A terahertz time-domain undersampling spectroscopy method and system for stress measurement

Abstract

The present invention provides a terahertz time-domain undersampling spectroscopy method and system for stress measurement. Undersampling is performed on a stressed specimen to obtain at least one set of terahertz time-domain undersampling spectral data. This data is then processed to obtain an error function describing the undersampling error caused by stress modulation. This error function is then processed to calculate the stress modulation coefficient and the change in the peak position of the terahertz signal. The specimen stress is then calculated based on the stress modulation coefficient and the change in the peak position of the terahertz time-domain spectrum. The present invention has the beneficial effects of effectively reducing the sampling window, minimizing delay line displacement, increasing measurement speed, and significantly shortening measurement time, while ensuring stress measurement accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of mechanics, and in particular relates to a terahertz time-domain undersampling spectroscopy method and system for stress measurement. Background Art

[0002] Terahertz time-domain spectroscopy can be used to probe the internal parameters of dielectric materials, such as their refractive index. Based on the stress-refractive index theory, the stress experienced by a material can be calculated from the change in refractive index. Using THz time-domain spectroscopy to characterize stress requires a polarized THz time-domain spectroscopy system. In 2007, Japanese researchers Shin-ichiro Ebara et al. constructed a polarized THz time-domain spectroscopy system and experimentally measured the refractive index change caused by stretching polytetrafluoroethylene (PTFE). In 2011, Tsuguhiro Takahashi et al. improved the experimental system, extracting information about internal stress from changes in the THz transmission signal intensity. More recently, Wang Zhiyong et al. at Tianjin University have used THz time-domain spectroscopy for mechanical measurements. In 2014, Song Wei et al. modified a conventional THz-TDS system and proposed a principle for experimental photoelasticity measurement in the THz band based on the laws of stress optics. They experimentally verified the photoelasticity theory in the THz band and used the improved experimental system to measure internal stress in PTFE. In 2021, Kang Kai, Wang Zhiyong and others proposed a method for measuring internal stress fields based on terahertz time-domain spectroscopy, and in 2022 combined it with CT algorithm to realize three-dimensional characterization of internal stress.

[0003] Research on stress measurement methods based on terahertz time-domain spectroscopy can be divided into two categories based on the arrangement of the polarized terahertz time-domain spectroscopy system: bright field (polarizer and analyzer polarization directions are consistent) and dark field (polarizer and analyzer polarization directions are perpendicular). Bright field terahertz measurement requires measuring the complete terahertz time-domain signal, performing a Fourier transform to obtain phase information, and then calculating stress based on this phase information; dark field terahertz measurement also requires a complete terahertz time-domain signal, and the peak-to-peak value of the signal is used to calculate the stress magnitude. However, both stress measurement methods require the acquisition of the complete terahertz time-domain signal, which takes a long time to sample. Summary of the Invention

[0004] In view of the above problems, the present invention provides a terahertz time-domain undersampling spectroscopy method and system for stress measurement to solve the above or other problems existing in the prior art.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is: a terahertz time-domain undersampling spectroscopy method for stress measurement, which uses an undersampling method to obtain at least one set of terahertz time-domain undersampling spectral data from a stressed specimen, processes the terahertz time-domain undersampling spectral data, obtains an error function for describing the undersampling error caused by stress modulation, processes the error function, calculates the stress modulation coefficient and the change in the peak position of the terahertz signal, and calculates the specimen stress based on the stress adjustment coefficient and the change in the peak position of the terahertz time-domain spectrum.

[0006] Furthermore, the terahertz time-domain undersampled spectral data is terahertz time-domain spectral data containing peak values and valley values.

[0007] Furthermore, the terahertz time-domain undersampling spectral data is processed to obtain an error function for describing the undersampling error caused by stress modulation, including:

[0008] Obtain terahertz time-domain spectroscopy data of the unstressed specimen;

[0009] The terahertz time-domain spectrum data of the unstressed specimen and the terahertz time-domain undersampled spectrum data of the stressed specimen are processed using a polynomial interpolation method to obtain processed terahertz time-domain spectrum data of the unstressed specimen and processed terahertz time-domain spectrum data of the stressed specimen;

[0010] Establish an error function and calculate the local minimum of the error function.

[0011] Furthermore, the step of establishing the error function includes:

[0012] Obtaining a segment of data S'c0(t) from the processed terahertz time-domain spectrum data of the unstressed specimen, where the data S'c0(t) is of the same length as the processed terahertz time-domain spectrum data of the stressed specimen;

[0013] Establish the error function Err(A,Δt), the error function Err(A,Δt) expression is:

[0014]

[0015] Wherein, A is the stress modulation coefficient, Δt is the change in the peak position of the terahertz time-domain spectrum, Δt=t1-t0, t1 is the starting time coordinate of the data S'c0(t), t0 is the starting time coordinate of the terahertz time-domain spectrum data of the stressed specimen after treatment, and S'(t) is the terahertz time-domain spectrum data of the stressed specimen after treatment.

[0016] Furthermore, in the step of calculating the local minimum value of the error function, a linear search algorithm is used to calculate the local minimum value of the error function.

[0017] Furthermore, the calculation of specimen stress includes:

[0018] According to the relationship between the refractive index change of the stressed specimen along different stress directions and the corresponding stress, the principal stress of the specimen is calculated;

[0019] Calculating the difference between the refractive index changes of the respective optical axes based on the peak position shift of the terahertz time-domain spectrum in a bright field mode; and / or

[0020] The principal stress difference of the specimen is calculated based on the amplitude of the terahertz time-domain spectroscopy data in the dark field mode.

[0021] Furthermore, the relationship between stress and refractive index change in bright field mode is:

[0022]

[0023] Where c is the speed of light, n0 and d0 are the initial refractive index and initial thickness of the specimen, respectively, μ is the Poisson’s ratio of the specimen material, E is the elastic modulus, σ is the specimen stress, and Δt is the peak position shift of the THz time-domain spectrum.

[0024] Furthermore, the amplitude calculation relationship of the composite wave signal synthesized by at least two polarized waves in the dark field method is:

[0025]

[0026] Among them, δ1-δ2 is the phase difference between the main optical axes caused by stress, is the polarization angle, θ is the first principal stress direction, and δ1-δ2 is the calculation relationship of the phase difference caused by stress between the principal optical axes: f is the frequency of the terahertz wave, c is the speed of light, and d is the thickness of the stressed specimen.

[0027] A terahertz time-domain undersampling spectroscopy system for stress measurement includes a laser emitting device, a terahertz wave generating device, a terahertz wave detecting device, an optical path conversion device, and a time delay control device. The terahertz wave generating device and the terahertz wave detecting device are respectively arranged on both sides of a test piece, the optical path conversion device is arranged on both sides of the test piece, and the time delay control device and the terahertz detecting device are arranged on the same side of the test piece. The light beam emitted by the laser emitting device is divided into two beams, one beam enters the terahertz wave detecting device through the time delay control device, and the other beam enters the terahertz wave generating device. The terahertz wave emitted from the terahertz wave detecting device and the terahertz wave emitted from the terahertz wave generating device act on the stressed test piece to interfere with each other, thereby obtaining terahertz time-domain undersampling spectroscopy data and performing stress measurement.

[0028] Furthermore, the time delay control device includes multiple reflectors arranged along the optical path, and the multiple reflectors can be movably arranged to change the optical path length; the optical path conversion device includes a polarizer arranged along the transmission direction of the terahertz wave and parabolic mirrors arranged on both sides of the polarizer.

[0029] Due to the adoption of the above technical solution, when the stress of the specimen is measured using terahertz time-domain spectroscopy technology, the terahertz time-domain undersampling spectroscopy method is applied to obtain the terahertz time-domain undersampling spectral data of the stressed specimen, and combined with the complete terahertz time-domain spectrum of the unstressed specimen, an error function is established to describe the undersampling error caused by stress modulation, the error function is processed to obtain the local minimum of the error function, and when the error function takes the local minimum, the stress modulation coefficient and the change in the peak position of the terahertz signal are obtained. The stress of the specimen is solved based on the stress modulation coefficient and the change in the peak position of the terahertz signal, which effectively reduces the sampling window, reduces the displacement of the delay line, improves the measurement speed, greatly shortens the measurement time, and ensures the stress measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 1 is a schematic structural diagram of a terahertz time-domain undersampling spectroscopy system for stress measurement according to an embodiment of the present invention;

[0031] Figure 2 2 is a schematic diagram of terahertz time-domain undersampling spectral data according to an embodiment of the present invention (the dotted line represents the terahertz time-domain spectral signal sampled using the traditional method, and the solid line represents the undersampling signal collected using the undersampling method);

[0032] Figure 3 1. It is a schematic diagram of an analytical solution of elastic mechanics theory based on stress characterization results of under-sampled terahertz signals according to an embodiment of the present invention;

[0033] Figure 4 1 is a schematic diagram of stress characterization results based on undersampled terahertz signals and experimental measurement values according to an embodiment of the present invention.

[0034] In the picture:

[0035] 1. Laser emitting device 2. Spectroscope 3. Time delay control device

[0036] 4. Terahertz wave detection device 5. Terahertz wave generation device 6. Parabolic mirror

[0037] 7. Polarizing filter DETAILED DESCRIPTION

[0038] The present invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0039] Figure 1A structural schematic diagram of an embodiment of the present invention is shown. This embodiment relates to a terahertz time-domain undersampling spectroscopy method and system for stress measurement, which is used to measure the stress of a stressed specimen, especially for measuring stress in dielectric materials. Terahertz time-domain undersampling spectroscopy is used to measure and analyze the stress of the stressed specimen, shortening the sampling time of terahertz time-domain spectroscopy measurement and ensuring the accuracy of stress measurement.

[0040] A terahertz time-domain undersampling spectroscopy method for stress measurement is disclosed. In a mechanical loading and measurement device, a stress test is performed on a specimen, and terahertz waves are applied to the stressed specimen for scanning. A terahertz time-domain undersampling spectrum is obtained through an undersampling method, and the terahertz time-domain undersampling spectrum is analyzed to further measure the stress of the stressed specimen.

[0041] The terahertz time-domain undersampling spectroscopy method for stress measurement specifically comprises the following steps: using an undersampling method to obtain at least one set of terahertz time-domain undersampling spectral data from a stressed specimen; processing the terahertz time-domain undersampling spectral data to obtain an error function for describing the undersampling error caused by stress modulation; processing the error function to calculate the stress modulation coefficient and / or the change in the peak position of the terahertz signal; and calculating the specimen stress based on the stress modulation coefficient and / or the change in the peak position of the terahertz signal.

[0042] The above-mentioned terahertz time-domain undersampled spectral data is terahertz time-domain spectral data containing peak values and valley values.

[0043] Processing terahertz time-domain undersampled spectral data to obtain an error function for describing the undersampling error caused by stress modulation includes:

[0044] Obtaining terahertz time-domain spectrum data of the unstressed specimen: Perform a test scan of the unstressed specimen's test area to collect a set of complete terahertz time-domain spectrum data through the unstressed specimen, denoted as S0(t), and determine the locations of the peaks and valleys of the complete terahertz time-domain spectrum.

[0045] Considering that the peak and valley positions of stress-modulated terahertz time-domain spectra change very little, an undersampling method is used for the stressed specimen. A test scan is performed on the test area of the stressed specimen to collect a set of undersampling data of the terahertz time-domain spectra containing peak and valley values, which is recorded as undersampling data S(t).

[0046] The terahertz time-domain undersampled spectral data of the unstressed specimen and the terahertz time-domain spectral data of the stressed specimen are processed using a polynomial interpolation method to obtain the processed terahertz time-domain spectral data of the unstressed specimen and the processed terahertz time-domain spectral data of the stressed specimen. Here, the polynomial interpolation method is preferably cubic polynomial interpolation to improve the time domain accuracy of the undersampled data.

[0047] The complete terahertz time-domain spectrum data of the unstressed specimen are processed by cubic polynomial interpolation, and the processed complete terahertz time-domain spectrum data of the unstressed specimen are S'0(t); the terahertz time-domain undersampled spectrum data of the stressed specimen are processed by cubic polynomial interpolation, and the processed terahertz time-domain undersampled spectrum data of the stressed specimen are S'(t);

[0048] Establish an error function and calculate the local minimum of the error function. The steps of establishing the error function include:

[0049] A segment of data S'c0(t) in the processed terahertz time-domain spectrum data of the unstressed specimen is obtained, where the data S'c0(t) is of the same length as the processed terahertz time-domain undersampled spectrum data of the stressed specimen, and the terahertz time-domain spectrum data is reconstructed, that is, the data S'c0(t) is of the same length as the terahertz time-domain undersampled spectrum data S'(t) of the stressed specimen.

[0050] Since stress will modulate the overall amplitude of the terahertz time-domain spectroscopy data, the stress modulation coefficient is set to A, and the value range of A is (0,1).

[0051] Establish the error function Err(A,Δt), the error function Err(A,Δt) expression is:

[0052]

[0053] Wherein, A is the stress modulation coefficient, Δt is the peak position movement of the terahertz time-domain spectrum, Δt=t1-t0, t1 is the starting time coordinate of the data S'c0(t), t0 is the starting time coordinate of the terahertz time-domain spectrum data of the stressed specimen after processing, and S'(t) is the terahertz time-domain undersampled spectrum data of the stressed specimen after processing.

[0054] In the step of calculating the local minimum of the error function, a linear search algorithm is used to calculate the local minimum of the error function based on the above-mentioned error function expression. When the error function Err(A, Δt) reaches its minimum, the stress modulation coefficient A and the peak position shift Δt of the terahertz time-domain spectrum are A0 and Δt0, respectively. Since the stress modulation of the terahertz time-domain spectrum is mainly reflected in the overall amplitude and time delay (the peak position shift of the terahertz time-domain spectrum), the overall amplitude change is determined by the stress modulation coefficient A0, that is, Sr = A0·S0.

[0055] When Δt<0, several zeros are added to the front of the reconstructed terahertz time-domain spectrum data, and several data are deleted at the end, so that the length of the data remains unchanged, and the peak value of the reconstructed terahertz time-domain spectrum data Sr coincides with the undersampled data; when Δt>0, several zeros are added to the end of the reconstructed terahertz time-domain spectrum data, and several data are deleted at the beginning. Similarly, the length of the data remains unchanged, and the peak value of the reconstructed terahertz time-domain spectrum data Sr coincides with the undersampled data.

[0056] Stress characterization is performed based on the reconstructed terahertz time-domain spectroscopy data. The calculation of specimen stress includes:

[0057] The principal stress of the specimen is calculated based on the relationship between the change in refractive index along different stress directions and the corresponding stress. According to the stress-optics law, the stress on the specimen material causes the originally isotropic material to become optically anisotropic. The principal optical axis of birefringence caused by stress is consistent with the principal direction of stress. If the specimen is in a plane stress state, the change in refractive index of the specimen can be expressed by the stress of the specimen as:

[0058] Δn1=Aσ1+Bσ2,

[0059] Δn2=Aσ2+Bσ1.

[0060] Among them, Δn1 and Δn2 are the changes in the refractive index of the material along the two plane principal stress directions, σ1 and σ2 are the first principal stress and the second principal stress, and A and B are stress-optical coefficients.

[0061] According to the calculation relationship of the refractive index change of the two main optical axes, the difference between the refractive index change of the two main optical axes can be obtained. The calculation relationship of the difference is:

[0062] Δn=Δn1-Δn2=C(σ1-σ2),

[0063] Wherein, C is the stress optical coefficient used in photoelastic stress analysis, C=AB.

[0064] There are two types of stress characterization methods based on terahertz time-domain spectroscopy: bright field and dark field. The difference between the refractive index changes of each optical axis is calculated based on the peak position shift of the terahertz time-domain spectrum in the bright field method; and / or the principal stress difference of the specimen is calculated based on the amplitude of the terahertz time-domain spectroscopy data in the dark field method.

[0065] Among them, the bright field measurement focuses on the peak position shift Δt of the terahertz time-domain spectrum. The relationship between stress and refractive index change in the bright field method is:

[0066]

[0067] Where c is the speed of light, n0 and d0 are the initial refractive index and initial thickness of the specimen, respectively, μ is the Poisson's ratio of the specimen material, E is the elastic modulus, σ is the specimen stress, and Δt is the peak position shift of the terahertz time-domain spectrum. The principal stress of the specimen can be calculated from the above formula.

[0068] Dark-field measurement focuses on the change in the overall amplitude (stress modulation coefficient) of the terahertz time-domain spectral data. When the terahertz wave passes through the stressed specimen, it is decomposed into two polarized waves due to stress birefringence. The different propagation speeds lead to a phase difference between the two polarized waves. After the two polarized terahertz waves pass through the stressed specimen, the interference of the two polarized terahertz waves causes a change in the amplitude of the composite wave signal E1. The amplitude calculation relationship of the composite wave signal E1 in the dark-field method is:

[0069]

[0070] Among them, δ1-δ2 is the phase difference between the main optical axes caused by stress, is the polarization angle, θ is the first principal stress direction, δ1-δ2 is the phase difference caused by stress between the principal optical axes, and the calculation relationship is:

[0071]

[0072] Where f is the frequency of the terahertz wave, c is the speed of light, d is the thickness of the stressed specimen, and Δn is the difference between the refractive index changes of the two main optical axes.

[0073] From the above calculation formula, it can be seen that the amplitude A contains information about the first principal stress direction θ and the principal stress difference Δσ. Therefore, the measurement results of the amplitude A under two different polarization states are required to solve the two unknowns θ and Δσ.

[0074] Such as: and Under the two polarization states, the measured amplitude A, the first principal stress direction θ and the principal stress difference Δσ can be calculated as:

[0075]

[0076] In this way, the stress modulation coefficient A (amplitude A) and the time delay (the shift in the peak position of the terahertz spectrum) Δt can be obtained, and the stress of the specimen can be analyzed.

[0077] like Figure 2Figure 2 shows terahertz time-domain spectroscopy data acquired using undersampling. Undersampling can significantly reduce the sampling window for terahertz time-domain spectroscopy signals. The dashed line in the figure represents the terahertz time-domain spectroscopy signal sampled using conventional methods, while the solid line represents the undersampled signal acquired using the aforementioned undersampling method. The figure shows that the signal sampling window is reduced from 12 ps to 2 ps. Because terahertz time-domain spectroscopy signals utilize coherent pump detection, the position of the time axis is controlled by the phase delay shift. During detection, the sampling time is proportional to the size of the signal sampling window. This undersampling method can significantly reduce the sampling time.

[0078] Based on the mentioned terahertz time-domain spectroscopy sampling method, the stress field characterization of the radially compressed disk of polytetrafluoroethylene material can be realized. Figure 3 and 4 As shown in the figure, the stress field extracted from undersampled terahertz time-domain spectroscopy data is compared with the analytical solution for a radially compressed disk derived from elastic mechanics. It is found that the undersampling method of terahertz time-domain spectroscopy can measure the stress field. At the same time, compared with the traditional sampling method based on complete terahertz time-domain spectroscopy data, the undersampling method has a significant advantage in acquisition speed.

[0079] A terahertz time-domain undersampling spectroscopy system for stress measurement, such as Figure 1 As shown, it includes a laser emitting device 1, a terahertz wave generating device 5, a terahertz wave detecting device 4, an optical path changing device and a time delay control device 3. The optical path changing device is arranged on both sides of the specimen, the terahertz wave generating device 5 and the terahertz wave detecting device 4 are respectively arranged on both sides of the specimen, and the time delay control device 3 and the terahertz wave detecting device 4 are arranged on the same side of the specimen. The light beam emitted by the laser emitting device 1 is divided into two beams. One light path enters the terahertz wave detecting device 4 through the time delay control device 3. The time delay control device 3 can move back and forth in the horizontal direction to change the optical path of the light path, and the other light path enters the terahertz wave generating device 5. The terahertz wave coming out of the terahertz wave detecting device 4 and the terahertz ratio coming out of the terahertz wave generating device 5 act on the stressed specimen through the optical path changing device respectively to interfere with each other, obtain terahertz time domain undersampling spectrum data, and perform stress measurement.

[0080] The above-mentioned laser emitting device 1 is a pulse laser, preferably a femtosecond laser. The emitting end of the pulse laser is provided with a spectroscope 2 to split the laser light emitted by the pulse laser. The laser light emitted by the pulse laser is divided into two optical paths by the spectroscope 2, one beam being the pump light, which enters the time delay control device 3, and the other beam being the detection light, which enters the terahertz wave generating device 5; on the transmission route of the first optical path, a plurality of reflectors are provided to reflect the optical path to control the transmission route of the optical path so that the light beam can enter the terahertz wave detecting device 4 through the time delay control device 3. At the same time, on the transmission route of the second optical path, a plurality of reflectors are also provided to reflect the optical path to control the transmission route of the optical path so that the light beam can enter the terahertz wave generating device 5. The multiple reflectors in the two optical paths are positioned according to actual needs, and no specific requirements are made here.

[0081] The time delay control device 3 is at least two reflectors arranged along the optical path. The multiple reflectors can be movably arranged and can be relatively close to or away from the test piece to change the optical path of the optical path.

[0082] In some feasible embodiments, preferably, the terahertz wave generating device 5 is a photoconductive antenna, which is a commercially available product and can be selected according to actual needs. A pulsed laser drives the photoconductive antenna to obtain a terahertz source and generate terahertz waves.

[0083] In some feasible embodiments, preferably, the above-mentioned terahertz wave detection device 4 is a photoconductive detector, which is a commercially available product and is selected according to actual needs.

[0084] An optical path conversion device is provided on both sides of the specimen. The optical path conversion device includes a polarizer 7 and a parabolic mirror 6 provided on both sides of the polarizer 7. The optical path conversion device changes the transmission path of the terahertz wave so that the terahertz wave output from the terahertz wave generating device 5 and the terahertz wave detecting device 4 acts on the specimen. Through undersampling, terahertz time-domain spectrum data is obtained and analyzed to perform stress testing on the specimen.

[0085] In some feasible embodiments, the parabolic mirror 6 , the polarizer 7 and the parabolic mirror 6 are arranged in sequence along the vertical direction.

[0086] Due to the adoption of the above technical solution, when the stress of the specimen is measured using terahertz time-domain spectroscopy technology, the terahertz time-domain undersampling spectroscopy method is applied to obtain the terahertz time-domain undersampling spectral data of the stressed specimen, and combined with the complete terahertz time-domain spectrum of the unstressed specimen, an error function is established to describe the undersampling error caused by stress modulation, the error function is processed to obtain the local minimum of the error function, and when the error function takes the local minimum, the stress modulation coefficient and the change in the peak position of the terahertz signal are obtained. The stress of the specimen is solved based on the stress modulation coefficient and the change in the peak position of the terahertz signal, which effectively reduces the sampling window, reduces the displacement of the delay line, improves the measurement speed, greatly shortens the measurement time, and ensures the stress measurement accuracy.

[0087] The embodiments of the present invention are described in detail above, but the contents described are only preferred embodiments of the present invention and should not be considered to limit the scope of the present invention. All equivalent changes and improvements made within the scope of the present invention should still fall within the scope of the patent coverage of the present invention.

Claims

1. A terahertz time-domain undersampling spectroscopy method for stress measurement, characterized by: Obtaining at least one set of terahertz time-domain undersampling spectrum data from the stressed specimen using an undersampling method, processing the terahertz time-domain undersampling spectrum data to obtain an error function for describing an undersampling error caused by stress modulation, processing the error function to calculate a stress modulation coefficient and a change in the peak position of the terahertz signal, and calculating the specimen stress based on the stress adjustment coefficient and the change in the peak position of the terahertz time-domain spectrum; Processing the terahertz time-domain undersampling spectrum data to obtain an error function for describing the undersampling error caused by stress modulation includes: Obtain terahertz time-domain spectroscopy data of the unstressed specimen; The terahertz time-domain spectrum data of the unstressed specimen and the terahertz time-domain undersampled spectrum data of the stressed specimen are processed using a polynomial interpolation method to obtain processed terahertz time-domain spectrum data of the unstressed specimen and processed terahertz time-domain spectrum data of the stressed specimen; Establishing the error function and calculating the local minimum of the error function; The steps to establish the error function include: Obtain a segment of data S'c0(t) from the processed terahertz time-domain spectrum data of the unstressed specimen, where the data S'c0(t) is equal in length to the processed terahertz time-domain undersampled spectrum data of the stressed specimen, and the processed terahertz time-domain undersampled spectrum data of the stressed specimen is S'(t); The error function Err(A,Δt) is established. The error function Err(A,Δt) is expressed as follows: Wherein, A is the stress modulation coefficient, Δt is the peak position change of the terahertz time-domain spectrum, Δt=t1-t0, t1 is the starting time coordinate of the data S'c0(t), t0 is the starting time coordinate of the terahertz time-domain undersampling spectrum data of the stressed specimen after processing, and S'(t) is the terahertz time-domain undersampling spectrum data of the stressed specimen after processing.

2. The terahertz time-domain undersampling spectroscopy method for stress measurement according to claim 1, characterized in that: The terahertz time-domain undersampled spectral data is terahertz time-domain spectral data containing peak values and valley values.

3. The terahertz time-domain undersampling spectroscopy method for stress measurement according to claim 1, characterized in that: In the step of calculating the local minimum value of the error function, a linear search algorithm is used to calculate the local minimum value of the error function.

4. The terahertz time-domain undersampling spectroscopy method for stress measurement according to any one of claims 1 to 3, characterized in that: The calculation of specimen stress includes: According to the relationship between the refractive index change of the specimen along different stress directions and the corresponding stress, the principal stress of the specimen is calculated; Calculating the difference between the refractive index changes of the respective optical axes based on the peak position shift of the terahertz time-domain spectrum in a bright field mode; and / or The principal stress difference of the specimen is calculated based on the amplitude of the terahertz time-domain spectroscopy data in the dark field mode.

5. The terahertz time-domain undersampling spectroscopy method for stress measurement according to claim 4, characterized in that: The relationship between stress and refractive index change in bright field mode is: Where c is the speed of light, n0 and d0 are the initial refractive index and initial thickness of the specimen, respectively, μ is the Poisson’s ratio of the specimen material, E is the elastic modulus, σ is the specimen stress, and Δt is the peak position shift of the THz time-domain spectrum.

6. The terahertz time-domain undersampling spectroscopy method for stress measurement according to claim 5, characterized in that: The calculation formula for the amplitude of the composite wave signal synthesized by at least two polarized waves in the dark field method is: Among them, δ1-δ2 is the phase difference between the main optical axes caused by stress, is the polarization angle, θ is the first principal stress direction, and δ1-δ2 is the calculation relationship of the phase difference caused by stress between the principal optical axes: f is the frequency of the terahertz wave, c is the speed of light, and d is the thickness of the stressed specimen.

7. A terahertz time-domain undersampling spectroscopy system for stress measurement, characterized by: Stress measurement is performed using the terahertz time-domain undersampling spectroscopy method for stress measurement according to any one of claims 1 to 6, comprising a laser emitting device, a terahertz wave generating device, a terahertz wave detecting device, an optical path conversion device, and a time delay control device, wherein the terahertz wave generating device and the terahertz wave detecting device are respectively arranged on both sides of the specimen, the optical path conversion device is arranged on both sides of the specimen, and the time delay control device and the terahertz wave detecting device are arranged on the same side of the specimen. The light beam emitted by the laser emitting device is divided into two beams, one light path enters the terahertz wave detecting device through the time delay control device, and the other light path enters the terahertz wave generating device. The terahertz wave coming out of the terahertz wave detecting device and the terahertz wave coming out of the terahertz wave generating device act on the stressed specimen, interfere with each other, obtain terahertz time-domain undersampling spectral data, and perform stress measurement.

8. The terahertz time-domain undersampling spectroscopy system for stress measurement according to claim 7, characterized in that: The time delay control device includes multiple reflectors arranged along the light path, and the multiple reflectors can be movably arranged to change the light path length; the light path conversion device includes a polarizer arranged along the transmission direction of the terahertz wave and parabolic mirrors arranged on both sides of the polarizer.

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