A terahertz coating detection method and system based on sparse reconstruction algorithm

Abstract

The present invention designs a terahertz coating detection method and system based on a sparse reconstruction algorithm. First, a sparse representation algorithm is used 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 reflection model, and the geometric thickness of the thermal expansion coating is calculated based on the refractive index and the time interval of the reflection peak.

Description

Technical Field

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

[0002] With technological advancements, coating technology is increasingly being used in industry and manufacturing, particularly in the aviation, automotive, and petrochemical sectors. Common coating types include thermal barrier coatings, paint coatings, anti-corrosion coatings, and automotive coatings, each with distinct functions and applications. Thermal barrier coatings are widely used in aircraft engines and gas turbines, forming a thermal barrier layer on the surface of high-temperature components, reducing substrate temperatures and improving corrosion and wear resistance. The thickness of the ceramic layer, the primary thermal insulation structure, directly impacts the coating's performance and lifespan. Too thin provides insufficient insulation, while too thick can easily cause stress concentration and lead to delamination. Additionally, paint coatings are commonly used on buildings, ships, and equipment to protect the substrate from environmental corrosion. Anti-corrosion coatings are used in corrosive environments such as the marine and petrochemical industries, effectively extending the service life of equipment. Automotive coatings enhance vehicle durability by providing a wear-resistant, weather-resistant, and aesthetically pleasing exterior. With the increasing application of coatings, monitoring coating thickness and integrity has become crucial, especially in harsh environments, where performance directly determines the reliability and lifespan of equipment.

[0003] Terahertz waves are a general term for electromagnetic waves with frequencies between 0.1THz and 10THz. They lie between the infrared and microwave bands on the electromagnetic spectrum, thus serving as a bridge between electronics and photonics. Terahertz waves have very low photon energy, making them very safe. They can penetrate most non-metallic and non-polar materials that are opaque to visible light and infrared radiation, making them suitable for detecting hidden objects. Furthermore, due to their electromagnetic properties, terahertz waves can be detected and received contactlessly. Combined with these unique advantages, terahertz waves have shown considerable potential for application in industrial inspection. Traditional terahertz time-domain spectroscopy thickness measurement is based on the time-of-flight method, but this method can only directly measure the optical thickness of a coating and requires the additional measurement of the coating's refractive index to calculate its geometric thickness. Patent CN114111604A proposes a thermal barrier coating inspection algorithm that does not require a reference sample. However, this requires manual location of the reflection peak's timing and amplitude, which is slow and subject to significant errors. In practical applications, due to the aliasing of reflection peaks from thinner coatings, this method is only effective for coatings hundreds of microns thick and has low accuracy. To address these shortcomings, this study proposes a terahertz coating detection method based on a sparse reconstruction algorithm. Summary of the Invention

[0004] To overcome existing challenges, the present invention has designed a terahertz coating detection method based on a sparse reconstruction algorithm. This method first uses a sparse representation algorithm to decompose the reflected terahertz time-domain spectrum, effectively distinguishing aliased reflection signals. The resulting sparse solution is then processed using a reconstruction algorithm to automatically and accurately locate the amplitude and time interval of the reflection signal. Finally, the Fresnel formula is used to calculate the material's refractive index, and the coating's geometric thickness is then calculated based on the refractive index and the time interval between reflection peaks.

[0005] Based on the above-mentioned 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 is perpendicularly incident on the coating. The perpendicularly incident terahertz wave will be reflected multiple times within the coating. The reflected signal is collected and recorded 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 E0(t). Based on the reference signal, a dictionary matrix X is constructed using the Toeplitz matrix. Each column vector in matrix X is a delayed transformation of the reference signal E0(t), called an atom. The interval between two adjacent atoms is one sampling period, meaning that the subsequent atom is shifted down one unit relative to the previous atom.

[0008] Step 3: Calculate the sparse representation of the reflected signal based on the reflected signal in step 1 and the dictionary matrix X constructed in step 2. The reflected 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 an optimization problem of solving the minimum l0 norm of the vector:

[0011]

[0012] Where λ is the regularization parameter. Adjusting this parameter (usually around 0.001) based on the noise level and coating thickness can achieve a balance between measurement accuracy and noise immunity. The l0 norm of a vector is defined as the number of nonzero elements in the vector. For this type of problem, for ease of calculation, it can be converted into a LASSO regression model with l1 norm regularization constraints:

[0013]

[0014] Step 4: Sparse representation results The adjacent non-zero values ​​are grouped together. The impulse response sequences after grouping are denoted as h1, h2, h3, where 1, 2, and 3 represent the number of layers.

[0015] Step 5: Use the grouping results h1, h2, and h3 to reconstruct each reflected signal. The reflected signals are reconstructed in sequence using the following formula:

[0016]

[0017] Where h1, h2, and h3 represent the first, second, and third impulse response sequences after grouping, and y1, y2, and y3 represent the first, second, and third reflection peaks after reconstruction.

[0018] Step 6: Extract the amplitudes of the 1st, 2nd, and 3rd reflection peaks obtained in step 5 and the time when they reach the maximum amplitude in sequence. The amplitude of the 1st reflection peak is recorded as R1, the amplitude of the 2nd reflection peak is recorded as E2, the amplitude of the 3rd reflection peak is recorded as E3, and the time difference when adjacent reflection peaks reach the maximum amplitude is recorded as Δt.

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

[0020]

[0021] Where 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, that is, 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.

[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 allows us to 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 coating thickness. Based on this relationship and the refractive index, the coating thickness can be calculated as:

[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] This 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 spectroscopy system. 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 within the ceramic layer, and the reflected signal is collected and recorded as Y.

[0033] The sparse representation dictionary module is used to construct a sparse representation dictionary. The signal emitted by the terahertz time-domain spectrometer is used as the reference signal, denoted as E0(t). Based on the reference signal, the dictionary matrix X is constructed using the Toeplitz matrix form.

[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 grouping module, used to obtain the results of the sparse solution module Decompose, specifically Grouping is done by grouping adjacent non-zero values ​​into one group. The impulse response sequences after grouping are denoted as h1, h2, h3, where 1, 2, and 3 represent the number of layers.

[0036] 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 reconstructed first, second, and third reflection peaks.

[0037] The reflection signal information extraction module extracts the amplitudes of the first, second, and third reconstructed reflection peaks and the times 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, and the amplitude of the third reflection peak is recorded as E3. The time difference when adjacent reflection peaks reach the 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 coating thickness.

[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 patent CN114111604A, which is that it can only be used for thicker coatings and requires manual differentiation and positioning of reflection signals. It can simply, quickly and accurately separate the aliased terahertz time-domain reflection 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 reflection 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 following briefly introduces the drawings required for use in the embodiments or the description of the prior art. 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 any creative work.

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

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

[0046] Figure 3 The figure 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 Comparison of the simulation results of the coating refractive index and thickness using this method with 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 particular system structures and techniques are provided for purposes of illustration, not limitation, to facilitate a thorough understanding of the embodiments of the present invention. However, it will be apparent to those skilled in the art that the present invention may be practiced in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present invention with unnecessary detail.

[0051] The present invention will be further described in detail below with reference to the accompanying drawings. The material to be tested includes a base layer and a coating to be tested, and its structure is shown in FIG. Figure 1 A terahertz pulse (R0) emitted by a terahertz time-domain spectrometer is incident vertically from top to bottom on the coating to be inspected. Part of the energy is directly reflected by the air-coating interface and received by the detector (E1), while the remaining energy penetrates the coating and is reflected at the coating-substrate interface. When the pulse enters the coating and returns to the coating-air interface, part of the energy is transmitted into the air and received by the detector (E2), while the remaining energy is reflected back into the coating, where it continues to reflect back and forth.

[0052] Based on the above-mentioned 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, record it 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 E0(t), and 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 in Figure 2, each column vector in the matrix X is a delayed transformation of the reference signal E0(t), called an atom. The interval between two adjacent atoms is one sampling period, that is, the latter atom moves down one unit based on the previous atom.

[0055] Step 3: Calculate the sparse representation of the reflected signal based on the reflected signal in step 1 and the dictionary matrix X constructed in step 2. The reflected 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 an optimization problem of solving the minimum l0 norm of the vector:

[0058]

[0059] Where λ is the regularization parameter. Adjusting this parameter (usually around 0.001) based on the noise level and coating thickness can achieve a balance between measurement accuracy and noise immunity. The l0 norm of a vector is defined as the number of nonzero elements in the vector. For this type of problem, for ease of calculation, it can be converted into a LASSO regression model with l1 norm regularization constraints:

[0060]

[0061] Step 4: Sparse representation results Group the adjacent non-zero values ​​into one group, such as Figure 3 The impulse response sequences after grouping are denoted as h1, h2, h3, where 1, 2, and 3 represent the number of layers.

[0062] Step 5: Use the grouping results h1, h2, and h3 to reconstruct each reflected signal. The reflected signals are reconstructed in sequence using the following formula:

[0063]

[0064] Where h1, h2, and h3 represent the first, second, and third impulse response sequences after grouping, and y1, y2, and y3 represent the first, second, and third 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 R1, the amplitude of the second reflection peak is recorded as E2, and the amplitude of the third reflection peak is recorded as E3. The time difference between adjacent reflection peaks when they reach the maximum amplitude is recorded as Δt. Figure 3 、 Figure 4 It should be noted that due to the half-wave loss when reflecting on the interface with a low to high refractive index, the sign of E3 is opposite to that of E1 and E2.

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

[0067]

[0068] Where r ijIt 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, that is, 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.

[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 allows us to 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 coating thickness. Based on this relationship and the refractive index, the thickness of the coating material can be calculated as:

[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 this application specifically includes the following parts:

[0079] The sample signal acquisition module is used to measure the coating using a terahertz time-domain spectroscopy system. 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 within the ceramic layer, and the reflected signal is collected and recorded as Y.

[0080] The sparse representation dictionary module is used to construct a sparse representation dictionary. The signal emitted by the terahertz time-domain spectrometer is used as the reference signal, denoted as E0(t). Based on the reference signal, a dictionary matrix X is constructed using the Toeplitz matrix. Each column vector in matrix X is a delayed transformation of the reference signal E0(t), called an atom. The interval between two adjacent atoms is one sampling period, meaning that the subsequent atom is shifted down one unit relative to 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 an optimization problem of solving the minimum l0 norm of a vector:

[0084]

[0085] Where λ is the regularization parameter. Adjusting this parameter (usually around 0.001) based on the noise level and coating thickness can achieve a balance between measurement accuracy and noise immunity. The l0 norm of a vector is defined as the number of nonzero elements in the vector. For this type of problem, for ease of calculation, it can be converted into a LASSO regression model with l1 norm regularization constraints:

[0086]

[0087] Clustering grouping module, used to obtain the results of the sparse solution module Decompose, specifically Grouping is done by grouping adjacent non-zero values ​​into one group. The impulse response sequences after grouping are denoted as h1, h2, h3, where 1, 2, and 3 represent the number of layers.

[0088] The grouping and reconstructing reflected signal module is used to reconstruct the grouping results, that is, to reconstruct each reflected signal according to h1, h2, and h3 obtained by grouping. The reflected signals are reconstructed in sequence using the following formula:

[0089]

[0090] Where h1, h2, and h3 represent the first, second, and third impulse response sequences after grouping, and y1, y2, and y3 represent the first, second, and third reflection peaks after reconstruction.

[0091] Extract the reflection signal information module, and extract the amplitudes 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, and the amplitude of the third reflection peak is recorded as E3. The time difference when adjacent reflection peaks reach the maximum amplitude is recorded as Δt, as shown in 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 theoretically be expressed as:

[0093]

[0094] Where 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, that is, 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.

[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 allows us to 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 a terahertz pulse propagates in the coating is twice the coating thickness. 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 measuring range to within 1um, thereby achieving efficient, high-accuracy, and wide-range non-destructive testing of the coating, without the need for any other standard sample preparation and measurement work. In the simulation, the method designed by the present invention simulated 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 were 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 were 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 apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article or apparatus comprising the element.

[0107] The above description of the disclosed embodiments is intended to enable one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be readily 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 is not limited to the embodiments shown herein but is intended to conform 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 considered as equivalent replacement methods and are included in the scope of protection 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 they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention, and should all be included in the scope of protection 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 is vertically incident on the coating, and the reflected signal is collected, which is recorded as Y. Step 2: Construct a sparse representation dictionary. The signal emitted by the terahertz time-domain spectrometer is used as a reference signal, denoted as E0(y). Based on the reference signal, a dictionary matrix X is constructed in the form of a Toeplitz matrix. 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 Group the adjacent non-zero values ​​into one group; the impulse response sequences after grouping are recorded as h1, h2, h3, where 1, 2, and 3 represent the number of layers; Step 5: Use the grouping results h1, h2, and h3 to reconstruct each reflected signal. The reflected signals are reconstructed in sequence using the following formula: y1=Xh1 y2=Xh2 (1) y3=Xh3 Where h1, h2, h3 represent the first, second, and third impulse response sequences after grouping, and y1, y2, y3 represent the first, second, and third reflection peaks after reconstruction; Step 6: Extract the amplitudes of the first, second, and third reflection peaks obtained in step 5 and the times 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, and the amplitude of the third reflection peak is recorded as E3. The time difference between adjacent reflection peaks when they reach the maximum amplitude is recorded as Δt. Step 7, calculating the refractive index n of the coating material based on 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 coating thickness. Based on this relationship and the refractive index, the thickness of the coating material can be calculated as: 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. The terahertz coating detection method according to claim 1, wherein in 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 one sampling period, that is, the latter atom is shifted down one unit based on the previous atom.

3. The terahertz coating detection method according to claim 2, wherein 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, i.e. 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: Where λ is the regularization parameter, and the l0 norm of a vector is defined as the number of non-zero elements in the vector. For ease of calculation, it can be converted into a LASSO regression model under l1 norm regularization constraint: 。 4. The terahertz coating detection method according to claim 3, wherein the amplitude calculation method in step 6 is: Where 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, that is, 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. The terahertz coating detection method according to claim 4, wherein the refractive index of the coating material is calculated in step 7 by: 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 allows us to 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). Based on the reference signal, a dictionary matrix X is constructed in the form of a Toeplitz matrix. 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 grouping module, used to obtain the results of the sparse solution module Decompose, specifically Grouping, grouping adjacent non-zero values ​​into one group; the impulse response sequences after grouping are recorded as h1, h2, h3, where 1, 2, and 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 reconstructed first, second, and third reflection peaks; Extract the reflection signal information module, and extract the amplitudes of the first, second, and third reconstructed reflection peaks 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, and the amplitude of the third reflection peak is recorded as E3. The time difference when adjacent reflection peaks reach the maximum amplitude is recorded as Δt; A refractive index calculation module is 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 a terahertz pulse propagates in the coating is twice the coating thickness. 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. The terahertz coating detection system according to claim 6, wherein the sparse representation dictionary construction module constructs a dictionary matrix X in the form of a Toeplitz matrix based on the reference signal when constructing the sparse representation dictionary; 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 one sampling period, that is, the latter atom is shifted downward by 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, i.e. 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: Where λ is the regularization parameter, and the l0 norm of a vector is defined as the number of non-zero elements in the vector. For ease of calculation, it can be converted into a LASSO regression model under 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: Where 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, that is, 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 allows us to calculate the refractive index n of the coating material:

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