A transverse axis matching method based on material absorption spectrum of terahertz time domain signal

Abstract

The application discloses a kind of based on material absorption spectrum's terahertz time-domain signal horizontal axis matching method, the terahertz time-domain signal of measured material is obtained using terahertz time-domain spectroscopy system, obtains the sampling point number of terahertz time-domain signal;From the standard frequency domain signal of measured material in terahertz standard database is acquired, obtains the multiple absorption peaks of material and each absorption peak position;The frequency domain signal of test is obtained by fast fourier transform to measured terahertz time-domain signal;Equivalent sampling interval of time-domain signal is set as optimization target, the sum of the difference of all absorption peaks of the frequency domain signal of test and standard frequency domain signal is as error function and set error function convergence condition;Error function is optimized by random optimization algorithm, until error function reaches convergence condition, and the optimized time-domain equivalent sampling interval is output;Through the optimized time-domain equivalent sampling interval, frequency domain equivalent sampling range is calculated and obtained, combined with sampling point number, obtain the matched time, frequency domain horizontal axis.

Description

Technical Field

[0001] This invention belongs to the field of terahertz pulse signal sampling technology, and specifically relates to a terahertz time-domain signal horizontal axis matching method based on material absorption spectrum. Background Technology

[0002] Terahertz (THz) waves (or terahertz radiation) generally refer to electromagnetic waves with frequencies between 0.1 THz and 10 THz (wavelengths between 30 μm and 3 mm). They overlap with millimeter waves in the long-wavelength band and with infrared light in the short-wavelength band, representing a transitional region from electronics to photonics. Due to the unique position of terahertz waves in the electromagnetic spectrum, terahertz technology has demonstrated immense scientific research value and application prospects in numerous fields, including industry, basic research, military, and medicine.

[0003] A typical terahertz time-domain spectroscopy (THz-TDS) system mainly consists of four parts: a femtosecond pulsed laser, a THz pulse generation device, a THz pulse detection device, and a time delay device. The femtosecond laser pulse emitted by the femtosecond laser is split into pump and probe beams by a beam splitter. A transient current proportional to the terahertz radiation field is obtained using photoconductive detection technology. Since the terahertz time-domain signal is approximately on the picosecond scale or even shorter, the rise time of the current response is essentially on the sub-picosecond scale. Therefore, equivalent time sampling techniques are needed to extract the horizontal and vertical axes of the terahertz time-domain electric field signal. The horizontal axis is determined by changing the optical path difference between the probe and pump beams using a variable time delay device, and a series of equivalent sampling intervals (the flight time of the terahertz wave at different times) are calculated from the optical path difference. The vertical axis represents the amplitude of the transient current of the terahertz radiation.

[0004] For ordinary mechanical delay lines, the above method can be used for horizontal axis matching. However, for time delay devices such as involute and high-speed rotating types, their structures are more complex, making it difficult to obtain the horizontal axis of the terahertz time-domain signal using the optical path difference calculation formula to achieve horizontal axis matching. Therefore, this invention proposes a method for horizontal axis matching of terahertz time-domain signals based on material absorption spectra. Summary of the Invention

[0005] To address the challenge of matching the horizontal axis of terahertz time-domain signals obtained from complex time-delay devices, this invention provides a method for matching the horizontal axis of terahertz time-domain signals based on material absorption spectra. This method reduces the difficulty of horizontal axis matching in terahertz time-domain signal acquisition, enables the acquisition of terahertz time-domain signals from various time-delay systems, and improves the accuracy of horizontal axis matching for terahertz time-domain signals.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A terahertz time-domain signal horizontal axis matching method based on material absorption spectra includes the following steps:

[0008] Step 1: Obtain the terahertz time-domain signal of the material under test using a terahertz time-domain spectroscopy system, and obtain the number of terahertz time-domain signal sampling points;

[0009] Step 2: Obtain the standard frequency domain signal of the material under test from the terahertz standard database to obtain multiple absorption peaks of the material and the positions of each absorption peak; perform a fast Fourier transform on the measured terahertz time domain signal to obtain the test frequency domain signal;

[0010] Step 3: Set the equivalent sampling interval of the time domain signal as the optimization target, use the sum of the differences between all absorption peaks of the tested frequency domain signal and the standard frequency domain signal as the error function, and set the convergence condition of the error function.

[0011] Step 4: Optimize the error function using a stochastic optimization algorithm until the error function reaches the convergence condition, and output the optimized time-domain equivalent sampling interval.

[0012] Step 5: Calculate the equivalent sampling range in the frequency domain using the optimized time-domain equivalent sampling interval, and combine it with the number of sampling points to obtain the matched time and frequency domain horizontal axes.

[0013] Furthermore, the specific process of step two is as follows:

[0014] Obtain the standard frequency domain signal of the material under test from the terahertz standard database, and determine the positions P of the m and m>3 absorption peaks of the material. sta (m); The frequency domain signal of the measured terahertz time-domain signal is obtained by performing a fast Fourier transform on the measured terahertz signal using the following formula:

[0015] E(f)=F(E(t))

[0016] Where F is the Fast Fourier Transform; E(t) is the terahertz time-domain signal of the material under test.

[0017] Furthermore, the specific process of step three is as follows:

[0018] 3.1 Based on the time-domain equivalent sampling interval τ sample Given the number of sampling points N, the equivalent sampling range in the frequency domain is τ. s ′ ample =1 / (2·τ) sample At the same time, the frequency domain horizontal axis can be obtained as

[0019] 3.2 Obtain the number of sampling points corresponding to the m absorption peak positions of the test frequency domain signal and obtain the horizontal axis position P of the absorption peak. test (m);

[0020] 3.3 Calculate the sum of the differences between the m corresponding absorption peaks of the test frequency domain signal and the standard frequency domain signal using the following formula, and use it as the error function. Set the convergence condition for the error function:

[0021]

[0022] Furthermore, the specific process of step five is as follows:

[0023] Through the optimized time-domain equivalent sampling interval τ best The equivalent sampling range τ in the frequency domain is calculated. b ′ est =1 / (2·τ) best Combined with the number of sampling points N, the matched time-domain horizontal axis X is calculated using the following formula. time-domain and frequency domain horizontal axis X frequency-domain :

[0024] X time-domain =(0,τ) best ,2τ best ,3τ best ,...,Nτ best )

[0025]

[0026] Based on this, the time-domain signal and frequency-domain signal after absorption peak matching are obtained.

[0027] The present invention has the following beneficial effects:

[0028] This invention utilizes material absorption peaks from a standard database for terahertz time-domain signal horizontal axis matching, solving the problem of difficult horizontal axis registration for terahertz time-domain signals acquired by complex time-delay systems. This reduces the difficulty of horizontal axis matching in terahertz time-domain signal acquisition and enables the acquisition of terahertz time-domain signals from various time-delay systems, providing a foundation for coherent detection of terahertz time-domain signals.

[0029] This invention utilizes a stochastic optimization algorithm to optimize the equivalent sampling interval in the time domain, solving the problem of manually matching the equivalent sampling interval. By setting an error function, it reduces the introduction of human error and improves the accuracy of the horizontal axis matching of terahertz time domain signals.

[0030] This invention can not only use materials (including silicon, quartz, etc.) for terahertz time-domain signal horizontal axis matching, but also use the absorption peaks of gases (including water vapor, carbon monoxide, etc.) for horizontal axis matching. It can be used in a variety of terahertz systems, and is highly practical and widely applicable. Attached Figure Description

[0031] Figure 1 This is a terahertz time-domain signal diagram of water vapor tested in Example 1;

[0032] Figure 2 This is a terahertz frequency domain signal diagram of water vapor tested in Example 1;

[0033] Figure 3(a) shows the terahertz time-domain signal after matching in Example 1;

[0034] Figure 3(b) shows the terahertz frequency domain signal after matching in Example 1;

[0035] Figure 4 This is a flowchart of a terahertz time-domain signal horizontal axis matching method based on material absorption spectrum according to the present invention. Detailed Implementation

[0036] To make the purpose, technical solution, and advantages of the invention clearer, the invention will be further described in detail below with reference to the accompanying drawings.

[0037] This invention relates to a terahertz time-domain signal horizontal axis matching method based on material absorption spectra, such as... Figure 4 As shown, it includes the following steps:

[0038] Step 1: Obtain the terahertz time-domain signal of the material under test using a terahertz time-domain spectroscopy system, denoted as E(t), and obtain the number of sampling points of the terahertz time-domain signal, denoted as N, that is, the length of E(t) is N.

[0039] Step 2: Obtain the standard frequency domain signal of the material under test from the terahertz standard database to obtain the m (m>3) absorption peak positions P of the material. sta (m); The measured terahertz time-domain signal is obtained by performing a fast Fourier transform on the measured terahertz time-domain signal using formula (1).

[0040] E(f)=F(E(t)) (1)

[0041] Where F is the Fast Fourier Transform.

[0042] Step 3: Set the equivalent sampling interval τ of the time-domain signal sample To optimize the objective, the sum of the differences between the m corresponding absorption peaks of the tested frequency domain signal and the standard frequency domain signal is used as the error function, and the convergence condition of the error function is set.

[0043] The specific operation process for step three is as follows:

[0044] 3.1 Based on the time-domain equivalent sampling interval τ sample Given the number of sampling points N, the equivalent sampling range in the frequency domain is τ. s ′ ample =1 / (2·τ) sample At the same time, the frequency domain horizontal axis can be obtained as

[0045] 3.2 Obtain the number of sampling points corresponding to the m absorption peak positions of the test frequency domain signal and obtain the horizontal axis position P of the absorption peak. test (m);

[0046] 3.3 Calculate the sum of the differences between the m corresponding absorption peaks of the test signal and the standard signal using formula (2) as the error function, and set the convergence condition of the error function.

[0047]

[0048] Step 4: Optimize the error function using a stochastic optimization algorithm until the error function reaches the convergence condition, and output the optimized parameters, i.e., the equivalent sampling interval τ in the time domain. best .

[0049] Step 5: Using the optimized time-domain equivalent sampling interval τ best The equivalent sampling range τ in the frequency domain is calculated. b ′ est =1 / (2·τ) best Combined with the number of sampling points N, the matched time-domain horizontal axis X can be calculated using equation (3). time-domain and frequency domain horizontal axis X frequency-domain Based on this, the time-domain signal and frequency-domain signal after absorption peak matching are obtained.

[0050]

[0051] Example 1:

[0052] This embodiment presents a terahertz time-domain signal horizontal axis matching method based on material absorption spectra, using water vapor as the analyte:

[0053] Step 1: Sample and obtain the water vapor terahertz time-domain signal, such as... Figure 1 As shown.

[0054] Step 2: Obtain the positions of different absorption peaks of water vapor in the standard frequency domain data from the terahertz standard database, as shown in Table 1. Perform a fast Fourier transform on the measured terahertz time-domain signal to obtain the tested frequency-domain signal, as shown in Table 1. Figure 2 As shown.

[0055] Table 1. Positions of the standard absorption peak of water vapor

[0056] Peak number Peak position (THz) 1. 0.557 2. 0.753 3. 0.989 4. 1.098 5. 1.164 6. 1.2264 7. 1.4116 8. 1.603 9. 1.67107 10. 1.718 11. 1.7984 12. 1.869 13. 1.9207

[0057] Step 3: Select the particle swarm optimization algorithm as the stochastic optimization algorithm. The error function is shown in formula (2). Set the error convergence condition as tol < 10. -4 .

[0058] Step 4: Optimize the error function using a stochastic optimization algorithm until the error function reaches the convergence condition, and obtain the time-domain equivalent sampling interval τ at this point. best =1.0022×10 -13 s, and simultaneously obtain the frequency domain equivalent sampling range τ′ best = 4.9889THz.

[0059] Step 5: Obtain the absorption peak data of the current terahertz frequency domain signal being tested, as shown in Table 2 (the number of decimal places is retained to be consistent with the standard absorption peak data). It can be seen that the matched absorption peak values ​​match the absorption peak values ​​in the standard database.

[0060] Table 2. Location of water vapor absorption peaks.

[0061]

[0062]

[0063] Step 5: Based on the time-domain sampling interval, the number of sampling points, and the frequency-domain sampling range, the time- and frequency-domain signals of the water vapor terahertz signal after matching can be plotted, as shown in Figure 3(a) and Figure 3(b).

[0064] The above description is only a preferred embodiment of the present invention. For those skilled in the art, there will be changes in the specific implementation and application scope based on the ideas of the present invention. The content of this specification should not be construed as a limitation of the present invention.

Claims

1. A terahertz time-domain signal horizontal axis matching method based on material absorption spectra, characterized in that, Includes the following steps: Step 1: Obtain the terahertz time-domain signal of the material under test using a terahertz time-domain spectroscopy system, and obtain the number of terahertz time-domain signal sampling points; Step 2: Obtain the standard frequency domain signal of the material under test from the terahertz standard database to obtain the multiple absorption peaks of the material and the positions of each absorption peak; perform a fast Fourier transform on the measured terahertz time domain signal to obtain the test frequency domain signal; Step 3: Set the equivalent sampling interval of the time domain signal as the optimization target, use the sum of the differences between all absorption peaks of the tested frequency domain signal and the standard frequency domain signal as the error function, and set the convergence condition of the error function. Step 4: Optimize the error function using a stochastic optimization algorithm until the error function reaches the convergence condition, and output the optimized time-domain equivalent sampling interval. Step 5: Calculate the equivalent sampling range in the frequency domain using the optimized time-domain equivalent sampling interval, and combine it with the number of sampling points to obtain the matched time and frequency domain horizontal axes.

2. The terahertz time-domain signal horizontal axis matching method based on material absorption spectrum as described in claim 1, characterized in that, The specific process of step two is as follows: Obtain the standard frequency domain signal of the material under test from the terahertz standard database to obtain the positions P of the m absorption peaks of the material. sta (m), where m > 3; The frequency domain signal of the measured terahertz time-domain signal is obtained by performing a fast Fourier transform on the measured terahertz signal using the following formula: E(f)=F(E(t)) Where F is the Fast Fourier Transform; E(t) is the terahertz time-domain signal of the material under test.

3. The terahertz time-domain signal horizontal axis matching method based on material absorption spectrum as described in claim 2, characterized in that, The specific process of step three is as follows: (3.1) Based on the time-domain equivalent sampling interval τ sample Given the number of sampling points N, the equivalent sampling range in the frequency domain is τ′. sample =1 / (2τ) sample At the same time, the frequency domain horizontal axis can be obtained as (3.2) Obtain the number of sampling points corresponding to the m absorption peak positions of the test frequency domain signal and obtain the horizontal axis position P of the absorption peak. test (m); (3.3) Calculate the sum of the differences between the m corresponding absorption peaks of the test frequency domain signal and the standard frequency domain signal using the following formula, and use it as the error function. Set the convergence condition for the error function:

4. The terahertz time-domain signal horizontal axis matching method based on material absorption spectrum as described in claim 3, characterized in that, The specific process of step five is as follows: Through the optimized time-domain equivalent sampling interval τ best The equivalent sampling range τ′ in the frequency domain is calculated. best =1 / (2τ) best Combined with the number of sampling points N, the matched time-domain horizontal axis X is calculated using the following formula. time-domain and frequency domain horizontal axis X frequency-domain : X time-domain =(0,τ best ,2t best ,3t best ,...,Nt best ) Based on this, the time-domain signal and frequency-domain signal after absorption peak matching are obtained.

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