Thermal aberration analysis method for high-precision image position alignment measurement lens

Abstract

The present invention relates to the field of thermal aberration analysis, and in particular to a thermal aberration analysis method for a high-precision image position alignment measurement lens, comprising: S1. constructing a geometric optical model of a double telecentric lens; S2. constructing a solid mechanics structure model based on the double telecentric lens and a lens barrel for fixing the double telecentric lens; S3. constructing a heat transfer model; S4. constructing an optical dispersion model; S5. using the above model to perform bidirectional coupled ray tracing and parametric scanning, respectively calculating two situations of adding only a geometric optical interface and adding both a geometric optical interface and a solid mechanics interface, and obtaining calculation results of the two situations; S6. using a point array diagram, a focus shift amount, and a wavefront aberration to compare and analyze the calculation results of the two situations, and evaluate the imaging performance of the double telecentric lens. The present invention analyzes the influence of various environmental factors on the imaging results through multi-physical field coupling.

Description

Technical Field

[0001] The invention belongs to the technical field of thermal aberration analysis, and in particular relates to a thermal aberration analysis method for a high-precision image position alignment measurement lens. Background Art

[0002] The rapid development of microelectronics and nanotechnology is continuously leading the innovation process of micro-nano manufacturing technology dominated by lithography. This innovative achievement has gradually become one of the key imaging performances to measure the national scientific and technological competitiveness. Alignment technology is one of the key sub-module technologies in the lithography process, and alignment technology directly determines the final effect after overlay. At present, the feature size that can be achieved by cutting-edge lithography equipment has reached the level below 10nm, the overlay accuracy of the lithography machine is 1 / 3 of the feature size, and the alignment measurement accuracy is about 1 / 5-1 / 3 of the overlay accuracy of the lithography machine. In view of the above basic requirements for alignment accuracy, lithography alignment technology with extremely high precision has received great attention. For the lithography machine image position alignment imaging system, it mainly includes four parts: pre-alignment and positioning of the mask, pre-alignment of the wafer, alignment of the mask workbench and the wafer workbench, and alignment of the mask and the wafer. Most of the current alignment technologies adopt large-volume, low-precision working modes, and the alignment technology based on video images is considered to be an alignment technology with great practical application prospects due to its advantages of simple operation, high accuracy and high robustness. Although a large number of related research results have been published, these studies mainly focus on improving the sensitivity and accuracy of measurements, and do not explore the potential impact of multiple environmental factors coupling on lithography alignment accuracy. In fact, video image-based alignment technology depends to a large extent on the performance of the lithography machine image position alignment imaging system, and is closely related to environmental factors.

[0003] The image position alignment imaging system of the lithography machine has a growing demand for high-precision optical performance analysis technology. The standards implemented by each optical lens in the material selection, design, manufacturing, debugging and assembly must be extremely rigorous. During the assembly process of the image position alignment imaging system of the lithography machine, the surface shape error caused by factors such as the optical lens' own weight, clamping method, and support structure will have an unpredictable impact on the imaging quality of the image position alignment imaging system of the lithography machine. In addition, during the operation of the lithography machine, the lens of the image position alignment imaging system of the lithography machine will be reflected, transmitted, and absorbed under the illumination of the lighting system, which will cause uneven temperature distribution on the lens surface and further cause deformation of the lens. Therefore, the stability of the optical lens and its supporting structure in the working environment will directly affect the positioning accuracy of the image position alignment imaging system of the lithography machine. However, this stability is closely related to many factors, such as the self-weight of the optical lens, the design of the support and clamping structure, the application of clamping force, slight fluctuations in ambient temperature, and heat source loading. These factors may cause the surface shape of the optical lens to change, and then cause problems such as visual axis drift and wavefront distortion in the lithography image alignment imaging system, and ultimately cause the entire optical path to change. In order to ensure the imaging quality of the lithography image alignment imaging system, the above-mentioned influencing factors must be coupled and analyzed and corresponding measures must be taken when necessary. Summary of the invention

[0004] In view of this, the present invention aims to provide a method for analyzing thermal aberration of a high-precision image position alignment measurement lens to solve the problem that the imaging performance of the current alignment method based on video images is easily affected by the environment.

[0005] To achieve the above object, the technical solution created by the present invention is implemented as follows:

[0006] A method for analyzing thermal aberration of a lens for high-precision image position alignment measurement comprises the following steps:

[0007] S1. Geometric optics modeling: Construct the geometric optics model of the bi-telecentric lens in COMSOL software;

[0008] S2. Solid mechanics structure modeling: A solid mechanics structure model is constructed in COMSOL software based on a bi-telecentric lens and a lens barrel for fixing the bi-telecentric lens;

[0009] ;

[0010] In the formula, is the initial mass density, is the structural displacement, the gradient operator is relative to the material coordinates, is the deformation gradient, is the second Piola-Kirchhoff stress tensor, is the body stress component in the current state;

[0011] S3. Heat transfer modeling: Construct a heat transfer model in COMSOL software;

[0012] ;

[0013] In the formula, is the specific heat capacity under constant stress, is the velocity vector of the translational motion, is the conductive heat flux, is the radiation heat flux, is the coefficient of thermal expansion, For external heat source.

[0014] S4. Optical dispersion modeling: Construct an optical dispersion model in COMSOL software;

[0015] ;

[0016] ;

[0017] In the formula, is the refractive index of the lens, is the ambient temperature, is the thermo-optical coefficient; is the expression of the refractive index changing with temperature, through the thermo-optic coefficient The dispersion formula is integrated to obtain: is the temperature difference, To calculate the temperature difference The reference temperature, is the thermo-optical dispersion coefficient;

[0018] S5. Optical and mechanical coupling calculation: The geometric optical model, solid mechanical structure model, heat transfer model, and optical dispersion model of the dual telecentric lens are used to perform bidirectional coupled ray tracing and parametric scanning, and two situations are calculated respectively: one is to add only the geometric optical interface and the other is to add both the geometric optical interface and the solid mechanical interface, to obtain the first calculation result and the second calculation result;

[0019] S6. Analysis of calculation results: The first calculation result and the second calculation result are compared and analyzed with the help of the point diagram, focus shift and wavefront aberration to evaluate the imaging performance of the bi-telecentric lens.

[0020] Furthermore, the double telecentric lens adopts asymmetrically distributed front lens group and rear lens group, the front lens group and the rear lens group respectively include five lenses, the image distance of the double telecentric lens is 20 mm, and the object distance of the double telecentric lens is 80 mm.

[0021] Furthermore, bidirectional coupled ray tracing is achieved by solving a set of coupled first-order ordinary differential equations to calculate the ray trajectories:

[0022] ;

[0023] ;

[0024] In the formula, Indicates the light position, represents the wave vector, represents angular frequency, t represents time;

[0025] Wave Vector and angular frequency The relationship is

[0026] ;

[0027] In the formula, represents the speed of light in a vacuum;

[0028] When light enters and leaves a lens, it refracts:

[0029] ;

[0030] In the formula, is the refractive index of the medium before entering the lens, is the refractive index of the lens, and are the angle of incidence and angle of refraction of the light respectively.

[0031] Furthermore, when only the geometric optical interface is added, the first calculation result only considers the influence of the refractive index change caused by temperature drift on the imaging performance of the bi-telecentric lens; when the geometric optical interface and the solid mechanics interface are added at the same time, the second calculation result considers the influence of the refractive index change caused by temperature drift coupled with thermal expansion on the imaging performance of the bi-telecentric lens.

[0032] Furthermore, based on the first calculation result, a point diagram that only considers the refractive index change caused by temperature drift is obtained, and the RMS, focal shift and wavefront aberration at different temperatures are obtained; based on the second calculation result, the point diagram after the refractive index change is coupled with thermal expansion is obtained, and the RMS, focal shift and wavefront aberration at different temperatures are obtained.

[0033] Compared with the prior art, the invention can achieve the following beneficial effects:

[0034] Based on the idea of ​​multi-physical field analysis, the geometric optical model, solid mechanics structure model, heat transfer model, and optical dispersion model of the dual-telecentric lens are constructed for multi-physical field coupling. Since the nature of each model is multi-dimensional and multi-scale, after coupling physical factors such as structural mechanics, heat transfer, and dispersion, the superposition effect of different physical fields can be obtained, thereby realizing the analysis of the influence of different environmental factors on the imaging performance of the dual-telecentric lens. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The drawings constituting part of the present invention are used to provide a further understanding of the present invention. The exemplary embodiments and descriptions of the present invention are used to explain the present invention and do not constitute an improper limitation on the present invention. In the drawings:

[0036] Figure 1 It is a flow chart of a method for analyzing thermal aberration of a lens with high-precision image position alignment measurement according to an embodiment of the invention;

[0037] Figure 2 is a schematic diagram of a fixing method of each lens according to an embodiment of the invention;

[0038] Figure 3 is a schematic diagram of a light trajectory after multi-physical field coupling calculation according to an embodiment of the invention;

[0039] Figure 4a-4c It is a point diagram under different ambient temperatures when only the refractive index change caused by temperature drift is considered according to the embodiment of the invention;

[0040] Figure 5a-5c is a schematic diagram of thermal stress distribution of the lens structure at different temperatures according to an embodiment of the invention;

[0041] Figure 6a-6c It is a point diagram under different ambient temperatures when the factors affecting the refractive index change and thermal expansion are considered simultaneously according to the embodiment of the invention;

[0042] Figure 7a-7c It is a schematic diagram of wavefront aberration under different ambient temperatures when only the refractive index change caused by temperature drift is considered according to an embodiment of the invention;

[0043] Figure 8a-8c It is a schematic diagram of wavefront aberration under different ambient temperatures when the factors affecting the refractive index change caused by temperature drift and thermal expansion are considered simultaneously according to an embodiment of the invention.

[0044] The reference numerals include: object plane 1, front lens group 2, rear lens group 3, image plane 4, lens 5, and lens barrel 6. DETAILED DESCRIPTION

[0045] In order to make the purpose, technical solution and advantages of the invention more clear, the invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described here are only used to explain the invention and do not constitute a limitation of the invention.

[0046] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0047] In the description of the present invention, it should be understood that the terms "center", "longitudinal", "lateral", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside" and the like indicate positions or positional relationships based on the positions or positional relationships shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as a limitation on the present invention. In addition, the terms "first", "second", etc. are only used for descriptive purposes, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, features defined as "first", "second", etc. may explicitly or implicitly include one or more of the features. In the description of the present invention, unless otherwise specified, "multiple" means two or more.

[0048] In the description of the invention, it should be noted that, unless otherwise clearly specified and limited, the terms "installation", "connection" and "connection" should be understood in a broad sense, for example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection, or it can be indirectly connected through an intermediate medium, or it can be the internal communication of two components. For ordinary technicians in this field, the specific meanings of the above terms in the invention can be understood according to specific circumstances.

[0049] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments.

[0050] like Figure 1 As shown, the present invention provides a method for analyzing thermal aberration of a lens for high-precision image position alignment measurement, comprising the following steps:

[0051] S1. Geometric optics modeling: Construct a geometric optics model of the bi-telecentric lens in COMSOL software.

[0052] Optical lens is an important guarantee to ensure the accuracy and stability of the position measurement system based on the centroid positioning principle. The factors that can affect the corresponding position relationship between the object point and the image point, such as lens distortion, resolution, and telecentricity, will affect the positioning accuracy of the light spot. In order to achieve micron-level precision position measurement, a double telecentric lens is designed. In order to compress the volume, reduce the weight, and achieve optical observation with large depth of field, low distortion, and large observation range, the entire double telecentric lens adopts asymmetrically distributed front and rear lens groups. Each lens group consists of 5 lenses, a total of 10 lenses. The double telecentric lens uses HLAK1 and HZF39 as the main lens materials, with ultra-high object telecentricity and image telecentricity. The image distance of the double telecentric lens is 20mm, and the object distance of the double telecentric lens is 80mm. For the specific design of the double telecentric lens, please refer to the patent with publication number CN118033878A and publication date July 2, 2024, so it will not be repeated here.

[0053] S2. Solid mechanics structure modeling: A solid mechanics structure model is constructed in COMSOL software based on the bi-telecentric lens and the lens barrel for fixing the bi-telecentric lens.

[0054] Light may interact with the deformed solid mechanical structure, causing it to be reflected or refracted in a direction different from that of the undeformed solid mechanical structure. Stress displacement is actually the result of all external forces applied to the solid mechanical structure. In this case, the solid mechanical structure mainly consists of a bi-telecentric lens and a lens barrel that holds it in place. The lens barrel has undergone a preliminary stress-deformation finite element analysis, and the deformation and strain caused by gravity do not affect the image quality. However, due to changes in temperature, solid mechanical structures may also deform due to thermal stress, as changes in temperature may cause them to expand or contract. As the temperature changes, the total inelastic strain in the lens also undergoes a thermal strain term. The change of thermal strain Defined as:

[0055] ;

[0056] In the formula, represents the thermal expansion coefficient, T represents the temperature of the thermo-optical dispersion medium, Indicates the reference temperature.

[0057] Thermal strain term Used to calculate the total inelastic strain in the lens, which is a parameter required in the calculation of solid mechanics structural model equations.

[0058] Set the effect of thermal expansion on the solid mechanics structure. Thermal expansion requires a solid mechanics interface and pays attention to the overall change of the ambient temperature. Add a subnode under the linear elastic material, add the linear elastic material under the subnode, and enter the required temperature here. In addition, in solid mechanics calculations, there must be a constraint. Here, the present invention chooses to apply a fixed constraint at the position of the lens barrel 6, which means that the middle lens 5 is deforming, but the lens barrel 6 remains stationary. The lens is fixed in the following way: Figure 2 shown.

[0059] The solid mechanics structure model constructed is:

[0060] ;

[0061] In the formula, is the initial mass density, is the structural displacement, the gradient operator is relative to the material coordinates, is the deformation gradient, is the second Piola-Kirchhoff stress tensor, is the body stress component in the current state.

[0062] S3. Heat transfer modeling: Construct a heat transfer model in COMSOL software.

[0063] The heat transfer model constructed is:

[0064] ;

[0065] In the formula, is the specific heat capacity under constant stress, is the velocity vector of the translational motion, is the conductive heat flux, is the radiation heat flux, is the coefficient of thermal expansion, For external heat source.

[0066] Temperature is often affected by many boundary conditions such as heat sources and heat sinks (such as Joule heating or chemical reactions) and heat exchange between the external environment such as convection or radiation. Temperature will directly affect the propagation path of light in the thermo-optical dispersive medium, and the refractive index is a function of temperature. In addition, temperature will also indirectly affect the path of light because thermal stresses may cause boundary deformation.

[0067] The temperature was set as the global parameter ambient temperature at the medium properties and was set to 22°C ± 1.5°C during the subsequent parametric scanning process.

[0068] S4. Optical dispersion modeling: Construct an optical dispersion model in COMSOL software.

[0069] The geometric optics interface is used to track the rays as they reflect and refract across the boundary. The refractive index of different materials is often affected by factors such as wavelength and temperature, and changes in a functional manner. Once the lens system is deformed, the light may interact with its deformed geometry. In this special case, the ray path is affected by both temperature and structural deformation.

[0070] The Medium Properties node of the Geometrical Optics interface allows the selection of an optical dispersion model that defines the refractive index as a function of the vacuum wavelength (or temperature) via a set of equations and coefficients.

[0071] The equation of the optical dispersion model gives the expression for the variation of refractive index with temperature , which is obtained by the thermo-optical coefficient It is obtained by integrating the dispersion formula.

[0072] The constructed optical dispersion model is:

[0073] ;

[0074] ;

[0075] In the formula, is the refractive index of the lens, is the ambient temperature, is the thermo-optical coefficient; is the expression of the refractive index changing with temperature, through the thermo-optic coefficient The dispersion formula is integrated to obtain: is the temperature difference, To calculate the temperature difference The reference temperature, is the thermo-optical dispersion coefficient.

[0076] Select Get dispersion model from material from the Optical dispersion model list to automatically detect the optical dispersion model based on the material properties defined for each material. This option allows you to create an optical dispersion model even if different glasses from different manufacturers have different standards for the optical dispersion model.

[0077] To set the effect of temperature on the refractive index, modify the reference temperature to directly adjust the refractive index. In the medium properties, set the input temperature , The temperature parameter that the present invention is concerned with can be defined in the parameters. If you want to see the effect of a specific temperature, just enter If you want to see the effect of a range of temperatures, you can perform a parameter sweep over the temperature. Here, define , respectively, in the parametric sweep , only the influence of the refractive index is considered. After completing the above settings, you can directly perform the calculation.

[0078] S5. Calculation of optical and mechanical coupling: The geometric optical model, solid mechanics structure model, heat transfer model, and optical dispersion model of the dual telecentric lens are used to perform bidirectional coupled ray tracing and parametric scanning. Two situations are calculated, one in which only the geometric optical interface is added, and the other in which both the geometric optical interface and the solid mechanics interface are added. The first calculation result and the second calculation result are obtained.

[0079] Bidirectional coupled ray tracing requires two key settings: 1. Check Include geometric nonlinearity, otherwise mechanical deformation will not affect optics; 2. Select a fixed number of iterations. The default value is 5. If you want a more accurate result, you can set it higher, but this will increase the calculation time, so here the default value of 3 is selected.

[0080] The ray trajectory is calculated by solving a set of coupled first-order ordinary differential equations. The ray trajectory after multi-physics field coupling calculation is as follows: Figure 3 As shown, Figure 3 From right to left in the figure are object plane 1, double front lens group 2, rear lens group 3 and image plane 4.

[0081] ;

[0082] ;

[0083] In the formula, Indicates the light position, represents the wave vector, represents angular frequency, t represents time;

[0084] Wave Vector and angular frequency The relationship is

[0085] ;

[0086] In the formula, represents the speed of light in a vacuum;

[0087] When light enters and leaves a lens, it refracts:

[0088] ;

[0089] In the formula, is the refractive index of the medium before entering the lens, is the refractive index of the lens, and are the angle of incidence and angle of refraction of the light respectively.

[0090] When only the geometric optics interface is added, the first calculation result only considers the influence of the refractive index change caused by temperature drift on the imaging result of the double telecentric lens; when both the geometric optics interface and the solid mechanics interface are added, the second calculation result considers the influence of the refractive index change caused by temperature drift coupled with thermal expansion on the imaging result of the double telecentric lens.

[0091] S6. Analysis of calculation results: The first calculation result and the second calculation result are compared and analyzed with the help of the point diagram, focus shift and wavefront aberration to evaluate the imaging performance of the bi-telecentric lens.

[0092] The first and second calculation results are analyzed in depth to predict the performance of the optical model. Two factors that affect the imaging results of the bi-telecentric lens are first quantitatively analyzed, namely the change in the lens refractive index and the distribution of its thermal stress. The imaging results of the bi-telecentric lens are then evaluated using the point diagram RMS, focal length shift, and wavefront aberration. A comparative analysis is performed in the following two cases: one is to consider only the effect of the refractive index change caused by temperature drift on the imaging results, and the other is to consider the combined effect of the refractive index change and thermal expansion on the imaging results.

[0093] The refractive index of the two lenses in the center varies with the ambient temperature as shown in Table 1. Magnitude.

[0094] Table 1 Changes of the refractive index of the two central lenses with ambient temperature

[0095]

[0096] Considering only the point diagram of the refractive index change caused by temperature drift, the results are as follows Figure 4a-4c The RMS and focal shift at different temperatures are shown in Table 2:

[0097] Table 2 RMS and focal shift when only considering the refractive index change caused by temperature drift

[0098]

[0099] Based on the above research, after adding solid mechanics calculation, the thermal stress distribution of the system is analyzed as follows: Figure 5a-5c As shown in Figure 3, the stress distribution is basically concentrated at the edge, and the stress in the middle of the lens is relatively small. The maximum stress values ​​at different temperatures are shown in Table 3:

[0100] Table 3 Maximum stress values ​​at different temperatures

[0101]

[0102] Considering the coupling of the refractive index change and the thermal expansion factor, the point diagram is obtained as follows Figure 6a-6cThe RMS and focal shift at different temperatures are shown in Table 4:

[0103] Table 4 RMS and focal shift under the influence of thermo-optical dispersion and thermal expansion factors

[0104]

[0105] For optical systems with very high imaging quality requirements, in most cases, it is necessary to evaluate the imaging quality of the optical system by studying the deformation of the light wavefront after passing through the optical system, that is, it is necessary to use wavefront aberration to evaluate. When only considering the refractive index change caused by temperature drift, the wavefront aberration at different ambient temperatures is as follows: Figure 7a-7c As shown, the present invention couples the refractive index change with the influence of thermal expansion factors, and the obtained wavefront aberration is as follows Figure 8a-8c Its maximum values ​​at different temperatures are shown in Table 5:

[0106] Table 5 Maximum wavefront aberration under the influence of thermo-optic dispersion and thermal expansion factors

[0107]

[0108] The present invention calculates two situations respectively, namely, adding only geometric optics interface and adding both geometric optics and solid mechanics interface. By analyzing the calculation results of these two situations, the influence of various factors on the imaging results in the thermal aberration phenomenon can be more clearly observed.

[0109] It should be understood that the various forms of processes shown above can be used to reorder, add or delete steps. For example, the steps described in the disclosure of the present invention can be performed in parallel, sequentially or in different orders, as long as the desired results of the technical solution disclosed in the present invention can be achieved, and this document does not limit this.

[0110] The above specific implementations do not constitute a limitation on the protection scope of the present invention. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for analyzing thermal aberration of a lens for high-precision image position alignment measurement, characterized in that: The steps include: S1. Geometric optics modeling: Construct the geometric optics model of the bi-telecentric lens in COMSOL software; S2. Solid mechanics structure modeling: A solid mechanics structure model is constructed in COMSOL software based on a bi-telecentric lens and a lens barrel for fixing the bi-telecentric lens: ； In the formula, is the initial mass density, is the structural displacement, the gradient operator is relative to the material coordinates, is the deformation gradient, is the second Piola-Kirchhoff stress tensor, is the body stress component in the current state; S3. Heat transfer modeling: Construct a heat transfer model in COMSOL software; ； In the formula, is the specific heat capacity under constant stress, is the velocity vector of the translational motion, is the conductive heat flux, is the radiation heat flux, is the coefficient of thermal expansion, For external heat source; S4. Optical dispersion modeling: Constructing the optical dispersion model in COMSOL software: ； ； In the formula, is the refractive index of the lens, is the ambient temperature, is the thermo-optical coefficient; is the expression of the refractive index changing with temperature, through the thermo-optic coefficient The dispersion formula is integrated to obtain: is the temperature difference, To calculate the temperature difference The reference temperature, is the thermo-optical dispersion coefficient; S5. Optical and mechanical coupling calculation: The geometric optical model, solid mechanical structure model, heat transfer model, and optical dispersion model of the dual telecentric lens are used to perform bidirectional coupled ray tracing and parametric scanning, and two situations are calculated respectively: one is to add only the geometric optical interface and the other is to add both the geometric optical interface and the solid mechanical interface, to obtain the first calculation result and the second calculation result; S6. Analysis of calculation results: The first calculation result and the second calculation result are compared and analyzed with the help of the point diagram, focus shift and wavefront aberration to evaluate the imaging performance of the bi-telecentric lens.

2. The method for analyzing thermal aberration of a lens for high-precision image position alignment measurement according to claim 1, characterized in that: The double telecentric lens adopts asymmetrically distributed front lens group and rear lens group. The front lens group and the rear lens group include five lenses respectively. The image distance of the double telecentric lens is 20mm, and the object distance of the double telecentric lens is 80mm.

3. The method for analyzing thermal aberration of a lens for high-precision image position alignment measurement according to claim 1, characterized in that: Bidirectional coupled ray tracing is achieved by solving a set of coupled first-order ordinary differential equations to calculate the ray trajectories: ； ； In the formula, Indicates the light position, represents the wave vector, represents angular frequency, t represents time; Wave Vector and angular frequency The relationship is ； In the formula, represents the speed of light in a vacuum; When light enters and leaves a lens, it refracts: ； In the formula, is the refractive index of the medium before entering the lens, is the refractive index of the lens, and are the angle of incidence and angle of refraction of the light respectively.

4. The method for analyzing thermal aberration of a lens for high-precision image position alignment measurement according to claim 3, characterized in that: When only the geometric optical interface is added, the first calculation result only considers the influence of the refractive index change caused by temperature drift on the imaging performance of the bi-telecentric lens; when both the geometric optical interface and the solid mechanics interface are added, the second calculation result considers the influence of the refractive index change caused by temperature drift coupled with thermal expansion on the imaging performance of the bi-telecentric lens.

5. The method for analyzing thermal aberration of a lens for high-precision image position alignment measurement according to claim 3, characterized in that: According to the first calculation result, a point diagram is obtained which only considers the refractive index change caused by temperature drift, and the RMS, focal shift and wavefront aberration at different temperatures are obtained; according to the second calculation result, a point diagram after the refractive index change is coupled with thermal expansion is obtained, and the RMS, focal shift and wavefront aberration at different temperatures are obtained.

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