Multi-layer medium optical parameter iterative extraction method and system

Abstract

The invention discloses a multilayer medium optical parameter iterative extraction method and system, and the method comprises the steps: receiving a terahertz pulse signal, and carrying out the preprocessing of the terahertz pulse signal, so as to obtain a frequency spectrum of a main reflection peak at an interface of each layer of medium in the terahertz pulse signal; obtaining a reference frequency spectrum of an ideal reflecting surface corresponding to the interface of each layer of medium, and calculating the ratio of the frequency spectrum of the main reflection peak at the interface of each layer of medium to the reference frequency spectrum of the corresponding ideal reflecting surface to obtain a reflection coefficient corresponding to each layer of medium; calculating a complex refractive index corresponding to each layer of medium according to the reflection coefficient corresponding to each layer of medium; and obtaining a time interval between adjacent pulse echoes in each layer of medium, and calculating the thickness of the corresponding medium layer according to the complex refractive index corresponding to each layer of medium and the time interval. According to the method and the system, the complex refractive index and the geometric thickness of the multilayer medium can be effectively extracted, and the calculation precision is improved through iterative optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of terahertz time-domain spectroscopy, and in particular to a method and system for iteratively extracting optical parameters of a multilayer medium. Background Art

[0002] Terahertz time-domain spectroscopy (THz-TDS) is a technology used to detect and analyze electromagnetic waves in the terahertz frequency range (0.1-10THz). Existing terahertz time-domain spectroscopy systems are mainly divided into two types: transmission and reflection. Transmission systems have been widely studied and applied in recent years, but for non-transparent samples or small-sized samples, reflection systems have unique advantages. Reflection systems can detect detailed information such as microstructure and defects on the surface of materials and have high spatial resolution.

[0003] However, existing reflective terahertz time-domain spectroscopy systems have certain limitations when extracting optical parameters of multilayer media. Existing methods are usually only applicable to the calculation of single-layer materials. For multilayer materials, the Fresnel equations are more complicated, and the subjective elimination of high-order reflection terms may cause additional errors. In addition, the existing methods do not consider the absorption of the medium during the calculation process, resulting in differences between the calculated results and the experimental results. Summary of the invention

[0004] In order to solve the technical problems existing in the background technology, the present invention proposes a method and system for iteratively extracting optical parameters of a multilayer medium.

[0005] The present invention proposes a method for iteratively extracting optical parameters of a multilayer medium, comprising the following steps: S1, receiving a terahertz pulse signal, and preprocessing the terahertz pulse signal to obtain a spectrum of a main reflection peak at an interface of each layer of the medium in the terahertz pulse signal; S2, obtaining the reference spectrum of the ideal reflection surface corresponding to each layer of the medium interface, and calculating the ratio of the spectrum of the main reflection peak at each layer of the medium interface to the reference spectrum of the corresponding ideal reflection surface to obtain the reflection coefficient corresponding to each layer of the medium; S3, calculating the complex refractive index corresponding to each layer of the medium according to the reflection coefficient corresponding to each layer of the medium; S4. Obtain the time interval between adjacent pulse echoes in each layer of the medium, and calculate the thickness of the corresponding medium layer according to the complex refractive index corresponding to each layer of the medium and the time interval.

[0006] Preferably, it also includes: S5. Extract corresponding optical parameters from the complex refractive index of each layer of the medium, iteratively optimize the optical parameters by gradient descent method, and iteratively update the thickness of the corresponding medium layer until the loss function converges to a preset threshold value. The optical parameters are specifically the real part n and the imaginary part k of the complex refractive index.

[0007] Preferably, the preprocessing specifically includes: After the received terahertz pulse signal is reflected by the multi-layer medium, a measured signal containing internal information of the multi-layer medium is obtained; Use Hanning window to design bandpass filter to extract the spectrum of impulse response function of the measured signal; The high-frequency noise in the spectrum of the impulse response function is removed by combining the stationary wavelet transform (SWT) and the Symlet wavelet to reconstruct the impulse response function and obtain the restored time domain spectrum. The reflection peaks of the measured signal at the interfaces of each layer of the medium are extracted from the restored time domain spectrum to obtain the spectrum of the main reflection peaks at the interfaces of each layer of the medium.

[0008] Preferably, the step of obtaining a reference spectrum of an ideal reflection surface corresponding to each medium interface comprises:

[0009] In the formula, when total reflection occurs at the interface between the kth layer and the k+1th layer of medium, represents the transmission coefficient into the next layer; Indicates the transmission coefficient of the previous layer returned; represents the reflection spectrum of the metal plate; The reference spectrum represents the ideal reflection surface of the k-th and k+1-th layers of the medium; is the thickness of the air layer; c is the speed of light; is the thickness of the i-th layer; is the wave vector.

[0010] Preferably, the ratio of the spectrum of the main reflection peak at the interface of each layer of medium to the reference spectrum of the corresponding ideal reflection surface is calculated to obtain the reflection coefficient corresponding to each layer of medium, which specifically includes: Get the spectrum of the main reflection peak at the interface between the kth layer and the k+1th layer of medium ; The spectrum of the main reflection peak at the interface between the kth layer and the k+1th layer medium is Reference spectrum with ideal reflecting surface Calculating the ratio, we can get the reflection coefficient of the interface between the kth layer and the k+1th layer of medium. .

[0011] Preferably, step S3 specifically includes: The numerical relationship between the reflection coefficient corresponding to each layer of medium and the complex refractive index corresponding to each layer of medium is specifically: ; in, is the reflection coefficient at the interface between the kth and k+1th layers of media; is the complex refractive index corresponding to the kth layer; is the complex refractive index corresponding to the k+1th layer.

[0012] Preferably, calculating the thickness of the corresponding medium layer according to the complex refractive index corresponding to each layer of the medium and the time interval specifically includes: ; in, is the time interval passing through the kth layer of medium; is the refractive index of the kth medium at the center frequency of the THz pulse, that is, the real part of the complex refractive index of the kth medium.

[0013] The present invention proposes a multi-layer medium optical parameter iterative extraction system, comprising: The first processing module is used to receive a terahertz pulse signal and pre-process the terahertz pulse signal to obtain a spectrum of a main reflection peak at each medium interface in the terahertz pulse signal; The second processing module is used to obtain the reference spectrum of the ideal reflection surface corresponding to each layer of the medium interface, and calculate the ratio of the spectrum of the main reflection peak at each layer of the medium interface to the reference spectrum of the corresponding ideal reflection surface to obtain the reflection coefficient corresponding to each layer of the medium; An optical parameter extraction module is used to calculate the complex refractive index corresponding to each layer of the medium according to the reflection coefficient corresponding to each layer of the medium; The optical parameter extraction module is also used to obtain the time interval between adjacent pulse echoes in each layer of the medium, and calculate the thickness of the corresponding medium layer according to the complex refractive index corresponding to each layer of the medium and the time interval.

[0014] Preferably, it also includes: The optimization module is used to extract the corresponding optical parameters from the complex refractive index of each layer of the medium, iteratively optimize the optical parameters by gradient descent method, and iteratively update the thickness of the corresponding medium layer until the loss function converges to a preset threshold.

[0015] In the present invention, the proposed method and system for iterative extraction of optical parameters of multilayer media include: receiving a terahertz pulse signal, and preprocessing the terahertz pulse signal to obtain the spectrum of the main reflection peak at the interface of each layer of media in the terahertz pulse signal; obtaining the reference spectrum of the ideal reflection surface corresponding to the interface of each layer of media, and respectively calculating the ratio of the spectrum of the main reflection peak at the interface of each layer of media with the reference spectrum of the corresponding ideal reflection surface to obtain the reflection coefficient corresponding to each layer of media; calculating the complex refractive index corresponding to each layer of media according to the reflection coefficient corresponding to each layer of media; obtaining the time interval between adjacent pulse echoes in each layer of media, and calculating the thickness of the corresponding medium layer according to the complex refractive index corresponding to each layer of media and the time interval. The optical parameters are iteratively optimized by the gradient descent method until the loss function converges to a preset threshold. The complex refractive index and geometric thickness of the multilayer media can be effectively extracted, and the calculation accuracy is improved through iterative optimization. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 A schematic diagram of the work flow structure of a multi-layer medium optical parameter iterative extraction method proposed by the present invention; Figure 2 A refractive index distribution diagram of the second layer of medium before optimization in a multi-layer medium optical parameter iterative extraction method proposed by the present invention; Figure 3 It is a refractive index distribution diagram of the second layer of medium after optimization in a multi-layer medium optical parameter iterative extraction method proposed by the present invention; Figure 4 A distribution diagram of the extinction coefficient of the second layer before optimization of an iterative extraction method of optical parameters of a multi-layer medium proposed by the present invention; Figure 5 This is a distribution diagram of the extinction coefficient of the second layer after optimization of the iterative extraction method of optical parameters of a multi-layer medium proposed by the present invention; Figure 6 A schematic diagram of the system architecture of a multi-layer medium optical parameter iterative extraction system proposed in the present invention. DETAILED DESCRIPTION

[0017] Reference Figure 1-6 The present invention proposes an iterative extraction method for optical parameters of a multilayer medium, comprising the following steps: S1. Receive a terahertz pulse signal and pre-process the terahertz pulse signal to obtain a spectrum of a main reflection peak at an interface between each layer of the medium in the terahertz pulse signal.

[0018] In this embodiment, before calculating the optical parameters, spectrum preprocessing is performed first, and then the position of the reflection peak of the terahertz wave at the interface between two media is extracted.

[0019] In this embodiment, the preprocessing specifically includes: After the received terahertz pulse signal is reflected by the multi-layer medium, a measured signal containing internal information of the multi-layer medium is obtained; Use Hanning window to design bandpass filter to extract the spectrum of impulse response function of the measured signal; The high-frequency noise in the spectrum of the impulse response function is removed by combining the stationary wavelet transform (SWT) and the Symlet wavelet to reconstruct the impulse response function and obtain the restored time domain spectrum. The reflection peaks of the measured signal at the interfaces of each layer of the medium are extracted from the restored time domain spectrum to obtain the spectrum of the main reflection peaks at the interfaces of each layer of the medium.

[0020] Specifically, ;in, represents the convolution operation, h(t) is the impulse response function; is the terahertz pulse signal; is the measured signal.

[0021] According to the time domain convolution theorem, the time domain response function can be obtained by the following formula: ; Where FT is Fourier transform, is the inverse Fourier transform. Since the FFT algorithm only transforms signals of finite length, spectrum leakage will occur. Generally, a window function is used to reduce spectrum leakage. The present invention uses a Hanning window, and the form of the Hanning window function in the frequency domain is as follows: ; The starting frequency is , the cut-off frequency is .

[0022] The present invention uses the Symlet wavelet function to perform stationary wavelet transform (SWT) on the signal. The formulas for wavelet decomposition and reconstruction are as follows: ; Among them, SWT is wavelet transform, cA is the approximation coefficient, cD is the detail coefficient, and the threshold function is used. Remove coefficients with smaller absolute values ​​and then use the function The signal is reconstructed to improve the signal-to-noise ratio.

[0023] When the medium is a multi-layer uniform structure, different interfaces will generate reflection signals. Let the reflection signal be , and perform Fourier transform on it to get the following formula: ; In the formula, represents the spectrum of a terahertz pulse; is the frequency response function of the pulse propagating in the multilayer medium; An interface function that represents refraction or reflection at an interface.

[0024] S2. Obtain the reference spectrum of the ideal reflection surface corresponding to each layer of the medium interface, and calculate the ratio of the spectrum of the main reflection peak at each layer of the medium interface to the reference spectrum of the corresponding ideal reflection surface to obtain the reflection coefficient corresponding to each layer of the medium.

[0025] In this embodiment, the spectrum from each reflection surface inside the sample can be expressed by the following formula: ; Assuming that there is an ideal total reflection surface between each layer in the sample, we get:

[0026] In the formula, when total reflection occurs at the interface between the kth layer and the k+1th layer of medium, represents the transmission coefficient into the next layer; Indicates the transmission coefficient of the previous layer returned; represents the reflection spectrum of the metal plate; The reference spectrum represents the ideal reflection surface of the k-th and k+1-th layers of the medium; is the thickness of the air layer; c is the speed of light; is the thickness of the i-th layer; is the wave vector.

[0027] From this we can get, .

[0028] In this embodiment, the spectrum of the main reflection peak at the interface of each layer of the medium is respectively compared with the reference spectrum of the corresponding ideal reflection surface to obtain the reflection coefficient corresponding to each layer of the medium, which specifically includes: Get the spectrum of the main reflection peak at the interface between the kth layer and the k+1th layer of medium ; The spectrum of the main reflection peak at the interface between the kth layer and the k+1th layer medium is Reference spectrum with ideal reflecting surface Calculating the ratio, we can get the reflection coefficient of the interface between the kth layer and the k+1th layer of medium. .

[0029] S3. Calculate the complex refractive index corresponding to each layer of the medium according to the reflection coefficient corresponding to each layer of the medium.

[0030] In this embodiment, step S3 specifically includes: The numerical relationship between the reflection coefficient corresponding to each layer of medium and the complex refractive index corresponding to each layer of medium is specifically: ; The iterative formula for the complex refractive index obtained from the above formula is as follows: ; in, is the reflection coefficient at the interface between the kth and k+1th layers of media; is the complex refractive index corresponding to the kth layer; is the complex refractive index corresponding to the k+1th layer. ; The macroscopic optical properties of a sample are generally described by complex refractive index, where n is the real refractive index and k is the extinction coefficient. c represents the propagation speed of THz electromagnetic waves in a vacuum. The initial values ​​of the sample's refractive index and extinction coefficient are calculated according to the above process, where: Figure 2 and Figure 3 are the calculated results of the refractive index coefficient and extinction coefficient of the second layer of medium before optimization, Figure 4 and Figure 5 They are the calculation results of the refractive index coefficient and extinction coefficient of the second layer of medium after optimization.

[0031] S4. Obtain the time interval between adjacent pulse echoes in each layer of the medium, and calculate the thickness of the corresponding medium layer according to the complex refractive index and time interval corresponding to each layer of the medium.

[0032] In this embodiment, the thickness of the corresponding medium layer is calculated according to the complex refractive index and time interval corresponding to each layer of the medium, specifically including: ; in, is the time interval passing through the kth layer of medium; is the refractive index of the kth medium at the center frequency of the THz pulse, that is, the real part of the complex refractive index of the kth medium.

[0033] S5. Extract the corresponding optical parameters from the complex refractive index of each layer of the medium, iteratively optimize the optical parameters by gradient descent method, and iteratively update the thickness of the corresponding medium layer until the loss function converges to a preset threshold.

[0034] In this embodiment, in order to verify the accuracy of the optical parameters, the propagation process of electromagnetic waves being refracted or reflected in a multilayer medium is simulated.

[0035] In this embodiment, in order to quantitatively measure the accuracy of the optical parameters, the L1 norm of the simulated spectrum and the experimental spectrum is used as the loss function. The loss function directly characterizes the difference between the spectra and is used to evaluate the accuracy of the optical parameters. The loss function is specifically:

[0036] In the formula, let n and k be optimization parameters, and the learning rate decay strategy is used in the gradient descent method to find the optimal solution. The geometric thickness of the medium is continuously updated after each iteration and does not directly participate in the optimization.

[0037] In this embodiment, the initial values ​​of the refractive index coefficient and the extinction coefficient are calculated according to a given algorithm.

[0038] After the signal and the calculated optical parameters are input into the simulation program, the simulation results can be obtained. The waveform is quite different from the experimental data, and the loss function is 0.007. After the reference signal and the optimized optical parameters are input into the simulation program, the simulation results can be obtained, and the loss function is reduced to 0.0003.

[0039] Reference Figure 1-6 The present invention proposes a multi-layer medium optical parameter iterative extraction system, comprising: The first processing module is used to receive a terahertz pulse signal and pre-process the terahertz pulse signal to obtain a spectrum of a main reflection peak at each medium interface in the terahertz pulse signal; The second processing module is used to obtain the reference spectrum of the ideal reflection surface corresponding to each layer of the medium interface, and calculate the ratio of the spectrum of the main reflection peak at each layer of the medium interface to the reference spectrum of the corresponding ideal reflection surface to obtain the reflection coefficient corresponding to each layer of the medium; An optical parameter extraction module is used to calculate the complex refractive index corresponding to each layer of the medium according to the reflection coefficient corresponding to each layer of the medium; The optical parameter extraction module is also used to obtain the time interval between adjacent pulse echoes in each layer of the medium, and calculate the thickness of the corresponding medium layer according to the complex refractive index and time interval corresponding to each layer of the medium.

[0040] The optimization module is used to extract the corresponding optical parameters from the complex refractive index of each layer of the medium, iteratively optimize the optical parameters through the gradient descent method, and iteratively update the thickness of the corresponding medium layer until the loss function converges to a preset threshold.

[0041] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for iteratively extracting optical parameters of a multilayer medium, characterized in that: The following steps are involved: S1, receiving a terahertz pulse signal, and preprocessing the terahertz pulse signal to obtain a spectrum of a main reflection peak at an interface of each layer of the medium in the terahertz pulse signal; S2, obtaining the reference spectrum of the ideal reflection surface corresponding to each layer of the medium interface, and calculating the ratio of the spectrum of the main reflection peak at each layer of the medium interface to the reference spectrum of the corresponding ideal reflection surface to obtain the reflection coefficient corresponding to each layer of the medium; S3, calculating the complex refractive index corresponding to each layer of the medium according to the reflection coefficient corresponding to each layer of the medium; S4. Obtain the time interval between adjacent pulse echoes in each layer of the medium, and calculate the thickness of the corresponding medium layer according to the complex refractive index corresponding to each layer of the medium and the time interval.

2. The method for iteratively extracting optical parameters of a multilayer medium according to claim 1, characterized in that: Also includes: S5. Extract corresponding optical parameters from the complex refractive index of each layer of the medium, iteratively optimize the optical parameters by gradient descent method, and iteratively update the thickness of the corresponding medium layer until the loss function converges to a preset threshold value. The optical parameters are specifically the real part n and the imaginary part k of the complex refractive index.

3. The method for iteratively extracting optical parameters of a multilayer medium according to claim 1, characterized in that: The pre-processing specifically includes: After the received terahertz pulse signal is reflected by the multi-layer medium, a measured signal containing internal information of the multi-layer medium is obtained; Use Hanning window to design bandpass filter to extract the spectrum of impulse response function of the measured signal; The high-frequency noise in the spectrum of the impulse response function is removed by combining the stationary wavelet transform (SWT) and the Symlet wavelet to reconstruct the impulse response function and obtain the restored time domain spectrum. The reflection peaks of the measured signal at the interfaces of each layer of the medium are extracted from the restored time domain spectrum to obtain the spectrum of the main reflection peaks at the interfaces of each layer of the medium.

4. The method for iteratively extracting optical parameters of a multilayer medium according to claim 1, characterized in that: The step of obtaining a reference spectrum of an ideal reflection surface corresponding to each layer of the medium interface specifically includes: In the formula, when total reflection occurs at the interface between the kth layer and the k+1th layer of medium, represents the transmission coefficient into the next layer; Indicates the transmission coefficient of the previous layer returned; represents the reflection spectrum of the metal plate; The reference spectrum represents the ideal reflection surface of the k-th and k+1-th layers of the medium; is the thickness of the air layer; c is the speed of light; is the thickness of the i-th layer; is the wave vector.

5. The method for iteratively extracting optical parameters of a multilayer medium according to claim 1, characterized in that: The ratio of the spectrum of the main reflection peak at the interface of each layer of medium is calculated with the reference spectrum of the corresponding ideal reflection surface to obtain the reflection coefficient corresponding to each layer of medium, specifically including: Get the spectrum of the main reflection peak at the interface between the kth layer and the k+1th layer of medium ; The spectrum of the main reflection peak at the interface between the kth layer and the k+1th layer medium is Reference spectrum with ideal reflecting surface Calculating the ratio, we can get the reflection coefficient of the interface between the kth layer and the k+1th layer of medium. .

6. The method for iteratively extracting optical parameters of a multilayer medium according to claim 1, characterized in that: Step S3 specifically includes: The numerical relationship between the reflection coefficient corresponding to each layer of medium and the complex refractive index corresponding to each layer of medium is specifically: ； The iterative formula for the complex refractive index obtained from the above formula is as follows: ; in, is the reflection coefficient at the interface between the kth and k+1th layers of media; is the complex refractive index corresponding to the kth layer; is the complex refractive index corresponding to the k+1th layer.

7. The method for iteratively extracting optical parameters of a multilayer medium according to claim 1, characterized in that: The step of calculating the thickness of the corresponding medium layer according to the complex refractive index corresponding to each layer of the medium and the time interval specifically includes: ; in, is the time interval passing through the kth layer of medium; is the refractive index of the kth medium at the center frequency of the THz pulse, that is, the real part of the complex refractive index of the kth medium.

8. A multi-layer medium optical parameter iterative extraction system, characterized in that: include: The first processing module is used to receive a terahertz pulse signal and pre-process the terahertz pulse signal to obtain a spectrum of a main reflection peak at each medium interface in the terahertz pulse signal; The second processing module is used to obtain the reference spectrum of the ideal reflection surface corresponding to each layer of the medium interface, and calculate the ratio of the spectrum of the main reflection peak at each layer of the medium interface to the reference spectrum of the corresponding ideal reflection surface to obtain the reflection coefficient corresponding to each layer of the medium; An optical parameter extraction module is used to calculate the complex refractive index corresponding to each layer of the medium according to the reflection coefficient corresponding to each layer of the medium; The optical parameter extraction module is also used to obtain the time interval between adjacent pulse echoes in each layer of the medium, and calculate the thickness of the corresponding medium layer according to the complex refractive index corresponding to each layer of the medium and the time interval.

9. The multi-layer medium optical parameter iterative extraction system according to claim 8, characterized in that: Also includes: The optimization module is used to extract the corresponding optical parameters from the complex refractive index of each layer of the medium, iteratively optimize the optical parameters by the gradient descent method, and iteratively update the thickness of the corresponding medium layer until the loss function converges to a preset threshold. The optical parameters are specifically the real part n and the imaginary part k of the complex refractive index.

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