A plastic film thickness measurement system and method based on transmission spectrum

Abstract

This invention discloses a plastic film thickness measurement system and method based on transmission spectroscopy, belonging to the field of thin film optics and optical measurement. The thickness measurement system includes a light source, an incident converging lens, a film sample, a receiving converging lens, a miniature spectrometer, and a data processing unit. The light source and the incident converging lens are connected via optical fiber. The principal optical axes of the incident and receiving converging lenses are aligned. The focal points of the incident and receiving converging lenses are adjusted to infinity. The film sample is placed between the incident and receiving converging lenses. The angle between the normal of the film sample and the principal optical axes of the incident and receiving lenses is the angle of incidence. The receiving converging lens is connected to the miniature spectrometer via optical fiber, and the miniature spectrometer is connected to the data processing unit via a USB data cable. This invention, based on the existing full-spectrum fitting method, combines the measurement of the refractive index of the film using the transmittance envelope, realizing the thickness measurement of films with unknown refractive indices.

Description

Technical Field

[0001] This invention relates to a method for measuring the thickness of plastic films based on transmission spectroscopy, belonging to the field of thin film optics and optical measurement. Background Technology

[0002] Since the beginning of the 21st century, the plastics industry and plastic film technology have developed rapidly. With the advancements in processing technologies such as radiation curing and multilayer co-extrusion, as well as functional materials, the functionality of these polymer film materials has been further improved, increasing their application value. Functional films typically possess one or more special functions, including electrical, magnetic, optical, acoustic, mechanical, chemical, and biological functions, thus offering broad application prospects in emerging industries such as energy conservation and environmental protection, new energy, high-end equipment manufacturing, and biotechnology. Existing methods for measuring film thickness mainly include the probe method, wavelength extremum method, quartz crystal oscillator method, interferometric spectroscopy, and elliptic polarization method. Among these, non-contact, non-destructive thickness measurement methods primarily include broadband spectral analysis and elliptic polarization. The elliptic polarization method utilizes the principle of changes in the polarization state of light reflected from the film for measurement. It can measure the refractive index and thickness of the film with a measurement error of less than 1 nm and repeatability of less than 0.01 nm, making it the most accurate method currently available. However, the equipment is expensive and complex, requiring the rotation of waveplates and adjustment of the incident angle, making the process cumbersome and time-consuming, and preventing rapid measurement. The wavelength extremum method is commonly used to monitor thin film growth. When the optical thickness of the thin film reaches an integer multiple of 1 / 4 of the monitoring light wavelength, the transmittance of the thin film exhibits an extreme value. Because the rate of change in transmittance at the extreme point is low, the measurement accuracy of the wavelength extremum method is limited. Interference spectroscopy analysis, based on the principles of reflection and interference, shows that after light undergoes multiple reflections and transmissions through the upper and lower surfaces of the thin film, the optical path differences between the light rays cause mutual interference, resulting in different reflectance or transmittance of the thin film for different wavelengths. By collecting the reflection or transmission spectra of the thin film, the thickness can be analyzed. This method is easy to implement and can achieve measurement speeds down to the millisecond level. This invention studies the interference spectroscopy analysis method.

[0003] Existing methods for measuring the refractive index and thickness of thin films using transmittance rely on precise values ​​of transmittance extrema for thickness calculation, without utilizing complete spectral data. Currently, the widely used method is the full-spectrum fitting method, which, based on the inverse relationship between the rate of change of transmittance and wavelength, calculates the thickness by taking the reciprocal of the transmittance and estimating the period. These methods using interferometric spectroscopy primarily employ perpendicular incidence reflection spectroscopy and treat the film's refractive index as a known quantity, making it impossible to simultaneously determine both the refractive index and thickness. Therefore, to simultaneously measure the refractive index and thickness of thin films, this invention utilizes transmission interferometric spectroscopy to measure the refractive index and employs the full-spectrum fitting method to calculate the film thickness. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and effectively solve the problems of dependence on the accuracy of extreme points in existing refractive index and film thickness calculation methods and the inability of the full spectrum fitting method to measure the refractive index of thin films. This invention provides a method for measuring the thickness of plastic films based on transmission spectroscopy, which calculates the refractive index using the relationship between transmittance and refractive index, and then substitutes the calculated refractive index into the full spectrum fitting method to solve for the film thickness.

[0005] The above objectives are achieved through the following technical solutions:

[0006] A method for measuring the thickness of plastic films based on transmission spectroscopy, the method comprising the following steps:

[0007] (1) According to Figure 1 As shown, a plastic film thickness measurement system based on transmission spectroscopy is constructed. The system comprises a light source 1, an incident converging lens 2, a film sample 3, a receiving converging lens 4, a miniature spectrometer 5, and a data processing unit 6. The light source 1 and the incident converging lens 2 are connected via optical fiber. The principal optical axes of the incident converging lens 2 and the receiving converging lens 4 are aligned. The focal points of the incident converging lens 2 and the receiving converging lens 4 are adjusted to infinity. The film sample 3 is placed between the incident converging lens 2 and the receiving converging lens 4. The angle between the normal of the film sample 3 and the principal optical axes of the incident converging lens 2 and the receiving converging lens 4 is the angle of incidence. The receiving converging lens 4 and the miniature spectrometer 5 are connected via optical fiber. The miniature spectrometer 5 and the data processing unit 6 are connected via a USB data cable. When the light emitted from the light source 1 passes through the incident converging lens 2 and strikes the film sample 3, the receiving converging lens 4 on the other side of the film sample 3 receives the transmitted light, and the miniature spectrometer 5 measures the transmission interference spectrum P. t (λ), the transmission interference spectrum P t (λ) Transmitted to data processing unit 6;

[0008] (2) Remove the thin film sample 3 described in step (1). When the light emitted from the light source passes through the incident converging lens 2 and is directed towards the receiving converging lens 4, use a miniature spectrometer to measure the light source spectrum P. o (λ), the light source spectrum P o (λ) Transmitted to data processing unit 6;

[0009] (3) The transmission interference spectrum P obtained in steps (1) and (2) t (λ) and the light source spectrum P o Dividing by (λ), we obtain the transmittance T(λ) of the thin film sample. The transmittance T(λ) is a function of the incident angle, the incident wavelength, the refractive index of the thin film sample, and the thickness of the thin film sample, i.e.:

[0010]

[0011] In the formula, r1 is the reflection coefficient of the interface between air and thin film sample, r2 is the reflection coefficient of the interface between thin film sample and air, and δ is the phase difference between two adjacent transmitted rays, expressed as:

[0012]

[0013] In the formula, n(λ) is the refractive index of the thin film sample, h is the thickness of the thin film sample in meters, θ is the incident angle in degrees or radians, and λ is the wavelength of the light source in meters.

[0014] (4) Preferably, when the light from the light source is incident perpendicularly on the thin film sample 3, the reflection coefficients r1 and r2 are expressed as:

[0015]

[0016] In the formula, n0 is the refractive index of the incident medium, n(λ) is the refractive index of the thin film sample, and n G Let be the refractive index of the exit-side medium; then the transmittance T(λ) is expressed as:

[0017]

[0018] In the formula, n0 is the refractive index of the incident medium, n(λ) is the refractive index of the thin film sample, and n G Let α be the refractive index of the exit-side medium, h be the film thickness in meters, λ be the wavelength of the light source in meters, and α, C1, and C2 be intermediate values ​​used to simplify calculations and have no physical meaning. Furthermore, α = exp(-4πnh / λ) and C1 = (n + n0)(n G +n), C2=(n-n0)(n G -n).

[0019] Therefore, the refractive index n(λ) of the thin film sample can be calculated as follows:

[0020]

[0021] In the formula, n0 is the refractive index of the incident medium, n G Let N(λ) be the refractive index of the exit-side medium, and N(λ) be an intermediate quantity used to simplify calculations and has no physical meaning.

[0022]

[0023] In the formula, T max (λ) is the upper envelope passing through all the maxima of transmittance T(λ), T min (λ) is the lower envelope that passes through all the minimum points of transmittance T(λ);

[0024] (5) Perform empirical mode decomposition on the transmittance T(λ) obtained in step (3), and express the transmittance T(λ) as the sum of q eigenmode functions. The specific method for solving the eigenmode functions is as follows:

[0025] (5.1) Using all the maxima and minima of transmittance T(λ), the upper envelope e of transmittance T(λ) is fitted by a cubic spline function. max (λ) and lower envelope e min (λ); Calculate the mean value of the upper and lower envelopes as the mean envelope m of the transmittance T(λ). 11 (λ)=[e max (λ)+e min (λ)] / 2, where the subscript ij of m represents the j-th filtering of the i-th component;

[0026] (5.2) The first component h obtained from the decomposition 11 (λ) can be expressed as h using the original signal and the mean envelope. 11 (λ)=T(λ)-m 11 (λ);

[0027] (5.3) Check the first component h obtained. 11 Does (λ) satisfy the two conditions of an intrinsic mode function? That is, on an intrinsic mode function, the number of local extrema and the number of zeros should be equal or differ by 1; and for any time, the local mean of the maximum envelope and the minimum envelope is 0.

[0028] If it does not meet the requirements, repeat the screening process in (5.1) and (5.2) k times until the obtained component h is obtained. 1k (λ)=h 1(k-1) (λ)-m 1k If (λ) satisfies the two constraints of the intrinsic mode function, then h 1k (λ) is the first intrinsic mode function IMF1(λ) obtained from the empirical mode decomposition of transmittance T(λ);

[0029] (5.4) Subtracting the first intrinsic mode function from the transmittance T(λ) yields the residual signal r1(λ) = T(λ) - IMF1(λ). Repeating the filtering process (5.1)-(5.3) on the residual signal, we can decompose it into q intrinsic mode functions IMF. q (λ), until the margin r q (λ)=r q-1 (λ)-IMF q When (λ) is a monotonic function or a constant function, the EMD decomposition process terminates.

[0030] (6) Adaptively select the q intrinsic mode functions obtained in step (5). The specific steps are as follows:

[0031] (6.1) The transmittance T(λ) is smoothed using a five-point cubic Savitzky-Golay filter fitting method. The length of the sliding window is 5. When the center of the sliding window moves to the j-th position of the transmittance T(λ), the data point x within the sliding window is used as the basis for the smoothing process. j-2 ,x j-1 ,x j ,x j+1 ,x j+2 Construct a cubic polynomial:

[0032] f(x j )=a0+a1j+a2j 2 +a3j 3 (17)

[0033] The coefficients a0, a1, a2, a3 are solved using the least squares method, and then the j-th element of the smoothed transmittance T(λ) is calculated using equation (7); the smoothed transmittance is denoted as T. s (λ);

[0034] (6.2) Search for smoothed transmittance T s All local maxima of (λ), i.e., when x i-1 <x i And x i >x i+1 At that time, it was believed that x i For each local maximum, cubic spline interpolation is performed to obtain the smoothed transmittance T. s The upper envelope T of (λ) s + (λ);

[0035] (6.3) Search for smoothed transmittance T s All local minima of (λ), i.e., when x i-1 >x i And x i <x i+1 At that time, it was believed that x i For each local minimum, cubic spline interpolation is performed to obtain the smoothed transmittance T. s The lower envelope T of (λ) s - (λ);

[0036] (6.4) The upper envelope T obtained in step (6.2) s + (λ) Subtract the lower envelope T obtained in step (6.3) s - (λ), to obtain the smoothed transmittance T s The amplitude R of (λ) Ts (λ);

[0037] (6.5) Obtain the upper envelope of the q intrinsic mode functions obtained in step (5) using the methods described in steps (6.2) and (6.3). and lower envelope The amplitude R of the q intrinsic mode functions obtained in step (5) is then obtained using the method described in step (6.4). IMF1 (λ),…,R IMFq (λ);

[0038] (6.6) Calculate the smoothed transmittance T obtained in step (6.4) respectively. s The amplitude R of (λ) Ts (λ) and the amplitude R of the q eigenmode functions obtained in step (6.5) IMF1 (λ),…,R IMFq The mean square error of (λ) will be related to the smoothed transmittance T. s The eigenmode function with the smallest mean square error of amplitude (λ) is denoted as T. c (λ), T c (λ) serves as the data for subsequent steps to calculate the film thickness.

[0039] (7) When the thin film sample 3 described in step (1) is placed in the air, the reflection coefficient satisfies the relationship r1 = -r2, denoted as r = r1 = -r2, and the T obtained in step (6) is... c (λ) undergoes the following transformation:

[0040]

[0041] K1 = 2πn(λ)cosθ / λ, where n(λ) is the refractive index of the thin film obtained in step (4), θ is the angle of incidence in degrees or radians, λ is the wavelength of light in meters, and h is the thickness of the thin film sample in meters.

[0042] Transmittance T after transformation by equation (8) K1 The transmittance T is the sum of a constant and a cosine function with K1 as the independent variable, where the frequency of the cosine function is determined by the film thickness. The Lomb-Scargle periodogram method is used to solve for the transformed transmittance T. K1 Power spectrum P T (ω):

[0043]

[0044] In the formula, ω is the transmittance T after transformation by equation (8). K1 The frequency, N is the number of pixels in the spectrometer, that is, the number of data in the transmittance T(λ) obtained in step (3), T K1 (j) is T K1Let K1(j) be the j-th data in K1, and let the redundancy parameter τ be defined as:

[0045]

[0046] (8) Extract the power spectrum P obtained in step (7) T The frequency ω0 at the peak (ω) is used to calculate the thickness of the thin film sample as ω0π.

[0047] Beneficial effects:

[0048] Compared with existing technologies, this invention overcomes the shortcomings of existing thin film thickness measurement methods. Based on the existing full-spectrum fitting method, it combines the measurement of the refractive index of the thin film with the transmission envelope, realizing the thickness measurement of thin films with unknown refractive indices. After applying empirical mode decomposition to decompose the transmission index into several intrinsic mode functions, the amplitude matching method is used to adaptively select the correct intrinsic mode functions as data for subsequent thin film thickness calculations. This avoids the interference of peak values ​​caused by low-frequency components of the light source spectrum in the power spectrum on the thin film thickness calculation results. At the same time, it avoids the manual selection of intrinsic mode functions, effectively solving the problem of high-frequency noise being incorrectly used as valid data for thin film thickness calculation, and improving the robustness of the thin film thickness calculation method. Attached Figure Description

[0049] Figure 1 This is a schematic diagram of a plastic film thickness measurement system.

[0050] Figure 2 This is a schematic diagram of the process of the present invention;

[0051] Figure 3 The above is a simulation result diagram of the method for calculating the refractive index of the thin film described in the embodiments of the present invention;

[0052] Figure 4 The method described in this embodiment of the invention measures the transmittance and power spectrum of the thin film thickness. Detailed Implementation

[0053] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings.

[0054] Example 1:

[0055] like Figure 1As shown, the plastic film thickness measurement system mainly consists of a light source, an incident converging lens, a film sample to be measured, a receiving converging lens, a miniature spectrometer, and a data processing unit. The light source emits light with a certain spectral width, and the spectral range of the light source should correspond to the measurement range of the miniature spectrometer to ensure that the light emitted by the light source can be measured by the miniature spectrometer after transmission through the film. The incident converging lens is connected to the light source via optical fiber. Adjusting the focal length of the incident converging lens focuses the light emitted by the light source to infinity, so that the light is approximately parallel when transmitted through the film. The receiving converging lens receives the transmitted light through the film and connects it to the miniature spectrometer via optical fiber. The grating beam splitting system inside the miniature spectrometer diffracts light of different wavelengths into different directions, and then the focusing lens inside the miniature spectrometer focuses the separated light onto a photodetector and outputs spectral data. The data is presented as a light intensity value corresponding to each pixel. Based on the known relationship between the pixels and wavelength of the miniature spectrometer, the spectral data can be obtained. The data processing unit processes and calculates the spectral data obtained from the miniature spectrometer to obtain the film refractive index and thickness results.

[0056] This invention primarily targets the data processing unit. To overcome the shortcomings of existing technologies and achieve thickness measurement of thin films with unknown refractive indices, it calculates the refractive index of the thin film using the transmittance envelope function and applies the obtained refractive index result to the thin film thickness calculation. After decomposing the transmittance into several intrinsic mode functions using empirical mode decomposition, an amplitude matching method is used to adaptively select the correct intrinsic mode function as the data for subsequent thin film thickness calculation. This avoids the interference of peak values ​​caused by low-frequency components of the light source spectrum in the power spectrum on the thin film thickness calculation results, effectively improving the reliability of intrinsic mode function selection and enhancing the robustness of thin film thickness measurement.

[0057] like Figure 2 As shown, the specific steps include the following:

[0058] (1) According to Figure 1 As shown, a plastic film thickness measurement system based on transmission spectroscopy is constructed. The involved components include a light source 1, an incident converging lens 2, a film sample 3, a receiving converging lens 4, a miniature spectrometer 5, and a data processing unit 6. When the light emitted from the light source 1 passes through the incident converging lens 2 and strikes the film sample 3, the receiving converging lens 4 on the other side of the film sample 3 receives the transmitted light, and the miniature spectrometer 5 measures the transmission interference spectrum P. t (λ), the transmission interference spectrum P t (λ) Transmitted to data processing unit 6;

[0059] (2) Remove the thin film sample 3 described in step (1). When the light emitted from the light source passes through the incident converging lens and is directed to the receiving converging lens, use a miniature spectrometer to measure the light source spectrum P. o (λ), the light source spectrum Po (λ) Transmitted to data processing unit 6;

[0060] (3) The transmission interference spectrum P obtained in steps (1) and (2) t (λ) and the light source spectrum P o Dividing by (λ), we obtain the transmittance T(λ) of the thin film sample. The transmittance T(λ) is a function of the incident angle, the incident wavelength, the refractive index of the thin film sample, and the thickness of the thin film sample, i.e.:

[0061]

[0062] In the formula, r1 is the reflection coefficient of the interface between air and thin film sample, r2 is the reflection coefficient of the interface between thin film sample and air, and δ is the phase difference between two adjacent transmitted rays, expressed as:

[0063]

[0064] In the formula, n(λ) is the refractive index of the thin film sample, h is the thickness of the thin film sample in meters, θ is the incident angle in degrees or radians, and λ is the wavelength of the light source in meters.

[0065] (4) Preferably, when the light from the light source is incident perpendicularly on the thin film sample 3, the refractive index n(λ) of the thin film sample 3 is calculated as follows:

[0066]

[0067] In the formula, n0 is the refractive index of the incident medium, n G Let N(λ) be the refractive index of the exit-side medium, and N(λ) be an intermediate quantity used to simplify calculations and has no physical meaning.

[0068]

[0069] In the formula, T max (λ) is the upper envelope passing through all the maxima of transmittance T(λ), T min (λ) is the lower envelope that passes through all the minimum points of transmittance T(λ);

[0070] (5) Perform empirical mode decomposition on the transmittance T(λ) obtained in step (3), and express the transmittance T(λ) as the sum of q intrinsic mode functions, which are expressed as: IMF1(λ),…,IMF q (λ);

[0071] (6) Adaptively select the q intrinsic mode functions obtained in step (5). First, smooth the transmittance T(λ) using the five-point cubic Savitzky-Golay filter fitting method, and find its upper and lower envelopes to obtain the amplitude R of the transmittance T(λ).Ts (λ), and calculate the amplitude R of each of the q eigenmode functions. IMF1 (λ),…,R IMFq (λ), select the amplitude R with respect to the emissivity T(λ). Ts (λ) is the eigenmode function with the smallest mean square error;

[0072] (7) Preferably, when the thin film sample 3 is placed in the air, the reflection coefficient satisfies the relationship r1=-r2, denoted as r=r1=-r2, and the T obtained in step (6) is... c (λ) undergoes the following transformation:

[0073]

[0074] Where K1 = 2πn(λ)cosθ / λ, n(λ) is the refractive index of the thin film obtained in step (4), θ is the angle of incidence in degrees or radians, λ is the wavelength of light in meters, and h is the thickness of the thin film in meters. The transformed transmittance T is solved using the Lomb-Scargle periodogram method. K1 Power spectrum P T (ω):

[0075]

[0076] In the formula, ω is the transmittance T after transformation by equation (8). K1 The frequency, N is the number of pixels in the spectrometer, that is, the number of data in the transmittance T(λ) obtained in step (3), T K1 (j) is T K1 Let K1(j) be the j-th data in K1, and let the redundancy parameter τ be defined as:

[0077]

[0078] (8) Extract the power spectrum P obtained in step (7) T The frequency ω0 at the peak value is used to calculate the thickness of the thin film sample, K. 1p π.

[0079] Simulation experiment:

[0080] Taking the transmission interferometry measurement of the thickness of a plastic film placed in air as an example, the wavelength range of the light source of the measurement system is set to 505 nm to 638 nm. The spectrometer has 2048 effective pixels within this wavelength range. The refractive index of the film is expressed using the Cauchy dispersion model. The air refractive index is 1, and light is incident perpendicularly on the thin film sample to be tested. Calculate the transmittance curve and add a mean of 0 and a variance of 10. -6The Gaussian noise was used as the transmittance T(λ). Sample thicknesses of 10 μm, 20 μm, 35 μm, 50 μm, 100 μm, 150 μm, 200 μm, and 300 μm were set, and the refractive index and thickness were calculated respectively. The simulation results are shown in Table 1.

[0081] Table 1: Simulation measurement results of film sample thickness

[0082]

[0083] As shown in Table 1, the maximum absolute error between the simulation calculation results and the set values ​​for the above eight types of film samples is 2.23 micrometers, and the maximum relative error is 5.75%, which can meet the requirements for measuring the thickness of plastic films with unknown refractive indices.

[0084] The calculated refractive index of the thin film is as follows when the film thickness is set to 10 micrometers. Figure 3 As shown, due to the presence of noise, there is a certain deviation between the calculated refractive index and the set refractive index, but the overall deviation is small and has little impact on the calculation results of the film thickness.

[0085] Film thickness measurement experiment:

[0086] Taking the transmission interferometry measurement of the thickness of a plastic film placed in air as an example, according to Figure 1 A transmission spectroscopy system for measuring the thickness of plastic films was constructed. A film thickness measurement experiment was conducted on a plastic film sample with a thickness of approximately 362 micrometers. The emission wavelength range of the test light source was between 820 nm and 870 nm, the air refractive index was 1, and the light was incident perpendicularly on the film sample. The transmittance and power spectra are shown below. Figure 4 As shown, where Figure 4 (a) is the transmittance curve obtained in step (3), where the solid line is the transmittance and the dashed line is the upper and lower envelope of the transmittance described in step (4). Figure 4 (b) shows the power spectrum obtained in step (7). Peak extraction was performed on the power spectrum obtained in step (7), and the film thickness measurement result was 365.88 micrometers. The thickness measurement result of the same film sample using a mirror positioning instrument was 363.24 micrometers, and the error analysis results are shown in Table 2:

[0087] Table 2: Thickness Measurement Results of Thin Film Samples

[0088]

[0089] As described above, although the invention has been shown and described with reference to specific preferred embodiments, it should not be construed as limiting the invention itself. Various changes in form and detail may be made without departing from the spirit and scope of the invention as defined in the appended claims.

Claims

1. A method for measuring the thickness of plastic films based on transmission spectroscopy, characterized in that, A plastic film thickness measurement system based on transmission spectroscopy is employed. This system includes a light source, an incident converging lens, a film sample, a receiving converging lens, a miniature spectrometer, and a data processing unit. The light source and the incident converging lens are connected via optical fiber. The principal optical axes of the incident and receiving converging lenses are aligned. The focal points of the incident and receiving converging lenses are adjusted to infinity. The film sample is placed between the incident and receiving converging lenses. The angle between the normal of the film sample and the principal optical axes of the incident and receiving lenses is the angle of incidence. The receiving converging lens and the miniature spectrometer are connected via optical fiber, and the miniature spectrometer and the data processing unit are connected via a USB data cable. The measurement method includes the following steps: S1. Construct a plastic film thickness measurement system based on transmission spectroscopy. When the light emitted from the light source passes through the incident converging lens and is incident on the film sample, a receiving converging lens is used on the other side of the film sample to receive the transmitted light, and a miniature spectrometer is used to measure the transmission interference spectrum. Transmission interference spectrum Transmitted to the data processing department; S2. Remove the thin film sample described in step S1. When the light emitted from the light source passes through the incident converging lens and is directed to the receiving converging lens, measure the light source spectrum using a miniature spectrometer. , the spectrum of the light source Transmitted to the data processing department; S3. The transmission interference spectra obtained in steps S1 and S2 are... and light source spectrum Divide the phase to obtain the transmittance of the thin film sample. ; S4. Based on the transmittance obtained in step S3 Calculate the refractive index of the thin film sample ; S5. The transmittance obtained in step S3 Perform empirical mode decomposition to determine the transmittance. It is expressed as the sum of q eigenmode functions; S6. Adaptively select the q eigenmode functions obtained in step S5 to obtain an eigenmode function for a film thickness. ; S7. Adaptively select the eigenmode function of the thin film thickness obtained in step S6. Transform into a constant and a... The sum of the cosine functions of the independent variable The transformed transmittance was solved using the Lomb-Scargle periodogram method. power spectrum ,in , The refractive index of the thin film obtained in step S4 is... The angle of incidence is expressed in degrees or radians. Wavelength of light, measured in meters; S8. Extract the power spectrum obtained in step S7. frequency at peak The required thickness of the thin film sample is calculated as follows: .

2. The method for measuring the thickness of plastic films based on transmission spectroscopy according to claim 1, characterized in that, The incident angle is 0 degrees.

3. The method for measuring the thickness of plastic films based on transmission spectroscopy according to claim 2, characterized in that, Transmittance in step S3 It is a function of the incident angle, the incident light wavelength, the refractive index of the thin film sample, and the thickness of the thin film sample, that is: In the formula, The reflectance coefficient at the interface between air and the thin film sample is denoted as . The reflectance coefficient at the interface between the thin film sample and the air is denoted as . Let be the phase difference between two adjacent transmitted rays, expressed as: In the formula, Let be the refractive index of the thin film sample, and h be the thickness of the thin film sample, in meters. The angle of incidence is expressed in degrees or radians. The wavelength of the light source is expressed in meters.

4. The method for measuring the thickness of plastic films based on transmission spectroscopy according to claim 3, characterized in that, The specific method for step S4 is as follows: when the light from the light source is incident perpendicularly on the thin film sample, the reflectance coefficient... and Represented as: In the formula, Let be the refractive index of the incident medium. Let be the refractive index of the thin film sample. The refractive index of the exit-side medium; At this time, transmittance Represented as: In the formula, Let be the refractive index of the incident medium. Let be the refractive index of the thin film sample. Here, h represents the refractive index of the exit-side medium, and h represents the film thickness in meters. Wavelength of the light source, measured in meters; α, C1, and C2 are intermediate quantities introduced to simplify calculations; they have no physical meaning and , , ; The refractive index of the thin film sample was thus calculated. for: In the formula Let be the refractive index of the incident medium. The refractive index of the exit-side medium. These are intermediate quantities set up to simplify calculations; they have no physical meaning, and In the formula, For transmittance The upper envelope of all maxima, For transmittance The lower envelope of all local minima.

5. The method for measuring the thickness of plastic films based on transmission spectroscopy according to claim 3, characterized in that, The specific method for step S5 is as follows: S51. Utilizing transmittance Transmittance is obtained by fitting all maxima and minima using a cubic spline function. upper envelope and lower envelope The mean of the upper and lower envelopes is used as the transmittance. mean envelope , where the subscript ij of m represents the j-th filtering of the i-th component; S52. The first component obtained from decomposition Expressed using the original signal and the mean envelope: ; S53. Check the first component obtained. Whether it meets the two conditions of an intrinsic mode function, namely, the number of local extrema and the number of zeros on an intrinsic mode function should be equal or differ by 1; and for any time, the local mean of the maximum envelope and the minimum envelope is 0. If it does not meet the requirements, repeat the screening process of S51-S52 k times until the desired component is obtained. If the two constraints of the intrinsic mode function are satisfied, then Transmittance The first eigenmode function derived from empirical mode decomposition ; S54. Transmittance Subtracting the first intrinsic mode function yields the margin signal. Repeat the filtering process of S51-S53 on the residual signal to decompose it into q intrinsic mode functions. until the remaining amount When the function is a monotonic function or a constant function, the EMD decomposition process terminates.

6. The method for measuring the thickness of plastic films based on transmission spectroscopy according to claim 3, characterized in that, The specific method for step S6 is as follows: S61. Transmittance was measured using a five-point cubic Savitzky-Golay filter fitting method. Smoothing is performed, and the length of the sliding window is set to 5. When the center of the sliding window moves to the transmittance... At the j-th position, based on the data points within the sliding window Construct a cubic polynomial: Solve for the coefficients using the least squares method. Then, the smoothed transmittance is calculated using equation (7). The j-th position; the smoothed transmittance is denoted as ; S62. Search for smoothed transmittance All local maxima, i.e., when and At that time, it was believed For local maxima, cubic spline interpolation is performed on all local maxima to obtain the smoothed transmittance. upper envelope ; S63. Search for smoothed transmittance All local minima, i.e., when and At that time, it was believed For local minima, cubic spline interpolation is performed on all local minima to obtain the smoothed transmittance. lower envelope ; S64. The upper envelope obtained in S62 The lower envelope obtained by subtracting S63 The smoothed transmittance was obtained. amplitude ; S65. Obtain the upper envelope of the q eigenmode functions obtained in step S5 using the methods described in S62 and S63. and lower envelope The amplitudes of the q intrinsic mode functions obtained in step S5 are then calculated using the method described in S64. ; S66. Calculate the smoothed transmittance obtained in S64 respectively. amplitude The amplitudes of the q eigenmode functions obtained from S65 The mean square error will be related to the smoothed transmittance. The eigenmode function with the smallest mean square error of amplitude is denoted as ,Will This data will be used as a basis for calculating the film thickness in subsequent steps.

7. The method for measuring the thickness of plastic films based on transmission spectroscopy according to claim 3, characterized in that, The specific method for step S7 is as follows: when the thin film sample is placed in air, the reflectance satisfies the relationship ,make The result obtained in step S6 Perform the following transformation: h represents the thickness of the thin film sample, in meters; Transmittance after transformation by equation (8) For a constant and a Let be the sum of the cosine functions of the independent variable, where the frequency of the cosine function is determined by the film thickness. The transformed transmittance is then solved using the Lomb-Scargle periodogram method. power spectrum : In the formula, Transmittance after transformation by equation (8) The frequency, where N is the number of pixels in the spectrometer, which is also the transmittance obtained in step S3. The number of data in the middle, for The j-th data in for The j-th data in the data, redundant parameter Defined as: 。

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