Terahertz coating detection method and system based on sparse reconstruction algorithm

Abstract

The invention designs a terahertz coating detection method and system based on a sparse reconstruction algorithm, and the method comprises the steps: decomposing a reflected terahertz time-domain spectrum through employing a sparse representation algorithm, and effectively distinguishing aliasing reflection signals; processing a sparse solution obtained by decomposition through a reconstruction algorithm, and automatically and accurately positioning the amplitude and the time interval of a reflected signal; and finally, calculating the refractive index of the material by using a Fresnel formula and a reflection model, and further calculating the geometric thickness of the thermal expansion coating according to the refractive index and the time interval of a reflection peak.

Description

Technical Field

[0001] The present invention belongs to the field of nondestructive testing, and in particular relates to a terahertz coating detection method and system based on a sparse reconstruction algorithm. Background Art

[0002] With the advancement of science and technology, coating technology is increasingly used in industry and manufacturing, especially in the fields of aviation, automobiles, petrochemicals, etc. Common types of coatings include thermal barrier coatings, paint coatings, anti-corrosion coatings and automotive coatings, which have different functions and application scenarios. Thermal barrier coatings are widely used in aircraft engines and gas turbines. By forming an insulation layer on the surface of high-temperature components, the substrate temperature is reduced and the corrosion and wear resistance is improved. As the main insulation structure, the thickness of the ceramic layer directly affects the performance and life of the coating. If it is too thin, it cannot insulate, and if it is too thick, it is easy to cause stress concentration and fall off. In addition, paint coatings are often used on the surface of buildings, ships and equipment to prevent the external environment from eroding the substrate; anti-corrosion coatings are used in corrosive environments such as the ocean and petrochemicals to effectively extend the service life of the equipment; automotive coatings improve the durability of vehicles by providing a wear-resistant, weather-resistant and beautiful outer layer. With the increasing application of coatings, the detection of coating thickness and integrity has become crucial, especially when working in harsh environments, where its performance directly determines the reliability and life of the equipment.

[0003] Terahertz waves are a general term for electromagnetic waves with a frequency range of 0.1THz-10THz. They are located between the infrared band and the microwave band on the electromagnetic spectrum, so they have become a bridge between electronics and photonics. Terahertz waves have very low photon energy and are a very safe electromagnetic wave. They can penetrate most non-metallic and non-polar substances that are opaque to visible light and infrared rays, so they can be used to detect hidden objects. In addition, due to the electromagnetic wave properties of terahertz waves, their detection and reception can be contactless. Combined with the unique advantages of the above-mentioned terahertz waves, they have also shown certain application potential in the field of industrial inspection. The traditional terahertz time-domain spectroscopy thickness measurement method is based on the time-of-flight method, but this method can only directly detect the optical thickness of the coating, and the refractive index of the coating needs to be measured separately to calculate its geometric thickness. Patent CN114111604A proposes a thermal barrier coating detection algorithm that does not require a reference sample, but it requires manual positioning of the time and amplitude of the reflection peak, which is slow and has large errors. In practical applications, due to the aliasing of reflection peaks of thinner coatings, this method is only effective for coatings hundreds of microns thick and has low accuracy. In view of the above defects, this study proposes a terahertz coating detection method based on sparse reconstruction algorithm. Summary of the invention

[0004] In order to overcome the existing problems, the present invention designs a terahertz coating detection method based on a sparse reconstruction algorithm. The present invention first uses a sparse representation algorithm to decompose the reflected terahertz time domain spectrum, which can effectively distinguish the aliased reflection signals. Then, the sparse solution obtained by the decomposition is processed by a reconstruction algorithm to automatically and accurately locate the amplitude and time interval of the reflection signal. Finally, the refractive index of the material is calculated using the Fresnel formula, and then the geometric thickness of the coating is calculated based on the refractive index and the time interval of the reflection peak.

[0005] Based on the above terahertz pulse reflection principle, the terahertz coating detection method based on the sparse reconstruction algorithm of the present application specifically includes the following steps:

[0006] Step 1: Use a terahertz time-domain spectrometer to measure the coating. The terahertz pulse emitted by the terahertz time-domain spectrometer system is vertically incident on the coating. The vertically incident terahertz wave will be reflected multiple times in the coating; collect the reflected signal and record it as Y.

[0007] Step 2: Construct a sparse representation dictionary. The signal emitted by the terahertz time-domain spectrometer is used as the reference signal, denoted as E 0 (t). Based on the reference signal, the dictionary matrix X is constructed in the form of a Toeplitz matrix. Each column vector in the matrix X is the reference signal E 0 The delay transformation of (t) is called an atom, and the interval between two adjacent atoms is 1 sampling period, that is, the latter atom moves down one unit based on the previous atom.

[0008] Step 3: Calculate the sparse representation result of the reflection signal based on the reflection signal in step 1 and the dictionary matrix X constructed in step 2. The reflection signal of the sample can be expressed in the following matrix form:

[0009] Y=Xh+e (1)

[0010] Where h represents the impulse response sequence, represents the solution of h, i.e. the sparse representation result; e represents the allowable calculation and measurement error. This formula is a typical problem of signal processing in sparse representation theory. The problem is transformed into solving the vector minimum l 0 Norm optimization problem:

[0011]

[0012] Where λ is the regularization parameter. By adjusting this parameter (usually taking a value of about 0.001) according to the noise level and coating thickness, a balance between measurement accuracy and noise resistance can be achieved. 0 The definition of the norm is the number of non-zero elements in the vector. For this type of problem, in order to simplify the calculation, it can be converted into l1 LASSO regression model under norm regularization constraint:

[0013]

[0014] Step 4: Sparse representation results The adjacent non-zero values ​​are grouped together. The impulse response sequences after grouping are denoted as h 1 、h 2 、h 3 ,1,2,3 represent the number of layers.

[0015] Step 5: Use the grouping result h 1 、h 2 、h 3 Reconstruct each reflected signal. Reconstruct the reflected signals one by one using the following formula:

[0016]

[0017] In the formula, h 1 、h 2 、h 3 represents the impulse response sequences of the first, second and third groups after grouping, y 1 ,y 2 ,y 3 Indicates the 1st, 2nd, and 3rd reflection peaks after reconstruction.

[0018] Step 6: Extract the amplitudes of the first, second, and third reflection peaks obtained in step 5 and the time when they reach the maximum amplitude. The amplitude of the first reflection peak is recorded as R 1 , the amplitude of the second reflection peak is recorded as E 2 , the amplitude of the third reflection peak is recorded as E 3 The time difference between adjacent reflection peaks reaching their maximum amplitude is recorded as Δt.

[0019] Step 7: Calculate the refractive index of the material based on the amplitudes of the reflection peaks obtained in step 6. The amplitudes of the first three echo signals can be theoretically expressed as:

[0020]

[0021] In the formula, r ij It represents the ratio of the amplitude of the reflected wave to the amplitude of the incident wave when the terahertz pulse is reflected from the i-th layer to the j-th layer, i.e., the reflection ratio; t ij It represents the ratio of the amplitude of the transmitted wave to the amplitude of the incident wave when the terahertz pulse is transmitted from the i-th layer to the j-th layer, that is, the transmittance; t 1 Represents the loss ratio generated when the terahertz pulse propagates in the coating.

[0022] Assuming the refractive index of the coating material is n and the refractive index of air is 1, according to the Fresnel formula, the reflectance and transmittance can be expressed as:

[0023]

[0024] By calculation, the relationship between the reflectance, transmittance and refractive index between the coating and the air can be obtained, namely:

[0025]

[0026] Solving this equation and discarding unreasonable solutions, we can calculate the refractive index n of the coating material:

[0027]

[0028] Step 8: The distance that the terahertz pulse propagates in the coating is twice the thickness of the coating. Based on this relationship, the thickness of the coating can be calculated using the refractive index:

[0029]

[0030] Where d is the thickness of the coating, c is the speed of light in a vacuum, and Δt is the time difference between adjacent reflection peaks when they reach their maximum amplitude.

[0031] The present application also includes a terahertz coating detection system based on a sparse reconstruction algorithm, which specifically includes the following parts:

[0032] The sample signal acquisition module is used to measure the coating using a terahertz time-domain spectrometer. The terahertz pulse emitted by the terahertz time-domain spectrometer system is vertically incident on the coating. The vertically incident terahertz wave will be reflected multiple times in the ceramic layer, and the reflected signal is collected and recorded as Y.

[0033] Construct a sparse representation dictionary module to construct a sparse representation dictionary. The signal emitted by the terahertz time-domain spectrometer is used as the reference signal, denoted as E 0 (t). Based on the reference signal, a dictionary matrix X is constructed in the form of a Toeplitz matrix.

[0034] The sparse solution module solves the sparse representation result of the reflection signal based on the reflection signal Y obtained in the sample signal acquisition module and the sparse representation dictionary matrix X

[0035] Clustering module, used to obtain the results of sparse solution module Decompose it into Grouping, grouping the adjacent non-zero values ​​into one group. The impulse response sequences after grouping are denoted as h 1 、h 2 、h 3,1,2,3 represent the number of layers.

[0036] The grouping reconstruction reflected signal module is used to reconstruct the grouping results, that is, according to the h obtained by grouping 1 、h 2 、h 3 Reconstruct each reflection signal to obtain the reconstructed 1st, 2nd, and 3rd reflection peaks.

[0037] Extract the reflection signal information module, extract the amplitude of the first, second, and third reconstructed reflection peaks and the time when they reach the maximum amplitude, and the amplitude of the first reflection peak is recorded as E 1 , the amplitude of the second reflection peak is recorded as E 2 , the amplitude of the third reflection peak is recorded as E 3 The time difference between adjacent reflection peaks reaching their maximum amplitude is recorded as Δt.

[0038] The refractive index calculation module is used to calculate the refractive index of the coating material according to the reconstructed reflection signal amplitude.

[0039] The thickness calculation module calculates the thickness of the coating using the refractive index of the coating material based on the relationship that the distance the terahertz pulse propagates in the coating is twice the thickness of the coating.

[0040] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0041] (1) The method designed in the present invention overcomes the drawbacks of CN114111604A that it can only be used for thicker coatings and requires manual differentiation and positioning of reflected signals. It can simply, quickly and accurately separate the aliased terahertz time-domain reflected signals and retain their relative position, amplitude and phase information. After reconstruction, each reflection peak is no longer limited to the atoms in the dictionary, but retains its own unique time and phase information, which can be used for further analysis. Using the reconstructed terahertz time-domain reflected signal, the refractive index and thickness of coatings of various thicknesses can be accurately calculated.

[0042] (2) The method designed in the present invention is not only applicable to relatively thick thermal barrier ceramic coating materials, but also provides good effects for other thinner coatings such as anti-corrosion coatings, radar absorbing coatings, and automobile paints. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0044] Figure 1 This is the propagation model of terahertz waves in coatings.

[0045] Figure 2 This is the time domain waveform of the reference signal and sample reflection signal when testing a coating with a refractive index of 3.45 and a thickness of 20um.

[0046] Figure 3 The present invention is a flow chart of the method proposed in the present invention.

[0047] Figure 4 The terahertz time domain signal reflected by the sample and the time domain waveform of the first three reflection peaks after reconstruction.

[0048] Figure 5 This is a comparison between the simulation calculation results of the coating refractive index and thickness using this method and the reference values.

[0049] Figure 6 This is a schematic diagram of the system flow proposed by the present invention. DETAILED DESCRIPTION

[0050] In the following description, specific details such as specific system structures, technologies, etc. are provided for the purpose of illustration rather than limitation, so as to provide a thorough understanding of the embodiments of the present invention. However, it should be clear to those skilled in the art that the present invention may be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to prevent unnecessary details from obstructing the description of the present invention.

[0051] The present invention is further described in detail below with reference to the accompanying drawings. The material to be detected includes a base layer and a coating to be detected, and its structure is shown in FIG. Figure 1 The terahertz pulse (R 0 ) is incident vertically from top to bottom on the coating to be tested, and part of the energy is directly reflected by the air-coating interface and received by the detector (E 1 ), and the other part is transmitted into the coating and reflected at the coating-substrate interface. When the pulse entering the coating returns to the coating-air interface, part of the energy is transmitted into the air and received by the detector (E 2 ), and another part of the energy is reflected back into the coating and continues to reflect back and forth in the coating.

[0052] Based on the above terahertz pulse reflection principle, the terahertz coating detection method based on the sparse reconstruction algorithm of the present application specifically includes the following steps:

[0053] Step 1: Use a terahertz time-domain spectrometer to measure the coating. The terahertz pulse emitted by the terahertz time-domain spectrometer is vertically incident on the coating. The vertically incident terahertz wave will be reflected multiple times in the ceramic layer. Collect the reflected signal, recorded as Y, and its time-domain spectrum is as follows: Figure 2 Shown as solid line.

[0054] Step 2: Construct a sparse representation dictionary. The signal emitted by the terahertz time-domain spectrometer is used as the reference signal, denoted as E 0 (t), its time domain spectrum is as follows Figure 2 The dotted line shows that the dictionary matrix X is constructed based on the reference signal in the form of a Toeplitz matrix, as shown in Figure 3 As shown. Each column vector in the matrix X is the reference signal E 0 The delay transformation of (t) is called an atom, and the interval between two adjacent atoms is 1 sampling period, that is, the latter atom moves down one unit based on the previous atom.

[0055] Step 3: Calculate the sparse representation result of the reflection signal based on the reflection signal in step 1 and the dictionary matrix X constructed in step 2. The reflection signal of the sample can be expressed in the following matrix form:

[0056] Y=Xh+e (1)

[0057] Where h represents the impulse response sequence, represents the solution of h, i.e. the sparse representation result; e represents the allowable calculation and measurement error. This formula is a typical problem of signal processing in sparse representation theory. The problem is transformed into solving the vector minimum l 0 Norm optimization problem:

[0058]

[0059] Where λ is the regularization parameter. By adjusting this parameter (usually taking a value of about 0.001) according to the noise level and coating thickness, a balance between measurement accuracy and noise resistance can be achieved. 0 The definition of the norm is the number of non-zero elements in the vector. For this type of problem, in order to simplify the calculation, it can be converted into l 1 LASSO regression model under norm regularization constraint:

[0060]

[0061] Step 4: Sparse representation results Group the adjacent non-zero values ​​into one group, such as Figure 3 As shown. The impulse response sequences after grouping are recorded as h 1 、h 2 、h 3 ,1,2,3 represent the number of layers.

[0062] Step 5: Use the grouping result h 1 、h2 、h 3 Reconstruct each reflected signal. Reconstruct the reflected signals one by one using the following formula:

[0063]

[0064] In the formula, h 1 、h 2 、h 3 represents the impulse response sequences of the first, second and third groups after grouping, y 1 ,y 2 ,y 3 Indicates the 1st, 2nd, and 3rd reflection peaks after reconstruction.

[0065] Step 6: Extract the amplitudes of the first, second, and third reflection peaks obtained in step 5 and the time when they reach the maximum amplitude. The amplitude of the first reflection peak is recorded as R 1 , the amplitude of the second reflection peak is recorded as E 2 , the amplitude of the third reflection peak is recorded as E 3 , the time difference when the adjacent reflection peaks reach the maximum amplitude is recorded as Δt, such as Figure 3 , Figure 4 It should be noted that due to the half-wave loss when reflecting on the interface with a low refractive index to a high refractive index, E 3 With E 1 、E 2 The signs of are opposite.

[0066] Step 7: Calculate the refractive index of the coating material based on the amplitudes of the reflection peaks obtained in step 6. The amplitudes of the first three echo signals can be theoretically expressed as:

[0067]

[0068] In the formula, r ij It represents the ratio of the amplitude of the reflected wave to the amplitude of the incident wave when the terahertz pulse is reflected from the i-th layer to the j-th layer, i.e., the reflection ratio; t ij It represents the ratio of the amplitude of the transmitted wave to the amplitude of the incident wave when the terahertz pulse is transmitted from the i-th layer to the j-th layer, that is, the transmittance; t 1 Represents the loss ratio generated when the terahertz pulse propagates in the coating.

[0069] Assuming the refractive index of the coating material is n and the refractive index of air is 1, according to the Fresnel formula, the reflectance and transmittance can be expressed as:

[0070]

[0071] By calculation, the relationship between the reflectance, transmittance and refractive index between the coating and the air can be obtained, namely:

[0072]

[0073] Solving this equation and discarding unreasonable solutions, we can calculate the refractive index n of the coating material:

[0074]

[0075] Step 8: The distance that the terahertz pulse propagates in the coating is twice the thickness of the coating. Based on this relationship, the thickness of the coating material can be calculated using the refractive index:

[0076]

[0077] Where d is the thickness of the coating material, c is the speed of light in a vacuum, and Δt is the time difference between adjacent reflection peaks when they reach their maximum amplitude.

[0078] like Figure 6 As shown, the terahertz coating detection system based on the sparse reconstruction algorithm of the present application specifically includes the following parts:

[0079] The sample signal acquisition module is used to measure the coating using a terahertz time-domain spectrometer. The terahertz pulse emitted by the terahertz time-domain spectrometer system is vertically incident on the coating. The vertically incident terahertz wave will be reflected multiple times in the ceramic layer, and the reflected signal is collected and recorded as Y.

[0080] Construct a sparse representation dictionary module to construct a sparse representation dictionary. The signal emitted by the terahertz time-domain spectrometer is used as the reference signal, denoted as E 0 (t). Based on the reference signal, the dictionary matrix X is constructed in the form of a Toeplitz matrix. Each column vector in the matrix X is the reference signal E 0 The delay transformation of (t) is called an atom, and the interval between two adjacent atoms is 1 sampling period, that is, the latter atom moves down one unit based on the previous atom.

[0081] The sparse solution module solves the sparse representation result of the reflection signal based on the reflection signal obtained in the sample signal acquisition module and the sparse representation dictionary The reflection signal of the sample can be expressed in the following matrix form:

[0082] Y=Xh+e (11)

[0083] Where h represents the impulse response sequence, represents the solution of h, and e represents the allowable calculation and measurement error. This formula is a typical problem of signal processing in sparse representation theory, which can be transformed into solving the minimum vector l 0 Norm optimization problem:

[0084]

[0085] Where λ is the regularization parameter. By adjusting this parameter (usually taking a value of about 0.001) according to the noise level and coating thickness, a balance between measurement accuracy and noise resistance can be achieved. 0 The definition of the norm is the number of non-zero elements in the vector. For this type of problem, in order to simplify the calculation, it can be converted into l 1 LASSO regression model under norm regularization constraint:

[0086]

[0087] Clustering module, used to obtain the results of sparse solution module Decompose it into Grouping, grouping the adjacent non-zero values ​​into one group. The impulse response sequences after grouping are denoted as h 1 、h 2 、h 3 ,1,2,3 represent the number of layers.

[0088] The grouping reconstruction reflected signal module is used to reconstruct the grouping results, that is, according to the h obtained by grouping 1 、h 2 、h 3 Reconstruct each reflected signal. Reconstruct the reflected signals one by one using the following formula:

[0089]

[0090] In the formula, h 1 、h 2 、h 3 represents the impulse response sequences of the first, second and third groups after grouping, y 1 ,y 2 ,y 3 Indicates the 1st, 2nd, and 3rd reflection peaks after reconstruction.

[0091] Extract the reflection signal information module, extract the amplitude of the first, second, and third reconstructed reflection peaks and the time when they reach the maximum amplitude, and the amplitude of the first reflection peak is recorded as E 1 , the amplitude of the second reflection peak is recorded as E 2 , the amplitude of the third reflection peak is recorded as E 3 , the time difference when the adjacent reflection peaks reach the maximum amplitude is recorded as Δt, such as Figure 3 , Figure 4 shown.

[0092] The refractive index calculation module is used to calculate the refractive index of the coating material based on the reconstructed reflection signal amplitude. The amplitude of the first three echo signals can be theoretically expressed as:

[0093]

[0094] In the formula, r ij It represents the ratio of the amplitude of the reflected wave to the amplitude of the incident wave when the terahertz pulse is reflected from the i-th layer to the j-th layer, i.e., the reflection ratio; t ij It represents the ratio of the amplitude of the transmitted wave to the amplitude of the incident wave when the terahertz pulse is transmitted from the i-th layer to the j-th layer, that is, the transmittance; t 1 Represents the loss ratio generated when the terahertz pulse propagates in the coating.

[0095] Assuming the refractive index of the coating material is n and the refractive index of air is 1, according to the Fresnel formula, the reflectance and transmittance can be expressed as:

[0096]

[0097]

[0098] By calculation, the relationship between the reflectance, transmittance and refractive index between the coating and the air can be obtained, namely:

[0099]

[0100] Solving this equation and discarding unreasonable solutions, we can calculate the refractive index n of the coating material:

[0101]

[0102] The thickness calculation module calculates the thickness of the coating using the refractive index of the coating material, based on the relationship that the distance that the terahertz pulse propagates in the coating is twice the thickness of the coating. Specifically:

[0103]

[0104] Where d is the thickness of the coating, c is the speed of light in a vacuum, and Δt is the time difference between adjacent reflection peaks when they reach their maximum amplitude.

[0105] The method designed by the present invention still maintains good resolution for materials as thin as 15um and with a refractive index of 3.45, and controls the measurement error of the coating thickness within the range to within 1um, thereby realizing efficient, high-accuracy, and wide-range non-destructive testing of the coating, without any other standard sample preparation and measurement work. In the simulation, the method designed by the present invention simulates coatings with a refractive index of 3.45 and thicknesses of 15um, 20um, 30um, 40um, 50um, 60um, 70um, and 80um, respectively. The calculated results of the coating thickness are 15.28um, 19.43um, 30.38um, 40.17um, 49.57um, 60.34um, 70.60um, and 80.05um, respectively, and the calculated results of the refractive index are 3.34, 3.55, 3.41, 3.47, 3.48, 3.43, 3.42, and 3.45, respectively. Figure 5 shown.

[0106] It should also be noted that in this specification, terms such as "comprises", "includes" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of more restrictions, an element defined by the sentence "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or device including the element.

[0107] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

[0108] The above embodiments are preferred implementation modes of the present invention, but the implementation modes of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications that do not deviate from the spirit and principles of the present invention should be equivalent replacement methods and are included in the protection scope of the present invention.

[0109] The embodiments described above are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included in the protection scope of the present invention.

Claims

1. A terahertz coating detection method based on sparse reconstruction algorithm, characterized in that: The detection method comprises the following steps: Step 1: Use a terahertz time-domain spectrometer to measure the coating; specifically, the terahertz pulse emitted by the terahertz time-domain spectrometer system is vertically incident on the coating, and the reflected signal is collected, which is recorded as Y; Step 2: construct a sparse representation dictionary; use the signal emitted by the terahertz time-domain spectrometer as a reference signal, denoted as E0(y); construct a dictionary matrix X in the form of a Toeplitz matrix based on the reference signal; Step 3: Based on the reflection signal Y in step 1 and the dictionary matrix X constructed in step 2, the sparse representation result of the reflection signal is solved. Step 4: sparse representation result in step 3 Grouping is performed, and adjacent non-zero values ​​are grouped together; the impulse response sequences after grouping are recorded as h1, h2, h3, where 1, 2, 3 represent the number of layers; Step 5: Reconstruct each reflected signal using the grouping results h1, h2, and h3; reconstruct the reflected signals in sequence using the following formula: y1=Xh1 y2=Xh2 (1) y3=Xh3 Where, h1, h2, h3 represent the 1st, 2nd, and 3rd group of impulse response sequences after grouping, and y1, y2, and y3 represent the 1st, 2nd, and 3rd reflection peaks after reconstruction; Step 6, extracting the amplitudes of the first, second, and third reflection peaks obtained in step 5 and the time when they reach the maximum amplitude, the amplitude of the first reflection peak is recorded as E1, the amplitude of the second reflection peak is recorded as E2, the amplitude of the third reflection peak is recorded as E3, and the time difference when adjacent reflection peaks reach the maximum amplitude is recorded as Δt; Step 7, calculating the refractive index n of the coating material according to the amplitudes of the reflection peaks obtained in step 6; Step 8: The distance that the terahertz pulse propagates in the coating is twice the thickness of the coating. Based on this relationship, the thickness of the coating material can be calculated using the refractive index: Where d is the thickness of the coating, c is the speed of light in a vacuum, and Δt is the time difference between adjacent reflection peaks when they reach their maximum amplitude.

2. According to the terahertz coating detection method of claim 1, in the step 2, when constructing a sparse representation dictionary, a dictionary matrix X is constructed in the form of a Toeplitz matrix based on the reference signal; each column vector in the matrix X is a delayed transformation of the reference signal E0(t), called an atom, and the interval between two adjacent atoms is 1 sampling period, that is, the latter atom moves down one unit based on the previous atom.

3. According to the terahertz coating detection method of claim 2, the reflected signal in step 3 can be expressed in the following matrix form: Y=Xh+e (3) Where h represents the impulse response sequence, represents the solution of h, that is, the sparse representation result; e represents the allowable calculation and measurement error; Will solve The problem is transformed into an optimization problem of solving the minimum l0 norm of the vector: In the formula, λ is the regularization parameter, and the definition of the l0 norm of a vector is the number of non-zero elements in the vector; for the sake of simplicity of calculation, it can be converted into a LASSO regression model under the l1 norm regularization constraint:

4. According to the terahertz coating detection method of claim 3, the amplitude calculation method in step 6 is: In the formula, r ij It represents the ratio of the amplitude of the reflected wave to the amplitude of the incident wave when the terahertz pulse is reflected from the i-th layer to the j-th layer, i.e., the reflection ratio; t ij It represents the ratio of the amplitude of the transmitted wave to the amplitude of the incident wave when the terahertz pulse is transmitted from the i-th layer to the j-th layer, that is, the transmittance; t1 represents the loss ratio generated when the terahertz pulse propagates in the coating.

5. According to the terahertz coating detection method of claim 4, the specific method of calculating the refractive index of the coating material in step 7 is: Assuming the refractive index of the coating material is n and the refractive index of air is 1, according to the Fresnel formula, the reflectance and transmittance can be expressed as: By calculation, the relationship between the reflectance, transmittance and refractive index between the coating and the air can be obtained, namely: Solving this equation and discarding unreasonable solutions, we can calculate the refractive index n of the coating material:

6. A terahertz coating detection system based on sparse reconstruction algorithm, characterized in that: The detection system specifically includes the following parts: a sample signal acquisition module for measuring the coating using a terahertz time-domain spectrometer; The terahertz pulse emitted by the terahertz time-domain spectroscopy system is vertically incident on the coating. The vertically incident terahertz wave will be reflected multiple times in the ceramic layer, and the reflected signal is collected and recorded as Y; A sparse representation dictionary module is constructed to construct a sparse representation dictionary; the signal emitted by the terahertz time-domain spectrometer is used as a reference signal, denoted as E0(t); a dictionary matrix X is constructed in the form of a Toeplitz matrix based on the reference signal; The sparse solution module solves the sparse representation result of the reflection signal based on the reflection signal Y obtained in the sample signal acquisition module and the sparse representation dictionary matrix X Clustering module, used to obtain the results of sparse solution module Decompose it into Grouping, grouping adjacent non-zero values ​​into one group; the impulse response sequences after grouping are recorded as h1, h2, h3, where 1, 2, 3 represent the number of layers; The grouping and reconstruction reflection signal module is used to reconstruct the grouping results, that is, to reconstruct each reflection signal according to h1, h2, and h3 obtained by grouping, and obtain the first, second, and third reflection peaks after reconstruction; Extract reflection signal information module, extract the amplitude of the first, second and third reconstructed reflection peaks and the time when they reach the maximum amplitude in turn, the amplitude of the first reflection peak is recorded as E1, the amplitude of the second reflection peak is recorded as E2, the amplitude of the third reflection peak is recorded as E3, and the time difference when adjacent reflection peaks reach the maximum amplitude is recorded as Δt; A refractive index calculation module, used to calculate the refractive index n of the coating material according to the reconstructed reflection signal amplitude; The thickness calculation module calculates the thickness of the coating using the refractive index of the coating material, based on the relationship that the distance that the terahertz pulse propagates in the coating is twice the thickness of the coating. Specifically: Where d is the thickness of the coating, c is the speed of light in a vacuum, and Δt is the time difference between adjacent reflection peaks when they reach their maximum amplitude.

7. According to the terahertz coating detection system of claim 6, when constructing the sparse representation dictionary, the sparse representation dictionary construction module constructs a dictionary matrix X in the form of a Toeplitz matrix based on the reference signal; each column vector in the matrix X is a delayed transformation of the reference signal E0(t), called an atom, and the interval between two adjacent atoms is 1 sampling period, that is, the latter atom moves down one unit based on the previous atom.

8. The terahertz coating detection system according to claim 7, wherein the reflection signal in the sparse solution module can be expressed in the following matrix form: Y=Xh+e (2) Where h represents the impulse response sequence, represents the solution of h, that is, the sparse representation result; e represents the allowable calculation and measurement error; Will solve The problem is transformed into an optimization problem of solving the minimum l0 norm of the vector: In the formula, λ is the regularization parameter, and the definition of the l0 norm of a vector is the number of non-zero elements in the vector; for the sake of simplicity of calculation, it can be converted into a LASSO regression model under the l1 norm regularization constraint:

9. The terahertz coating detection system according to claim 8, wherein the amplitude calculation method in the reflection signal information extraction module is: In the formula, r ij It represents the ratio of the amplitude of the reflected wave to the amplitude of the incident wave when the terahertz pulse is reflected from the i-th layer to the j-th layer, i.e., the reflection ratio; t ij It represents the ratio of the amplitude of the transmitted wave to the amplitude of the incident wave when the terahertz pulse is transmitted from the i-th layer to the j-th layer, that is, the transmittance; t1 represents the loss ratio generated when the terahertz pulse propagates in the coating.

10. The terahertz coating detection system according to claim 9, wherein the refractive index in the refractive index calculation module is specifically calculated as follows: Assuming the refractive index of the coating material is n and the refractive index of air is 1, according to the Fresnel formula, the reflectance and transmittance can be expressed as: By calculation, the relationship between the reflectance, transmittance and refractive index between the coating and the air can be obtained, namely: Solving this equation and discarding unreasonable solutions, we can calculate the refractive index n of the coating material:

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