This indicates the number of multiple reflected signals.

[0008] Preferably, the dispersion correction sub-model in step S23 includes: ; In the formula, Represents the equivalent dispersion parameter. This represents the dispersion transfer function of terahertz waves in the coating. It represents angular frequency.

[0009] Preferably, in step S23, the formula for calculating the total fitted signal by combining the three sub-models is as follows: ; In the formula, Represents the total fitted signal. This represents the Fourier transform.

[0010] Preferably, the objective function in step S25 includes: ; In the formula, This represents the fitted signal value. Indicates the value of the measured signal. Indicates the overall goal.

[0011] Preferably, in step S3, the Differential Evolutionary Algorithm (DE) and the Covariance Matrix Adaptive Evolutionary Strategy (CMA-ES) are used to solve for the optimal solution of the inversion parameters, wherein the inversion parameters include , , , , .

[0012] Preferably, step S4, which involves retrieving the thickness of each coating layer based on the optimal solution, includes: The time-of-flight difference between the reflected echo signal and the reference signal at each layer is obtained based on the optimal solution. and refractive index ; according to and The thickness of each coating layer is calculated. The formula is: ; In the formula, y is the speed at which light travels through the air.

[0013] Preferably, the coating has a maximum of four layers.

[0014] Therefore, the present invention employs the above-described method for measuring the thickness of multilayer coatings based on terahertz time-domain spectroscopy, which has the following beneficial effects: (1) Based on terahertz time-domain spectroscopy, this invention realizes self-consistent measurement of the thickness of multilayer coatings through coating thickness inversion model and hybrid optimization algorithm, thereby improving the intelligence and practicality of terahertz thickness measurement technology in the detection of complex multilayer coating structures. (2) Non-destructive measurement has been achieved, which solves the problem that existing methods cannot achieve non-destructive testing.

[0015] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method of the present invention; Figure 2 The following is a physical image of the coating sample of the present invention, wherein (a) represents a double-layer coating and (b) represents a triple-layer coating; Figure 3This is a schematic diagram of the principle of measuring coating thickness using terahertz time-domain spectroscopy according to the present invention, wherein (a) represents a double-layer coating and (b) represents a triple-layer coating; Figure 4 This is a flowchart of the optimization algorithm solution of the present invention; Figure 5 This is the experimental fitting result of the test signal for the double-layer coating of the present invention; Figure 6 This is a thickness distribution diagram of the double-layer coating sample of the present invention; Figure 7 The above is a comparison diagram of the measured signal and the fitted signal of the double coating of the present invention. (a) represents the measured signal and (b) represents the fitted signal. Figure 8 This is the experimental fitting residual plot of the double coating of the present invention; Figure 9 This is the experimental fitting result of the test signal for the three-layer coating of the present invention; Figure 10 This is a thickness distribution diagram of the three-layer coating sample of the present invention; Figure 11 This is a comparison diagram of the measured signal and the fitted signal of the three-layer coating of the present invention. (a) represents the measured signal and (b) represents the fitted signal. Figure 12 This is the experimental fitting residual plot of the three-layer coating of the present invention. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can be arranged and designed in various different configurations, and therefore should not be construed as limiting the present invention.

[0018] Example 1 like Figure 1 As shown, this invention provides a method for measuring the thickness of multilayer coatings based on terahertz time-domain spectroscopy, comprising the following steps: S1. Measure the signals on the metal plate with and without coating using a reflective terahertz time-domain spectroscopy system. The signal with coating is used as the measurement signal. The signal without coating is used as a reference signal. In this embodiment, the coating consists of two layers, with the first layer having a thickness of 86 μm and the second layer having a thickness of 35 μm.

[0019] S2. Establish a coating thickness inversion model and fit the double-layer coating signal. The specific process includes: S21. Establish a multivariate reflection signal regression sub-model to calculate the time-of-flight difference and refractive index between the reflected echo signal and the reference signal for each layer. For double-coated samples, such as... Figure 2 As shown in (a) above, according to Figure 3 As shown in the schematic diagram of (a) terahertz time-domain spectroscopy for measuring coating thickness, there are three main reflected echoes; therefore, N=3 in the multivariate reflection signal regression model. Thus, the formula for the multivariate reflection signal regression sub-model is: ; In the formula, This represents the fitted signal of the three reflected echo signals. Indicates the first One reflected echo signal, For the first The reflected echo signal and the reference signal The time difference between the flights, Given the coefficients of each reflected pulse, the refractive index of each layer is calculated using Fresnel's law based on these coefficients. .

[0020] S22. Considering multiple reflections of the signal between layers, establish a multiple reflection correction sub-model. In the multiple reflection correction model, the number of multiple echoes of the terahertz signal is defined as 5, therefore the parameters... =5. Therefore, the formula for the multiple reflection correction sub-model is: ; In the formula, This represents the time delay between multiple reflected signals, where the multiple reflected signals have the same time delay. Indicates the total signal from multiple reflections. The multi-reflection amplitude attenuation coefficient represents the loss of terahertz waves due to multiple reflections within the coating. For multiple reflection pulse coefficients, This represents the time delay between the reflected echo signal from the metal substrate and the reference signal. Indicates the first Multiple reflections.

[0021] S23. Establish a dispersion correction sub-model to correct the dispersion effect of terahertz waves propagating in the coating.

[0022] Specifically, the dispersion correction sub-model includes: ; In the formula, Represents the equivalent dispersion parameter. This represents the dispersion transfer function of terahertz waves in the coating. It represents angular frequency.

[0023] S24. Combining the three sub-models, the total fitted signal is obtained. The formula for calculating the total fitted signal is: ; In the formula, Represents the total fitted signal. This represents the Fourier transform.

[0024] By establishing a multiple reflection correction sub-model and a dispersion correction sub-model, the multivariate reflection signal regression model is modified to improve the solution. and The results are more accurate.

[0025] S25. Based on the total fitted signal and the measurement signal, the fitting error is defined as the objective function of the coating thickness inversion model. The objective function includes: ; In the formula, This represents the fitted signal value. Indicates the value of the measured signal. Indicates the overall goal.

[0026] S3. Input the measured and reference signals into the coating thickness inversion model, and solve it using an evolutionary optimization algorithm to obtain the optimal solution for the inversion parameters. Specifically, the differential evolution algorithm (DE) and the covariance matrix adaptive evolutionary strategy (CMA-ES) are used to solve the objective function to obtain the solution that optimizes the objective function. The optimal solution that achieves the minimum , , , , The differential evolution algorithm performs a global search, while the covariance matrix adaptive evolution strategy performs a local search. Integrating these two algorithms through a hybrid optimization algorithm achieves a balance between the global and local search results. Finally, the experimental fitting results for the double-layer coating signal are as follows: Figure 5 As shown.

[0027] Specifically, such as Figure 4 As shown, the process of solving the objective function using the Differential Evolutionary Algorithm (DE) and the Covariance Matrix Adaptive Evolutionary Strategy (CMA-ES) includes: Randomly initialize the population and generate the population. The population is then assigned to the DE algorithm for initial global search.

[0028] population After performing a global search for a specified number of generations using the DE algorithm, an evolved population is formed. At this point, the algorithm has found the approximate range of the optimal solution, therefore from A suitable population range is selected for local search.

[0029] The population after DE evolution Select an optimal solution from the pool, and then select the surrounding area centered on this optimal solution. The initial population of CEA-ES is formed by the solutions, and a local search is performed, while the final results are preserved. Next, the searched population is unswapped, and a new population is selected from it and reassigned to DE for a global search. The new population is selected from... and Generated from [the source]. The DE-CMA-ES algorithm first selects from [the source]. a =N Choose the best individual, and then select from the remaining individuals. b =N (1- A diverse range of individuals forms a new population. ', and perform a global DE search as a new population, This is the selection ratio. This selection is repeated until the maximum number of iterations is met.

[0030] S4. Based on the optimal solution, the thickness of each coating layer is derived, and the thickness distribution of the double-layer coating sample is obtained as follows: Figure 6 As shown.

[0031] Step S4 specifically includes the following processes: The time-of-flight difference between the reflected echo signal and the reference signal at each layer is obtained based on the optimal solution. and refractive index ; according to and The thickness of each coating layer is calculated. The formula is: ; In the formula, y is the speed at which light travels through the air.

[0032] In this embodiment, the refractive index of the first layer The second layer of refractive index 2.286, thickness of the first layer The thickness of the second layer Dispersion parameters , , Fit quality , The comparison graphs of the fitted signal and the measured signal, and the fitting residual graph are shown below. Figure 7 , Figure 8 As shown, where, Figure 7 In the diagram, (a) represents the measurement signal. Figure 7 In the diagram, (b) represents the fitted signal. According to... , As can be seen from the comparison chart and the fitting residual plot, the fitted signal and the measured signal highly overlap in waveform evolution trend, and the fitting residual fluctuates randomly within a very small range. This indicates that the model can accurately describe the physical process in this embodiment, and the extracted structural parameters such as refractive index and thickness of each layer have high reliability and accuracy.

[0033] Example 2 This invention provides a method for measuring the thickness of multilayer coatings based on terahertz time-domain spectroscopy, comprising the following steps: S1. Measure the signals on the metal plate with and without coating using a reflective terahertz time-domain spectroscopy system. The signal with coating is used as the measurement signal. The signal without coating is used as a reference signal. In this embodiment, the coating consists of three layers, wherein the thickness of the first layer is 96 μm, the thickness of the second layer is 93 μm, and the thickness of the third layer is 39 μm.

[0034] S2. Establish a coating thickness inversion model and fit the signals of the three coating layers. The specific process includes: S21. Establish a multivariate reflection signal regression sub-model to calculate the time-of-flight difference and refractive index between the reflected echo signal and the reference signal for each layer. For a three-layer coated sample, such as... Figure 2 As shown in (b) above, according to Figure 3 As shown in the schematic diagram of (b) terahertz time-domain spectroscopy for measuring coating thickness, there are four main reflected echoes; therefore, N=4 in the multivariate reflection signal regression model. Thus, the formula for the multivariate reflection signal regression sub-model is: ; In the formula, This represents the fitted signal of the four reflected echo signals. Indicates the first One reflected echo signal, For the first The reflected echo signal and the reference signal The time difference between the flights, Given the coefficients of each reflected pulse, the refractive index of each layer is calculated using Fresnel's law based on these coefficients. .

[0035] S22. Considering multiple reflections of the signal between layers, establish a multiple reflection correction sub-model. In the multiple reflection correction model, the number of multiple echoes of the terahertz signal is defined as 5, therefore the parameters... =5. Therefore, the formula for the multiple reflection correction sub-model is: ; In the formula, This represents the time delay between multiple reflected signals, where the multiple reflected signals have the same time delay. Indicates the total signal from multiple reflections. The multi-reflection amplitude attenuation coefficient represents the loss of terahertz waves due to multiple reflections within the coating. For multiple reflection pulse coefficients, This represents the time delay between the reflected echo signal from the metal substrate and the reference signal. Indicates the first Multiple reflections.

[0036] S23. Establish a dispersion correction sub-model to correct the dispersion effect of terahertz waves propagating in the coating.

[0037] Specifically, the dispersion correction sub-model includes: ; In the formula, Represents the equivalent dispersion parameter. This represents the dispersion transfer function of terahertz waves in the coating. It represents angular frequency.

[0038] S24. Combining the three sub-models, the total fitted signal is obtained. The formula for calculating the total fitted signal is: ; In the formula, Represents the total fitted signal. This represents the Fourier transform.

[0039] By establishing a multiple reflection correction sub-model and a dispersion correction sub-model, the multivariate reflection signal regression model is modified to improve the solution. and The results are more accurate.

[0040] S25. Based on the total fitted signal and the measurement signal, the fitting error is defined as the objective function of the coating thickness inversion model. The objective function includes: ; In the formula, This represents the fitted signal value. Indicates the value of the measured signal. Indicates the overall goal.

[0041] S3. Input the measured and reference signals into the coating thickness inversion model, and solve it using an evolutionary optimization algorithm to obtain the optimal solution for the inversion parameters. Specifically, the differential evolution algorithm (DE) and the covariance matrix adaptive evolutionary strategy (CMA-ES) are used to solve the objective function to obtain the solution that optimizes the objective function. The optimal solution that achieves the minimum , , , , The differential evolution algorithm performs a global search, while the covariance matrix adaptive evolution strategy performs a local search. Integrating these two algorithms through a hybrid optimization algorithm achieves a balance between the global and local search results. Finally, the experimental fitting results for the three-layer coating signal are as follows: Figure 9 As shown.

[0042] S4. Based on the optimal solution, the thickness of each coating layer is derived, and the thickness distribution of the double-layer coating sample is obtained as follows: Figure 10 As shown.

[0043] Step S4 specifically includes the following processes: The time-of-flight difference between the reflected echo signal and the reference signal at each layer is obtained based on the optimal solution. and refractive index ; according to and The thickness of each coating layer is calculated. The formula is: ; In the formula, y is the speed at which light travels through the air.

[0044] In this embodiment, the refractive index of the first layer The second layer of refractive index 1.666, third layer refractive index 2.372, thickness of the first layer The thickness of the second layer The thickness of the third layer Dispersion parameters , , , Fit quality , The comparison graphs of the fitted signal and the measured signal, and the fitting residual graph are shown below. Figure 11 , Figure 12 As shown, where, Figure 11 In the diagram, (a) represents the measurement signal. Figure 11 In the diagram, (b) represents the fitted signal. According to... , As can be seen from the comparison chart and the fitting residual plot, the fitted signal and the measured signal highly overlap in waveform evolution trend, and the fitting residual fluctuates randomly within a very small range. This indicates that the model can accurately describe the physical process in this embodiment, and the extracted structural parameters such as refractive index and thickness of each layer have high reliability and accuracy.

[0045] Therefore, the present invention adopts the above-mentioned method for measuring the thickness of multilayer coatings based on terahertz time-domain spectroscopy. Based on terahertz time-domain spectroscopy, the method achieves self-consistent and non-destructive measurement of the thickness of multilayer coatings through a coating thickness inversion model and a hybrid optimization algorithm, with small error.

[0046] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for measuring the thickness of multilayer coatings based on terahertz time-domain spectroscopy, characterized in that, Including the following steps: S1. Measure the signals on the metal plate with and without coating using a reflective terahertz time-domain spectroscopy system, and use them as the measurement signal and reference signal, respectively. S2. Establish a coating thickness inversion model and fit the multilayer coating signal; S3. Input the measured signal and reference signal into the coating thickness inversion model, and solve it through an evolutionary optimization algorithm to obtain the optimal solution of the inversion parameters; S4. Calculate the thickness of each coating layer based on the optimal solution.

2. The method for measuring the thickness of a multilayer coating based on terahertz time-domain spectroscopy according to claim 1, characterized in that: Step S2, establishing the coating thickness inversion model, includes: S21. Establish a multivariate reflection signal regression sub-model and calculate the time-of-flight difference and refractive index between the reflection echo signal and the reference signal in each layer. S22. Considering multiple reflections of the signal between layers, establish a multi-reflection correction sub-model. S23. Establish a dispersion correction sub-model to correct the dispersion effect when terahertz waves propagate in the coating. S24. Combining the three sub-models, we obtain the total fitted signal; S25. Based on the total fitted signal and the measurement signal, the fitting error is defined as the objective function of the coating thickness inversion model.

3. The method for measuring the thickness of a multilayer coating based on terahertz time-domain spectroscopy according to claim 2, characterized in that: The multivariate reflection signal regression sub-model in step S21 includes: ； In the formula, express The fitted signal of the reflected echo signal, Indicates the first One reflected echo signal, For the first Each reflected echo signal and the reference signal The time difference between the flights, Indicates the number of reflected echoes. Given the coefficients of each reflected pulse, the refractive index of each layer is calculated using Fresnel's law based on these coefficients. .

4. The method for measuring the thickness of a multilayer coating based on terahertz time-domain spectroscopy according to claim 3, characterized in that, The multiple reflection correction sub-model in step S22 includes: ； In the formula, This represents the time delay between multiple reflected signals, where the multiple reflected signals have the same time delay. Indicates the total signal from multiple reflections. The multi-reflection amplitude attenuation coefficient represents the loss of terahertz waves due to multiple reflections within the coating. For multiple reflection pulse coefficients, This represents the time delay between the reflected echo signal from the metal substrate and the reference signal. Indicates the first Multiple reflections This indicates the number of multiple reflected signals.

5. The method for measuring the thickness of a multilayer coating based on terahertz time-domain spectroscopy according to claim 4, characterized in that, The dispersion correction sub-model in step S23 includes: ； In the formula, Represents the equivalent dispersion parameter. This represents the dispersion transfer function of terahertz waves in the coating. It represents angular frequency.

6. The method for measuring the thickness of a multilayer coating based on terahertz time-domain spectroscopy according to claim 5, characterized in that, In step S23, combining the three sub-models, the formula for calculating the total fitted signal is as follows: ； In the formula, Represents the total fitted signal. This represents the Fourier transform.

7. The method for measuring the thickness of a multilayer coating based on terahertz time-domain spectroscopy according to claim 6, characterized in that, The objective function in step S25 includes: ； In the formula, This represents the fitted signal value. Indicates the value of the measured signal. Indicates the overall goal.

8. The method for measuring the thickness of a multilayer coating based on terahertz time-domain spectroscopy according to claim 7, characterized in that: In step S3, the Differential Evolutionary Algorithm (DE) and the Covariance Matrix Adaptive Evolutionary Strategy (CMA-ES) are used to solve the problem and obtain the optimal solution for the inversion parameters. The inversion parameters include... , , , , .

9. The method for measuring the thickness of a multilayer coating based on terahertz time-domain spectroscopy according to claim 6, characterized in that, Step S4, which involves retrieving the thickness of each coating layer based on the optimal solution, includes: The time-of-flight difference between the reflected echo signal and the reference signal at each layer is obtained based on the optimal solution. and refractive index ; according to and The thickness of each coating layer is calculated. The formula is: ； In the formula, y is the speed at which light travels through the air.

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