A synchronous measurement method for two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states

Abstract

This invention belongs to the field of two-dimensional lateral offset measurement technology, and provides a method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states. The method includes: acquiring a metasurface lattice sample containing dual markers; determining the band structure of the quasi-continuous domain bound states and its corresponding resonant electric field distribution through electromagnetic field simulation; determining the correlation between the normalized coupling amplitude component and the overall bias vector direction through electromagnetic field simulation; establishing a multi-solution correspondence between the incident light polarization direction and the overall bias direction; determining a unique overall bias direction from the multi-solution correspondence based on the chiral spectral differences and full width at half maximum (FWHM) response exhibited by the dual markers under oblique incidence of circularly polarized light; and calculating the two-dimensional overlay error by combining the determined overall bias direction with the preset artificial bias information. Compared with traditional methods, this application achieves synchronous measurement of two-dimensional displacement in characterizing overlay errors in photolithography processes.

Description

Technical Field

[0001] This invention belongs to the field of two-dimensional lateral offset measurement technology, specifically relating to a method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states. Background Technology

[0002] In micro- and nano-scale manufacturing, accurately and synchronously characterizing the two-dimensional lateral offset between adjacent functional layers within an integrated structure is a fundamental challenge in modern precision manufacturing. This interlayer displacement not only determines the intrinsic configuration of multilayer devices but also directly affects their performance. Therefore, achieving high-precision synchronous acquisition of this parameter is crucial for ensuring the performance and manufacturing yield of high-end devices. For example, in advanced lithography processes, in-plane interlayer displacement typically manifests as overlay error; exceeding the allowable range will lead to device malfunction. In multilayer superlenses, excessive interlayer displacement introduces wavefront aberrations that cannot be corrected by subsequent optical methods. In MEMS devices, interlayer displacement caused by residual stress directly affects their mechanical stability and operational lifespan.

[0003] Currently, existing technologies still face numerous limitations in the synchronous and precise measurement of two-dimensional displacement between adjacent layers within integrated structures. Taking the interlayer displacement control of multilayer metalenses as an example, patent CN202410115266.4 proposes using fabrication positioning marks within the structural plane to align windows and control interlayer displacement, but it does not address synchronous measurement methods. In measuring overlay errors in advanced lithography processes, most techniques still employ separate measurements of x and y displacements, making true synchronous two-dimensional measurement difficult. Although some studies have proposed methods for synchronously acquiring two-dimensional overlay errors, such as the scheme proposed by Rohrich et al., their accuracy and efficiency are limited by the size and quality of the pre-stored signal library, making it difficult to achieve both simultaneously. In recent years, metasurface technology has provided new possibilities for synchronous two-dimensional displacement measurement, but existing research largely focuses on the relative displacement measurement between external objects and metasurfaces. For example, the technical solutions of patents CN202210022572.4, CN202310597156.1, CN201822012776.1, CN201811466247.7 are all dedicated to measuring the two-dimensional displacement of the metasurface relative to the optical axis, but have not yet effectively addressed the measurement needs of interlayer offset within the integrated structure.

[0004] Therefore, there is an urgent need to develop a new measurement scheme that can simultaneously measure the two-dimensional displacement inside an integrated structure. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states, thereby resolving the issues in the prior art. The technical solution adopted by this invention is as follows: A method for synchronous measurement of two-dimensional displacement on metasurfaces based on quasi-continuous domain bound states includes: A meta-lattice sample with dual labels is obtained, where each label is pre-biased; then, the band position of the quasi-continuous bound state of the meta-lattice sample and its corresponding resonant electric field distribution are determined by electromagnetic field simulation. The correlation between the normalized coupled amplitude components and the overall bias vector direction was determined through electromagnetic field simulation. By changing the polarization state of the incident light and analyzing the changes in the full width at half maximum (FWHM) of the spectrum, a multi-solution correspondence between the polarization direction of the incident light and the overall bias vector direction is established. Based on the chiral spectral differences and full width at half maximum (FWHM) responses exhibited by the dual-labeled array under oblique incidence of circularly polarized light, the overall bias vector direction is determined from the aforementioned multi-solution correspondence. The two-dimensional overlay error is calculated by combining the overall offset vector direction with the artificial offset.

[0006] Furthermore, the correlation between the normalized coupled amplitude components and the overall bias vector direction is determined through electromagnetic field simulation, including: Based on the resonant electric field distribution, the magnitudes of the coupled amplitude components corresponding to the quasi-continuous domain bound states under different overall bias vector directions are calculated and expressed as follows: in, Let D be the resonant field, D be the normalized coupled amplitude component, and r be the spatial position vector. It represents an infinitesimal volume element in three-dimensional space.

[0007] Furthermore, when the metalattice sample is a bilayer cylindrical metasurface with a lattice period of a, if the resonant electric field is in The irreducible representation under the symmetric group is , A symmetry group is a geometric symmetry structure with a fourfold rotation axis and four mirrors including that axis. As a symmetry breaking condition, OVL represents the overlay error, where... The magnitude of the two-dimensional overlay error. For the overlay error and the direction angle in the x-direction, the normalized coupled amplitude components satisfy the following relationship: If the resonant electric field is The irreducible representation under the symmetric group is Then, by introducing the overall bias vector direction as a symmetry breaking condition, the normalized coupled amplitude components satisfy: .

[0008] Furthermore, by changing the polarization state of the incident light and analyzing the changes in the full width at half maximum (FWHM) of the spectrum, based on the temporal coupled-mode theory, it can be expressed as: in Let be the resonant frequency, where d and u represent the wave amplitudes propagating downwards and upwards, respectively; subscripts x and y represent the polarization components of the wave in different directions, r and t represent the background non-resonant reflection and transmission amplitudes of the metastructure lattice, respectively, and A is the normalization coefficient; subscripts 1 and 2 represent the amplitudes calculated directly above and below the outer boundary of the structure, respectively. It is the angular frequency of the incident light. , These are the x and y components of the normalized coupled amplitude. Under unilateral incidence, the wave amplitude vector is ,in The polarization angle; when the incident light polarization angle satisfies , At this point, the reflectivity is at its maximum, and the full width at half maximum (FWHM) extends to its maximum value.

[0009] Furthermore, half-height full-width It satisfies a square-proportional relationship with the direction of the overall offset vector, expressed as: K is a proportional parameter.

[0010] Furthermore, a multi-solution correspondence is established between the incident light polarization direction and the overall bias vector direction, including: Incident light polarization angle Overall bias vector direction ,when , At that time, the incident light polarization angle Two global bias vector directions are generated: , ,in: ; Calculate the acute angle between each marked solution and its respective artificial bias direction. , .

[0011] Furthermore, based on the chiral spectral differences and full width at half maximum (FWHM) responses exhibited by the dual-labeled array under oblique incidence of circularly polarized light, the overall bias vector direction is determined from the multiple-solution correspondence, including: Judgment if > , < Is it valid? If true, then the angle between the acute angle and the direction of the artificial bias is... The solution is the true solution of one of the labels; If this is not the case, then the angle between the angle and the preset artificial bias direction is... The solution is the true solution of one of the labels; Finally, a true solution with a label is obtained; By observing the chiral distribution corresponding to the two labels through oblique incident circularly polarized light and rotating the azimuth angle, the angle between the chiral responses of the two labels is obtained as follows: ; Combine the obtained true solution with Angle coupling, as the true solution for another label.

[0012] Furthermore, by combining the overall offset vector direction with the artificial offset, the two-dimensional overlay error is calculated and expressed as: in, , This is a preset, artificial bias. , The angle between the directions of the overall offset vector; This refers to the overlay error obtained from the measurement.

[0013] Furthermore, when At that time, the one-dimensional overlay error was solved.

[0014] This invention offers the following advantages: Leveraging the unique optical properties of quasi-continuous bound states (quasi-BIC), it achieves high-precision synchronous measurement of displacements in the X and Y directions within a two-dimensional plane. Compared to traditional interlayer displacement measurement methods, this invention overcomes the technical limitations of single-direction measurement and multi-step detection, enabling the simultaneous acquisition of displacement information in two orthogonal directions during a single measurement. This significantly improves the overall efficiency and accuracy of displacement measurement and allows for precise characterization at the nanoscale.

[0015] In the specific technical solution, the present invention adopts a dual-marker measurement method, which combines the polarization difference and spectral intensity characteristics of chiral spectra for analysis. By identifying the characteristic chiral response signals under different displacement states, the uniqueness and reliability of displacement measurement results are guaranteed from the measurement principle.

[0016] Furthermore, this invention establishes a quantitative relationship between the normalized coupling amplitude components and the overall bias direction between metasurface layers, and derives and verifies the intrinsic correlation between the two. This method not only provides a new theoretical framework for characterizing interlayer displacement in bilayer metasurface structures, but also offers important technical references for the structural characterization, performance optimization, and precision manufacturing of micro / nano devices.

[0017] Therefore, this invention can achieve high-precision synchronous measurement of multidimensional displacement in complex micro-nano structures, which has good theoretical innovation significance and broad engineering application prospects. Attached Figure Description

[0018] Figure 1 This is a flowchart illustrating a synchronous measurement of two-dimensional displacement of a metasurface based on a quasi-continuous domain bound state, according to an embodiment of this application. Figure 2 This is a schematic diagram of the metasurface measurement sample marking structure according to an embodiment of this application; wherein, (a) is a three-dimensional view of the metasurface marking; and (b) is a cross-sectional view of the overlay marking. Figure 3 The intrinsic properties of the metasurface according to the embodiments of this application are: (a) the band structure of the BIC; (b) the corresponding quality factor; (c) the Ey component corresponding to point T in the band structure; and (d) the coupling amplitude components (Dx, Dy) of the mode under different bias vector directions. Figure 4 The behavior of the metasurface in the present application embodiment of the full width at half maximum (FWHM) under the scanning incident polarization state is shown; wherein, (a) the behavior of FWHM marked 1 as a function of the polarization angle; and (b) the behavior of FWHM marked 2 as a function of the polarization angle.

[0019] Figure 5 The intrinsic polarization states and chiral distribution of the metasurface in momentum space according to the embodiments of this application are shown; wherein, (a) the intrinsic polarization state of marker 1 in momentum space; (b) the distribution of chirality of marker 1 with azimuth angle; (c) the intrinsic polarization state of marker 2 in momentum space; and (d) the distribution of chirality of marker 2 with azimuth angle. Detailed Implementation

[0020] The following will be described in conjunction with embodiments of the present invention. Figures 1-2 The technical solutions in the embodiments of the present invention will be clearly and completely described. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Unless otherwise specified, the technical means used in the embodiments are conventional means well known to those skilled in the art.

[0021] like Figure 1 This invention proposes a method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states, comprising the following steps: S1. Obtain a meta-lattice sample containing double markers. The double markers are a pair of markers with the same overlay error. An artificial bias is preset on them with the same magnitude and opposite direction. Each marker is preset with an artificial bias. Then, the band position of the quasi-continuous domain bound state (q-BIC) and its corresponding resonant electric field distribution are determined by electromagnetic field simulation.

[0022] In this embodiment, for a given pair of metasurface samples, each marker is pre-set with an artificial bias of equal size and opposite direction. Under the known prior distribution information, computational electromagnetic field simulation is performed to determine the band position of the quasi-continuous domain bound state (q-BIC) of the metasurface sample and its corresponding resonant electric field distribution, while giving an irreducible representation of the resonant electric field distribution.

[0023] S2, through electromagnetic field simulation, determines the correlation between the normalized coupled amplitude components and the overall bias vector direction, i.e., the mapping model. .

[0024] In this embodiment, the overall offset vector direction (in The size of the two-dimensional bias. (where the direction angle is relative to the x-direction) Specifically, the calculation of the normalized coupled amplitude components is characterized by the following integral formula: The coupled amplitude components have been normalized. Let D be the resonant field, D be the normalized coupled amplitude component, and r be the spatial position vector. Let represent an infinitesimal volume element in three-dimensional space, and let be the integral performed on the unit cell volume of the superlattice.

[0025] When the metalattice sample is a bilayer cylindrical metasurface with a lattice period of a, if the resonant electric field is distributed in... The irreducible representation under the symmetric group is Then, the direction of the global bias vector is introduced as a symmetry breaking condition. A symmetry group is a geometric symmetry structure with a fourfold rotation axis and four mirrors including that axis. As a symmetry breaking condition, OVL represents the overlay error, where... The magnitude of the two-dimensional overlay error. Let the overlay error be related to the direction angle in the x-direction; at this time, the normalized coupled amplitude component D satisfies the following relationship: If the resonant electric field is distributed in The irreducible representation under the symmetric group is When the overall bias vector direction is introduced as a symmetry breaking condition, the normalized coupled amplitude component D satisfies: The above relationship is derived under the condition of first-order perturbation and is applicable to... In this case, the method does not require the mapping model of step S2. This allows for the direct establishment of the correlation between the normalized coupled amplitude components and the overall bias vector direction.

[0026] S3, the correlation between the normalized coupled amplitude components and the overall bias vector direction is determined through electromagnetic field simulation; Specifically, by scanning the polarization state of the incident light, the polarization angle corresponding to the maximum full width at half maximum (FWHM) is found. The overall bias vector direction is then solved according to the mapping model. However, there is a double solution, namely, the overall bias vector direction angle marked at 1 / 2. , , .

[0027] In this embodiment, by changing the polarization state of the incident light and analyzing the changes in the full width at half maximum (FWHM) of the spectrum, the physical process is described using the temporal coupled-mode theory: in Let be the resonant frequency, where d and u represent the wave amplitudes propagating downwards and upwards, respectively. The subscripts x and y represent the polarization components of the wave in different directions, r and t are the background non-resonant reflection and transmission amplitudes of the metastructure lattice, respectively, and A is the normalization coefficient. Subscripts 1 and 2 represent the amplitudes calculated directly above and below the outer boundary of the structure, respectively. It is the angular frequency of the incident light. , These are the x and y components of the normalized coupled amplitude.

[0028] This theoretical framework is used to describe the polarization-selective coupling behavior between the metalattice markers and the optical field in the quasi-BIC resonance mode, under unilateral incidence conditions, where the wave amplitude vector is... ,in Let be the polarization angle. Theoretical models can derive that when the incident light polarization angle satisfies ... , When the polarization angle of the incident light reaches its maximum value of 1, the full width at half maximum (FWHM) is broadened to its maximum value, thus establishing a mapping model between the polarization angle of the incident light and the coupling amplitude.

[0029] The above S2 has established a mapping model between the normalized coupled amplitude components and the overall bias vector direction. Based on the two mapping relationships above, the polarization angle can be obtained. To the overall offset direction Complete parsing mapping The overall bias direction can be obtained based on the mapping relationship. However, due to the polarization angle ,but This method has a double solution problem when determining the direction of the overlay error vector, namely, the overall offset direction angle of the mark 1 / 2. , And both satisfy Simultaneously, the acute angle between each marked solution and its respective preset artificial bias direction is calculated. , .

[0030] In this example, the full width at half maximum (FWHM) of the spectral response is measured using a micro-area angular-resolved scatterometer. It satisfies a square-proportional relationship with the direction of the overall offset vector, that is: S4. By changing the polarization state of the incident light and analyzing the changes in the full width at half maximum (FWHM) of the spectrum, a multi-solution correspondence between the polarization direction of the incident light and the overall bias direction is established. Specifically, the two full widths and heights obtained through double marking , We obtain a true direction solution for the label.

[0031] In this example, by judging if > , < Is it true? If so, then the acute angle between it and the preset artificially biased direction is... The solution is the true solution marked 1. If it is not, the acute angle between it and the preset artificially biased direction is... The solution is the true solution marked 2.

[0032] S5 introduces external chirality to solve for the true direction solution of another marker.

[0033] In this example, an extrinsic chirality mechanism is introduced to determine the true orientation of the other marker. By obliquely incident circularly polarized light and rotating the azimuth angle, the chiral distributions corresponding to the two markers are observed, and the angle between their chiral responses is obtained. The true direction solution for the other marker is the angle between the true directions obtained from S4. The solution.

[0034] S6. Based on the obtained true orientation of the double marks, perform OVL calculation to obtain the two-dimensional overlay error.

[0035] In this embodiment, the formula for calculating the two-dimensional overlay error is: In the formula, The overlay error obtained by measurement, To pre-set a human bias, , The angle between the directions of the overall offset vector of the double marker. When this is done, the corresponding solution method for one-dimensional overlay error is adopted.

[0036] The present invention provides the following specific embodiments: The structural design and material selection referenced existing research. This metasurface consists of a two-layer structure, each layer composed of a square array (spacing p) of silicon (TiO2) disks (radius R, thickness h). The bottom disk is completely embedded in fused silica, while the top disk is located in air above the fused silica separator layer. Figure 2 As shown. The total offset δ includes the preset offset (d) and the overlay error (OVL) generated during manufacturing. Two opposite preset offsets are considered in the simulation, where the preset offset... = , OVL= The linewidths or critical dimensions (CD) of the two gratings are the same. The optical constants of TiO2 and SiO2 are taken from T. Siefke, et al. Adv. Opt. Mater. 4, 1780–1786 and G. Jungk, et al. Phys. Status Solidi B215(1), 731–736(1999), respectively.

[0037] S1, through electromagnetic field simulation, determines the band structure of the quasi-continuous bound state (q-BIC) and its corresponding resonant electric field distribution, such as... Figure 3 As shown in (a)-(c), Figure 3 (a) shows the band structure of the BIC, with an extremely high quality factor Q at the Γ point ( Figure 3 (b) confirms the existence of BIC. Figure 3 (c) shows the electric field component distribution of this mode in the xz plane, indicating that this band is the TE band, and its irreducible expression is: model.

[0038] S2, determining the mapping model between the normalized coupled amplitude components and the overall bias vector direction through electromagnetic field simulation. Its mapping model is as follows Figure 3 As shown in (d), it satisfies For a double-layered cylindrical metasurface, the irreducible representation that meets the conditions can be directly obtained from the mapping model. Skip step S2.

[0039] S3, by scanning the polarization state of the incident light, the polarization angle that maximizes the full width at half maximum (FWHM) can be found, such as... Figure 4 As shown, the behavior of FWHM for labels 1 and 2 as the polarization angle changes is given. It can be seen that when the polarization angle reaches , The FWHM corresponding to markers 1 and 2 reaches its maximum, according to = This means that the overlay error vectors corresponding to marks 1 and 2 at this time are respectively in the direction of... , Simultaneously, the acute angle between each marked solution and its respective preset artificial bias direction is calculated. , Next, we will conduct a selection process for the two solutions.

[0040] S4, the two full width at half maximum (FWHM) values ​​obtained through double marking. ,at this time Then at this time, the one marked 1 .

[0041] S5, given the incident angle as At that time, the chiral distribution diagrams of markers 1 and 2 in real space are different, derived from circular dichroism. To express, , Let be the reflectance of the incident circularly polarized light, such as Figure 5 As shown, (a) and (c) are the intrinsic polarization states in momentum space corresponding to the two labels, and (b) and (d) are the CD distribution diagrams corresponding to the two labels. The red area represents right circular polarization. It can be seen that the angle between the chiral distributions of label 1 and label 2 is acute, thus indicating... .

[0042] S6. Based on the obtained true orientation of the double marks, perform OVL calculation to obtain the two-dimensional overlay error. The final result is then obtained. nm, nm, total OVL=50.5nm, it can be seen that the error is only 0.5nm at this time, and the error in both directions is less than 1nm.

[0043] The above embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Any modifications, alterations, or substitutions made by those skilled in the art to the technical solutions of the present invention without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states, characterized in that, include: Obtain hyperlattice samples including dual-labeled samples, where each label is pre-biased. Then, the band structure of the quasi-continuous bound state of the meta-lattice sample and its corresponding resonant electric field distribution are determined by electromagnetic field simulation. The correlation between the normalized coupled amplitude components and the overall bias vector direction was determined through electromagnetic field simulation. By changing the polarization state of the incident light and analyzing the changes in the full width at half maximum (FWHM) of the spectrum, a multi-solution correspondence between the polarization direction of the incident light and the overall bias vector direction is established. Based on the chiral spectral differences and full width at half maximum (FWHM) responses exhibited by the dual-labeled array under oblique incidence of circularly polarized light, the overall bias vector direction is determined from the aforementioned multi-solution correspondence. The two-dimensional overlay error is calculated by combining the overall offset vector direction with the artificial offset.

2. The method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states according to claim 1, characterized in that, The correlation between the normalized coupled amplitude components and the overall bias vector direction was determined through electromagnetic field simulation, including: Based on the resonant electric field distribution, the magnitudes of the coupled amplitude components corresponding to the quasi-continuous domain bound states under different overall bias vector directions are calculated and expressed as follows: in, Let D be the resonant field, D be the normalized coupled amplitude component, and r be the spatial position vector. It represents an infinitesimal volume element in three-dimensional space.

3. The method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states according to claim 2, characterized in that, When the metalattice sample is a bilayer cylindrical metasurface with a lattice period of a, if the resonant electric field is in The irreducible representation under the symmetric group is , A symmetry group is a geometric symmetry structure with a fourfold rotation axis and four mirrors including that axis. As a symmetry breaking condition, OVL represents the overlay error, where... The magnitude of the two-dimensional overlay error. For the overlay error and the direction angle in the x-direction, the normalized coupled amplitude components satisfy the following relationship: If the resonant electric field is The irreducible representation under the symmetric group is Then, by introducing the overall bias vector direction as a symmetry breaking condition, the normalized coupled amplitude components satisfy: 。 4. The method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states according to claim 1, characterized in that, When the polarization state of the incident light is changed and the change in the full width at half maximum (FWHM) of the spectrum is analyzed, based on the temporal coupled-mode theory, it can be expressed as: in Let be the resonant frequency, where d and u represent the wave amplitudes propagating downwards and upwards, respectively; subscripts x and y represent the polarization components of the wave in different directions, r and t represent the background non-resonant reflection and transmission amplitudes of the metastructure lattice, respectively, and A is the normalization coefficient; subscripts 1 and 2 represent the amplitudes calculated directly above and below the outer boundary of the structure, respectively. It is the angular frequency of the incident light. , These are the x and y components of the normalized coupled amplitude. Under unilateral incidence, the wave amplitude vector is ,in The polarization angle; when the incident light polarization angle satisfies , At this point, the reflectivity is at its maximum, and the full width at half maximum (FWHM) extends to its maximum value.

5. The method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states according to claim 4, characterized in that, Half height full width It satisfies a square-proportional relationship with the direction of the overall offset vector, expressed as: K is a proportional parameter.

6. The method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states according to claim 4, characterized in that, Establishing multiple possible correspondences between the incident light polarization direction and the overall bias vector direction, including: Incident light polarization angle Overall bias vector direction ,when , At that time, the incident light polarization angle Two global bias vector directions are generated: , ,in: ; Calculate the acute angle between each marked solution and its respective artificial bias direction. , .

7. The method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states according to claim 6, characterized in that, Based on the chiral spectral differences and full width at half maximum (FWHM) responses exhibited by the dual-labeled array under oblique incidence of circularly polarized light, the overall bias vector direction is determined from the multiple-solution correspondence, including: Judgment if > , < Is it valid? If true, then the angle between the acute angle and the direction of the artificial bias is... The solution is the true solution of one of the labels; If this is not the case, then the angle between the angle and the preset artificial bias direction is... The solution is the true solution of one of the labels; Finally, a true solution with a label is obtained; By observing the chiral distribution corresponding to the two labels through oblique incident circularly polarized light and rotating the azimuth angle, the angle between the chiral responses of the two labels is obtained as follows: ; Combine the obtained true solution with Angle coupling, as the true solution for another label.

8. The method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states according to any one of claims 1-7, characterized in that, Combining the overall offset vector direction and the artificial offset, the two-dimensional overlay error is calculated and expressed as: in, , This is a preset, artificial bias. , The angle between the directions of the overall offset vector; This refers to the overlay error obtained from the measurement.

9. The method for synchronous measurement of two-dimensional displacement of metasurfaces based on quasi-continuous domain bound states according to claim 8, characterized in that, when At that time, the one-dimensional overlay error was solved.

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