Single-frame snapshot type rear focal plane ellipsometry method based on Mueller matrix

Abstract

The invention belongs to the technical field of optical measurement, and particularly discloses a Mueller matrix-based single-frame snapshot rear focal plane ellipsometry method, which comprises the following steps of: constructing a Mueller matrix response model of a rear focal plane ellipsometry system based on an angular spectrum kernel function and a sample Mueller matrix, the angular spectrum kernel function is used for describing the angular spectrum mapping weight of the rear focal plane ellipsometry system for sample polarization response under the conditions of different incident angles and azimuth angles; obtaining a normalized spectral image of the sample based on the back focal plane angle resolution spectral image of the sample, the back focal plane angle resolution spectral image of the reference substance and the angular spectrum kernel function; and traversing the effective radiuses of the normalized spectral image, and determining sample Mueller matrix elements under each effective radius through a Mueller matrix response model. According to the method and the device, the solution of the Mueller matrix elements of the sample can be completed only by acquiring the rear focal plane angle resolution spectral image of the single measured sample, and single-frame snapshot type rear focal plane ellipsometry is realized.

Description

Technical Field

[0001] This application belongs to the field of optical measurement technology, and more specifically, relates to a single-frame snapshot-type back focal plane ellipticity measurement method based on the Mueller matrix. Background Technology

[0002] Elliptic polarization (EL) measurement is a key technology for measuring thin film thickness, material optical constants, and characterizing the microstructure of sample surfaces. It is widely used in cutting-edge fields such as the semiconductor industry, materials science, and biosensing. Back focal plane elliptic polarization measurement utilizes the azimuth polarization modulation characteristics of the objective lens's back focal plane to acquire polarization response information of the sample at different incident angles in a single measurement.

[0003] To achieve high-precision measurements, an accurate optical system model is required. The Mueller matrix can comprehensively describe polarization effects such as polarization, birefringence, and even depolarization during the interaction between light and the sample and the optical system. Therefore, the modeling method based on the Mueller matrix is ​​the foundation for achieving high-precision measurements.

[0004] How to achieve single-frame snapshot-style back focal plane ellipticity measurement based on the Mueller matrix is ​​a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0005] In view of the shortcomings of the existing technology, the purpose of this application is to realize single-frame snapshot-type back focal plane ellipsometric measurement based on the Mueller matrix.

[0006] To achieve the above objectives, in a first aspect, this application provides a single-frame snapshot-based back focal plane ellipsometric measurement method based on the Mueller matrix, comprising: Based on the angular spectrum kernel function and the sample Mueller matrix, a Mueller matrix response model of the back focal plane ellipsometric measurement system is constructed. The angular spectrum kernel function is used to describe the angular spectrum mapping weights of the back focal plane ellipsometric measurement system to the sample polarization response under different incident angles and azimuth angles. Based on the back focal plane angle-resolved spectral image of the sample, the back focal plane angle-resolved spectral image of the reference material, and the angular spectral kernel function, the normalized spectral image of the sample is obtained. Traverse the effective radius of the normalized spectral image, and calculate the sample Mueller matrix elements for each traversed effective radius; The calculation of the sample Mueller matrix elements includes: determining the effective angle of incidence based on the effective radius and the radius-angle of incidence mapping relationship, which is used to characterize the mapping relationship between the effective radius and the effective angle of incidence; extracting the corresponding omnidirectional annular angle-resolved spectral signal from the normalized spectral image based on the effective radius and the effective angle of incidence; and determining the sample Mueller matrix elements under the effective radius based on the omnidirectional annular angle-resolved spectral signal and the Mueller matrix response model.

[0007] In one possible implementation, the Mueller matrix response model is determined by the following formula: ; in, Characterizing the Mueller matrix response, Indicates the angle of incidence. Indicates azimuth. Represents the angular spectrum kernel function. This represents the index of the element in the sequence of elements formed after the Mueller matrix is ​​flattened. Indicates at the specified angle of incidence The first sample Mueller matrix Each element.

[0008] In one possible implementation, when the sample is isotropic, the Mueller matrix response model simplifies to the following formula: ; in, Characterizing the Mueller matrix response of isotropic samples, This represents the angular spectrum kernel function corresponding to the Mueller matrix elements of an isotropic sample. The Mueller matrix elements represent isotropic samples.

[0009] In one possible implementation, the Mueller matrix of the isotropic sample is as follows: .

[0010] In one possible implementation, a normalized spectral image of the sample is obtained based on the back focal angle-resolved spectral image of the sample, the back focal angle-resolved spectral image of the reference material, and the angular spectral kernel function, including calculating the normalized spectral image of the sample using the following formula. ; in, This represents the normalized spectral image of the sample. This represents the angular-resolved spectral image of the sample's back focal plane. This represents the back focal plane angular-resolved spectral image of the reference material. The theoretical reflectivity of the reference material. It is determined based on the angular spectral kernel function and the column vectors of the Mueller matrix of the reference material, and the calculation symbols are... Dot product symbol To indicate division, add a square bracket before the calculation sign. This indicates that calculations are performed on each element of the matrix.

[0011] In one possible implementation, It is determined by the following formula: ; in, Indicates the angle of incidence. Indicates azimuth. express The range of values ​​for , This represents the index of the element in the sequence of elements formed after the Mueller matrix is ​​flattened. Represents the angular spectrum kernel function. The column vectors of the Mueller matrix represent the reference material.

[0012] In one possible implementation, before acquiring the normalized spectral image of the sample, the following is also included: Determine the center of the circle and the pupil radius of the back focal plane angle-resolved spectral image of the sample, and determine the center of the circle and the pupil radius of the back focal plane angle-resolved spectral image of the reference material. The smaller of the pupil radius of the back focal plane angle-resolved spectral image of the sample and the pupil radius of the back focal plane angle-resolved spectral image of the reference material is determined as the target pupil radius, which represents the upper limit of the effective radius. Align the back focal angle-resolved spectral images of the sample and the reference material by using the center of the circle of the back focal angle-resolved spectral image of the sample and the back focal angle-resolved spectral image of the reference material.

[0013] In one possible implementation, the effective radius can take values ​​ranging from 1 to 2. , Indicates the first One effective radius, The smaller of the pupil radius of the back focal angle-resolved spectral image of the sample and the pupil radius of the back focal angle-resolved spectral image of the reference material is given.

[0014] In one possible implementation, the radius-angle of incidence mapping is determined by the following radius-angle of incidence formula: ; in, Indicates the first One effective radius, express The corresponding effective angle of incidence, These are preset parameters.

[0015] In a second aspect, this application provides an electronic device, including: a memory and one or more processors; the memory is coupled to the one or more processors, the memory is used to store computer program code, the computer program code including computer instructions; the one or more processors invoke the computer instructions to cause the electronic device to perform the method described in the first aspect or any possible implementation of the first aspect.

[0016] Overall, the technical solutions conceived in this application have the following beneficial effects compared with the prior art: (1) Only one back focal plane angle-resolved spectral image of the sample needs to be acquired to solve the sample Mueller matrix elements, and the sample thickness, material optical constants and other parameters can be calculated quickly and accurately (the elements of the sample Mueller matrix include these parameters), realizing single-frame snapshot back focal plane ellipsometric measurement.

[0017] (2) During the calibration process, the kernel function can be calibrated once and in one go by measuring the back focal angle-resolved spectral image of a reference material with known optical properties, without having to calibrate each optical component in the system individually and tediously.

[0018] (3) Compared with the existing full Mueller matrix modeling method, this application adopts the angular spectrum kernel function. It represents the part other than the sample that can cause changes in the polarization state of the system's probe light. It can avoid modeling the Mueller matrix of each optical component in the system, thereby reducing model complexity and computing power requirements, and is suitable for large-scale data computing. Attached Figure Description

[0019] Figure 1 This is a flowchart illustrating the single-frame snapshot-based back focal plane ellipticity measurement method based on the Mueller matrix provided in this application embodiment; Figure 2 This is a schematic diagram of the structure of the back focal plane ellipticity measurement system provided in the embodiments of this application; Figure 3 This is a schematic diagram of the back focal plane angle-resolved spectral image of the sample provided in the embodiments of this application; Figure 4 This is a schematic diagram of some Mueller matrix elements under different incident angles provided in the embodiments of this application; Figure 5 This is a schematic diagram of the structure of the electronic device provided in the embodiments of this application.

[0020] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein: 1 is the polarization generator; 2 is the non-polarization beam splitter; 3 is the first lens; 4 is the back focal plane; 5 is the objective lens; 6 is the sample; 7 is the polarization analyzer; 8 is the second lens; 9 is the CMOS camera; 10 is the motion controller. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0022] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0023] In the description of the embodiments of this application, unless otherwise stated, "multiple" means two or more, for example, multiple processing units means two or more processing units, multiple elements means two or more elements, etc.

[0024] The embodiments of this application are described below with reference to the accompanying drawings.

[0025] Figure 1 This is a flowchart illustrating the single-frame snapshot-based back focal plane ellipsometric measurement method based on the Mueller matrix provided in this application embodiment, as shown below. Figure 1 As shown, the method includes steps S101 to S103.

[0026] Step S101, based on the angular spectrum kernel function (a kernel function related to the angular spectrum distribution, denoted as...) The Mueller matrix response model of the back focal plane ellipsometric measurement system is constructed using the sample Mueller matrix and the sample Mueller matrix. The angular spectrum kernel function is used to describe the angular spectrum mapping weights of the back focal plane ellipsometric measurement system to the sample polarization response under different incident angles and azimuth angles.

[0027] Figure 2 This is a schematic diagram of the structure of the back focal plane ellipticity measurement system provided in the embodiments of this application, as shown below. Figure 2 As shown, the back focal plane ellipsometric measurement system includes a polarization generator 1, a non-polarization beam splitter 2, a first lens 3, a back focal plane 4, an objective lens 5, a sample 6, a polarization analyzer 7, a second lens 8, a CMOS camera 9, and a motion controller 10.

[0028] Step S102, based on the back focal plane angular-resolved spectral image of the (tested) sample ( ), back focal plane angle-resolved spectral image of the reference material ( ) and angular spectral kernel function to obtain the normalized spectral image of the sample ( ).

[0029] Figure 3 This is a schematic diagram of the back focal plane angular-resolved spectral image of the sample provided in the embodiments of this application, wherein the radius is azimuth angle is (range 0~) (See attached image) The meaning of "@c-Si": On a silicon substrate The thin film has a thickness of 25 nm.

[0030] Step S103, traverse the effective radius of the normalized spectral image (denoted as ). For each effective radius traversed, the sample Mueller matrix elements are calculated. The calculation of the sample Mueller matrix elements includes: determining the effective incident angle (denoted as ) based on the effective radius and the radius-incident angle mapping relationship. The radius-incident angle mapping relationship is used to characterize the mapping relationship between the effective radius and the effective incident angle; based on the effective radius and the effective incident angle, the corresponding omnidirectional annular angle-resolved spectral signal (denoted as ) is extracted from the normalized spectral image. , The value range is 0~2 Based on the omnidirectional annular angle-resolved spectral signal and the Mueller matrix response model, the sample Mueller matrix elements (denoted as ) under the effective radius are determined. The elements of the sample Mueller matrix are used as the measured ellipticity parameters.

[0031] Figure 4 This is a schematic diagram of some Mueller matrix elements under different incident angles provided in the embodiments of this application. Figure 4 The red curve in the middle represents the measured values ​​of the Mueller matrix elements obtained by the method of this application. Figure 4 The black curve in the middle represents the theoretical value of the Mueller matrix element. The measured value is close to the theoretical value, which verifies the accuracy of the method in this application.

[0032] Specifically, the angular spectrum kernel function describing the polarization transmission characteristics of the system is obtained through pre-calibration. Based on this, a Mueller matrix response model of the system is constructed. During measurement, a back focal plane angular-resolved spectral image of the sample is acquired. And using the back focal plane angle-resolved spectral image of the reference material. Normalization processing is performed to obtain a normalized spectral image. Then, traverse The middle corresponds to different incident angles effective radius Extract each Lower all-around angle (0~2π) ring spectral signal Due to the angular spectrum kernel function It is known that for each fixed , to loop signal With angular spectrum kernel function By substituting the elements into the Mueller matrix response model, we can construct and solve for the Mueller matrix elements of the sample at that incident angle. The system of equations is used to resolve the complete Mueller matrix of the sample at different incident angles in one go.

[0033] Therefore, only a single back focal plane angle-resolved spectral image of the sample needs to be acquired to solve for the elements of the sample Mueller matrix, and the sample thickness, material optical constants and other parameters (the elements of the sample Mueller matrix contain these parameters) can be calculated quickly and accurately, realizing single-frame snapshot back focal plane ellipsometric measurement.

[0034] In one possible implementation, the Mueller matrix response model is determined by the following formula: ; in, Characterizing the Mueller matrix response, It represents the angle of incidence (the angle between the direction of light propagation and the surface normal of the sample being measured). Indicates azimuth. Represents the angular spectrum kernel function. This represents the index of the element in the sequence of elements formed after flattening the Mueller matrix. The value range is 1 to 16. Indicates at the specified angle of incidence The first sample Mueller matrix Each element.

[0035] Understandably, based on the Mueller matrix beam vector propagation theory, by introducing a kernel function related to the angular spectrum distribution (angular spectrum kernel function)... (This allows for the establishment of a Mueller matrix response model for the back focal plane ellipsometric measurement system.) .

[0036] The Mueller matrix response model is derived from the angular spectrum kernel function. Muller matrix elements Composed of. The inherent polarization modulation characteristics of the system are decoupled from the Mueller matrix response of the sample, and a method is adopted. This represents the components, excluding the sample, that can cause a change in the polarization state of the system's probe light. During calibration, by measuring the back focal plane angle-resolved spectrum of a reference material with known optical properties, the kernel function can be calibrated in a single, holistic manner, without requiring independent and tedious individual calibration of each optical component in the system (unlike existing full Mueller matrix modeling methods, which typically require independent and tedious individual calibration of each optical component). This system-wide calibration method ensures the integrity of the calibration, thereby improving the accuracy of the Mueller matrix response model.

[0037] Furthermore, in the known Under the premise of inverting measurement data This allows for the high-precision analysis of the Mueller matrix elements of the sample itself. .

[0038] Furthermore, compared to existing full Mueller matrix modeling methods, this application employs angular spectrum kernel functions. It represents the part other than the sample that can cause changes in the polarization state of the system's probe light. It can avoid modeling the Mueller matrix of each optical component in the system, thereby reducing model complexity and computing power requirements, and is suitable for large-scale data computing.

[0039] Therefore, compared with existing full Mueller matrix modeling methods, the Mueller matrix response model in this application has higher accuracy and lower complexity.

[0040] Optionally, the angular spectral kernel function can be calibrated by analyzing the back focal plane angular-resolved spectral image of the reference material. Specifically, one or more reference materials with precisely known optical parameters (such as refractive index and thickness) are selected, and the Mueller matrix response data of the reference material are obtained. Simultaneously, based on the known parameters of the reference material, its properties at various incident angles are calculated using a theoretical model. The Mueller matrix elements are obtained by substituting the Mueller matrix response data and Mueller matrix elements of the reference material into the above Mueller matrix response model, and then calibrating the angular spectrum kernel function.

[0041] For example, the angular spectrum kernel function can specifically be a multidimensional discrete numerical lookup table, which has three dimensions, each corresponding to a discretized incident angle. Azimuth and the element numbers of the Mueller matrix The lookup table stores different dimensions. The weights (i.e., the angular spectrum mapping weights for the sample polarization response) are used as the angular spectrum kernel function. In dimensions The values ​​are determined by this lookup table. In practical applications, when measuring any sample, the corresponding dimension can be quickly obtained based on this lookup table through table lookup and interpolation (such as bilinear interpolation). The weights below.

[0042] In one possible implementation, when the sample is isotropic, the Mueller matrix response model simplifies to the following formula: ; in, Characterizing the Mueller matrix response of isotropic samples, This represents the angular spectrum kernel function corresponding to the Mueller matrix elements of an isotropic sample. The Mueller matrix elements represent isotropic samples.

[0043] Understandably, the angular spectral kernel function can simplify the redundant features of the Mueller matrix of isotropic samples. Specifically, the simplification method involves modifying the elements of the Mueller matrix of isotropic samples. The corresponding angular spectrum kernel functions are combined to form a new angular spectrum kernel function. .

[0044] In one possible implementation, the Mueller matrix of the isotropic sample is as follows: .

[0045] In one possible implementation, the above-mentioned normalized spectral image of the sample is obtained based on the back focal plane angle-resolved spectral image of the sample, the back focal plane angle-resolved spectral image of the reference material, and the angular spectral kernel function, including calculating the normalized spectral image of the sample using the following formula. ; in, This represents the normalized spectral image of the sample. This represents the angular-resolved spectral image of the sample's back focal plane. This represents the back focal plane angular-resolved spectral image of the reference material. The theoretical reflectivity of the reference material. It is determined based on the angular spectral kernel function and the column vectors of the Mueller matrix of the reference material, and the calculation symbols are... Dot product symbol To represent division, the calculation symbol ( or Add before) This indicates that calculations are performed on each element of the matrix (implementing calculations for each incident angle and each azimuth angle).

[0046] It should be noted that a plus sign is added before the calculation symbol. This is the code representation method in MATLAB.

[0047] It is understandable that by calculating the normalized spectral image of the sample using the above formula, the range of the normalized spectral image can at least cover the smaller pupil radius (the smaller of the pupil radius of the back focal angle-resolved spectral image of the sample and the pupil radius of the back focal angle-resolved spectral image of the reference material).

[0048] In one possible implementation, It is determined by the following formula: ; in, It represents the angle of incidence (the angle between the direction of light propagation and the surface normal of the sample being measured). Indicates azimuth. express The range of values ​​for , This represents the index of the element in the sequence of elements formed after the Mueller matrix is ​​flattened. Represents the angular spectrum kernel function. The column vectors of the Mueller matrix represent the reference material.

[0049] In one possible implementation, before acquiring the normalized spectral image of the sample, the following is also included: Determine the back focal plane angular-resolved spectral image of the sample ( The center and pupil radius of the circle were determined, and the back focal plane angular-resolved spectral image of the reference material was determined. The center and pupil radius of the circle; The smaller of the pupil radius of the back focal plane angular-resolved spectral image of the sample and the pupil radius of the back focal plane angular-resolved spectral image of the reference material is determined as the target pupil radius. The target pupil radius represents the upper limit of the effective radius; Align the back focal angle-resolved spectral images of the sample and the reference material (at the incident angle and azimuth angle) based on the center of the back focal angle-resolved spectral image of the sample and the back focal angle-resolved spectral image of the reference material.

[0050] In one possible implementation, the effective radius can take values ​​ranging from 1 to 2. , Indicates the first One effective radius, The smaller of the pupil radius of the back focal angle-resolved spectral image of the sample and the pupil radius of the back focal angle-resolved spectral image of the reference material is given.

[0051] In one possible implementation, the radius-angle of incidence mapping is determined by the following radius-angle of incidence formula: ; in, Indicates the first One effective radius, express The corresponding effective angle of incidence, Preset parameters (obtained through calibration) ).

[0052] Based on the methods in the above embodiments, this application provides an electronic device, such as... Figure 5 As shown, the electronic device may include a processor 810, a communications interface 820, a memory 830, and a communication bus 840, wherein the processor 810, the communications interface 820, and the memory 830 communicate with each other through the communication bus 840. The processor 810 can call logical instructions in the memory 830 to execute the methods in the above embodiments.

[0053] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this application.

[0054] Based on the methods in the above embodiments, this application provides a computer-readable storage medium storing a computer program that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0055] Based on the methods in the above embodiments, this application provides a computer program product that, when run on a processor, causes the processor to execute the methods in the above embodiments.

[0056] It is understood that the processor in the embodiments of this application 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, transistor logic devices, hardware components, or any combination thereof. A general-purpose processor can be a microprocessor or any conventional processor.

[0057] The method steps in this application embodiment can be implemented in hardware or by a processor executing software instructions. The software instructions can consist of corresponding software modules, which can be stored in random access memory (RAM), flash memory, read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), registers, hard disks, portable hard disks, CD-ROMs, or any other form of storage medium known in the art. An exemplary storage medium is coupled to the processor, enabling the processor to read information from and write information to the storage medium. Of course, the storage medium can also be a component of the processor. The processor and the storage medium can reside in an ASIC.

[0058] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially as a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted through the computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0059] It is understood that the various numerical designations used in the embodiments of this application are merely for the convenience of description and are not intended to limit the scope of the embodiments of this application.

[0060] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A single-frame snapshot-based back focal plane ellipticity measurement method based on the Mueller matrix, characterized in that, include: Based on the angular spectrum kernel function and the sample Mueller matrix, a Mueller matrix response model of the back focal plane ellipsometric measurement system is constructed. The angular spectrum kernel function is used to describe the angular spectrum mapping weights of the back focal plane ellipsometric measurement system to the sample polarization response under different incident angles and azimuth angles. Based on the back focal plane angle-resolved spectral image of the sample, the back focal plane angle-resolved spectral image of the reference material, and the angular spectral kernel function, the normalized spectral image of the sample is obtained. Traverse the effective radius of the normalized spectral image, and calculate the sample Mueller matrix elements for each traversed effective radius; The calculation of the sample Mueller matrix elements includes: determining the effective angle of incidence based on the effective radius and the radius-angle of incidence mapping relationship, wherein the radius-angle of incidence mapping relationship is used to characterize the mapping relationship between the effective radius and the effective angle of incidence; Based on the effective radius and effective incident angle, the corresponding omnidirectional annular angle-resolved spectral signal is extracted from the normalized spectral image; based on the omnidirectional annular angle-resolved spectral signal and the Mueller matrix response model, the sample Mueller matrix elements under the effective radius are determined.

2. The single-frame snapshot-based back focal plane ellipsometric measurement method based on the Mueller matrix according to claim 1, characterized in that, The Mueller matrix response model is determined by the following formula: ； in, Characterizing the Mueller matrix response, Indicates the angle of incidence. Indicates azimuth. Represents the angular spectrum kernel function. This represents the index of the element in the sequence of elements formed after the Mueller matrix is ​​flattened. Indicates at the specified angle of incidence The first sample Mueller matrix Each element.

3. The single-frame snapshot-based back focal plane ellipticity measurement method based on the Mueller matrix according to claim 2, characterized in that, When the sample is isotropic, the Mueller matrix response model simplifies to the following formula: ； in, Characterizing the Mueller matrix response of isotropic samples, This represents the angular spectrum kernel function corresponding to the Mueller matrix elements of an isotropic sample. The Mueller matrix elements represent isotropic samples.

4. The single-frame snapshot-based back focal plane ellipsometric measurement method based on the Mueller matrix according to claim 3, characterized in that, The Mueller matrix of the isotropic sample is as follows: 。 5. The single-frame snapshot-based back focal plane ellipsometric measurement method based on the Mueller matrix according to claim 1, characterized in that, The normalized spectral image of the sample is obtained based on the back focal plane angle-resolved spectral image of the sample, the back focal plane angle-resolved spectral image of the reference material, and the angular spectral kernel function, including calculating the normalized spectral image of the sample using the following formula. ； in, This represents the normalized spectral image of the sample. This represents the angular-resolved spectral image of the sample's back focal plane. This represents the back focal plane angular-resolved spectral image of the reference material. The theoretical reflectivity of the reference material. It is determined based on the angular spectral kernel function and the column vectors of the Mueller matrix of the reference material, and the calculation symbols are... Dot product symbol To indicate division, add a square bracket before the calculation sign. This indicates that calculations are performed on each element of the matrix.

6. The single-frame snapshot-based back focal plane ellipsometric measurement method based on the Mueller matrix according to claim 5, characterized in that, It is determined by the following formula: ； in, Indicates the angle of incidence. Indicates azimuth. express The range of values ​​for , This represents the index of the element in the sequence of elements formed after the Mueller matrix is ​​flattened. Represents the angular spectrum kernel function. The column vectors of the Mueller matrix represent the reference material.

7. The single-frame snapshot-based back focal plane ellipsometric measurement method based on the Mueller matrix according to claim 1, characterized in that, Before obtaining the normalized spectral image of the sample, the following steps are also included: Determine the center of the circle and the pupil radius of the back focal plane angle-resolved spectral image of the sample, and determine the center of the circle and the pupil radius of the back focal plane angle-resolved spectral image of the reference material. The smaller of the pupil radius of the back focal plane angle-resolved spectral image of the sample and the pupil radius of the back focal plane angle-resolved spectral image of the reference material is determined as the target pupil radius, which represents the upper limit of the effective radius. Align the back focal angle-resolved spectral images of the sample and the reference material by using the center of the circle of the back focal angle-resolved spectral image of the sample and the back focal angle-resolved spectral image of the reference material.

8. The single-frame snapshot-based back focal plane ellipsometric measurement method based on the Mueller matrix according to claim 1, characterized in that, The effective radius can take values ​​ranging from 1 to 10. , Indicates the first One effective radius, The smaller of the pupil radius of the back focal angle-resolved spectral image of the sample and the pupil radius of the back focal angle-resolved spectral image of the reference material is given.

9. The single-frame snapshot-based back focal plane ellipsometric measurement method based on the Mueller matrix according to claim 1, characterized in that, The radius-angle of incidence mapping relationship is determined by the following radius-angle of incidence formula: ； in, Indicates the first One effective radius, express The corresponding effective angle of incidence, These are preset parameters.

10. An electronic device, characterized in that, include: Memory and one or more processors; The memory is coupled to the one or more processors, and the memory is used to store computer program code, the computer program code including computer instructions; The one or more processors invoke the computer instructions to cause the electronic device to perform the method as described in any one of claims 1-9.

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