Method for simultaneously testing thickness and refractive index of material based on terahertz time-domain spectroscopy

Abstract

The invention discloses a method for simultaneously testing the thickness and refractive index of a material based on terahertz time-domain spectroscopy, which relates to the technical field of material testing and comprises the following steps: acquiring a reference signal and a sample signal by using a transmission-type terahertz time-domain spectroscopy system, and positioning a key pulse peak through an automatic peak value recognition algorithm; frequency domain phase information is obtained by combining fast Fourier transform, and then the phase difference between the main pulse and the echo is calculated; based on an optical path difference model, a relation equation set of the double-pulse phase difference and material parameters is established, the material thickness and the refractive index are obtained through inversion, and prior refractive index information is not needed; and finally, processing the data by adopting a local weighted regression smoothing algorithm to obtain comprehensive characterization parameters of the material. By adopting the method, high-precision, rapid and lossless thickness and refractive index measurement is realized, the applicability and the flexibility of measurement are remarkably improved, and the method has a wide industrial popularization prospect.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of material testing, in particular to a method for simultaneously testing material thickness and refractive index based on terahertz time-domain spectroscopy. BACKGROUND

[0002] In today's aerospace, new energy vehicles, semiconductor technology and other high-end manufacturing fields, the thickness control of material surface coating has a key influence on the performance, safety and stability of the product. For example, the thickness of the aircraft surface corrosion-resistant coating, the automobile battery pack insulating coating, the chip packaging layer, etc. is directly related to the durability, thermal conductivity, insulation and service life of the product. Therefore, developing a high-precision, fast and non-destructive thickness detection technology has become an urgent need in the field of new materials and advanced manufacturing.

[0003] Currently, the commonly used thickness measurement methods in industry mainly include ultrasonic thickness measurement, X-ray fluorescence thickness measurement, laser interference or confocal thickness measurement, eddy current and magnetic induction thickness measurement, etc. Although these traditional thickness measurement techniques can obtain the thickness information of unknown materials under certain conditions, they still have the following problems: slow test speed, high equipment cost, weak material adaptability, unstable measurement accuracy, etc., which still cannot meet the actual needs of fast online thickness detection in the field of advanced manufacturing. SUMMARY

[0004] The purpose of the present application is to solve the problems of slow test speed, high equipment cost, weak material adaptability, etc. of traditional thickness measurement methods, and to provide a method for simultaneously testing material thickness and refractive index based on terahertz time-domain spectroscopy.

[0005] To achieve the above purpose, the present application provides a method for simultaneously testing material thickness and refractive index based on terahertz time-domain spectroscopy, comprising the following steps:

[0006] S1, using a transmission type terahertz time-domain spectroscopy system to measure a sample with relatively weak terahertz absorption, obtaining a terahertz reference signal and a terahertz experimental signal, time synchronization correction is performed on the signals, and an equal-interval time sampling vector is established;

[0007] S2, using an automatic peak detection algorithm to locate the key pulse peaks in the time-domain waveform, and automatically identifying the peak values;

[0008] S3, at the located peak time point, setting a fixed width time window, intercepting the corresponding pulse signal, and performing windowing processing on the intercepted signal using a Hamming window;

[0009] S4, performing fast Fourier transform on the windowed signal to obtain a frequency-domain complex spectrum containing amplitude information and phase information;

[0010] S5, based on the optical path difference model, the relationship between the double pulse phase difference and the material parameters is established; the material thickness and the refractive index are inversely calculated by using the double pulse phase difference;

[0011] S6, the local weighted regression smoothing algorithm is used to smooth the refractive index and thickness curve, the weighted average value of the refractive index and the weighted average value of the thickness are calculated, and the measurement result is output.

[0012] Preferably, the sample to be measured in S1 is a sample with relatively weak terahertz absorption.

[0013] Preferably, the peak positioning in S2 is realized by a maximum value search algorithm combined with a preset time window limit.

[0014] Preferably, the specific steps of the signal windowing processing in S3 are:

[0015] For each pulse, the signal segment E(t) is intercepted, and a window function ω(t) is applied to generate a windowed signal:

[0016] E ω (t) = E(t) x ω(t).

[0017] Preferably, the fast Fourier transform of the windowed signal in S4 is that the frequency domain phase corresponding to the sample main pulse is phi0_sam, the phase of the reference signal corresponding to the sample main pulse is phi0_ref, the frequency domain phase corresponding to the sample echo pulse is phi1_sam, and the phase of the reference signal corresponding to the sample echo pulse is phi1_ref.

[0018] The main pulse phase difference is Δφ0(f) = phi0_sam-phi0_ref.

[0019] The echo phase difference is Δφ1(f) = phi1_sam-phi1_ref.

[0020] Preferably, the specific steps of S6 include:

[0021] The reference signal E ref (t) and the sample signal E sam (t) are subjected to fast Fourier transform to obtain E ref (ω) and E sam (ω), respectively, to obtain the complex transmission function of the sample, and the formula is:

[0022]

[0023] The complex transmission function is transformed to obtain the complex transmission function corresponding to the multiple reflection signals of the sample main peak in the sample:

[0024]

[0025] In the formula, p represents the pth echo, p=0 represents the main peak of the sample, is the complex refractive index of the sample, L0 is the thickness of the sample, ω is the angular frequency, and c is the speed of light in vacuum;

[0026] According to the complex transmission formula, T p (ω) modulus ρ p (ω) and amplitude angle φ p (ω);

[0027]

[0028] Under the condition of weak absorption approximation (κ0 / n0<<1), the amplitude angle φ p (ω) formula can be simplified as:

[0029]

[0030] The main pulse optical path difference corresponds to the signal propagation through the material thickness d and the refractive index n(f), and the main pulse phase difference Δφ0(f) of the material and the phase difference Δφ1(f) of the echo satisfy the following equation set:

[0031]

[0032] Where c is the speed of light, and f is the frequency;

[0033] The equation set is solved to obtain the expressions of the thickness d(f) and the refractive index n(f):

[0034]

[0035] Preferably, the S6 calculates the weighted average value n avg of the refractive index and the weighted average value d avg of the thickness:

[0036]

[0037] Where f1 and f2 are frequency boundaries, and F=f1-f2.

[0038] Therefore, the present application adopts the above-mentioned method for simultaneously testing the thickness and refractive index of a material based on terahertz time domain spectroscopy, and has the following beneficial effects:

[0039] (1) Breaking through the limitation of traditional refractive index dependence: the traditional THz thickness measurement technology needs to know the refractive index of the material in advance, while the present application constructs a double-pulse phase difference equation set based on the main pulse and echo signals, and can jointly invert the refractive index and thickness of the material without prior refractive index, breaking the dependence of the traditional model on optical parameters.

[0040] (2)High degree of automation, easy to system integration: combined with time window automatic positioning and peak recognition algorithm, can realize pulse intelligent extraction and signal processing without manual intervention, greatly improve the operation convenience and measurement consistency, at the same time, the algorithm supports the spectrum processing and statistical average based on LOESS etc. Smoothing technology, the output result is stable and reliable.

[0041] (3)Micron resolution, high precision: using frequency domain phase difference analysis and window function windowing processing, significantly improve the stability of frequency response signal, thickness measurement can realize micron or even sub-micron resolution, suitable for ultra-thin material, high precision detection scene.

[0042] The technical solutions of the present application will be described in detail below with the help of drawings and examples. BRIEF DESCRIPTION OF DRAWINGS

[0043] Figure 1 It is a method flowchart for simultaneously testing material thickness and refractive index based on terahertz time domain spectrum;

[0044] Figure 2 is a terahertz experimental signal waveform diagram;

[0045] Figure 3 is a peak interval diagram of automatically detecting reference signal and sample signal;

[0046] Figure 4 is a diagram of Hamming window (Hamming Window) windowing the intercepted signal;

[0047] Figure 5 is a phase difference diagram of sample signal relative to reference signal;

[0048] Figure 6 is a curve diagram of inverted refractive index n(f);

[0049] Figure 7 is a curve diagram of inverted thickness d(f);

[0050] Figure 8 It is a schematic diagram of terahertz wave through flat and uniform sample. DETAILED DESCRIPTION

[0051] EMBODIMENT

[0052] As shown in Figure 1 and Figure 8 The present application provides a method for simultaneously testing material thickness and refractive index based on terahertz time domain spectrum, characterized in that it comprises the following steps:

[0053] S1, material sample preparation and experimental data acquisition: using a transmission type terahertz time domain spectrum system to measure the sample to be measured, obtaining a terahertz reference signal and a terahertz experimental signal, correcting the time synchronization of the signal, and establishing an equal interval time sampling vector;

[0054] S2, automatic peak recognition: In order to accurately extract the pulse information related to the material, an automatic peak detection algorithm is used to locate the key pulse peaks in the time-domain waveform. Specifically, it includes: ① Peak value of reference signal: defined as the main pulse peak when there is no sample. ② Sample main pulse peak value: the first main peak in the sample signal, corresponding to the transmitted signal generated by the incident terahertz wave passing through the sample. ③ Peak value of sample echo signal: the second main peak of the sample signal, corresponding to the first reflection of the terahertz signal inside the material. Peak detection is realized by a maximum value search algorithm combined with a preset time window limit, ensuring accurate positioning of the target peak and avoiding misjudgment.

[0055] S3, signal windowing processing: In the vicinity of the determined peak time point, a fixed-width time window is set to intercept the corresponding pulse signal. In order to reduce the frequency domain leakage caused by time domain truncation, a Hamming window is used to perform windowing processing on the intercepted signal, making the time domain signal smooth decay, effectively improving the stability and accuracy of the frequency spectrum calculation. The specific steps are: for each pulse intercepted signal segment E(t), apply the window function ω(t), and the generated windowed signal is E ω (t) = E(t) x ω(t).

[0056] S4, Fourier transform and phase calculation: Perform fast Fourier transform (FFT) on the windowed signal to obtain the frequency domain complex spectrum, which contains amplitude information and phase information. The frequency domain phase corresponding to the sample main pulse is phi0_sam, the phase of the reference signal is phi0_ref, and the frequency domain phase corresponding to the sample echo pulse is phi1_sam, and the phase of the reference signal is phi1_ref.

[0057] The main pulse phase difference is Δφ0(f) = phi0_sam - phi0_ref;

[0058] The echo phase difference is Δφ1(f) = phi1_sam - phi1_ref.

[0059] S5, joint inversion of material thickness and refractive index: Based on the optical path difference model, the relationship between the double-pulse phase difference and the material parameters is established, and the thickness and refractive index are calculated. The specific steps include: for the reference signal E ref (t) and the sample signal E sam (t), perform fast Fourier transform on both to obtain E ref (ω) and E sam (ω), respectively, to obtain the complex transmission function of the sample, and the formula is:

[0060]

[0061] The complex transmission function contains the main peak of the sample and the multiple reflection signal in the sample, and the complex transmission function corresponding to the multiple reflection signal of the main peak in the sample can be obtained by transformation:

[0062]

[0063] In the formula, p represents the pth echo, p=0 represents the main peak of the sample, is the complex refractive index of the sample, L0 is the thickness of the sample, ω is the angular frequency, and c is the speed of light in vacuum;

[0064] According to the complex transmission formula, the modulus ρ p (ω) and the amplitude angle φ p (ω) of T p (ω) can be obtained.

[0065]

[0066] Under the condition of weak absorption approximation (k0 / n0<<1), the amplitude angle φ p (ω) formula can be simplified as:

[0067]

[0068] The main pulse optical path difference corresponds to the signal propagation through the material thickness and the refractive index, and the main pulse phase difference Δφ0(f) of the material and the phase difference Δφ1(f) of the echo satisfy the following equation set:

[0069]

[0070] Where c is the speed of light, and f is the frequency;

[0071] The equation set is solved to obtain the expressions of the thickness d(f) and the refractive index n(f):

[0072]

[0073] S6, smoothing processing: in order to eliminate the phase jump and high frequency oscillation caused by measurement noise and calculation error, the local weighted regression smoothing algorithm (such as LOESS) is used to smooth the refractive index n(f) and the thickness d(f) curve. The smoothed curve has good continuity and physical rationality, which is beneficial to the subsequent material property analysis. Finally, in the set effective frequency range (such as 0.2THz to 2.0THz), the weighted average value of the refractive index and the thickness is calculated as the comprehensive characterization parameter of the material, and the measurement result is output:

[0074] And

[0075] Where f1, f2 are the frequency boundaries, and F=f1-f2.

[0076] To verify the effectiveness of the method of the present application, specific examples are used for illustration.

[0077] Example 1

[0078] 1. Sample preparation and data acquisition: Quartz wafer was prepared as sample (thickness d = 510 pm, refractive index n = 1.96), and the sample was measured by a transmission terahertz time-domain spectroscopy system to obtain a terahertz reference signal and a terahertz experimental signal. To ensure uniformity of processing, the signals were time-synchronized and corrected, and an equally spaced time sampling vector was established. The results are shown in FIG. 2(a).

[0079] 2. Automatic peak identification: In order to accurately extract the pulse information related to the material, an automatic peak detection algorithm was used to locate the key pulse peaks in the time-domain waveform. The peak detection was realized by a maximum value search algorithm combined with a preset time window limit, which ensured accurate positioning of the target peak and avoided misjudgment. The results are shown in FIG. 3(a).

[0080] 3. Windowing processing of signals: In the vicinity of the determined peak time point (±0.5 ps), a fixed-width time window was set to intercept the corresponding pulse signal. In order to reduce the frequency domain leakage caused by time domain truncation, a Hamming window was used to process the intercepted signal, which made the time-domain signal smooth and decayed, effectively improving the stability and accuracy of the frequency spectrum calculation. The results are shown in FIG. 4(a).

[0081] 4. Fourier transform and phase calculation: Fast Fourier transform (FFT) was performed on the windowed signal to obtain the frequency-domain complex spectrum, which contained amplitude information and phase information. The obtained phase difference results are shown in FIG. 5(a).

[0082] 5. Joint inversion of material thickness and refractive index: Based on the optical path difference model, the relationship between the double-pulse phase difference and the material parameters was established, and the thickness and refractive index were calculated. A local weighted regression smoothing algorithm (such as LOESS) was used to smooth the refractive index n(f) and thickness d(f) curves. Finally, the weighted average values of the refractive index and thickness were calculated in the set effective frequency range (0.2 THz to 2.0 THz). The results are shown in FIG. 6(a) and FIG. 7(a).

[0083] Example 2

[0084] 1、Material sample preparation and experimental data acquisition: Prepare silicon wafer as sample (thickness d = 500 μm, refractive index n = 3.4), use the transmission terahertz time-domain spectroscopy system to measure the sample, obtain the terahertz reference signal and the terahertz experimental signal, in order to ensure the uniformity of processing, the signal is time synchronized and corrected, and the equally spaced time sampling vector is established. The results are shown in Figure 2(b).

[0085] 2、Automatic peak identification: In order to accurately extract the pulse information related to the material, an automatic peak detection algorithm is used to locate the key pulse peak in the time domain waveform. The peak detection is realized by combining the maximum value search algorithm with the preset time window limit, which ensures the accurate positioning of the target peak and avoids misjudgment. The results are shown in Figure 3(b).

[0086] 3、Signal windowing processing: In the vicinity of the determined peak time point (± 0.5 ps), a fixed width time window is set, and the corresponding pulse signal is intercepted. In order to reduce the frequency domain leakage caused by time domain truncation, Hamming window is used for windowing processing of the intercepted signal, which makes the time domain signal smooth decay, effectively improves the stability and accuracy of frequency spectrum calculation. The results are shown in Figure 4(b).

[0087] 4、Fourier transform and phase calculation: The windowed signal is subjected to fast Fourier transform (FFT) to obtain the frequency domain complex spectrum, which contains amplitude information and phase information. The obtained phase difference results are shown in Figure 5(b).

[0088] 5、Joint inversion of material thickness and refractive index: Based on the optical path difference model, the relationship between the double pulse phase difference and the material parameters is established, and the thickness and refractive index are calculated. The local weighted regression smoothing algorithm (such as LOESS) is used to smooth the refractive index n(f) and thickness d(f) curves. Finally, in the set effective frequency range (0.2 THz to 2.0 THz), the weighted average value of the refractive index and the thickness is calculated. The results are shown in Figures 6(b) and 7(b).

[0089] Therefore, the present application adopts the above-mentioned method for simultaneously testing the thickness and refractive index of the material based on terahertz time-domain spectroscopy, which breaks through the dependence on external means to obtain the refractive index in the traditional method, realizes self-consistent measurement completely relying on the terahertz time-domain spectroscopy signal itself, and significantly improves the applicability and flexibility of the measurement.

[0090] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for simultaneously measuring material thickness and refractive index based on terahertz time-domain spectroscopy, characterized in that, Includes the following steps: S1. Measure the sample under test using a transmission terahertz time-domain spectroscopy system, obtain the terahertz reference signal and the terahertz experimental signal, perform time synchronization correction on the signal, and establish an equally spaced time sampling vector. S2. An automatic peak detection algorithm is used to locate key pulse peaks in the time-domain waveform and automatically identify peak values; S3. At the located peak time point, set a time window of fixed width, extract the corresponding pulse signal, and perform windowing processing on the extracted signal using a Hamming window. S4. Perform a fast Fourier transform on the windowed signal to obtain a complex spectrum in the frequency domain containing amplitude and phase information. S5. Based on the optical path difference model, establish the relationship between the phase difference of the double pulse and the material parameters, and use the relationship between the phase difference of the double pulse and the material parameters to jointly inversely deduce the material thickness and refractive index; S6. Use a local weighted regression smoothing algorithm to smooth the refractive index and thickness curves, calculate the weighted average of the refractive index and the weighted average of the thickness, and output the measurement results.

2. The method for simultaneously measuring material thickness and refractive index based on terahertz time-domain spectroscopy according to claim 1, characterized in that: The sample to be tested in S1 is a sample with relatively weak terahertz absorption.

3. The method for simultaneously measuring material thickness and refractive index based on terahertz time-domain spectroscopy according to claim 1, characterized in that, In S2, peak positioning is achieved by combining a maximum value search algorithm with a preset time window limit.

4. The method for simultaneously measuring material thickness and refractive index based on terahertz time-domain spectroscopy according to claim 1, characterized in that, The specific steps for windowing the S3 signal are as follows: For each pulse, a segment E(t) is extracted, and a window function ω(t) is applied to generate a windowed signal: E ω (t)=E(t)×ω(t)。 5. The method for simultaneously measuring material thickness and refractive index based on terahertz time-domain spectroscopy according to claim 1, characterized in that, In S4, the fast Fourier transform of the windowed signal is performed as follows: the frequency domain phase corresponding to the sample main pulse is phi0_sam, the phase of the reference signal corresponding to the sample main pulse is phi0_ref, the frequency domain phase corresponding to the sample echo pulse is phi1_sam, and the phase of the reference signal corresponding to the sample echo pulse is phi1_ref. The phase difference of the main pulse is Δφ0(f) = phi0_sam - phi0_ref; The phase difference of the echo is Δφ1(f)=phi1_sam-phi1_ref.

6. The method for simultaneously measuring material thickness and refractive index based on terahertz time-domain spectroscopy according to claim 5, characterized in that, The specific steps of S5 include: For reference signal E ref (t) and sample signal E sam (t), performing fast Fourier transform on both yields E ref (ω) and E sam (ω), the complex transmission function of the sample is obtained, and the formula is: The complex transmission function is transformed to obtain the complex transmission functions corresponding to the multiple reflection signals of the main peak in the sample: In the formula, p represents the p-th echo, and p = 0 represents the main peak of the sample. L0 is the complex refractive index of the sample, L0 is the thickness of the sample, ω is the angular frequency, and c is the speed of light in a vacuum. T is obtained from the complex transmission formula. p The modulus ρ of (ω) p (ω) and argument φ p (ω); Under the weak absorption approximation (k0 / n0 << 1), the argument φ p The formula (ω) can be simplified to: The optical path difference of the main pulse corresponds to the signal propagation through the material thickness and refractive index. The phase difference Δφ0(f) of the main pulse of the material and the phase difference Δφ1(f) of the echo satisfy the following system of equations: Where c is the speed of light and f is the frequency; Solving the system of equations, we obtain expressions for the thickness d(f) and the refractive index n(f):

7. The method for simultaneously measuring material thickness and refractive index based on terahertz time-domain spectroscopy according to claim 6, characterized in that, S6 calculates the weighted average of the refractive index n avg The weighted average of thickness d avg The expression is: Where f1 and f2 are frequency boundaries, and F = f1 - f2.

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