Terahertz thickness parameter extraction method based on dispersion compensation optimization

Abstract

The invention relates to a terahertz thickness parameter extraction method based on dispersion compensation optimization, and the method comprises the steps: carrying out the processing according to the intensity of a dispersion effect: for a sample with a weaker dispersion effect, converting a sample signal from a time domain to a spatial domain, and determining the thickness of the sample through the time delay of a time domain peak value of the signal; for a sample with a strong dispersion effect, the reference signal is compensated in the same dispersion mode to overcome time delay, and the thickness of the sample is determined according to the peak position difference of the dispersion compensation signal. According to the terahertz thickness parameter extraction method based on dispersion compensation optimization provided by the invention, the problem of time domain peak nonlinear offset caused by a material dispersion effect is solved, and the precision of material thickness parameter extraction in terahertz nondestructive testing is greatly improved.

Description

Technical Field

[0001] The present invention relates to the field of terahertz band material thickness detection, and particularly to a terahertz thickness parameter extraction method based on dispersion compensation optimization. Background Art

[0002] Terahertz waves refer to electromagnetic waves in the frequency band of 0.1 THz - 10 THz. Due to their characteristics of low photon energy and higher frequency than microwave band detection means, the thickness detection technology based on terahertz waves is widely used in the thickness detection of non-polar materials and surface coatings, providing a non-contact detection means for fields such as aerospace, biomedicine, and chip design. The fiber optic terahertz time-domain spectrometer (THz-TDS) based on photoconductive antennas is a terahertz detection instrument suitable for industrial scenarios, capable of stably exciting broadband terahertz waves in the range of 0.2 THz - 3 THz. By adjusting the optical path of the terahertz time-domain spectrometer, transmission measurement and reflection measurement of samples can be carried out. During the detection, usually two measurements of the reference signal and the sample signal are performed. By calculating the time difference between the peak positions of the reference signal and the sample signal, and combining with the refractive index of the sample, the sample thickness is inversely calculated. This method is very simple, but due to the dispersion effect and non-linear absorption effect of the material, it will cause the broadening of the overall waveform and the passivation of the peak position, resulting in the shift or even unidentifiability of the terahertz wave peak position, which will lead to inaccurate calculation of the material thickness. The material dispersion effect is caused by the inherent characteristics of the material, and the refractive index of the material varies at different frequencies. For materials with a large dispersion coefficient, such as many crystal materials, the refractive index in the terahertz band has a large change, so it has a strong broadening effect on broadband terahertz waves, and there is a large non-linear shift in the peak position of the sample signal in THz-TDS measurement. Since the spectrum of the terahertz time-domain spectrometer is wide and asymmetric, the broadening of the signal cannot be described by the group velocity. Therefore, for dispersive materials, simply using the average refractive index of the material or the refractive index corresponding to the central frequency to estimate the material thickness by the time-of-flight method may cause obvious measurement errors. The inaccurate extraction of the material thickness will greatly affect the accuracy of terahertz non-destructive testing. Summary of the Invention

[0003] In view of the deficiencies of the above methods, the present invention proposes a terahertz thickness parameter extraction method based on dispersion compensation optimization. In terahertz time-domain reflectance spectroscopy measurement, the signal on the lower surface of the sample propagates a distance equal to twice the thickness of the sample relative to the signal on the upper surface. In terahertz time-domain transmission spectroscopy measurement, the sample signal can be equivalently considered as propagating a distance equal to its own thickness in a sample with a refractive index reduced by one relative to the reference signal. For samples with known refractive indices in the terahertz band, the present invention uses a dispersion compensation algorithm based on reverse transmission to perform signal propagation in the opposite direction to the original propagation direction on the received sample signal, which is equivalent to performing dispersion compensation on the sample signal based on the nonlinear wave number. By performing linear interpolation on the linear angular frequency based on the relationship of the nonlinear wave number, the wave number domain signal after dispersion compensation is obtained, and then the inverse Fourier transform is performed to convert the wave number domain signal into the spatial domain signal. To solve the problem of signal distortion caused by interpolation, the sampling signal and the reference signal are interpolated in the same dispersion mode. The peak positions of the reference signal and the sample signal in the spatial domain directly correspond to the thickness of the sample. During this process, the signal is converted from the time domain to the spatial domain, and the dispersion effect of the sample signal is compensated. When the sample has a strong dispersion effect or the sample is relatively thick, the broadening effect of the sample signal makes the thickness estimation based on the time of flight inaccurate. After using the method of the present invention, the difference in the peak positions of the reference signal and the sample signal in the spatial domain directly corresponds to the thickness of the sample. When the absorption coefficient of the sample is large, an amplitude compensation method based on the reference signal is used to solve the nonlinear absorption problem of thick samples, which expands the test range for samples with different characteristics. Generally speaking, the terahertz thickness parameter extraction method based on dispersion compensation optimization proposed by the present invention solves the nonlinear offset of the time-domain peak caused by the material dispersion effect and greatly improves the accuracy of material thickness parameter extraction in terahertz non-destructive testing.

[0004] The technical solution adopted by the present invention to solve its technical problems is: a terahertz thickness parameter extraction method based on dispersion compensation optimization, specifically including the following steps:

[0005] S1. Obtain the refractive index of the sample in the terahertz band;

[0006] S2. Test the sample based on a time-domain spectrometer to respectively obtain the reference signal and the sample signal in the reflectance and transmittance modes; respectively calculate the signal transfer functions in the reflectance and transmittance modes; determine the dispersion factors affecting the reflectance and transmittance transmissions;

[0007] S3. Process according to the dispersion effect: a. For samples that do not produce a dispersion effect, convert the sample signal from the time domain to the spatial domain, and then determine the sample thickness through the time delay of the time-domain peak of the signal; b. For samples that produce a dispersion effect, perform dispersion compensation in the same dispersion mode in combination with the dispersion factor, and determine the thickness of the sample according to the peak position difference of the sample dispersion compensation signal.

[0008] The refractive index of the sample is calculated by transmission testing and the iterative method.

[0009] It also includes zero-padding the obtained reference signal and sample signal in the time domain to improve the frequency-domain resolution and prevent signal aliasing in subsequent signal dispersion compensation.

[0010] Under reflectance measurement, the transfer function H of the reference signal and the sample signal r (ω) is:

[0011]

[0012] where G s (ω) and G r (ω) are the frequency-domain transforms of the reference signal and the sample signal.

[0013] Under transmission measurement, the transfer function H of the reference signal and the sample signal t (ω) is:

[0014]

[0015] For a sample that does not produce a dispersion effect, the sample thickness is determined according to the following formula:

[0016] x = v gr t(9)

[0017] where v gr is the group velocity of the center frequency of the terahertz signal.

[0018] The dispersion compensation with the combined dispersion factor in the same dispersion mode includes:

[0019] Combining the dispersion factor, calculating the group velocity and phase velocity of the terahertz wave transmitted in the sample according to the refractive index, and inferring the nonlinear wave number;

[0020] Performing uniform interpolation of the nonlinear wave number to transform the time-domain signal into a wave-number domain signal;

[0021] Performing an inverse Fourier transform to convert the wave-number domain signal into a spatial domain, and respectively obtaining the reflectance and transmittance sample dispersion compensation signals after dispersion compensation.

[0022] The signal compensation in the same dispersion mode includes:

[0023] Propagating the signal in the opposite direction along the propagation direction to compensate for an integer multiple of the sample thickness d for the nonlinear wave number k at each frequency;

[0024] Then, the reflectance distance-domain signal h in the wave-number domain for dispersion compensation r (x) and the transmittance distance-domain signal ht (x):

[0025]

[0026]

[0027] Wherein:

[0028] ω = v ph (ω)k (12)

[0029] dω = v gr (ω)dk (13)

[0030] v ph (ω) and v gr (ω) is the phase velocity and group velocity related to the frequency;

[0031] Nonlinear wavenumber is used for uniform interpolation, and equations (10) and (11) are adjusted to the inverse Fourier transform formula through the relationship between angular frequency and wavenumber, which is used to transform the wavenumber domain into the spatial domain signal;

[0032] Then, the reflected and transmitted sample signals after dispersion compensation are obtained respectively; that is: the reflected distance domain signal h r (x) and the transmitted distance domain signal h t (x):

[0033]

[0034]

[0035] Wherein:

[0036] H(k) = G(ω)v gr (ω) (16)

[0037] ω = ω(k) (17)

[0038] G(ω) is the frequency domain signal uniformly obtained based on the equally spaced points in the frequency domain. However, for the wavenumber k, it is not equally spaced. Therefore, it is necessary to interpolate G(ω) according to the dispersion relationship between frequency and wavenumber to obtain the equally spaced wavenumber domain signal.

[0039] When considering the influence of sample thickness on dispersion, the amplitude of the sampling signal is compensated by the amplitude of the reference signal, and (16) is rewritten as:

[0040] H(k) = G r (ω)v gr (ω) (18)

[0041] After dispersion compensation by (14) and (15), the waveform becomes a non-dispersive signal in the distance domain.

[0042] Determining the thickness of the sample according to the peak position difference of the dispersion compensation signal includes:

[0043] Substituting the obtained reflected and transmitted sample signals after dispersion compensation into the following formula respectively:

[0044]

[0045] where h(x) is the distance that the sample signal travels under the dispersion mapping, and h o (x) is the reference signal transmission distance under the dispersion mapping.

[0046] The present invention has the following beneficial effects and advantages:

[0047] 1. The terahertz thickness parameter extraction method based on dispersion compensation optimization proposed by the present invention corrects the non-linear peak shift in the time domain caused by the material dispersion effect, and improves the accuracy of thickness parameter extraction based on time of flight in terahertz non-destructive testing.

[0048] 2. The terahertz thickness parameter extraction method based on dispersion compensation optimization proposed by the present invention is applicable to both transmissive and reflective terahertz time-domain spectroscopy systems, and has good universality.

[0049] 3. The terahertz thickness parameter extraction method based on dispersion compensation optimization proposed by the present invention still maintains high accuracy when the material to be measured has strong non-linear absorption. Therefore, the present invention can handle materials with relatively large thickness or absorption coefficient.

[0050] 4. The terahertz thickness parameter extraction method based on dispersion compensation optimization proposed by the present invention has strong robustness. Even under low signal-to-noise ratio conditions, it can quickly and accurately obtain the sample thickness. Description of the Drawings

[0051] Figure 1 is the flow chart of the terahertz thickness parameter extraction method based on dispersion compensation optimization proposed by the present invention;

[0052] Figure 2 is the measurement illustration of the reference signal and the sample signal in the transmissive and reflective terahertz time-domain spectroscopy systems;

[0053] Figure 3 is the real part and the imaginary part of the refractive index of the simulated sample 1 and sample 2 in the electromagnetic simulation;

[0054] Figure 4 is the normalized sample signal and the reference signal of the electromagnetic simulation;

[0055] Figure 5 These are the reference signal and the sample signal after dispersion compensation, which are the thickness measurement results of (a) Sample 1 and (b) Sample 2 respectively; Detailed implementation manners

[0056] In order to make the objectives, technical solutions and advantages of the invention more clear and understandable, the following further details the present invention in conjunction with the accompanying drawings and embodiments.

[0057] In the thickness detection of terahertz time-domain spectroscopy materials, a broadband terahertz time-domain pulse propagates a distance that is an integer multiple of the thickness within a substance. When the measurement method is a reflection measurement, the echo on the upper surface of the sample is the reference signal, and the echo on the lower surface of the substance is the sample signal. Therefore, the reference signal in the time domain obtained by the terahertz receiver is:

[0058]

[0059]

[0060] R 12 (ω) is the complex reflection coefficient at the junction of air and the upper surface of the material, ω is the angular frequency, F(ω) is the frequency-domain transform of the emission signal of the photoconductive antenna, and L is the distance between the photoconductive antenna at the emission end and the lower surface of the sample. k air is the wave number of air, c air is the speed of light in air, which is related to the refractive index n of air air and the speed of light c.

[0061] Without considering the multiple reflection effect, the sample signal in the time domain obtained by the terahertz receiver is:

[0062]

[0063]

[0064] wherein, R 21 (ω) is the complex reflection coefficient from the material to air, T 12 (ω) and T 21 (ω) are the complex reflection coefficients at the junctions of air with the upper and lower surfaces of the material, A(ω) is the total amplitude attenuation of the sample signal during transmission, and d is the thickness of the sample. k sample is the wave number corresponding to the sample, which is related to the refractive index n of the sample sample and the speed of light c.

[0065] It can be deduced that the transfer function H of the reference signal and the sample signal under the reflection measurement r (ω) is:

[0066]

[0067] Among them, G s (ω) and G r (ω) are the frequency-domain transforms of the reference signal and the sample signal, T 1 (ω) and T 2 (ω) are the frequency-domain transform values of the complex reflection coefficients at the interface between the upper and lower surfaces, R 1 (ω) is the frequency-domain transform value of the complex reflection coefficient from the material to the air, exp(2ik sample d) is the dispersion factor affecting the reflection transmission function.

[0068] Similarly, when the measurement method is transmission measurement, only air is measured as the reference signal, and the signal transmitted through the sample is the sample signal. At this time, the reference signal in the time domain obtained by the terahertz receiver is:

[0069]

[0070] Among them, in the formula, F(ω) is the frequency-domain conversion of the photoconductive antenna for the transmitted signal. x is the distance between the transmitter and the receiver. k air is the wave number of air, which is related to the refractive index of air.

[0071] Without considering the multiple reflection effect, the sample signal in the time domain obtained by the terahertz receiver is:

[0072]

[0073] It can be deduced that the transmission function H t (ω) of the reference signal and the sample signal under transmission measurement is:

[0074]

[0075] Among them, exp[i(k sample -k air )d] is the dispersion factor affecting the transmission function of transmission measurement;

[0076] Generally speaking, for samples with weak dispersion effects, it can be simply regarded as the time delay and amplitude reduction of the reference signal relative to the sample signal. Therefore, the following formula can be directly used to convert the sample signal from the time domain to the spatial domain, and then the thickness x of the sample with weak dispersion can be determined by the time delay of the time-domain peak of the signal.

[0077] x = v gr t (9)

[0078] Among them, v gr is the group velocity of the central frequency of the terahertz signal.

[0079] When considering the sample dispersion effect, that is, when the test sample has a large dispersion effect, the complex wave excited by the terahertz time-domain spectrometer propagates at its respective phase velocity, resulting in the broadening of the time-domain waveform. This broadening effect is exacerbated in samples with a larger thickness or a larger dispersion coefficient. Directly using formula (9) for conversion will result in a large error in the measurement of the thickness.

[0080] Therefore, the dispersion compensation optimization method proposed by the present invention is used for correction. It can be seen that in the propagation function of the reflection measurement, the dispersion is caused by the coefficient exp(2ik sample d), and relatively, in the propagation function of the transmission measurement, the dispersion is caused by the coefficient exp[i(k sample -k air )d]. To compensate for the dispersion effect, the signal is propagated in the opposite direction along the propagation direction, which is equivalent to compensating for an integer multiple of the sample thickness d of the nonlinear wave number k at each frequency. The reflection distance-domain signal h r (x) and the transmission distance-domain signal h t (x) of the dispersion compensation are as follows:

[0081]

[0082]

[0083] Where:

[0084] ω = v ph (ω)k (12)

[0085] dω = v gr (ω)dk (13)

[0086] v ph (ω) and v gr (ω) are the phase velocity and group velocity related to the frequency.

[0087] The distance-domain dispersion compensation signal in the above formula can be directly calculated by superposition calculation, but the calculation amount is too large. Therefore, for this formula, uniform interpolation of the nonlinear wave number can be used to solve it. By the relationship between the angular frequency and the wave number, the above formula is adjusted to the inverse Fourier transform formula. In this process, the wave number domain is transformed into the spatial domain. Therefore, the integration variable needs to be adjusted from ω to k, and the integration variable is adjusted according to the following relationship to obtain the reflected and transmitted sample signals after dispersion compensation respectively:

[0088]

[0089]

[0090] Where:

[0091] H(k) = G(ω)v gr (ω) (16)

[0092] ω = ω(k) (17)

[0093] G(ω) is a frequency-domain signal obtained uniformly at equally spaced points in the frequency domain. However, for the wave number k, it is not equally spaced. Therefore, it is necessary to interpolate G(ω) according to the dispersion relationship between frequency and wave number to obtain an equally spaced wave number domain signal.

[0094] In addition, for thinner materials, the waveform distortion caused by absorption is often ignored.

[0095] On the contrary, when considering the influence of sample thickness on dispersion, that is, when testing samples with a relatively thick or large absorption coefficient, there is still a large distortion in the dispersion compensation waveform. Additional amplitude compensation should be introduced. The signal amplitude is attenuated by the absorption characteristics, and the phase information is not affected. Therefore, the amplitude of the sampled signal is compensated by the amplitude of the reference signal, and (16) is rewritten as:

[0096] H(k) = G r (ω)v gr (ω) (18)

[0097] where G r (ω) is the Fourier transform of the sample signal.

[0098] After the dispersion compensation of (14) and (15), the waveform becomes a non-dispersive signal in the distance domain. Therefore, a simple method to determine the material thickness is to use the position of the peak point. Before dispersion compensation, regardless of whether the maximum position of the sample signal is translated to the time zero point, the peak position of the compensated signal includes not only the sample thickness but also the distance of the reference signal corresponding to the initial time delay. This is because after performing FFT processing on the time signal, the time information of the signal has been lost. A simple method is to compensate for the initial transmission distance with (9), but it is still affected by the distance error caused by the dispersion relationship. Therefore, the reference signal is compensated in the same dispersion mode accordingly, which is equivalent to determining the distance that the reference signal propagates in this dispersion mode. After the above signal dispersion compensation, the thickness d of the sample with large dispersion is determined by the difference in the maximum position between h(x) and h 0 (x), expressed as:

[0099]

[0100] where h(x) is the distance that the sample signal is transmitted under the dispersion mapping (substitute the reflected and transmitted sample signals obtained by compensating the dispersion in formulas 14 and 15 respectively), h o(x) is the transmission distance of the reference signal under dispersion mapping (substitute the reference signals of the reflection type and the transmission type after dispersion compensation obtained from Formulas 10 and 11 respectively).

[0101] In the above process, the multiple echoes caused by the multiple reflection effect will also be correspondingly dispersion-compensated because they have the same dispersion relationship, and their peak positions appear at integer multiples of the sample thickness. Therefore, the terahertz thickness parameter extraction method optimized based on dispersion compensation includes the following steps, as Figure 1 shown.

[0102] First, determine the refractive index of the sample in the terahertz frequency band. For samples that are known or calibrated by other institutions, their refractive indices can be directly used. For unknown samples, use a sample with a standard thickness for transmission testing, and calculate the refractive index of the sample through the iterative method. Then, perform tests on the sample based on a time-domain spectrometer, and the reference signal and the sample signal need to be obtained. In the transmission test, the reference signal is obtained without placing the sample between the terahertz transmitter and the receiver, and the sample signal is obtained by placing the sample at the focal point. In the reflection test, the echo signal from the front surface of the substance is the reference signal, and the echo from the back surface of the substance is the sample signal, as Figure 2 shown. To prevent signal aliasing in the subsequent signal dispersion compensation, zero-padding in the time domain needs to be performed on the obtained reference signal and sample signal to improve the frequency-domain resolution.

[0103] After that, based on the measured refractive index, the group velocity and phase velocity of the terahertz wave transmitted in the sample can be inferred, and then the nonlinear wave number can be calculated. Uniform sampling of the nonlinear wave number is performed, and then the distance-domain coordinate x is deduced through the relationship between the wave number domain and the spatial domain. Through linear interpolation, the time-domain signal can be transformed into a wave number-domain signal, and then an inverse Fourier transform is performed to convert the wave number-domain signal into a spatial domain.

[0104] Because there is an initial time delay in the time-domain peak of the reference signal, the reference signal needs to be compensated under the same dispersion mode. Finally, the thickness of the sample can be determined according to the peak position difference of the dispersion-compensated signal. Specific Example 1:

[0106] 1. Conduct electromagnetic simulations based on transmission terahertz time-domain spectroscopy on Samples 1 and 2 with different dispersion and absorption characteristics, and use the simulation results to complete the thickness testing of the two samples. The theoretical thickness of the sample is set to 4.1 mm. The real part of its refractive index and the absorption coefficient are as Figure 3 shown.

[0107] 2. Figure 4, (a) Terahertz signal test sample 1 (without considering absorption effect), (b) Terahertz signal test sample 1 (considering absorption effect), (c) Terahertz signal test sample 2 (without considering absorption effect), and (d) Terahertz signal test sample 2 (considering absorption effect). Since the two simulated samples have different dispersion and absorption characteristics, after the terahertz wave penetrates the sample, it will broaden due to the dispersion effect, which is very obvious in Figure 4 (a) and (c), and the oscillation at the tail intensifies, making it very inaccurate to calculate the material thickness using the TOF algorithm. To separate the dispersion effect, the absorption effect of the sample is not considered in these two figures. When the absorption effect is considered, the absorption effect of the broadband spectrum significantly deforms the waveform, as shown in Figure 4 (b) and (d). Therefore, it is necessary to compensate for the dispersion and absorption effects.

[0108] 3. After obtaining the simulation results, the corresponding nonlinear wave number, phase velocity, and group velocity were obtained based on the real part of the refractive index of the material, and interpolation was performed according to the relationship between the wave number and the angular frequency to complete Figure 1 the corresponding steps, and the dispersion-compensated waveform was obtained as shown in Figure 5 . Accordingly, the material thicknesses of sample 1 and sample 2 were obtained as 4.0995 mm and 4.0999 mm respectively, and the deviation percentages were 0.0122% and 0.0024% respectively. Compared with the thicknesses of 3.8999 mm and 3.5958 mm calculated by the time of flight using the group velocity of the central frequency, the errors were only 0.24% and 0.02% of the original.

Claims

1. A method for extracting terahertz thickness parameters optimized based on dispersion compensation, characterized in that, it includes the following steps: S1. Obtain the refractive index of the sample in the terahertz frequency band; S2. Test the sample based on a time-domain spectrometer, respectively obtain the reference signals and sample signals in reflection and transmission modes; calculate the signal transfer functions in reflection and transmission modes respectively; determine the dispersion factors affecting reflection and transmission; S3. Process according to the dispersion effect: a. For a sample without considering the dispersion effect, convert the sample signal from the time domain to the spatial domain, and then determine the sample thickness through the time delay of the time-domain peak of the signal; b. For a sample considering the dispersion effect, perform dispersion compensation in the same dispersion mode in combination with the dispersion factor, and determine the thickness of the sample according to the peak position difference of the sample dispersion compensation signal.

2. The method for extracting terahertz thickness parameters optimized based on dispersion compensation according to claim 1, characterized in that, the refractive index of the sample is calculated by transmission testing and the iterative method.

3. The method for extracting terahertz thickness parameters optimized based on dispersion compensation according to claim 1, characterized in that, it further includes zero-padding the obtained reference signal and sample signal in the time domain to improve the frequency-domain resolution and prevent signal aliasing in subsequent signal dispersion compensation.

4. The method for extracting terahertz thickness parameters optimized based on dispersion compensation according to claim 1, characterized in that, The transfer function H of the reference signal and the sample signal under reflective measurement r (ω) is as follows: Among them, G s (ω) and G r (ω) are the frequency-domain transforms of the reference signal and the sample signal.

5. The method for extracting terahertz thickness parameters optimized based on dispersion compensation according to claim 1, characterized in that, The transfer function H of the reference signal and the sample signal under transmissive measurement t (ω) is as follows:

6. The method for extracting terahertz thickness parameters optimized based on dispersion compensation according to claim 1, characterized in that, for a sample without generating a dispersion effect, the sample thickness is determined according to the following formula: x = v gr t (9) Among them, v gr is the group velocity of the center frequency of the terahertz signal.

7. The method for extracting terahertz thickness parameters optimized based on dispersion compensation according to claim 1, characterized in that, the performing dispersion compensation in the same dispersion mode in combination with the dispersion factor includes: Combining the dispersion factor, calculating the group velocity and phase velocity of the terahertz wave transmitted in the sample according to the refractive index, and inferring the nonlinear wave number; Performing uniform interpolation of the nonlinear wave number to transform the time-domain signal into a wave number-domain signal; Performing an inverse Fourier transform to convert the wave number-domain signal into the spatial domain, and respectively obtaining the sample dispersion compensation signals in reflection and transmission modes after dispersion compensation.

8. The method for extracting terahertz thickness parameters optimized based on dispersion compensation according to claim 7, characterized in that, compensating the signal in the same dispersion mode includes: Propagating the signal in the opposite direction along the propagation direction to compensate for an integer multiple of the sample thickness d for the nonlinear wave number k at each frequency; Then, the reflected distance-domain signal h r (x) and the transmitted distance-domain signal h t (x): wherein: ω = v ph (ω)k (12) dω = v gr (ω)dk (13) v ph (ω) and v gr (ω) is the phase velocity and group velocity related to the frequency; Performing uniform interpolation using the nonlinear wave number, and adjusting equations (10) and (11) to an inverse Fourier transform formula through the relationship between the angular frequency and the wave number for converting the wave number domain into a spatial domain signal; Then, the reflected and transmitted sample signals after dispersion compensation are obtained respectively; that is: the reflected distance-domain signal h r (x) and the transmitted distance-domain signal h t (x): wherein: H(k) = G(ω)v gr (ω) (16) ω = ω(k) (17) G(ω) is a frequency-domain signal uniformly obtained based on equally spaced points in the frequency domain. However, for the wave number k, it is not equally spaced. Therefore, it is necessary to interpolate G(ω) according to the dispersion relationship between the frequency and the wave number to obtain an equally spaced wave number-domain signal.

9. The terahertz thickness parameter extraction method based on dispersion compensation optimization according to claim 1, wherein, when considering the influence of sample thickness on dispersion, the amplitude of the sampled signal is compensated by the amplitude of the reference signal, and (16) is rewritten as: H(k) = G r (ω)v gr (ω) (18) After the dispersion compensation of (14) and (15), the waveform becomes a non-dispersive signal in the distance domain.

10. The terahertz thickness parameter extraction method based on dispersion compensation optimization according to claim 8 or 9, wherein, determining the thickness of the sample according to the peak position difference of the dispersion compensation signal includes: substituting the obtained reflected and transmitted sample signals after dispersion compensation into the following formula respectively: Among them, h(x) is the distance that the sample signal travels under the dispersion mapping, and h o (x) is the distance that the reference signal travels under the dispersion mapping.

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