A method for extracting the thickness of multilayer coatings on anisotropic substrates

Abstract

The present invention discloses a method for extracting the thickness of a multilayer coating on an anisotropic substrate, comprising step S1: using a first TPX lens to project a terahertz wave at a position on the substrate to be measured, thereby obtaining first information; step S2: using a second TPX lens to project a terahertz wave at the same position on the substrate to be measured, thereby obtaining second information; step S3: creating an equivalent matrix value for the anisotropic substrate that is independent of the test position; step S4: repeating steps S1 and S2 on a substrate with a coating, thereby obtaining the coating thickness of the substrate. The method for extracting the thickness of a multilayer coating on an anisotropic substrate disclosed by the present invention greatly simplifies the coating thickness measurement process and effectively eliminates the difficult and time-consuming step of rotating the sample or test equipment to collect a large amount of data during measurement. The equivalent parameters of the anisotropic substrate are obtained, and the multilayer thickness extraction process is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of thickness extraction, and in particular relates to a method for extracting the thickness of a multilayer coating on an anisotropic substrate. Background Art

[0002] Surface coatings are crucial to the performance of a wide range of products in industries such as automotive, aerospace, and turbines. Furthermore, surface coatings on various products must achieve an optimal thickness to function properly. For example, paint thickness is crucial to aircraft safety and performance. It determines the extent of damage to an aircraft in the event of a lightning strike. Paint thickness is particularly critical near fuel tanks, as lightning can create sparks that ignite the fuel. Several factors can contribute to coating thinning over time.

[0003] Environmental exposure: UV radiation and adverse weather conditions

[0004] Chemical exposure: Exposure to corrosive chemicals or pollutants

[0005] Mechanical stress: Physical wear or abrasion and poor flexibility can lead to cracking or delamination

[0006] Substrate compatibility: poor coating adhesion and high stress

[0007] Microbial growth: mold or mildew, causing discoloration and degradation.

[0008] Temperature extremes: Repeated exposure to temperature fluctuations and overheating

[0009] Aging and material breakdown: Coatings may break down chemically or physically, reducing their effectiveness.

[0010] Aircraft are therefore regularly repainted to ensure adequate paint thickness. Measuring paint thickness is a crucial step in repainting aircraft fuselages. Accurately measuring paint thickness helps ensure that paint thickness is kept to a minimum to reduce unnecessary payload, while not falling below the limits mandated by safety regulations. A coating that is too thin puts the aircraft at risk of damage from lightning strikes or UV radiation, while a coating that is too thick can hinder the aircraft's aerodynamic performance. Therefore, assessing aircraft paint thickness during maintenance and manufacturing is crucial.

[0011] During the measurement process, problems arise if the material to be measured has anisotropy, such as uneven refractive index in different directions. The problem with anisotropic samples is that various parameters such as the refractive index can vary greatly at every point in the sample. In previous work, the terahertz frequency range of 0.1THz to 1.2THz was used to determine the thickness of paint. However, the above method is difficult to apply in real life because it is difficult and time-consuming to collect a large amount of data by rotating the sample or testing equipment. Therefore, the substrate problem hinders the commercialization of the technology. In addition, when the beam size becomes larger, the signal-to-noise ratio decreases significantly.

[0012] Therefore, further improvements are made to the above problems. Summary of the Invention

[0013] The primary objective of this invention is to provide a method for extracting the thickness of multilayer coatings on anisotropic substrates. This method significantly simplifies the coating thickness measurement process, effectively eliminating the difficult and time-consuming step of rotating the sample or test equipment to collect large amounts of data during measurement. This method obtains equivalent parameters for anisotropic substrates and improves the multilayer thickness extraction process. The algorithm developed for multilayer thickness extraction can be further extended to anisotropic substrates.

[0014] To achieve the above objectives, the present invention discloses a method for extracting the thickness of a multilayer coating on an anisotropic substrate, comprising the following steps:

[0015] Step S1: Use a first TPX lens to project a terahertz wave onto a position on a substrate to be measured (without a coating), and the beam size of the first TPX lens matches the characteristic size of the position (the beam size is slightly larger), thereby obtaining first information including the optical path length L0, the refractive index n0, and the peak frequency f0;

[0016] Step S2: Projecting a terahertz wave onto the same position of the substrate to be measured (without coating) using a second TPX lens, wherein the beam size of the second TPX lens is larger than the beam size of the first TPX lens (twice or larger), thereby obtaining second information including the optical path length L1, the refractive index n1, and the peak frequency f1;

[0017] Step S3: analyzing the spectral data measured by the first information and the second information, creating an equivalent matrix value for the anisotropic substrate that is independent of the test position, and using the equivalent matrix value as an equivalent index of the substrate;

[0018] Step S4: Repeat steps S1 and S2 on the substrate with the coating, thereby obtaining the coating thickness of the substrate.

[0019] As a further preferred technical solution of the above technical solution, for step S3:

[0020] Since the projection is performed on the same position of the substrate and the beam size of the second TPX lens is larger than that of the first TPX lens, an overlapping area is generated. The first information and the second information are respectively converted into frequency domain signals using Fourier transform. The frequency domain signals are then integrated, and the power per unit area is calculated and normalized. The specific implementation is as follows:

[0021] After obtaining the time domain spectrum through the first information, Fourier transform is performed to obtain the first frequency spectrum F1;

[0022] After obtaining the time domain spectrum through the second information, Fourier transform is performed to obtain the second spectrum F2;

[0023] Integrating the first spectrum F1 and the second spectrum F2 respectively to obtain a first spectrum intensity I1 and a second spectrum intensity I2;

[0024] Based on the measurement results of the two TPX lenses, the integrated intensity achieves a constant I2-I1 (subtraction), and this result is used as an equivalent indicator of the substrate (the signals of the two circles are sensitive to the information of the center point, and the signal of the small circle (i.e., the aperture projected by the first TPX lens) is greatly affected by the anisotropy of the substrate. The outer ring signal is stable after subtraction).

[0025] As a further preferred technical solution of the above technical solution, in step S4, the parameters of the substrate and each coating material are input through a numerical simulation method, and the thickness of each coating is obtained through simulation and calculation.

[0026] As a further preferred technical solution of the above technical solution, the terahertz wave beam projected by the first TPX lens is smaller than the characteristic size of the (anisotropic) substrate.

[0027] As a further preferred technical solution of the above technical solution, the beam size of the second TPX lens is twice the beam size of the first TPX lens. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 Schematic diagram of projecting a light beam through the first / second TPX lens of the present invention.

[0029] Figure 2 This is the relationship between the amplitude and frequency of the two light beams of the 5 mm signal and the 8 mm signal of the present invention.

[0030] Figure 3 It is the signal processing result of the 5 mm spot size, the 8 mm spot size and the comprehensive information of the 5 mm and 8 mm spot sizes of the present invention. DETAILED DESCRIPTION

[0031] The following description is intended to disclose the present invention so that those skilled in the art can implement the present invention. The preferred embodiments described below are for illustrative purposes only, and those skilled in the art will readily appreciate other obvious variations. The basic principles of the present invention defined in the following description may be applied to other embodiments, variations, improvements, equivalents, and other technical solutions that do not depart from the spirit and scope of the present invention.

[0032] In the preferred embodiment of the present invention, those skilled in the art should note that the substrate and the like involved in the present invention may be regarded as prior art.

[0033] Preferred embodiment.

[0034] like Figure 1-3 As shown, the present invention discloses a method for extracting the thickness of a multilayer coating on an anisotropic substrate, comprising the following steps:

[0035] Step S1: Use a first TPX lens to project a terahertz wave onto a position on a substrate to be measured (without a coating), and the beam size of the first TPX lens matches the characteristic size of the position (the beam size is slightly larger), thereby obtaining first information including the optical path length L0, the refractive index n0, and the peak frequency f0;

[0036] Step S2: Projecting a terahertz wave onto the same position of the substrate to be measured (without coating) using a second TPX lens, wherein the beam size of the second TPX lens is larger than the beam size of the first TPX lens (twice or larger), thereby obtaining second information including the optical path length L1, the refractive index n1, and the peak frequency f1;

[0037] Step S3: analyzing the spectral data measured by the first information and the second information, creating an equivalent matrix value for the anisotropic substrate that is independent of the test position, and using the equivalent matrix value as an equivalent index of the substrate;

[0038] Step S4: Repeat steps S1 and S2 on the substrate with coating to obtain the coating thickness of the substrate. Repeat steps S1 and S2 on the substrate with coating and use the same calculation method as step S3 for the coating. These values ​​will be further input into the thickness extraction algorithm. Based on the obtained information such as optical path length and refractive index, according to the formula:

[0039] L = n × d

[0040] Where L is the optical path length, n is the refractive index, and d is the thickness, this provides preliminary thickness data. It can be observed that the signals collected from small focal points can vary significantly. For larger focal points, while covering a larger area, the signals collected from different locations on the anisotropic substrate still vary, but the variation is smaller.

[0041] like Figure 2As shown in Figure 2, using this information, two smaller focal spots (5 mm and 8 mm) can be used to obtain stable equivalent information, similar to the 13 mm focal spot size information, which is independent of the anisotropic substrate position. To obtain a stable result with 13 mm spot size information, the sample must be rotated 360 degrees to obtain the average value. The new measurement scheme makes it possible to achieve the same effect without rotating the sample.

[0042] like Figure 3 As shown, the relationship between the THz TDS amplitude and frequency of the 5 mm signal and the 8 mm signal is shown. Figure 3 Processed data from three measurement points is shown. The signals for a 5 mm spot size and an 8 mm spot size are also plotted for comparison. Using the same legend for the three measurement points with the same spot size demonstrates that similar and stable results can be obtained for the same spot size but different measurement points.

[0043] The results show that the signal varies significantly for spot sizes of 5 mm and 8 mm. However, for processed data containing information about the 5 mm and 8 mm spot sizes, the signal becomes very stable, with very little variation. These processed values ​​can be considered as average information for the anisotropic substrate, thereby obtaining equivalent parameters for the anisotropic CFRP substrate and further input into the thickness measurement algorithm.

[0044] Specifically, for step S3:

[0045] Since the projection is performed on the same position of the substrate and the beam size of the second TPX lens is larger than that of the first TPX lens, an overlapping area is generated. The first information and the second information are respectively converted into frequency domain signals using Fourier transform. The frequency domain signals are then integrated, and the power per unit area is calculated and normalized. The specific implementation is as follows:

[0046] After obtaining the time domain spectrum through the first information, Fourier transform is performed to obtain the first frequency spectrum F1;

[0047] After obtaining the time domain spectrum through the second information, Fourier transform is performed to obtain the second spectrum F2;

[0048] Integrating the first spectrum F1 and the second spectrum F2 respectively to obtain a first spectrum intensity I1 and a second spectrum intensity I2;

[0049] Based on the measurement results of the two TPX lenses, the integrated intensity achieves a constant I2-I1 (subtraction), and this result is used as an equivalent indicator of the substrate (the signals of the two circles are sensitive to the information of the center point, and the signal of the small circle (i.e., the aperture projected by the first TPX lens) is greatly affected by the anisotropy of the substrate. The outer ring signal is stable after subtraction).

[0050] More specifically, in step S4, the parameters of the substrate (equivalent matrix value) and each coating material (including n, k and dielectric constant, etc.) are input through a numerical simulation method, and the thickness of each coating is obtained through simulation and calculation, where:

[0051] Furthermore, the terahertz wave beam projected by the first TPX lens is relatively small relative to the characteristic size of the (anisotropic) substrate.

[0052] Furthermore, the beam size of the second TPX lens is twice the beam size of the first TPX lens.

[0053] Inverse modeling: Using a common optimization procedure, experimental results are compared with the simulation model. Input parameters for the substrate and layer materials, as well as material parameters such as n, k, and dielectric constant, are used. To minimize the discrepancy, a particle swarm optimization (PSO) method is used. Once the error is minimized, the thickness can be derived from this optimal set of parameters.

[0054] In the inverse modeling process, the error function defines the error between the experimental output and the simulation model. If defined properly, the objective function can significantly improve the accuracy and precision of the optimization protocol. The error function defined in the method is the cross-correlation between the experimental results and the simulation model. The mathematical form of the cross-correlation operation is:

[0055]

[0056] and its Fourier transform pair:

[0057]

[0058] To better demonstrate the nature of the error function, an analytical model with two layers of paint on a substrate is assumed as the “experimental input” to the optimization process.

[0059] The “experimental input” is the amplitude of the wave reflected by the paint structure, which is swept as a function of THz frequency. The method uses the amplitude of the reflected wave |R input |, and use Fourier transform to map it to the time domain. |R input The Fourier transform of | is

[0060]

[0061] The method then removes components in the time domain that are several orders of magnitude lower than the components at t = 0. These components are unimportant and do not contribute to the reconstruction of the reflection curve in the frequency domain. This helps prevent inaccurate results due to these non-essential components.

[0062] The next step in the method is to calculate the cross-correlation error between the input function and the test function. The error is divided into two parts, magnitude and phase. The magnitude error between the input function and the test function is defined as:

[0063]

[0064] Phase error:

[0065]

[0066] When the error reaches a minimum, the solution is found.

[0067] It is worth mentioning that the technical features such as the substrate involved in the patent application of this invention should be regarded as prior art. The specific structure, working principle and possible control method and spatial layout method of these technical features can be selected by conventional means in the field and should not be regarded as the inventive point of this patent. This patent will not be further elaborated.

[0068] For those skilled in the art, it is still possible to modify the technical solutions described in the aforementioned embodiments, or to make equivalent replacements for some of the technical features therein. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for extracting the thickness of a multilayer coating on an anisotropic substrate, characterized in that: The following steps are involved: Step S1: Projecting a terahertz wave onto a position of a substrate to be measured using a first TPX lens, wherein the beam size of the first TPX lens matches the characteristic size of the position, thereby obtaining first information including optical path length L0, refractive index n0, and peak frequency f0; Step S2: Projecting a terahertz wave onto the same position of the substrate to be measured using a second TPX lens, wherein the beam size of the second TPX lens is larger than the beam size of the first TPX lens, thereby obtaining second information including optical path length L1, refractive index n1, and peak frequency f1; Step S3: analyzing the spectral data measured by the first information and the second information, creating an equivalent matrix value for the anisotropic substrate that is independent of the test position, and using the equivalent matrix value as an equivalent index of the substrate; Step S4: Repeating steps S1 and S2 on the substrate with the coating, thereby obtaining the coating thickness of the substrate.

2. The method for extracting the thickness of a multilayer coating on an anisotropic substrate according to claim 1, characterized in that: For step S3: Since the projection is performed on the same position of the substrate and the beam size of the second TPX lens is larger than that of the first TPX lens, an overlapping area is generated. The first information and the second information are respectively converted into frequency domain signals using Fourier transform. The frequency domain signals are then integrated, and the power per unit area is calculated and normalized. The specific implementation is as follows: After obtaining the time domain spectrum through the first information, Fourier transform is performed to obtain the first frequency spectrum F1; After obtaining the time domain spectrum through the second information, Fourier transform is performed to obtain the second spectrum F2; Integrating the first spectrum F1 and the second spectrum F2 respectively to obtain a first spectrum intensity I1 and a second spectrum intensity I2; Based on the results of the two TPX lens measurements, the integrated intensity achieves a constant I2-I1, and this result is used as an equivalent indicator of the substrate.

3. The method for extracting the thickness of a multilayer coating on an anisotropic substrate according to claim 1, characterized in that: In step S4, the parameters of the substrate and each coating material are input through a numerical simulation method, and the thickness of each coating is obtained through simulation and calculation.

4. The method for extracting the thickness of a multilayer coating on an anisotropic substrate according to claim 1, characterized in that: The terahertz wave beam projected by the first TPX lens is smaller than the characteristic size of the substrate.

5. The method for extracting the thickness of a multilayer coating on an anisotropic substrate according to claim 4, characterized in that: The beam size of the second TPX lens is twice the beam size of the first TPX lens.

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