A Miniaturized and Fast System for Thin Film Thickness Measurement

Transparent films are significant industrial components that are widely used in modern optics, microelectronics, optical engineering, and other related fields. There is an urgent need for the fast and stable thickness measurement of industrial films at the micron-grade. This paper built a miniaturized and low-cost film thickness measurement system based on confocal spectral imaging and the principle of thin-film spectral interference. The reflection interference spectrum was analyzed to extract the phase term introduced by the film thickness from the full spectrum information, where local spectral noise can be better corrected. An efficient and robust film thickness calculation algorithm was realized without any calibrating sample. The micron-grade thickness measurement system had an industrial property with a measurement range of up to 75 μm with a measurement uncertainty of 0.1 μm, presenting a good performance in single-layer film thickness measurement with high efficiency.


Introduction
Transparent film, as an important industrial component, is widely used in modern optics, microelectronics, optical engineering, and other related scientific and technological fields. Various films produced by physical or chemical deposition methods can use interference effects to change optical properties, such as antireflection, filtering, and polarization. Meanwhile, their protection characteristics such as high-temperature resistance, corrosion, and abrasion play a decisive role in the quality of optical instruments in the fields of communication, display, storage, etc. [1,2] However, film preparation is affected by process parameters such as emission characteristics, relative position placement, and surface shape of the plated parts, resulting in uneven thickness distribution, which affects the barrier performance and tensile properties of subsequent applications [3]. Therefore, the measurement and evaluation of film thickness are particularly important in the production process, especially for the thickness measurement of micron-grade industrial films. Limited by the irregular industrial environment, there is an urgent need for a fast, stable, and robust high-resolution film thickness measurement system.
Based on the characteristics of light absorption, reflection, and polarization, the optical measurement methods of film thickness can be divided into spectrophotometry [4,5], ellipsometry [6][7][8], interferometry [9][10][11], and multiple compound methods [12][13][14]. Although the measurement methods based on ellipsometry and interferometry have high resolution and accuracy, the disadvantages of large system size, high price, and strict environmental conditions do not meet the rapid and stable application requirement of industrial measurement. The spectrophotometry is more widely used due

Measurement Scheme
Based on the principle of thin-film interference and confocal spectral imaging, this paper built a low-cost and fast-speed thin-film thickness measurement system to study the thickness calculation algorithm of the thin film. As shown in Figure 1, a Light Emitting Diode (LED), a micro-spectrometer, and a self-designed confocal achromatic probe are used to realize the miniaturization of the measurement system.
The light intensity changes periodically in a coherent region with destructive and constructive phenomena. For dielectric films, if the absorption of light by the film is not considered, the total interference intensity of the reflected light beam incident on the film can be approximately expressed as I r (z, λ) = I r1 + I r2 + 2 √ I r1 · I r2 · cos(2πz/λ + φ 0 ) = I 0 (λ) · R 01 + I 0 (λ) · T 01 R 1s T 10 + 2I 0 (λ) √ R 01 T 01 R 1s T 10 · cos(2πz/λ + φ 0 ) (1) where λ is the wavelength and φ 0 is the additional phase. R 01 and T 01 , respectively, represent the reflectance and transmittance from the air to the film. R 1s and T 10 , respectively, represent the reflectance from the film to the substrate and the transmittance from the film to the air. For the case of normal incidence, the optical path difference z = 2n 1 × d is determined by the film's refractive index n 1 and thickness d, where the refractive index is treated as a constant to improve computational efficiency. The envelope of the spectral interference signal measured by the spectrometer is approximately a Gaussian distribution. The phase term 2πz/λ + φ 0 caused by the optical path difference z determines the density of the interference fringes. As the core algorithm of the PPS analysis, Empirical Mode Decomposition (EMD) and Lomb-Scargle periodogram (LSP) process the high-frequency spectral interference information successively to extract the film thickness.  Figure 2 is the flow chart of the core algorithm in this paper. Firstly, aiming at the original interference signal collected by a spectrometer, EMD is used as a high-pass filter to extract highfrequency interference components, adaptively eliminating the influence of the non-uniform intensity distribution of the LED source. Second, to obtain the phase term introduced by film thickness, the interference component is transformed into the wavenumber domain through reciprocal of wavelength λ. Third, through the spectral analysis method, we extract the phase term from the full spectrum to effectively avoid the interference of local noise. However, conventional spectral analysis methods, such as Fourier transform, cannot handle the problem of non-equal interval sampling of signals caused by the λ− transformation. In this paper, the phase term is solved by the LSP spectrum analysis and illustrated by phase power spectral density distribution. Finally, the peak value of the power spectral density function is extracted by the maximum value method to calculate the film thickness. The detailed flow of the proposed algorithm is as follows.

Film Thickness Calculation Algorithm
EMD, as the preprocessing algorithm of Hilbert Huang Transform (HHT) [17], can adaptively decompose the complex nonlinear and non-stationary signal into a limited number of Intrinsic Mode Function (IMF). In this paper, EMD is used as a high-pass filter [18] to automatically filter out the high-frequency principal component of the reflectance spectrum signal. The mirror extending method [19] assists in processing the endpoint data of the original signal to eliminate the boundary oscillation effect caused by the third-order spline interpolation in EMD.  Figure 2 is the flow chart of the core algorithm in this paper. Firstly, aiming at the original interference signal collected by a spectrometer, EMD is used as a high-pass filter to extract high-frequency interference components, adaptively eliminating the influence of the non-uniform intensity distribution of the LED source. Second, to obtain the phase term introduced by film thickness, the interference component is transformed into the wavenumber σ domain through reciprocal of wavelength λ. Third, through the spectral analysis method, we extract the phase term from the full spectrum to effectively avoid the interference of local noise. However, conventional spectral analysis methods, such as Fourier transform, cannot handle the problem of non-equal interval sampling of signals caused by the λ−σ transformation. In this paper, the phase term is solved by the LSP spectrum analysis and illustrated by phase power spectral density distribution. Finally, the peak value of the power spectral density function is extracted by the maximum value method to calculate the film thickness. The detailed flow of the proposed algorithm is as follows.

Film Thickness Calculation Algorithm
EMD, as the preprocessing algorithm of Hilbert Huang Transform (HHT) [17], can adaptively decompose the complex nonlinear and non-stationary signal into a limited number of Intrinsic Mode Function (IMF). In this paper, EMD is used as a high-pass filter [18] to automatically filter out the high-frequency principal component of the reflectance spectrum signal. The mirror extending method [19] assists in processing the endpoint data of the original signal to eliminate the boundary oscillation effect caused by the third-order spline interpolation in EMD. Appl. Sci. 2020, 10, x FOR PEER REVIEW 4 of 13 The reflectance spectrum signal ISI is a discrete function of the uniform sampled pixels for being collected by Charge Coupled Device (CCD) array in a micro spectrometer. After EMD filtering, ISI is disassembled into a set of IMF components Imfk, k = 1, 2, …, m of different frequency ranges, and a monotonic trend function Res, as shown in Figure 3b. Imf1 is the first component to be filtered out with the highest signal frequency. In the case with no high-frequency noise, Imf1 is the film interference principal component. Then, according to the corresponding relationship between the pixel index and the wavelength of CCD array in the spectrometer, the intensity Ii of each i, i = 1, 2, …, N, is obtained by converting Imf1 from the λ to the domain. N is the number of pixels of the spectrometer. Due to the wavelength drift of the spectrometer and the reciprocal transformation from the λ to the domain, the non-uniform sampled characteristic of i made Ii unable to be directly analyzed by the conventional spectral analysis method. Therefore, it is necessary to preprocess Ii before performing spectral analysis to obtain film thickness information We adopt the cubic spline The reflectance spectrum signal I SI is a discrete function of the uniform sampled pixels for being collected by Charge Coupled Device (CCD) array in a micro spectrometer. After EMD filtering, I SI is disassembled into a set of IMF components Imf k , k = 1, 2, . . . , m of different frequency ranges, and a monotonic trend function Res, as shown in Figure 3b. Imf 1 is the first component to be filtered out with the highest signal frequency. In the case with no high-frequency noise, Imf 1 is the film interference principal component. Then, according to the corresponding relationship between the pixel index and the wavelength of CCD array in the spectrometer, the intensity I i of each σ i , i = 1, 2, . . . , N, is obtained by converting Imf 1 from the λ to the σ domain. N is the number of pixels of the spectrometer. The reflectance spectrum signal ISI is a discrete function of the uniform sampled pixels for being collected by Charge Coupled Device (CCD) array in a micro spectrometer. After EMD filtering, ISI is disassembled into a set of IMF components Imfk, k = 1, 2, …, m of different frequency ranges, and a monotonic trend function Res, as shown in Figure 3b. Imf1 is the first component to be filtered out with the highest signal frequency. In the case with no high-frequency noise, Imf1 is the film interference principal component. Then, according to the corresponding relationship between the pixel index and the wavelength of CCD array in the spectrometer, the intensity Ii of each i, i = 1, 2, …, N, is obtained by converting Imf1 from the λ to the domain. N is the number of pixels of the spectrometer. Due to the wavelength drift of the spectrometer and the reciprocal transformation from the λ to the domain, the non-uniform sampled characteristic of i made Ii unable to be directly analyzed by the conventional spectral analysis method. Therefore, it is necessary to preprocess Ii before performing spectral analysis to obtain film thickness information We adopt the cubic spline Due to the wavelength drift of the spectrometer and the reciprocal transformation from the λ to the σ domain, the non-uniform sampled characteristic of σ i made I i unable to be directly analyzed by the conventional spectral analysis method. Therefore, it is necessary to preprocess I i before performing spectral analysis to obtain film thickness information We adopt the cubic spline interpolation combined Appl. Sci. 2020, 10, 7284 5 of 13 fast Fourier transform (CIFFT) and LSP [20,21] as two representative methods to process I i , and finally choose the LSP after comparing the solution results. In particular, inspired by the time-frequency domain (t−f ) transformation [22], we rewrite the LSP function into the wavenumber-phase factor domain (σ−z) transformation form, as Equations (2) and (3).
where δ is specified for each z to ensure time-shift invariance, Under normal circumstances, the full width at half maximum of the single-layer film interference spectrum after LSP transformation is small (30-50 nm) as shown in Figure 4. Therefore, the peak value z peak can be directly extracted by the maximum value method. The built-in false alarm probability of LSP evaluates the significance of the peak value to further ensure the correct extraction. If n 1 is the refractive index of the film, the film thickness d is Appl. Sci. 2020, 10, x FOR PEER REVIEW 5 of 13 interpolation combined fast Fourier transform (CIFFT) and LSP [20,21] as two representative methods to process Ii, and finally choose the LSP after comparing the solution results. In particular, inspired by the time-frequency domain (t−f) transformation [22], we rewrite the LSP function into the wavenumber-phase factor domain ( −z) transformation form, as Equations (2) and (3).
where δ is specified for each z to ensure time-shift invariance, Under normal circumstances, the full width at half maximum of the single-layer film interference spectrum after LSP transformation is small (30-50 nm) as shown in Figure 4. Therefore, the peak value zpeak can be directly extracted by the maximum value method. The built-in false alarm probability of LSP evaluates the significance of the peak value to further ensure the correct extraction. If n1 is the refractive index of the film, the film thickness d is  In the PPS algorithm, EMD as a self-adaptive high-pass filter realizes the non-destructive extraction of spectral interference terms. While expanding the measurement range of the film, it effectively reduces the influence of the non-uniform distribution of the light source spectrum. The essence of LSP is to fit the data with a single sine function y = acos (ωt) + bsin (ωt) with the same frequency [20], which implicitly requiring the mean value of the measurement data to be zero. The IMF components after EMD filtering approximately meet this requirement, thus the combination of EMD and LSP can obtain a significant deterministic solution. Besides, LSP uses full range spectrum data and thus can better correct the gross errors introduced by local spectral noise. At the same time, using the built-in statistical tool of LSP to evaluate the reliability of the solution can greatly eliminate the false frequency interference caused by environmental noise and improve the stability of the system.

Simulation
The following problems have been found in the actual measurement of various types of films.
(1) The absorption and reflection coefficients varying with film materials, which results in different fringe contrast of the actual film interference signal; (2) the influence of external stray light causes local noise in the reflected spectrum signal, which have an impact on the film thickness calculation. Besides, to clarify the effective range, inherent error, and the feasibility of this system, we conduct a simulation analysis based on the thin-film interference model. By adjusting the fringe contrast, the In the PPS algorithm, EMD as a self-adaptive high-pass filter realizes the non-destructive extraction of spectral interference terms. While expanding the measurement range of the film, it effectively reduces the influence of the non-uniform distribution of the light source spectrum. The essence of LSP is to fit the data with a single sine function y = acos (ωt) + bsin (ωt) with the same frequency [20], which implicitly requiring the mean value of the measurement data to be zero. The IMF components after EMD filtering approximately meet this requirement, thus the combination of EMD and LSP can obtain a significant deterministic solution. Besides, LSP uses full range spectrum data and thus can better correct the gross errors introduced by local spectral noise. At the same time, using the built-in statistical tool of LSP to evaluate the reliability of the solution can greatly eliminate the false frequency interference caused by environmental noise and improve the stability of the system.

Simulation
The following problems have been found in the actual measurement of various types of films.
(1) The absorption and reflection coefficients varying with film materials, which results in different fringe contrast of the actual film interference signal; (2) the influence of external stray light causes local noise in the reflected spectrum signal, which have an impact on the film thickness calculation. Besides, to clarify the effective range, inherent error, and the feasibility of this system, we conduct a simulation analysis based on the thin-film interference model. By adjusting the fringe contrast, the thickness, and the noise of the interference signal, we clarify the error influence of different measurement conditions, thus verify the robustness of the algorithm.

Verification of the Thin-Film Interference Model
We use the thin-film interference model R 01 T 01 R 1s T 10 , A, B∈(0,1], and suppose the light source intensity distribution conforms to the Gaussian distribution G(λ; µ, η 2 ) with mathematical expectation µ and standard variance η 2 , The reflected spectrum signal can be abbreviated as below, where C is the maximum intensity amplitude of the light spectrum, We take A = 0.5, B = 0.2, C = 18000, µ = 660 nm, η = 80 nm, φ 0 = π, and z = 9 µm. The simulated interference spectrum is shown in Figure 5a and compared with the measured data in Figure 5b. The simulation signal is consistent with the actual measurement signal, which verifies the correctness of the simulation model.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 6 of 13 thickness, and the noise of the interference signal, we clarify the error influence of different measurement conditions, thus verify the robustness of the algorithm.

Verification of the Thin-Film Interference Model
We use the thin-film interference model Ir (z, λ) of Equation (1) The reflected spectrum signal can be abbreviated as below, where C is the maximum intensity amplitude of the light spectrum, We take A = 0.5, B = 0.2, C = 18000, µ = 660 nm, η = 80 nm, ϕ0 = π, and z = 9 μm. The simulated interference spectrum is shown in Figure 5a and compared with the measured data in Figure 5b. The simulation signal is consistent with the actual measurement signal, which verifies the correctness of the simulation model.

Influence of Thin-Film Thickness
Using 0.1 μm as the interval of thickness value in Ir (z, λ) to simulate the reflection spectrum of 1-100 μm film. The simulation result in Figure 6 shows the inherent error of the algorithm changes periodically within ± 50 nm in the effective range of 1-75 μm. The current measurement range is also limited by the wavelength resolution of the spectrometer, resulting in the failure calculation of the film thickness over 75 μm.

Influence of Thin-Film Thickness
Using 0.1 µm as the interval of thickness value in I r (z, λ) to simulate the reflection spectrum of 1-100 µm film. The simulation result in Figure 6 shows the inherent error of the algorithm changes periodically within ±50 nm in the effective range of 1-75 µm. The current measurement range is also limited by the wavelength resolution of the spectrometer, resulting in the failure calculation of the film thickness over 75 µm. Appl. Sci. 2020, 10, x FOR PEER REVIEW 7 of 13

Influence of Thin-Film Materials
Based on the simulation signal of Ir (z, λ), we change signal contrast K = B/A to analyze the influence caused by various absorption and reflection coefficients under different film materials. Figure 7a illustrates the reflection spectrum signals with of 0.1, 0.5, and 1, respectively. For a particular thickness, the amplitude of the signal gets higher when contrast increases, while the period remains nearly constant. The thickness calculation deviations under different contrasts are shown in Figure 7b. The deviations keep the value of 16.61 nm, which proves that the interference signal contrast does not relate to the thickness calculation deviation.

Influence of Noise
Irregular local Gaussian noise is added to the basic interference signal based on Ir (z, λ) to simulate the noise introduced by CCD pixel data packet loss or environmental vibration to verify the robustness of the algorithm. As shown in Figure 8b, the calculation result of LSP is closer to the true value of the thickness than CIFFT. Although the noise components are still contained in power spectrum density, whose density is much smaller compared to the peak value especially after LSP.

Influence of Thin-Film Materials
Based on the simulation signal of I r (z, λ), we change signal contrast K = B/A to analyze the influence caused by various absorption and reflection coefficients under different film materials. Figure 7a illustrates the reflection spectrum signals with of 0.1, 0.5, and 1, respectively. For a particular thickness, the amplitude of the signal gets higher when contrast increases, while the period remains nearly constant. The thickness calculation deviations under different contrasts are shown in Figure 7b. The deviations keep the value of 16.61 nm, which proves that the interference signal contrast does not relate to the thickness calculation deviation.

Influence of Thin-Film Materials
Based on the simulation signal of Ir (z, λ), we change signal contrast K = B/A to analyze the influence caused by various absorption and reflection coefficients under different film materials. Figure 7a illustrates the reflection spectrum signals with of 0.1, 0.5, and 1, respectively. For a particular thickness, the amplitude of the signal gets higher when contrast increases, while the period remains nearly constant. The thickness calculation deviations under different contrasts are shown in Figure 7b. The deviations keep the value of 16.61 nm, which proves that the interference signal contrast does not relate to the thickness calculation deviation.

Influence of Noise
Irregular local Gaussian noise is added to the basic interference signal based on Ir (z, λ) to simulate the noise introduced by CCD pixel data packet loss or environmental vibration to verify the robustness of the algorithm. As shown in Figure 8b, the calculation result of LSP is closer to the true value of the thickness than CIFFT. Although the noise components are still contained in power spectrum density, whose density is much smaller compared to the peak value especially after LSP.

Influence of Noise
Irregular local Gaussian noise is added to the basic interference signal based on I r (z, λ) to simulate the noise introduced by CCD pixel data packet loss or environmental vibration to verify the robustness of the algorithm. As shown in Figure 8b, the calculation result of LSP is closer to the true value of the thickness than CIFFT. Although the noise components are still contained in power spectrum density, whose density is much smaller compared to the peak value especially after LSP. Therefore, the combination of EMD and LSP has sufficient robustness by reducing the misjudgment rate. Therefore, the combination of EMD and LSP has sufficient robustness by reducing the misjudgment rate.

Experiments and Discussion
To verify the correctness and effectiveness of the proposed algorithm, this paper built a miniaturized thin film thickness measurement system as shown in Figure 9. The experimental system consists of a three-axis translation stage, a commercial fiber spectrometer, and a self-developed small achromatic microscope probe. The probe is mounted on the Z-axis guide rail and the Z-axis guide rail is fixed on the XY table. The X, Y, and Z-axis guide rails drive the translation and lifting of the probe, to realize the rapid and high-precision scanning measurement of the film sample. To ensure the measurement accuracy of the system, the experiment performs wavelength calibration on the spectrometer and eliminate high-order diffraction by measuring the spectral line of a mercury-argon standard light source in the range of 300-1000 nm. The standard wavelength values of the characteristic spectral line of the light source are provided by the National Institute of

Experiments and Discussion
To verify the correctness and effectiveness of the proposed algorithm, this paper built a miniaturized thin film thickness measurement system as shown in Figure 9. The experimental system consists of a three-axis translation stage, a commercial fiber spectrometer, and a self-developed small achromatic microscope probe. The probe is mounted on the Z-axis guide rail and the Z-axis guide rail is fixed on the XY table. The X, Y, and Z-axis guide rails drive the translation and lifting of the probe, to realize the rapid and high-precision scanning measurement of the film sample.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 8 of 13 Therefore, the combination of EMD and LSP has sufficient robustness by reducing the misjudgment rate.

Experiments and Discussion
To verify the correctness and effectiveness of the proposed algorithm, this paper built a miniaturized thin film thickness measurement system as shown in Figure 9. The experimental system consists of a three-axis translation stage, a commercial fiber spectrometer, and a self-developed small achromatic microscope probe. The probe is mounted on the Z-axis guide rail and the Z-axis guide rail is fixed on the XY table. The X, Y, and Z-axis guide rails drive the translation and lifting of the probe, to realize the rapid and high-precision scanning measurement of the film sample. To ensure the measurement accuracy of the system, the experiment performs wavelength calibration on the spectrometer and eliminate high-order diffraction by measuring the spectral line of a mercury-argon standard light source in the range of 300-1000 nm. The standard wavelength values of the characteristic spectral line of the light source are provided by the National Institute of To ensure the measurement accuracy of the system, the experiment performs wavelength calibration on the spectrometer and eliminate high-order diffraction by measuring the spectral line of a mercury-argon standard light source in the range of 300-1000 nm. The standard wavelength values of the characteristic spectral line of the light source are provided by the National Institute of Standards and Technology (NIST) [23]. The corresponding relationship between the wavelength and the index of each CCD pixel is obtained by the second-order fitting.

Standard Film Samples Measurement
A set of Polyvinyl chloride (PVC) standard film samples with a thickness range of 2-50 (±0.3 + 0.5% H) µm are fixed by a custom film clamping device as shown in Figure 9. First, we measure the standard film of 18 µm thickness at a random point for 20 times to verify the single point repeatability of the system. After EMD filtering, CIFFT and LSP algorithms are adopted to calculate the thickness, respectively. As shown in Figure 10a, the measurement result indicates that the thickness deviation of LSP fluctuates in the range of ±0.1 µm. The mean deviation of LSP is −0.038 µm, while the mean deviation of CIFFT is −0.147 µm. Comparing to CIFFT, LSP has a lower uncertainty and a smaller deviation for film thickness, which proves that the system has good repeatability in the single-point thickness measurement. Secondly, to further verify the stability of the area measurement of the experimental system, we measure 16 signals in different areas in a circular hole with a diameter of 7 mm in the standard film sample group. The measurement results of the 4 × 4 grid uniformly distributed sampling points are shown in Figure 10b. The center point of the error bar and the longitudinal length of the shaded area represent the mean and standard deviation of the measurement error related to the standard value, respectively. The maximum absolute error of LSP is 0.9202 µm, and the repeatability is no more than 2.5%. The experiment result proves that the proposed PPS algorithm is stable and reliable and meets industrial requirement repeatability. The average calculation time is 0.01 s for each measurement. Due to the anisotropic tensile forces in the clamping process of the standard film, the wrinkles and uneven thickness distribution of film are inevitable, which causes the measurement results of several film thicknesses in this experiment to be too large. Overall, the measurement uncertainty of the PPS algorithm proposed in this paper is stable at 0.1 µm.
Appl. Sci. 2020, 10, x FOR PEER REVIEW 9 of 13 Standards and Technology (NIST) [23]. The corresponding relationship between the wavelength and the index of each CCD pixel is obtained by the second-order fitting.

Standard Film Samples Measurement
A set of Polyvinyl chloride (PVC) standard film samples with a thickness range of 2-50 (± 0.3 + 0.5% H) μm are fixed by a custom film clamping device as shown in Figure 9. First, we measure the standard film of 18 μm thickness at a random point for 20 times to verify the single point repeatability of the system. After EMD filtering, CIFFT and LSP algorithms are adopted to calculate the thickness, respectively. As shown in Figure 10a, the measurement result indicates that the thickness deviation of LSP fluctuates in the range of ± 0.1 μm. The mean deviation of LSP is − 0.038 μm, while the mean deviation of CIFFT is − 0.147 μm. Comparing to CIFFT, LSP has a lower uncertainty and a smaller deviation for film thickness, which proves that the system has good repeatability in the single-point thickness measurement. Secondly, to further verify the stability of the area measurement of the experimental system, we measure 16 signals in different areas in a circular hole with a diameter of 7 mm in the standard film sample group. The measurement results of the 4 × 4 grid uniformly distributed sampling points are shown in Figure 10b. The center point of the error bar and the longitudinal length of the shaded area represent the mean and standard deviation of the measurement error related to the standard value, respectively. The maximum absolute error of LSP is 0.9202 μm, and the repeatability is no more than 2.5%. The experiment result proves that the proposed PPS algorithm is stable and reliable and meets industrial requirement repeatability. The average calculation time is 0.01 s for each measurement. Due to the anisotropic tensile forces in the clamping process of the standard film, the wrinkles and uneven thickness distribution of film are inevitable, which causes the measurement results of several film thicknesses in this experiment to be too large. Overall, the measurement uncertainty of the PPS algorithm proposed in this paper is stable at 0.1 μm.

Germanium-Based 1 μm SiO2 Standard Film Measurement
Germanium is the most widely used infrared optical material and often covered with a thin film to enhance the transmittance and durability in harsh environments such as high temperature and acid. In this article, a 1 μm thickness SiO2 film sample on a germanium substrate with a stepped structure is measured to verify the accuracy of thickness control during the coating process. In Figure  11a, the stepped structure consists of an uncoated area, and a coated area is designed for the

Germanium-Based 1 µm SiO 2 Standard Film Measurement
Germanium is the most widely used infrared optical material and often covered with a thin film to enhance the transmittance and durability in harsh environments such as high temperature and acid. In this article, a 1 µm thickness SiO 2 film sample on a germanium substrate with a stepped structure is measured to verify the accuracy of thickness control during the coating process. In Figure 11a, the stepped structure consists of an uncoated area, and a coated area is designed for the measurement benchmark and measured by white light interference (WLI) 12 times. At the same time, the PPS performs a 12 points measurement on the coating part of the WLI measurement area.

Measurement Experiment of PCB Chip Film Thickness
To protect the key chips on semiconductor PCB, the surface is generally treated with coating or glue. The coating thickness is various in a different area, thus fast and non-destructive measurement has important engineering value. This paper aims at the needs of industrial PCB chip transparent film thickness measurement and uses the method to carry out experimental verification. For different areas of the PCB board, the transparent film with 1-30 μm thickness is measured multiple times. In After leveling and denoising, the vertical distance between the upper and lower fitting surfaces of the step shown in Figure 11b, is calculated to represent the WLI measurement result. The detailed measurement result is shown in Table 1. Comparing the PPS and WLI measurement data, the mean thickness of PPS is 0.892 µm and the standard deviation is 0.076 µm, while the mean thickness of WLI is 0.954 µm, and the standard deviation is 0.053 µm. The mean of PPS measurement results is about 50nm smaller than WLI, but the measurement speed is faster than WLI.

Measurement Experiment of PCB Chip Film Thickness
To protect the key chips on semiconductor PCB, the surface is generally treated with coating or glue. The coating thickness is various in a different area, thus fast and non-destructive measurement has important engineering value. This paper aims at the needs of industrial PCB chip transparent film thickness measurement and uses the method to carry out experimental verification. For different areas of the PCB board, the transparent film with 1-30 µm thickness is measured multiple times. In Figure 12, the measurement results at three points a, b, and c on the different electronic chips are 2.067 µm, 3.515 µm, and 24.910 µm, respectively, which match the reference values 2 µm, 3.5 µm, and 25 µm provided by the factory. The absolute thickness errors are 67 nm, 15 nm, and 90 nm, respectively. Figure 12, the measurement results at three points a, b, and c on the different electronic chips are 2.067 μm, 3.515 μm, and 24.910 μm, respectively, which match the reference values 2 μm, 3.5 μm, and 25 μm provided by the factory. The absolute thickness errors are 67 nm, 15 nm, and 90 nm, respectively.

Conclusions
Based on the reflection spectrum interference theory, this paper built a low-cost and miniaturized thin-film thickness measurement system with the measurement range of 1-75 μm, an angle of ± 5°, and an uncertainty of 0.1 μm. The measurement speed of 10 ms and no need of focusing within millimeter working distance met the efficient and convenient requirements of industrial-grade measurement. The validity of the system was verified by experiments of the standard PVC films, the micron-grade film layer on PCB chip, and Germanium-based SiO2 film. In the proposed phase power spectrum analysis method, the high-frequency spectral interference term was extracted adaptively from the full spectrum data through loop iterations, avoiding the use of the reference sample. For single-layer film thickness measurement, power spectrum analysis resolved the film thickness from the spectral interference term and corrected the gross error caused by local spectral noise, thereby ensuring the stability of the algorithm.
It is also clear that the industrial film thickness measurement results in this article need to be further optimized due to the lack of hardware performance. In the following work, the measurement range can be increased by selecting a high-resolution spectrometer. We can continue to optimize the algorithm model and the probe design to further improve the uncertainty of the measurement system.

Acknowledgments:
The authors express their sincere thanks to Yiting Duan, Yongbin Lu, and Boyang Shi for the preparation of the experiment and valuable discussions.

Conflicts of Interest:
The authors declare no conflict of interest.

Conclusions
Based on the reflection spectrum interference theory, this paper built a low-cost and miniaturized thin-film thickness measurement system with the measurement range of 1-75 µm, an angle of ±5 • , and an uncertainty of 0.1 µm. The measurement speed of 10 ms and no need of focusing within millimeter working distance met the efficient and convenient requirements of industrial-grade measurement. The validity of the system was verified by experiments of the standard PVC films, the micron-grade film layer on PCB chip, and Germanium-based SiO 2 film. In the proposed phase power spectrum analysis method, the high-frequency spectral interference term was extracted adaptively from the full spectrum data through loop iterations, avoiding the use of the reference sample. For single-layer film thickness measurement, power spectrum analysis resolved the film thickness from the spectral interference term and corrected the gross error caused by local spectral noise, thereby ensuring the stability of the algorithm.
It is also clear that the industrial film thickness measurement results in this article need to be further optimized due to the lack of hardware performance. In the following work, the measurement range can be increased by selecting a high-resolution spectrometer. We can continue to optimize the algorithm model and the probe design to further improve the uncertainty of the measurement system.