Anisotropic transparent material measurement methods, systems, apparatus, and storage media

Abstract

The application discloses a kind of anisotropic transparent material measurement method, system, device and storage medium, method includes establishing the optical theoretical model of sample to be measured;The transparent substrate formed by anisotropic transparent material is included in sample to be measured, and the multiple reflection light from the front surface and back surface between transparent substrate is incoherent light;Based on back reflection incoherent light superposition theory, the optical theoretical model is handled, and the theoretical Mueller matrix of sample to be measured is deduced;The measured Mueller matrix of sample to be measured is obtained, and the theoretical Mueller matrix and measured Mueller matrix are inversed and fitted, and the measurement result of sample to be measured is obtained.The application can effectively process incoherent back reflection light, and then the thickness parameter of anisotropic transparent material and complete optical tensor information can be accurately obtained, the measurement precision and inversion stability are significantly improved, with higher measurement reliability and practical value.

Description

Technical Field

[0001] This invention relates to the field of materials measurement technology, and specifically to a method, system, device, and storage medium for measuring anisotropic transparent materials. Background Technology

[0002] Optical ellipsometric measurement is a non-contact, high-precision measurement method that obtains parameters such as thin film thickness and optical constants (e.g., refractive index and extinction coefficient) by analyzing the change in polarization state of light waves after reflection or transmission on the sample surface. It has wide applications in semiconductors, optical coatings, materials science and other fields.

[0003] Anisotropic materials are those whose physical properties (including optical properties) vary with spatial orientation. Common examples include anisotropic transparent crystals, which exhibit properties such as birefringence and optical rotation. (Birefringence refers to the phenomenon where light propagating in a material is decomposed into two linearly polarized beams with different refractive indices due to different propagation directions, resulting in an optical path difference; optical rotation refers to the phenomenon where the vibration plane of linearly polarized light rotates after passing through the material.) The optical constants (such as refractive index and extinction coefficient) of such materials need to be fully described in the form of optical tensors, and their measurement is much more difficult than that of isotropic materials.

[0004] Currently, optical measurement techniques for anisotropic materials are mainly based on ellipsometrics. Traditional ellipsometric measurement models are typically based on the "semi-infinite substrate" approximation. This model is applicable to most substrates because substrate materials usually exhibit non-zero absorption, and their thickness is sufficiently large (e.g., hundreds of micrometers). This causes reflected light from the back of the substrate to be completely absorbed by the substrate material and unable to reach the detector as incident light propagates within the substrate. Therefore, the signal received by the detector originates only from a single reflection from the front surface of the sample (i.e., the incident interface), greatly simplifying the model. This approximation is valid for most substrates with intrinsic absorption or thick absorption layers (such as silicon wafers and common semiconductor substrates).

[0005] However, when the anisotropic material is anisotropic transparent crystal (such as sapphire, quartz, magnesium fluoride, etc.), its absorbance is approximately zero, and it absorbs almost no light. When the substrate thickness (usually several hundred micrometers) is greater than the coherence length of the light source, the "semi-infinite substrate" approximation model of traditional ellipsometric measurement technology will no longer be applicable. The defects and shortcomings of the existing technology will be significantly amplified. Specifically, the multiple reflections from the back of the substrate (reflected light from the back of the substrate, referred to as back reflection light) become incoherent due to the large optical path difference. Since the substrate is transparent and has no absorption properties, all these incoherent reflections will penetrate the substrate and enter the detector, superimposing with the reflected light from the sample surface. The traditional ellipsometric measurement technology, based on the "single reflection" measurement model, cannot effectively process these incoherent back reflections, causing significant interference to the measurement signal. This leads to measurement errors in sample thickness and optical constants, failing to meet the high-precision measurement requirements of anisotropic transparent crystals.

[0006] Therefore, the existing technology lacks an ellipsometric measurement theory and method that can specifically handle incoherent back reflection light in transparent anisotropic substrates, making it difficult to achieve high-precision and integrated measurement of the thickness and complete optical tensor of such materials. Summary of the Invention

[0007] In view of this, the present invention provides a method, system, device and storage medium for measuring anisotropic materials, in order to solve the problem in existing ellipsometric measurement technology that the inability to effectively process incoherent back-reflected light leads to the inability to accurately obtain the thickness parameters and complete optical tensor information of anisotropic transparent materials.

[0008] This invention provides a method for measuring anisotropic transparent materials, the method comprising: An optical theoretical model is established for the sample under test during the ellipsometric measurement process; wherein, the sample under test includes a transparent substrate formed of anisotropic transparent material, and in the optical theoretical model, the multiple reflected light from the front surface and the back surface of the transparent substrate is incoherent light; Based on the theory of superposition of incoherent back-reflection light, the optical theoretical model is processed to derive the theoretical Mueller matrix of the sample under test in the optical theoretical model. The measured Mueller matrix of the sample under test during the ellipsometric measurement process is obtained, and the theoretical Mueller matrix and the measured Mueller matrix are inverted and fitted to obtain the measurement result of the sample under test; wherein, the measurement result includes at least the thickness information and optical tensor information of the transparent substrate.

[0009] Optionally, the optical theoretical model includes three dielectric layers: an incident medium, an intra-substrate medium, and an exit medium. Based on the theory of superposition of incoherent back-reflected light, the optical theoretical model is processed to derive the theoretical Mueller matrix of the sample under test in the optical theoretical model, including: Using Euler angle transformation, the dielectric tensor of each dielectric layer in the optical theoretical model in the sample principal axis coordinate system is obtained; Based on the dielectric tensor of each dielectric layer in the principal axis coordinate system of the sample, the eigenvector matrix and eigenvalue matrix characterizing the light propagation properties of the corresponding dielectric layer are obtained respectively. Based on the eigenvector matrices of all dielectric layers, the reflection coefficient matrix and transmission coefficient matrix at each dielectric interface in the optical theoretical model are calculated respectively; and based on the eigenvalue matrix corresponding to the dielectric in the substrate, the single-layer film transfer matrix of the dielectric in the substrate is calculated. By using the single-layer film transfer matrix of the medium within the substrate and the reflection and transmission coefficient matrices at all medium interfaces, incoherent light superposition is performed to obtain the theoretical Mueller matrix in the optical theoretical model.

[0010] Optionally, based on the dielectric tensor of each dielectric layer in the principal axis coordinate system of the sample, the eigenvector matrix and eigenvalue matrix characterizing the light propagation properties of the corresponding dielectric layer are solved, including: Choose any dielectric layer and construct the generalized material matrix of the sample under test in the optical theoretical model based on the permittivity tensor of the selected dielectric layer in the principal axis coordinate system of the sample. Using the generalized material matrix, the Berreman differential transfer matrix of the corresponding dielectric layer is solved; The Berreman differential transfer matrix is ​​decomposed into eigenvectors, which are composed of the eigenvectors of the Berreman differential transfer matrix, and the corresponding eigenvalue matrix is ​​composed of the eigenvalues ​​of the Berreman differential transfer matrix.

[0011] Optionally, for any chosen dielectric layer, the expression for the corresponding generalized material matrix is ​​as follows: ; in, For the selected generalized material matrix of the dielectric layer, This represents the dielectric tensor of the selected medium in the principal axis coordinate system of the sample. and The optical rotation tensor of the selected dielectric layer, Let be the permeability tensor of the selected dielectric layer; In each medium layer, the corresponding eigenvector matrix is ​​specifically a column vector matrix composed of the eigenvectors of the corresponding Berreman differential transfer matrix; the corresponding eigenvalue matrix is ​​specifically a diagonal matrix.

[0012] Optionally, for the selected dielectric layer, the corresponding generalized material matrix is ​​specifically a 6×6 dimensional matrix, and the corresponding Berreman differential transfer matrix is ​​specifically a 4×4 dimensional matrix, and the expression for each element in the corresponding Berreman differential transfer matrix is: ; in, , ,...and For each element in the Berreman differential transfer matrix corresponding to the selected medium layer, , ,...and For each element in the generalized material matrix corresponding to the selected dielectric layer, The transverse wave vector component of the selected dielectric layer; a 3n and a 6n These are the first and second auxiliary vectors corresponding to the selected medium layer, respectively; n is the number of columns of the first and second auxiliary vectors; and b is the determinant factor corresponding to the selected medium layer. The first auxiliary vector a corresponding to the selected dielectric layer 3n Second auxiliary vector a 6n The expressions are as follows: ; ; The specific expression for the determinant factor b corresponding to the selected dielectric layer is as follows: .

[0013] Optionally, the reflection coefficient matrix at each medium interface includes a first reflection coefficient matrix from the incident medium incident to the front surface of the medium inside the substrate and reflected from the front surface of the medium inside the substrate, a second reflection coefficient matrix from the front surface of the medium inside the substrate incident to the back surface of the medium inside the substrate and reflected from the back surface of the medium inside the substrate, and a third reflection coefficient matrix from the back surface of the medium inside the substrate incident to the front surface of the medium inside the substrate and reflected from the front surface of the medium inside the substrate. The transmission coefficient matrix at each medium interface includes a first transmission coefficient matrix from the incident medium incident to the front surface of the medium inside the substrate and transmitted to the back surface of the medium inside the substrate, a second transmission coefficient matrix from the front surface of the medium inside the substrate incident to the back surface of the medium inside the substrate and transmitted to the exit medium, and a third transmission coefficient matrix from the back surface of the medium inside the substrate incident to the front surface of the medium inside the substrate and transmitted to the incident medium. Based on the eigenvector matrices of all dielectric layers, the reflection coefficient matrix and transmission coefficient matrix at each dielectric interface in the optical theoretical model are calculated, including: Based on the eigenvector matrix corresponding to the incident medium and the eigenvector matrix corresponding to the medium inside the substrate, the first reflection coefficient matrix, the first transmission coefficient matrix, the third reflection coefficient matrix and the third transmission coefficient matrix are calculated respectively. The second reflection coefficient matrix and the second transmission coefficient matrix are calculated based on the eigenvector matrix corresponding to the medium inside the substrate and the eigenvector matrix corresponding to the emitted medium.

[0014] Optionally, the formulas for calculating the first reflection coefficient matrix and the first transmission coefficient matrix are as follows: ; in, and These are the first reflection coefficient matrix and the first transmission coefficient matrix, respectively. Let be the eigenvector matrix of the incident medium. This is an inverse matrix operation. The eigenvector matrix of the dielectric within the substrate. , , and The first product matrix The top left matrix sub-block, top right matrix sub-block, bottom left matrix sub-block, and bottom right matrix sub-block in the matrix; The formulas for calculating the second reflection coefficient matrix and the second transmission coefficient matrix are as follows: ; in, and These are the second reflection coefficient matrix and the second transmission coefficient matrix, respectively. Let be the eigenvector matrix of the exiting medium. , , and The second product matrix The top left matrix sub-block, top right matrix sub-block, bottom left matrix sub-block, and bottom right matrix sub-block in the matrix; The formulas for calculating the third reflection coefficient matrix and the third transmission coefficient matrix are as follows: ; in, and These are the third reflection coefficient matrix and the third transmission coefficient matrix, respectively. , , and The third product matrix The top left matrix sub-block, top right matrix sub-block, bottom left matrix sub-block, and bottom right matrix sub-block.

[0015] Optionally, the monolayer film transfer matrix corresponding to the dielectric in the substrate includes a forward transfer matrix and a reverse transfer matrix; The specific formulas for calculating the forward and reverse transfer matrices corresponding to the dielectric within the substrate are as follows: ; Among them, P + and P - These are the forward transfer matrix and the reverse transfer matrix corresponding to the dielectric within the substrate, respectively. q is the diagonal element of the j-th row in the eigenvalue matrix corresponding to the dielectric within the substrate. j Let be the j-th eigenvalue of the Berreman differential transfer matrix corresponding to the medium in the substrate, and j satisfies j=1,2,3,4; k0 is the vacuum wavenumber, d is the physical thickness of the medium in the substrate, and i is the imaginary unit.

[0016] Optionally, by using the monolayer transfer matrix of the dielectric within the substrate and the reflection and transmission coefficient matrices at all dielectric interfaces, incoherent light superposition is performed to obtain the theoretical Mueller matrix in the optical theoretical model, including: Based on the reflection coefficient matrix at all media interfaces and the monolayer film transfer matrix of the medium within the substrate, the round-trip operator for one round trip in the medium within the substrate is calculated. Based on the single-layer film transfer matrix, the round-trip operator, and the reflection coefficient matrix and transmission coefficient matrix at all media interfaces, the Jones matrix of each reflection path in the optical theoretical model is calculated. Using the Kronecker product operation, the Jones matrix of each reflection path is converted into the corresponding coherence matrix; The total coherence matrix is ​​obtained from the coherence matrices of all reflection paths, and the total coherence matrix is ​​transformed to obtain the theoretical Mueller matrix.

[0017] Optionally, the formula for calculating the round-trip operator is as follows: ; in, For round-trip operators; The formula for calculating the theoretical Mueller matrix is ​​as follows: ; Where M is the theoretical Mueller matrix, C total Let A be the total coherence matrix and A be the preset transformation matrix.

[0018] Optionally, the theoretical Mueller matrix and the measured Mueller matrix are inverted and fitted to obtain the measurement results of the sample to be tested, including: Based on the thickness information and optical tensor information of the transparent substrate, a set of parameters to be fitted is constructed; Define the difference function between the theoretical Mueller matrix and the measured Mueller matrix; The set of parameters to be fitted is adjusted using an iterative optimization method to minimize the difference function, and the parameter values ​​corresponding to the set of parameters to be fitted that minimize the difference function are determined as the measurement results.

[0019] Furthermore, the present invention also provides an anisotropic transparent material measurement system, applied in the aforementioned anisotropic transparent material measurement method, the system comprising: The model building module is used to establish an optical theoretical model of the sample under test during the ellipsometric measurement process; wherein, the sample under test includes a transparent substrate formed of anisotropic transparent material, and in the optical theoretical model, the multiple reflected light from the front surface and the back surface of the transparent substrate is incoherent light; The theoretical derivation module is used to process the optical theoretical model based on the theory of superposition of back-reflection incoherent light and derive the theoretical Mueller matrix of the sample under test in the optical theoretical model. The inversion fitting module is used to obtain the measured Mueller matrix of the sample under test during the ellipsometric measurement process, and to perform inversion fitting between the theoretical Mueller matrix and the measured Mueller matrix to obtain the measurement result of the sample under test; wherein, the measurement result includes at least the thickness information and optical tensor information of the transparent substrate.

[0020] Furthermore, the present invention also provides an anisotropic transparent material measurement device, including a processor, a memory, and a computer program stored in the memory and executable on the processor. When the computer program is executed, it implements the method steps in the aforementioned anisotropic transparent material measurement method.

[0021] Furthermore, the present invention also provides a computer storage medium comprising: at least one instruction that, when executed by a computer, implements the method steps in the aforementioned anisotropic transparent material measurement method.

[0022] The beneficial effects of this invention are as follows: The sample to be tested includes a transparent substrate formed of anisotropic transparent material. First, an optical theoretical model of the sample during ellipsometric measurement is constructed. This model takes into account that the multiple reflections between the front and back surfaces of the transparent substrate are incoherent, which is more in line with the actual measurement situation. Subsequent theoretical derivation and inversion fitting based on this model can provide a more reliable model foundation. After establishing the optical theoretical model, the theoretical Mueller matrix of the sample to be tested in the optical theoretical model can be obtained based on the theory of superposition of incoherent back reflection light. This fully considers the characteristics of each dielectric layer and the propagation law of light in it, making the theoretical derivation more rigorous and accurate. Then, the derived theoretical Mueller matrix is ​​inverted and fitted with the measured Mueller matrix, which can simultaneously and accurately obtain the thickness parameters of the anisotropic transparent substrate or crystal material and complete optical tensor information. The anisotropic transparent material measurement method, system, device, and storage medium of the present invention can effectively process incoherent back-reflected light, thereby accurately obtaining the thickness parameters and complete optical tensor information of anisotropic transparent materials. It provides a complete solution for the measurement of anisotropic transparent materials, significantly improves measurement accuracy and inversion stability, expands the application scope of Mueller matrix ellipticization technology in the characterization of thick transparent anisotropic materials, and has higher measurement reliability and practical value. Attached Figure Description

[0023] The features and advantages of the invention will be more clearly understood by referring to the accompanying drawings, which are schematic and should not be construed as limiting the invention in any way. In the drawings: Figure 1 A flowchart of a method for measuring anisotropic transparent materials according to Embodiment 1 of the present invention is shown; Figure 2 The optical path diagram of the optical theoretical model in Embodiment 1 of the present invention is shown; Figure 3 A structural diagram of an anisotropic transparent material measurement system according to Embodiment 2 of the present invention is shown. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0025] In this embodiment of the invention, the term "and / or" describes the relationship between associated objects, indicating that three relationships can exist. For example, A and / or B can represent: A existing alone, A and B existing simultaneously, or B existing alone. The character " / " generally indicates that the preceding and following associated objects have an "or" relationship.

[0026] It should be noted that the terms "first," "second," etc., in the specification, claims, and drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0027] In this embodiment of the invention, the term "multiple" refers to two or more, and other quantifiers are similar.

[0028] Example 1 This embodiment provides a method for measuring anisotropic transparent materials, such as... Figure 1 As shown, the method includes: S1: Establish an optical theoretical model of the sample under test during the ellipsometric measurement process; wherein, the sample under test includes a transparent substrate formed of anisotropic transparent material, and in the optical theoretical model, the multiple reflected light from the front surface and the back surface of the transparent substrate is incoherent light; S2: Based on the theory of superposition of back-reflected incoherent light, the optical theoretical model is processed to derive the theoretical Mueller matrix of the sample under test in the optical theoretical model; S3: Obtain the measured Mueller matrix of the sample under test during the ellipsometric measurement process, and perform inversion fitting between the theoretical Mueller matrix and the measured Mueller matrix to obtain the measurement result of the sample under test; wherein, the measurement result includes at least the thickness information and optical tensor information of the transparent substrate.

[0029] In this embodiment, the sample under test includes a transparent substrate formed of anisotropic transparent material. First, an optical theoretical model of the sample during ellipsometric measurement is constructed. This model takes into account that the multiple reflections between the front and back surfaces of the transparent substrate are incoherent, which is closer to the actual measurement situation. Subsequent theoretical derivation and inversion fitting based on this model can provide a more reliable model foundation. After establishing the optical theoretical model, the theoretical Mueller matrix of the sample under test in the optical theoretical model can be obtained based on the theory of superposition of incoherent back reflection light. This fully considers the characteristics of each dielectric layer and the propagation law of light in it, making the theoretical derivation more rigorous and accurate. Then, the derived theoretical Mueller matrix is ​​inverted and fitted with the measured Mueller matrix, which can simultaneously and accurately obtain the thickness parameters of the anisotropic transparent substrate or crystal material and complete optical tensor information.

[0030] The anisotropic transparent material measurement method of this embodiment can effectively process incoherent back-reflected light, thereby accurately obtaining the thickness parameters and complete optical tensor information of the anisotropic transparent material. It provides a complete solution for the measurement of anisotropic transparent materials, significantly improves the measurement accuracy and inversion stability, expands the application scope of Mueller matrix ellipticization technology in the characterization of thick transparent anisotropic materials, and has higher measurement reliability and practical value.

[0031] The following is a detailed description of each step in the anisotropic transparent material measurement method of this embodiment.

[0032] In this embodiment S1, when establishing the optical theoretical model, multiple factors can be considered to ensure the accuracy and practicality of the model. Since the sample under test contains a transparent substrate formed by anisotropic transparent materials, it is necessary to focus on analyzing the characteristics of light propagation in different directions. Therefore, the basic parameters of the sample can be obtained by observing and measuring the sample under test, such as the physical structure of the transparent substrate, the distribution of anisotropy (including direction, intensity, etc.), and optical property parameters that will affect the reflection and refraction of light, laying the foundation for subsequent theoretical derivation and model construction.

[0033] In this embodiment, a professional optical modeling software can be used to simulate the optical theoretical model, combined with the parameters obtained above. The software can accurately simulate the propagation path, reflection, and refraction of light in anisotropic transparent substrates based on the input optical material properties and geometry. Furthermore, considering the fact that multiple reflections between the front and back surfaces of the transparent substrate are incoherent, the theory of incoherent light superposition is introduced during the modeling process to more accurately reflect the actual propagation and interaction of light.

[0034] Establishing a sound optical theoretical model provides a solid foundation for subsequent theoretical derivations and inversion fitting. Based on this model, the propagation patterns of light in anisotropic transparent materials can be analyzed more accurately, thus providing strong support for accurately measuring the thickness parameters and complete optical tensor information of anisotropic transparent materials.

[0035] The optical path diagram of the optical theoretical model in this embodiment is as follows: Figure 2 As shown, it includes three dielectric layers: incident medium M0, substrate inner medium M1, and exit medium M2. The interface between incident medium M0 and substrate inner medium M1 is the front surface of the transparent substrate, and the interface between substrate inner medium M1 and exit medium M2 is the back surface of the transparent substrate.

[0036] Preferably, step S2 in this embodiment includes: S21: Using Euler angle transformation, obtain the dielectric tensor of each dielectric layer in the optical theoretical model in the measurement coordinate system; S22: Based on the dielectric tensor of each dielectric layer in the measurement coordinate system, solve for the eigenvector matrix and eigenvalue matrix that characterize the light propagation properties of the corresponding dielectric layer. S23: Based on the eigenvector matrices of all dielectric layers, calculate the reflection coefficient matrix and transmission coefficient matrix at each dielectric interface in the optical theoretical model; and based on the eigenvalue matrix corresponding to the dielectric in the substrate, calculate the single-layer film transfer matrix of the dielectric in the substrate. S24: Using the single-layer film transfer matrix of the medium in the substrate and the reflection coefficient matrix and transmission coefficient matrix at all medium interfaces, incoherent light superposition is performed to obtain the theoretical Mueller matrix in the optical theoretical model.

[0037] In step S21 above, because the optical properties of anisotropic transparent materials differ in different directions, their dielectric tensor changes with the measurement coordinate system. Euler angle transformation can be used to obtain the dielectric tensor in the principal axis coordinate system of the sample. This ensures that subsequent calculations are based on a unified and accurate coordinate system, providing crucial data for subsequent analysis of the propagation characteristics of light in anisotropic media.

[0038] In step S22, the eigenvector matrix describes the polarization state and propagation direction of light in the medium, while the eigenvalue matrix is ​​related to factors such as the propagation speed and attenuation of light in the medium. After obtaining the dielectric tensor of each medium layer in the principal axis coordinate system of the sample, solving for the eigenvector and eigenvalue matrices characterizing light propagation properties provides a convenient way to understand the propagation laws of light in anisotropic media, providing necessary parameters for subsequent calculations of the reflection coefficient matrix, transmission coefficient matrix, and single-layer film transfer matrix.

[0039] In step S23, the reflection coefficient matrix and the transmission coefficient matrix describe the ratio of reflection and transmission of light at different medium interfaces and the changes in polarization state, while the monolayer film transfer matrix is ​​used to describe the state changes of light as it propagates in the medium within the substrate. Calculating the reflection coefficient matrix and transmission coefficient matrix at each medium interface based on the eigenvector matrices of all medium layers, and calculating the monolayer film transfer matrix of the medium within the substrate based on the corresponding eigenvalue matrix of the medium within the substrate, facilitates the subsequent superposition of incoherent light to obtain the theoretical Mueller matrix.

[0040] In step S24, since the multiple reflections between the front and back surfaces of the transparent substrate are incoherent, the incoherent light is superimposed using the single-layer film transfer matrix of the substrate medium and the reflection and transmission coefficient matrices at all medium interfaces. This yields the theoretical Mueller matrix in the optical model. This theoretical Mueller matrix integrates the propagation characteristics, reflection and refraction of light in anisotropic transparent materials, as well as the superposition effect of incoherent light, providing an important theoretical basis for subsequent inversion and fitting with the measured Mueller matrix. This approach fully considers the propagation and interaction of light in each medium layer, making the theoretical derivation more consistent with reality.

[0041] Specifically, in step S21, for anisotropic optical materials, their dielectric properties are described by the dielectric tensor. Let the three Euler angles be... ,in, , and These are the azimuth angle, tilt angle, and in-plane rotation angle, respectively. These three Euler angles form a 3×3 rotation matrix B as follows: ; Using this rotation matrix B, the dielectric tensor in the laboratory coordinate system can be... Convert to refractive index tensor in the principal axis coordinate system of the sample The calculation formula is as follows: ; , ; in, The dielectric tensor in the laboratory coordinate system. ~ These are elements in the dielectric tensor in the laboratory coordinate system; Let f(x) be a diagonal matrix representing the dielectric tensor in the principal axis coordinate system of the sample. Its diagonal elements include: , and B T Let B be the transpose of the rotation matrix B.

[0042] The dielectric tensor of each of the three dielectric layers was obtained in the principal axis coordinate system of the sample using the method described above.

[0043] Further, step S22 includes: S221: Select any dielectric layer and construct the generalized material matrix of the sample under test in the optical theoretical model based on the dielectric tensor of the selected dielectric layer in the principal axis coordinate system of the sample. S222: Using the generalized material matrix, solve for the corresponding Berreman differential transfer matrix of the dielectric layer; S223: Perform eigenvalue decomposition on the Berreman differential transfer matrix to obtain the eigenvector matrix consisting of the eigenvectors of the Berreman differential transfer matrix and the eigenvalue matrix consisting of the eigenvalues ​​of the Berreman differential transfer matrix corresponding to the medium layer.

[0044] In step S221, the generalized material matrix is ​​constructed based on the dielectric tensor of the dielectric layer in the principal axis coordinate system of the sample. This matrix comprehensively considers the optical properties of anisotropic materials and can more fully describe the propagation behavior of light in the medium. Through this construction, complex optical problems can be transformed into matrix form, which facilitates subsequent calculations and analysis.

[0045] In step S222, the Berreman differential transfer matrix contains important information such as the polarization change and propagation direction of light in the medium. Solving it using the generalized material matrix can provide a deeper understanding of the propagation law of light in anisotropic media, which is the key to describing the propagation process of light in the medium.

[0046] In step S223, the eigenvector matrix and eigenvalue matrix obtained by the eigenvalue decomposition of the Berreman differential transfer matrix correspond to the polarization state, propagation speed, attenuation and other characteristics of light propagating in the medium, respectively, providing the necessary parameters for subsequent calculation of the reflection coefficient matrix, transmission coefficient matrix and single-layer film transfer matrix.

[0047] Specifically, in step S221, any chosen dielectric layer is selected, and the expression for the corresponding generalized material matrix is ​​as follows: ; in, For the selected generalized material matrix of the dielectric layer, This represents the dielectric tensor of the selected medium in the principal axis coordinate system of the sample. and The optical rotation tensor of the selected dielectric layer, represents the permeability tensor of the selected dielectric layer.

[0048] In step S222, for the selected dielectric layer, the corresponding generalized material matrix Specifically, it is a 6×6 dimensional matrix, corresponding to the Berreman differential transfer matrix. Specifically, it is a 4×4 dimensional matrix derived from Maxwell's equations, describing the propagation characteristics of light waves in multilayer dielectric structures and their reflection and transmission behavior at interlayer interfaces. The corresponding Berreman differential transfer matrix... The expressions for each element in the expression are: ; in, , ,...and The Berreman differential transfer matrix corresponding to the selected medium layer. The elements in , ,...and The generalized material matrix corresponding to the selected dielectric layer The elements in The transverse wave vector component of the selected dielectric layer; a 3n and a 6n These are the first and second auxiliary vectors corresponding to the selected medium layer, respectively; n is the number of columns of the first and second auxiliary vectors; and b is the determinant factor corresponding to the selected medium layer. The first auxiliary vector a corresponding to the selected dielectric layer 3n Second auxiliary vector a 6n The expressions are as follows: ; ; The specific expression for the determinant factor b corresponding to the selected dielectric layer is as follows: .

[0049] In the above calculation formula, the transverse wave vector component of the selected dielectric layer is... As the incident condition, it satisfies , where n0 is the refractive index of the incident medium and θ0 is the incident angle of the incident light from the incident medium.

[0050] In step S223, the Berreman differential transfer matrix is ​​used. The eigenvalue decomposition yields an eigenvector matrix composed of the eigenvectors of the Berreman differential transfer matrix. And the eigenvalue matrix composed of the eigenvalues ​​of the Berreman differential transfer matrix. .in, It is a column vector matrix, and It is a diagonal matrix, whose diagonal elements are formed by... eigenvalues ​​q j Given the eigenvalue matrix Specifically, it is expressed as follows: ; in, The eigenvalue matrix corresponding to the dielectric in the substrate The diagonal element of the j-th row, q jLet be the j-th eigenvalue of the Berreman differential transfer matrix corresponding to the medium in the substrate, and j satisfies j=1,2,3,4; k0 is the vacuum wavenumber, d is the physical thickness of the medium in the substrate, and i is the imaginary unit.

[0051] The four eigenvalues ​​of the Berreman differential transfer matrix correspond to four intrinsic electromagnetic modes. Two of these eigenmodes have positive propagation constants, representing the refracted wave component propagating in the forward direction within the thin film; the other two eigenmodes have negative propagation constants, corresponding to the reflected wave component propagating in the reverse direction within the thin film. The magnitudes of these four eigenvalues ​​can be ordered as follows: .

[0052] It should be understood that, in this embodiment, since the multiple reflections from the front and back surfaces of the transparent substrate are incoherent, the eigenmodes propagating along the same propagation direction remain coherent, while the eigenmodes undergoing different propagation times are incoherent with each other. The mathematical expression for this condition is: ; ; ; ; Among them, t j Let be the time required for the j-th eigenmode to complete one propagation in the incident medium, which satisfies , t c s is the temporal coherence length of the incident light, c is the speed of light; j The equivalent lateral displacement of the j-th eigenmode in the incident medium satisfies s c denoted as the spatial coherence length of the incident light.

[0053] Preferably, in step S23, as Figure 2 As shown, the reflection coefficient matrix at each medium interface includes a first reflection coefficient matrix from the incident medium incident to the front surface of the medium inside the substrate and reflected from the front surface of the medium inside the substrate, a second reflection coefficient matrix from the front surface of the medium inside the substrate incident to the back surface of the medium inside the substrate and reflected from the back surface of the medium inside the substrate, and a third reflection coefficient matrix from the back surface of the medium inside the substrate incident to the front surface of the medium inside the substrate and reflected from the front surface of the medium inside the substrate. The transmission coefficient matrix at each medium interface includes a first transmission coefficient matrix from the incident medium incident to the front surface of the medium inside the substrate and transmitted to the back surface of the medium inside the substrate, a second transmission coefficient matrix from the front surface of the medium inside the substrate incident to the back surface of the medium inside the substrate and transmitted to the exit medium, and a third transmission coefficient matrix from the back surface of the medium inside the substrate incident to the front surface of the medium inside the substrate and transmitted to the incident medium. In step S23, based on the eigenvector matrices of all dielectric layers, the reflection coefficient matrix and transmission coefficient matrix at each dielectric interface in the optical theoretical model are calculated, including: S231: Calculate the first reflection coefficient matrix, the first transmission coefficient matrix, the third reflection coefficient matrix, and the third transmission coefficient matrix based on the eigenvector matrix corresponding to the incident medium and the eigenvector matrix corresponding to the medium inside the substrate, respectively. S232: Calculate the second reflection coefficient matrix and the second transmission coefficient matrix based on the eigenvector matrix corresponding to the medium inside the substrate and the eigenvector matrix corresponding to the emitted medium.

[0054] The eigenvector matrix of the incident medium reflects the polarization state and other characteristics of the incident light in the incident medium, while the eigenvector matrix of the substrate medium reflects the propagation characteristics of light in the substrate medium. In step S231, when calculating the first reflection coefficient matrix, the first transmission coefficient matrix, the third reflection coefficient matrix, and the third transmission coefficient matrix, it is necessary to utilize the properties and relationships of the corresponding eigenvector matrices of the incident medium and the substrate medium. By performing specific operations and analyses on these two matrices, the corresponding reflection coefficient matrix and transmission coefficient matrix can be accurately obtained.

[0055] The eigenvector matrix of the substrate medium contains key information about light propagation within the substrate, while the eigenvector matrix of the exiting medium determines the propagation characteristics of light when it enters the exiting medium from the substrate medium. In step S232, the calculation of the second reflection coefficient matrix and the second transmission coefficient matrix depends on the corresponding eigenvector matrices of the substrate medium and the exiting medium. By analyzing and calculating these two matrices, the reflection and transmission of light at the interface between the substrate medium and the exiting medium can be accurately calculated.

[0056] Specifically, in step S231, the formulas for calculating the first reflection coefficient matrix and the first transmission coefficient matrix are as follows: ; in, and These are the first reflection coefficient matrix and the first transmission coefficient matrix, respectively. Let be the eigenvector matrix of the incident medium. This is an inverse matrix operation. The eigenvector matrix of the dielectric within the substrate. , , and The first product matrix The top left matrix sub-block, top right matrix sub-block, bottom left matrix sub-block, and bottom right matrix sub-block.

[0057] The first product matrix mentioned above The four matrices in the image—the top-left, top-right, bottom-left, and bottom-right sub-matrices—are all 2×2 matrices. The first product matrix... It is divided into four parts to decouple the forward and backward propagation modes. The upper left matrix sub-block is one of them. Related to the forward transmission from M0 to M1, Related to the reverse pattern in M1, the lower left matrix sub-block Related to reflection from M0 to M1, the lower right matrix sub-block Related to the back propagation from M1 to M2.

[0058] The formulas for calculating the second reflection coefficient matrix and the second transmission coefficient matrix are as follows: ; in, and These are the second reflection coefficient matrix and the second transmission coefficient matrix, respectively. Let be the eigenvector matrix of the exiting medium. , , and The second product matrix The top left matrix sub-block, top right matrix sub-block, bottom left matrix sub-block, and bottom right matrix sub-block.

[0059] The second product matrix mentioned above The four matrices in the upper left, upper right, lower left, and lower right sub-matrices are similar to the four matrices in the first product matrix, and will not be described again here.

[0060] Specifically, in step S231, the formulas for calculating the third reflection coefficient matrix and the third transmission coefficient matrix are as follows: ; in, and These are the third reflection coefficient matrix and the third transmission coefficient matrix, respectively. , , and The third product matrix The top left matrix sub-block, top right matrix sub-block, bottom left matrix sub-block, and bottom right matrix sub-block.

[0061] Similarly, the third product matrix mentioned above The four matrices in the upper left, upper right, lower left, and lower right sub-matrices are similar to the four matrices in the first product matrix, and will not be described again here.

[0062] Specifically, in step 23, the monolayer film transfer matrix corresponding to the medium in the substrate includes a forward transfer matrix and a reverse transfer matrix; The specific formulas for calculating the forward and reverse transfer matrices corresponding to the dielectric within the substrate are as follows: ; Among them, P + and P - These are the forward and reverse transfer matrices corresponding to the dielectric within the substrate, respectively. As explained earlier, q j The j-th eigenvalue is the Berreman differential transfer matrix corresponding to the medium within the substrate, which will not be elaborated further here.

[0063] The above positive transfer matrix P + The amplitude vector acting on the forward propagation mode, where two eigenvalues ​​correspond to the eigenvalues ​​of the two forward propagation modes; the backward propagation matrix P - The amplitude vector acting on the backpropagation mode, where two eigenvalues ​​correspond to the eigenvalues ​​of the two backpropagation modes.

[0064] It should be understood that in the reverse transfer matrix P - In this context, since the eigenvalues ​​themselves are negative, the exponent in the vector is positive.

[0065] Preferably, step S24 includes: S241: Calculate the round-trip operator for one round trip in the medium within the substrate based on the reflection coefficient matrix at all medium interfaces and the monolayer film transfer matrix of the medium within the substrate. S242: Calculate the Jones matrix for each reflection path in the optical theoretical model based on the single-layer film transfer matrix, the round-trip operator, and the reflection coefficient matrix and transmission coefficient matrix at all media interfaces; S243: Using the Kronecker product operation, the Jones matrix of each reflection path is converted into the corresponding coherence matrix; S244: Obtain the total coherence matrix based on the coherence matrices of all reflection paths, and transform the total coherence matrix to obtain the theoretical Mueller matrix.

[0066] In step S241, the round-trip operator comprehensively considers the reflection of light on the front and back surfaces of the medium within the substrate, as well as the phase change of light as it propagates within the substrate. It describes the total effect of light undergoing one complete round trip within the transparent substrate. Therefore, by combining the reflection coefficient matrix at all medium interfaces with the single-layer film transfer matrix of the medium within the substrate, the process of light making one round trip within the substrate can be accurately described.

[0067] In step S242, the Jones matrix describes the polarization state change of light under different reflection paths, which is of great significance for studying the propagation of light in anisotropic transparent materials. In this embodiment, the monolayer film transfer matrix, the round-trip operator, and the reflection coefficient matrix and transmission coefficient matrix at all medium interfaces work together to provide the necessary information for accurately calculating the Jones matrix of each reflection path. By calculating the Jones matrix of each reflection path, the light propagation can be further analyzed in depth.

[0068] The coherence matrix can more comprehensively describe the polarization and coherence characteristics of light, laying the foundation for subsequent calculation of the total coherence matrix. In step S243, the Jones matrix is ​​converted into a coherence matrix using the Kronecker product operation, which facilitates better handling of the coherence problem of light in the future.

[0069] Finally, in step S244, the theoretical Mueller matrix is ​​an important tool for describing the change in polarization state after light interacts with materials. The total coherence matrix is ​​obtained based on the coherence matrices of all reflection paths and converted into the theoretical Mueller matrix. By analyzing the converted theoretical Mueller matrix, we can gain a deeper understanding of the optical properties of anisotropic transparent materials, such as the birefringence and optical rotation of the materials.

[0070] After obtaining the theoretical Mueller matrix through the above series of steps, this embodiment can be easily combined with the experimentally measured Mueller matrix for inversion fitting, thereby accurately determining the optical parameters of anisotropic transparent materials, such as refractive index and absorption coefficient.

[0071] Specifically, in step S241, the formula for calculating the round-trip operator is as follows: ; in, For round trip operators.

[0072] Specifically, in step S242, after the round-trip operator is calculated, the Jones matrix under each reflection path can be calculated by combining the round-trip operator with each reflection coefficient matrix and transmission coefficient matrix.

[0073] Path 0: Direct reflection (specifically, incident light is directly reflected on the front surface of the medium within the substrate) The Jones matrix J0 under this reflection path is: .

[0074] Path 1: Single back reflection (specifically: transmission into the substrate → back reflection → transmission from the front surface) The Jones matrix J1 under this reflection path is: .

[0075] Path 2: Three-stage reflection (specifically: transmission into the substrate → first reflection from the back surface → reflection from the front surface → second reflection from the back surface → transmission from the front surface) This process involves one complete round trip, and the Jones matrix J2 under this reflection path is: ; This is equivalent to inserting an additional round-trip process Q on top of J1, after entering the substrate and before completing the first back reflection.

[0076] Path 3: Five reflections (specifically, based on Path 2, one more complete round trip) The process involves two complete round trips, and the Jones matrix J2 under this reflection path is: ; The Jones matrix for the remaining reflection paths follows the same principle.

[0077] because Let I be the identity matrix, therefore the expression for the total Jones matrix is: ; Where I is a 2×2 dimensional identity matrix.

[0078] Specifically, in step S243, since the light in the medium inside the substrate is incoherent light (the substrate thickness is generally greater than the coherence length, which is usually only a few micrometers), the intensity of light is used instead of the amplitude when the incoherent light is superimposed. In this embodiment, the Kronecker product operation is used to convert each Jones matrix into a coherent matrix containing the intensity information.

[0079] For the Jones matrix J under any reflection path, the specific formula for performing the Kronecker product operation is as follows: ; C is the coherence matrix corresponding to the Jones matrix J under any reflection path. J represents the Kronecker product. * Let J be the complex conjugate matrix of J. 11 ~J 22 It is an element in the Jones matrix J, J * 11 ~J *22 J is a complex conjugate matrix * The elements in.

[0080] Following the method described above for calculating the coherence matrix, each coherence matrix can be calculated.

[0081] Then, in step S244, the total coherence matrix C is obtained by summing all the coherence matrices. total Finally, the total coherence matrix is ​​transformed to obtain the theoretical Mueller matrix. The specific formula for calculating the theoretical Mueller matrix is ​​as follows: ; Where M is the theoretical Mueller matrix, C total Let A be the total coherence matrix and A be the preset transformation matrix.

[0082] Preferably, embodiment S3 includes: S31: Construct a set of parameters to be fitted based on the thickness information and optical tensor information of the transparent substrate; S32: Define the difference function between the theoretical Mueller matrix and the measured Mueller matrix; S33: The set of parameters to be fitted is adjusted using an iterative optimization method to minimize the difference function, and the parameter values ​​corresponding to the set of parameters to be fitted that minimize the difference function are determined as the measurement results.

[0083] In step S31, the thickness information and optical tensor information of the transparent substrate are combined to construct the parameter set to be fitted. This comprehensively covers the key characteristics of anisotropic transparent materials, providing a rich and accurate information foundation for subsequent fitting work. In step S32, by defining a difference function, the difference between the theoretical and measured Mueller matrices is quantified using mathematical expressions. This allows for a more intuitive understanding of the degree of agreement between the current theoretical model and the actual situation, directly affecting the direction and effect of subsequent iterative optimization. In step S33, by continuously adjusting the parameter set to be fitted, the value of the difference function is gradually reduced until it is minimized, allowing the parameters to change in a direction that better reflects reality. When the difference function reaches its minimum, the parameter values ​​corresponding to the parameter set to be fitted are the required measurement results. These parameters can accurately describe the optical properties of anisotropic transparent materials, providing important data support for research and applications in related fields.

[0084] This embodiment effectively ensures the accuracy and reliability of the measurement results through the above-described inversion fitting steps. This method is not only suitable for laboratory research, but can also be used in industrial production for quality testing and performance evaluation of anisotropic transparent materials, and has broad application prospects.

[0085] Specifically, in step S31, the set of parameters to be fitted may include the thickness of the transparent substrate, the principal refractive index of the anisotropic material, the absorption coefficient, the element values ​​of the optical tensor, etc. These parameters are defined as a parameter vector and used as input variables for subsequent inversion fitting.

[0086] In step S32, the specific form of the defined difference function can be a weighted least squares function or other error analysis-based functions. The weighted least squares function assigns weights based on the importance of different data points, giving more attention to key data during the fitting process and thus improving fitting accuracy. For example, in the measurement of anisotropic transparent materials, certain data points may have a significant impact on specific optical properties of the material; weighting can more accurately reflect these properties. Other error analysis-based functions can be selected according to different measurement requirements and data characteristics. This embodiment does not limit the specific function form.

[0087] In step S33, commonly used iterative optimization methods include gradient descent and Newton's method, and this embodiment does not impose any restrictions.

[0088] Example 2 An anisotropic transparent material measurement system is applied to the anisotropic transparent material measurement method of Example 1, such as... Figure 3 As shown, the system includes: The model building module is used to establish an optical theoretical model of the sample under test during the ellipsometric measurement process; wherein, the sample under test includes a transparent substrate formed of anisotropic transparent material, and in the optical theoretical model, the multiple reflected light from the front surface and the back surface of the transparent substrate is incoherent light; The theoretical derivation module is used to process the optical theoretical model based on the theory of superposition of back-reflection incoherent light and derive the theoretical Mueller matrix of the sample under test in the optical theoretical model. The inversion fitting module is used to obtain the measured Mueller matrix of the sample under test during the ellipsometric measurement process, and to perform inversion fitting between the theoretical Mueller matrix and the measured Mueller matrix to obtain the measurement result of the sample under test; wherein, the measurement result includes at least the thickness information and optical tensor information of the transparent substrate.

[0089] In this embodiment, the sample to be tested includes a transparent substrate formed of anisotropic transparent material. First, an optical theoretical model of the sample during ellipsometric measurement is constructed using a model building module. This model takes into account that the multiple reflections between the front and back surfaces of the transparent substrate are incoherent, which is closer to the actual measurement situation. Subsequent theoretical derivation and inversion fitting based on this model can provide a more reliable model foundation. After the optical theoretical model is established, the theoretical derivation module is used to derive the theoretical Mueller matrix of the sample to be tested in the optical theoretical model based on the theory of superposition of incoherent back reflection light. This fully considers the characteristics of each dielectric layer and the propagation law of light in it, making the theoretical derivation more rigorous and accurate. Then, the inversion fitting module is used to invert and fit the derived theoretical Mueller matrix with the measured Mueller matrix, which can simultaneously and accurately obtain the thickness parameters of the anisotropic transparent substrate or crystal material and complete optical tensor information.

[0090] The anisotropic transparent material measurement system of this embodiment can effectively process incoherent back-reflected light, thereby accurately obtaining the thickness parameters and complete optical tensor information of the anisotropic transparent material. It provides a complete solution for the measurement of anisotropic transparent materials, significantly improves the measurement accuracy and inversion stability, expands the application scope of Mueller matrix ellipticization technology in the characterization of thick transparent anisotropic materials, and has higher measurement reliability and practical value.

[0091] The functions of each module in the anisotropic transparent material measurement system described in this embodiment are the same as the method steps of the anisotropic transparent material measurement method described in Embodiment 1. Therefore, for details not covered in this embodiment, please refer to Embodiment 1 and... Figures 1 to 2 The specific details will not be elaborated here.

[0092] Example 3 This embodiment also provides an anisotropic transparent material measurement device, including a processor, a memory, and a computer program stored in the memory and executable on the processor. When the computer program is executed, it implements the method steps in the anisotropic transparent material measurement method of Embodiment 1.

[0093] By using a computer program stored in memory and running on a processor, incoherent back-reflected light can be effectively processed, thereby accurately obtaining the thickness parameters and complete optical tensor information of anisotropic transparent materials. This provides a complete solution for the measurement of anisotropic transparent materials, significantly improves measurement accuracy and inversion stability, expands the application scope of Mueller matrix ellipticization technology in the characterization of thick transparent anisotropic materials, and has higher measurement reliability and practical value.

[0094] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor. The processor is the control center of the computer device, connecting all parts of the computer device through various interfaces and lines.

[0095] Memory can be used to store computer programs and / or models. The processor performs various functions of the computer device by running or executing the computer programs and / or models stored in the memory, and by accessing data stored in the memory. Memory can primarily include a program storage area and a data storage area. The program storage area can store the operating system and at least one application program required for a function (e.g., sound playback, image playback, etc.); the data storage area can store data created based on the use of the mobile phone (e.g., audio data, video data, etc.). Furthermore, memory can include high-speed random access memory, and can also include non-volatile memory, such as hard disks, RAM, plug-in hard disks, SmartMedia Cards (SMC), Secure Digital (SD) cards, Flash Cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0096] It should be understood that each block of a flowchart and / or block diagram, and combinations of blocks in a flowchart and / or block diagram, can be implemented by a computer program. These computer programs can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing device to produce a machine, such that instructions executable by the processor of the computer or other programmable data processing device generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0097] These computer programs may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0098] These computer programs may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0099] This embodiment also provides a computer storage medium, the computer storage medium including: at least one instruction, which, when executed by a computer, implements the method steps in the anisotropic transparent material measurement method of Embodiment 1.

[0100] By executing a computer storage medium containing at least one instruction, incoherent back-reflected light can be effectively processed, thereby accurately obtaining the thickness parameters and complete optical tensor information of anisotropic transparent materials. This provides a complete solution for the measurement of anisotropic transparent materials, significantly improves measurement accuracy and inversion stability, expands the application scope of Mueller matrix ellipticization technology in the characterization of thick transparent anisotropic materials, and has higher measurement reliability and practical value.

[0101] Similarly, for details not covered in this embodiment, please refer to Embodiment 1, Embodiment 2, and... Figures 1 to 3 The specific details will not be elaborated here.

[0102] Although embodiments of the invention have been described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. A method for measuring anisotropic transparent materials, characterized in that, The method includes: An optical theoretical model is established for the sample under test during the ellipsometric measurement process; wherein, the sample under test includes a transparent substrate formed of anisotropic transparent material, and in the optical theoretical model, the multiple reflected light from the front surface and the back surface of the transparent substrate is incoherent light; Based on the theory of superposition of incoherent back-reflection light, the optical theoretical model is processed to derive the theoretical Mueller matrix of the sample under test in the optical theoretical model. The measured Mueller matrix of the sample under test during the ellipsometric measurement process is obtained, and the theoretical Mueller matrix and the measured Mueller matrix are inverted and fitted to obtain the measurement result of the sample under test; wherein, the measurement result includes at least the thickness information and optical tensor information of the transparent substrate.

2. The method for measuring anisotropic transparent materials according to claim 1, characterized in that, The optical theoretical model includes three dielectric layers: the incident medium, the substrate medium, and the exit medium. Based on the theory of superposition of incoherent back-reflected light, the optical theoretical model is processed to derive the theoretical Mueller matrix of the sample under test in the optical theoretical model, including: Using Euler angle transformation, the dielectric tensor of each dielectric layer in the optical theoretical model in the sample principal axis coordinate system is obtained; Based on the dielectric tensor of each dielectric layer in the principal axis coordinate system of the sample, the eigenvector matrix and eigenvalue matrix characterizing the light propagation properties of the corresponding dielectric layer are obtained respectively. Based on the eigenvector matrices of all dielectric layers, the reflection coefficient matrix and transmission coefficient matrix at each dielectric interface in the optical theoretical model are calculated respectively; and based on the eigenvalue matrix corresponding to the dielectric in the substrate, the single-layer film transfer matrix of the dielectric in the substrate is calculated. By using the single-layer film transfer matrix of the medium within the substrate and the reflection and transmission coefficient matrices at all medium interfaces, incoherent light superposition is performed to obtain the theoretical Mueller matrix in the optical theoretical model.

3. The method for measuring anisotropic transparent materials according to claim 2, characterized in that, Based on the dielectric tensor of each dielectric layer in the principal axis coordinate system of the sample, the eigenvector matrix and eigenvalue matrix characterizing the light propagation properties of the corresponding dielectric layer are obtained, including: Choose any dielectric layer and construct the generalized material matrix of the sample under test in the optical theoretical model based on the dielectric tensor of the selected dielectric layer in the principal axis coordinate system of the sample. Using the generalized material matrix, the Berreman differential transfer matrix of the corresponding dielectric layer is solved; The Berreman differential transfer matrix is ​​decomposed into eigenvectors, which are composed of the eigenvectors of the Berreman differential transfer matrix, and the corresponding eigenvalue matrix is ​​composed of the eigenvalues ​​of the Berreman differential transfer matrix.

4. The method for measuring anisotropic transparent materials according to claim 3, characterized in that, For any chosen dielectric layer, the expression for the corresponding generalized material matrix is ​​as follows: ； in, For the selected generalized material matrix of the dielectric layer, This represents the dielectric tensor of the selected medium in the principal axis coordinate system of the sample. and The optical rotation tensor of the selected dielectric layer, Let be the permeability tensor of the selected dielectric layer; In each medium layer, the corresponding eigenvector matrix is ​​specifically a column vector matrix composed of the eigenvectors of the corresponding Berreman differential transfer matrix; the corresponding eigenvalue matrix is ​​specifically a diagonal matrix.

5. The method for measuring anisotropic transparent materials according to claim 2, characterized in that, For the selected dielectric layer, the corresponding generalized material matrix is ​​specifically a 6×6 dimensional matrix, and the corresponding Berreman differential transfer matrix is ​​specifically a 4×4 dimensional matrix. The expressions for each element in the corresponding Berreman differential transfer matrix are as follows: ； in, , ,...and For each element in the Berreman differential transfer matrix corresponding to the selected medium layer, , ,...and For each element in the generalized material matrix corresponding to the selected dielectric layer, The transverse wave vector component of the selected dielectric layer; a 3n and a 6n These are the first and second auxiliary vectors corresponding to the selected medium layer, respectively; n is the number of columns of the first and second auxiliary vectors; and b is the determinant factor corresponding to the selected medium layer. The first auxiliary vector a corresponding to the selected dielectric layer 3n Second auxiliary vector a 6n The expressions are as follows: ； ； The specific expression for the determinant factor b corresponding to the selected dielectric layer is as follows: 。 6. The method for measuring anisotropic transparent materials according to claim 3, characterized in that, The reflection coefficient matrix at each medium interface includes a first reflection coefficient matrix from the incident medium incident to the front surface of the medium inside the substrate and reflected from the front surface of the medium inside the substrate, a second reflection coefficient matrix from the front surface of the medium inside the substrate incident to the back surface of the medium inside the substrate and reflected from the back surface of the medium inside the substrate, and a third reflection coefficient matrix from the back surface of the medium inside the substrate incident to the front surface of the medium inside the substrate and reflected from the front surface of the medium inside the substrate. The transmission coefficient matrix at each medium interface includes a first transmission coefficient matrix from the incident medium incident to the front surface of the medium inside the substrate and transmitted to the back surface of the medium inside the substrate, a second transmission coefficient matrix from the front surface of the medium inside the substrate incident to the back surface of the medium inside the substrate and transmitted to the exit medium, and a third transmission coefficient matrix from the back surface of the medium inside the substrate incident to the front surface of the medium inside the substrate and transmitted to the incident medium. Based on the eigenvector matrices of all dielectric layers, the reflection coefficient matrix and transmission coefficient matrix at each dielectric interface in the optical theoretical model are calculated, including: Based on the eigenvector matrix corresponding to the incident medium and the eigenvector matrix corresponding to the medium inside the substrate, the first reflection coefficient matrix, the first transmission coefficient matrix, the third reflection coefficient matrix and the third transmission coefficient matrix are calculated respectively. The second reflection coefficient matrix and the second transmission coefficient matrix are calculated based on the eigenvector matrix corresponding to the medium inside the substrate and the eigenvector matrix corresponding to the emitted medium.

7. The method for measuring anisotropic transparent materials according to claim 5, characterized in that, The specific formulas for calculating the first reflection coefficient matrix and the first transmission coefficient matrix are as follows: ； in, and These are the first reflection coefficient matrix and the first transmission coefficient matrix, respectively. Let be the eigenvector matrix of the incident medium. This is an inverse matrix operation. The eigenvector matrix of the dielectric within the substrate. , , and The first product matrix The top left matrix sub-block, top right matrix sub-block, bottom left matrix sub-block, and bottom right matrix sub-block in the matrix; The formulas for calculating the second reflection coefficient matrix and the second transmission coefficient matrix are as follows: ； in, and These are the second reflection coefficient matrix and the second transmission coefficient matrix, respectively. Let be the eigenvector matrix of the exiting medium. , , and The second product matrix The top left matrix sub-block, top right matrix sub-block, bottom left matrix sub-block, and bottom right matrix sub-block in the matrix; The formulas for calculating the third reflection coefficient matrix and the third transmission coefficient matrix are as follows: ； in, and These are the third reflection coefficient matrix and the third transmission coefficient matrix, respectively. , , and The third product matrix The top left matrix sub-block, top right matrix sub-block, bottom left matrix sub-block, and bottom right matrix sub-block.

8. The method for measuring anisotropic transparent materials according to claim 6, characterized in that, The monolayer transfer matrix corresponding to the dielectric in the substrate includes the forward transfer matrix and the reverse transfer matrix; The specific formulas for calculating the forward and reverse transfer matrices corresponding to the dielectric within the substrate are as follows: ； Among them, P + and P - These are the forward transfer matrix and the reverse transfer matrix corresponding to the dielectric within the substrate, respectively. q is the diagonal element of the j-th row in the eigenvalue matrix corresponding to the dielectric within the substrate. j Let be the j-th eigenvalue of the Berreman differential transfer matrix corresponding to the medium in the substrate, and j satisfies j=1,2,3,4; k0 is the vacuum wavenumber, d is the physical thickness of the medium in the substrate, and i is the imaginary unit.

9. The method for measuring anisotropic transparent materials according to claim 7, characterized in that, By using the monolayer transfer matrix of the dielectric within the substrate and the reflection and transmission coefficient matrices at all dielectric interfaces, incoherent light superposition is performed to obtain the theoretical Mueller matrix in the optical theoretical model, including: Based on the reflection coefficient matrix at all media interfaces and the monolayer film transfer matrix of the medium within the substrate, the round-trip operator for one round trip in the medium within the substrate is calculated. Based on the single-layer film transfer matrix, the round-trip operator, and the reflection coefficient matrix and transmission coefficient matrix at all media interfaces, the Jones matrix of each reflection path in the optical theoretical model is calculated. Using the Kronecker product operation, the Jones matrix of each reflection path is converted into the corresponding coherence matrix; The total coherence matrix is ​​obtained from the coherence matrices of all reflection paths, and the total coherence matrix is ​​transformed to obtain the theoretical Mueller matrix.

10. The method for measuring anisotropic transparent materials according to claim 8, characterized in that, The formula for calculating the round-trip operator is as follows: ； in, For round-trip operators; The formula for calculating the theoretical Mueller matrix is ​​as follows: ； Where M is the theoretical Mueller matrix, C total Let A be the total coherence matrix and A be the preset transformation matrix.

11. The method for measuring anisotropic transparent materials according to any one of claims 1 to 9, characterized in that, The theoretical Mueller matrix and the measured Mueller matrix are inverted and fitted to obtain the measurement results of the sample to be tested, including: Based on the thickness information and optical tensor information of the transparent substrate, a set of parameters to be fitted is constructed; Define the difference function between the theoretical Mueller matrix and the measured Mueller matrix; The set of parameters to be fitted is adjusted using an iterative optimization method to minimize the difference function, and the parameter values ​​corresponding to the set of parameters to be fitted that minimize the difference function are determined as the measurement results.

12. A measurement system for anisotropic transparent materials, characterized in that, The system, applied in the method for measuring anisotropic transparent materials as described in any one of claims 1 to 10, comprises: The model building module is used to establish an optical theoretical model of the sample under test during the ellipsometric measurement process; wherein, the sample under test includes a transparent substrate formed of anisotropic transparent material, and in the optical theoretical model, the multiple reflected light from the front surface and the back surface of the transparent substrate is incoherent light; The theoretical derivation module is used to process the optical theoretical model based on the theory of superposition of back-reflection incoherent light and derive the theoretical Mueller matrix of the sample under test in the optical theoretical model. The inversion fitting module is used to obtain the measured Mueller matrix of the sample under test during the ellipsometric measurement process, and to perform inversion fitting between the theoretical Mueller matrix and the measured Mueller matrix to obtain the measurement result of the sample under test; wherein, the measurement result includes at least the thickness information and optical tensor information of the transparent substrate.

13. A measuring device for anisotropic transparent materials, characterized in that, It includes a processor, a memory, and a computer program stored in the memory and executable on the processor, wherein the computer program, when executed, implements the method steps of the ellipticity measurement de-biasing error correction method as described in any one of claims 1 to 10.

14. A computer storage medium, characterized in that, The computer storage medium includes at least one instruction that, when executed by a computer, implements the method steps of the anisotropic transparent material measurement method as described in any one of claims 1 to 10.

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