Ellipsoidal mirror surface thin film thickness distribution calculation method and system

Abstract

The application relates to an ellipsoidal mirror surface film thickness distribution calculation method and system, which comprises the following steps: firstly, calculating the radial light beam incidence angle distribution curve of the ellipsoidal optical element surface; then, respectively calculating the minimum and maximum light beam incidence angle corresponding optimization film thickness, which is used as the initial range of the film thickness distribution optimization; then, from the minimum light beam incidence angle, the optimization film thickness of the current incidence angle is used as the lower limit of the next incidence angle film thickness optimization range, the incidence angle is gradually increased, and the optimization film thickness under all angles is finally obtained through three-stage iteration; finally, the film thickness distribution and working wavelength reflectivity are visualized. The application avoids the cumbersome operation of independent optimization for each incidence angle in the traditional design, avoids the low efficiency and precision problem caused by the difficulty in accurately setting the optimization range during the artificial optimization, and significantly improves the calculation efficiency, automation degree and repeatability of the ellipsoidal mirror surface film thickness distribution.

Description

Technical Field

[0001] This invention belongs to the field of optical thin film design and optimization technology, specifically relating to a dynamic optimization calculation method and system for the thin film thickness distribution on the surface of an ellipsoidal mirror. It is applicable to the thin film thickness design and spectral characteristic optimization of complex curved surfaces such as ellipsoidal mirrors and aspherical optical elements, and can be widely used in fields such as laser optics, astronomical observation, and high-precision mirror manufacturing. Background Technology

[0002] Ellipsoidal mirrors, due to their unique curved surface structure, can focus light beams from different directions to a single focal point, playing an irreplaceable role in systems such as laser resonators and astronomical telescopes. However, because the incident angle of the light beam varies at different points on their surface, the thickness distribution of the thin film directly affects the reflectivity characteristics at the operating wavelength. Traditional thin film design methods typically optimize independently for a single incident angle or a limited angle range, resulting in problems such as low efficiency, limited accuracy, and poor repeatability. On the one hand, the film thickness needs to be optimized individually for each incident angle, which is computationally intensive and time-consuming, especially for high-precision sampling points (such as dozens of radial positions), making the optimization process cumbersome. On the other hand, manually setting the optimization range is prone to errors due to insufficient experience, leading to local optima that are difficult to coordinate globally with the film thickness distribution at different angles, affecting the uniformity of reflectivity. Furthermore, the optimization process relies on manual intervention, and the calculation results of different batches or operators may differ, making it difficult to ensure design consistency. While existing technologies can calculate reflectivity at specific angles using optical thin film characteristic matrix theory or commercial film system design software, they lack automated methods for dynamically coordinating film thickness distribution at multiple angles. This fails to meet the high-precision and high-efficiency thin film design requirements of ellipsoidal mirrors. Therefore, developing a method for calculating the film thickness distribution of ellipsoidal mirrors that can automatically calculate the dynamic optimization range and gradually approach the global optimal solution has become a key technical issue for improving the performance of optical systems. Summary of the Invention

[0003] The technical problem this invention aims to solve is to overcome the shortcomings of traditional methods and propose a dynamic optimization calculation method for the thin film thickness distribution on the surface of an ellipsoidal reflector. This method is implemented through the following steps: First, based on the geometric parameters of the ellipsoidal reflector (semi-major axis, semi-medium axis, semi-minor axis, aperture) and sampling positions, the radial beam incident angle distribution curve is calculated to provide an angular benchmark for film thickness optimization. Next, the maximum and minimum incident angles are extracted and their optimized film thicknesses are calculated respectively, using this interval as the initial range to avoid the subjectivity of manual setting. Then, starting from the minimum incident angle, the optimized film thickness at the current angle is used as the lower limit of the next angle optimization range. The incident angle is gradually increased, and through three levels of iteration—coarse optimization (large interval), fine optimization (small interval), and ultrafine optimization (micro interval)—the globally optimal film thickness distribution at all angles is finally obtained. Finally, a film thickness distribution curve and a working wavelength reflectivity distribution curve are generated, and interactive software allows users to input geometric parameters, film structure, and working wavelength, automatically completing the optimization calculation and dynamically updating the results. This invention eliminates the need for independent optimization of each incident angle by using a dynamic optimization range adjustment and a three-level iterative optimization mechanism, thus significantly shortening the calculation time. At the same time, by automatically coordinating the film thickness distribution at multiple angles through software, it eliminates errors caused by human intervention, significantly improving the automation and repeatability of ellipsoidal mirror film design, and providing an efficient and reliable solution for calculating film thickness distribution for high-precision optical systems.

[0004] The technical solution of the present invention is as follows:

[0005] A method for calculating the thickness distribution of a thin film on the surface of an ellipsoidal reflector, characterized by the following steps:

[0006] Step S1. Obtain the incident angle distribution of the beam:

[0007] Acquire multiple sampling points radially distributed on the surface of the ellipsoidal mirror. P i Corresponding beam incident angle AOI i Where i = 1, 2, 3...N, N is the number of sampling points, and the incident angle of the beam changes monotonically along the radial direction;

[0008] Step S2. Determine the initial film thickness optimization range:

[0009] The sampling point with the smallest incident angle of the light beam among the plurality of sampling points is the first sampling point. P 1. The sampling point with the largest incident angle of the beam, i.e., the Nth sampling point. P N Based on the preset membrane structure, material parameters, and operating wavelength λ, targetGiven the incident beam polarization state, the optimized film thickness corresponding to the first sampling point and the Nth sampling point is calculated respectively, and these are determined as the lower limit D of the film thickness optimization range. Ymin and upper limit value D Ymax This constructs an initial film thickness optimization space containing the potential optimal film thickness for all sampling points; where Y represents the material, which can be a high-refractive-index material layer or a low-refractive-index material layer.

[0010] Step S3. Dynamically and progressively optimize the film thickness at each sampling point:

[0011] From the first sampling point P Starting with point 1, following the order of increasing beam incident angle, perform the following optimization operations on each sampling point in sequence:

[0012] Within the current film thickness optimization range of the current sampling point, a scanning calculation is performed with a preset optimization step size to obtain the film thickness combination that maximizes the reflectivity of the sampling point at the working wavelength, which is taken as the optimal film thickness of the current sampling point.

[0013] The optimal film thickness is used as the lower limit of the film thickness optimization range for the next sampling point, while the upper limit remains unchanged, thereby dynamically updating the film thickness optimization range for the next sampling point.

[0014] Repeat the above steps until all N sampling points have been optimized, and the optimal film thickness D for each sampling point is obtained. Y-UltraFine-i and the corresponding working wavelength reflectivity R i ;

[0015] Step S4. Generate and output film thickness and reflectivity distribution curves: Using the sampling point location as the abscissa and the optimal film thickness and working wavelength reflectivity as the ordinate, generate and output the film thickness distribution curve and the working wavelength reflectivity distribution curve, respectively.

[0016] The incident angle of the beam in step S1 AOI i Obtain it through the following methods:

[0017] Read the geometric parameters of the ellipsoidal reflector, including at least the semi-major axis length. L MajorAxis Length of semi-central axis and semi-minor axis L MinorAxis Component diameter D and the lateral distance of each sampling point from the major axis r i ;

[0018] Calculate the incident angle of the beam at each sampling point. AOI i The formula is as follows:

[0019]

[0020] In the formula, Sampling points P i The vector to the point of incidence of the light ray. Sampling points P i The normal vector at that point.

[0021] Step S2, which involves calculating the optimized film thickness corresponding to the first sampling point and the Nth sampling point, specifically includes:

[0022] Calculate the angle of refraction of the light beam inside the film using Snell's law. AOI Yi The formula is as follows:

[0023] n 0×sin( AOI i )= n Y ×sin( AOI Yi )

[0024] in, n 0 is the refractive index of air. n Y Let Y be the refractive index of material Y at the working wavelength.

[0025] Based on the quarter-wavelength film thickness formula, the thickness coefficients of each tunable film layer corresponding to the first sampling point and the Nth sampling point are calculated respectively. d Yi And based on this, the initial coarse optimization range for each tunable film layer is set [0.65×]. d Yi 1.35× d Yi The formula is as follows:

[0026] d Yi =| λ target / (4× n Y ×cos( AOI Yi ))|

[0027] Within the initial coarse optimization range, at the first optimization interval Interval Coarse Using the step size, reflectivity scanning optimization is performed using the optical thin film feature matrix method to obtain the optimized film thickness corresponding to the first sampling point and the Nth sampling point, which are respectively used as the lower limit and upper limit of the film thickness optimization range.

[0028] First optimization interval Interval Coarse According to the operating wavelength λ target The order of magnitude is adaptively determined, as shown in the following formula:

[0029] Interval Coarse =10 log10(λtarget)-2

[0030] In the formula, This indicates rounding down to the nearest integer.

[0031] The optimization operation described in step S3 also includes performing a three-level precision-advancing optimization sub-step for each sampling point:

[0032] Level 1, coarse optimization sub-step: Within the current film thickness optimization range of the current sampling point, at the first optimization interval... Interval Coarse Scanning optimization is performed to obtain the coarsely optimized film thickness D. Y-Coarse-i ;

[0033] The second level, the fine-tuning sub-step: Using the coarse-optimized film thickness as the center, construct a reduced fine-tuning range [D]. Y-Coarse-i - Interval Coarse D Y-Coarse-i + Interval Coarse ], with the second optimization interval Interval Fine Scanning optimization was performed to obtain finely optimized film thickness D. Y-Fine-i ;in, Interval Fine No greater than 0.5× Interval Coarse ;

[0034] The third level, ultrafine optimization sub-step: Using the optimized film thickness as the center, construct a reduced ultrafine optimization range [D]. Y-Fine-i - Interval Fine D Y-Fine-i + Interval Fine ], with the third optimization interval Interval UltraFine The scanning step size is optimized to obtain the ultrafine optimized film thickness, i.e., the optimal film thickness D. Y-UltraFine-i and the reflectivity at the operating wavelength corresponding to this film thickness combination. R i ;in, Interval UltraFine No greater than 0.1× Interval Coarse .

[0035] A system for calculating the thickness distribution of a thin film on the surface of an ellipsoidal reflector, characterized in that it includes:

[0036] The parameter input module is used to receive user-inputted geometric parameters of the ellipsoidal reflector, membrane structure parameters, material parameters, and operating wavelength information.

[0037] The incident angle distribution calculation module, connected to the parameter input module, is used to calculate the incident angle of the beam at each sampling point according to the geometric parameters and a preset ellipsoid equation and vector operation rules. AOI i, and generate a sequence of incident beam angles distributed radially;

[0038] The initial optimization range determination module is connected to the incident angle distribution calculation module. It is used to calculate the optimized film thickness corresponding to the minimum and maximum incident angles based on the sampling points corresponding to the minimum and maximum incident angles in the incident angle sequence of the beam, combined with the film structure, material parameters and working wavelength, and set them as the lower limit and upper limit of the film thickness optimization range, respectively, so as to construct an initial film thickness optimization space covering the entire angle range.

[0039] Dynamic progressive optimization module: connected to the initial optimization range determination module and the incident angle distribution calculation module, used to calculate the final optimized film thickness and corresponding working wavelength reflectivity of each sampling point in order from small to large incident angle of the beam;

[0040] Visualization output module: Connected to the dynamic progressive optimization module, it is used to automatically generate and display the film thickness distribution curve and the working wavelength reflectance distribution curve based on the lateral distance of each sampling point from the major axis, the final optimized film thickness, and the corresponding working wavelength reflectance.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] 1) Improve computational efficiency: By dynamically optimizing the range and using a three-level iterative optimization mechanism, the independent optimization of each incident angle is eliminated, significantly shortening the computation time and improving the computational efficiency of the ellipsoidal reflector thin film thickness distribution. This is especially suitable for high-precision sampling points and reduces the tedious computation process.

[0043] 2) Enhanced automation and repeatability: The interactive software automatically coordinates the film thickness distribution at multiple angles, eliminating errors caused by human intervention. The calculation results of different batches or operators are highly consistent, significantly improving the automation and repeatability of the ellipsoidal mirror thin film design and providing a reliable guarantee for the stable fabrication of high-precision optical systems. Attached Figure Description

[0044] Figure 1 This is a flowchart of the method for calculating the thin film thickness distribution on the surface of the ellipsoidal reflector according to the present invention;

[0045] Figure 2 This is a film thickness distribution curve of Embodiment 1 of the present invention;

[0046] Figure 3 This is a working wavelength reflectance distribution curve of Embodiment 1 of the present invention;

[0047] Figure 4 This is a film thickness distribution curve of Embodiment 2 of the present invention;

[0048] Figure 5 This is a working wavelength reflectance distribution curve of Embodiment 2 of the present invention. Detailed Implementation

[0049] The present invention will now be described in detail with reference to the embodiments and accompanying drawings. Those skilled in the art will understand that the embodiments described herein are only for explaining the present invention and are not intended to limit its scope of protection.

[0050] like Figure 1 As shown, a method for calculating the thickness distribution of a thin film on the surface of an ellipsoidal reflector includes the following steps:

[0051] Step S1: Calculate the incident angle distribution curve of the beam;

[0052] S1.1 Read the geometric parameters of the ellipsoidal mirror: semi-major axis length L MajorAxis Length of semi-central axis and semi-minor axis L MinorAxis Component diameter D Number of sampling points N Sampling location P i (i=1, 2, 3...N) and their lateral distances from the major axis r i ;

[0053] S1.2 Calculate all sampling positions according to formula (1) P i Corresponding beam incident angle AOI i ;

[0054] (1)

[0055] in Sampling location P i The vector to the point of incidence of the light ray. Sampling locationP i The normal vector at that point.

[0056] ;

[0057] ;

[0058] Step S2: Calculate the initial film thickness optimization range based on the beam incident angle range;

[0059] S2.1 Read the operating wavelength of the ellipsoidal mirror λ target The polarization state of the incident beam, and the film structure (e.g., substrate |(HBL)). n H|Air or substrate|(LBH) n L|air), and substrate and film material parameters, including the refractive index of the substrate at the operating wavelength. n s The working wavelength refractive index of the H material layer n H The working wavelength refractive index of the L material layer n L The working wavelength refractive index of material layer B n B The film thickness of material B is fixed as follows: d B (≥0);

[0060] S2.2 Calculate the initial lower limit of optimization:

[0061] -make i =1, calculate the lower limit coefficient of H material layer thickness optimization according to formulas (2) and (3). d H1 The optimized thickness range for layer H is [0.65×]. d H1 1.35× d H1 ];

[0062] - The lower limit coefficient for the thickness optimization of the L material layer is calculated according to formulas (4) and (5). d L1 The optimized thickness range for layer L is [0.65×]. d L1 1.35× d L1 ];

[0063] n 0×sin( AOI i )= n H ×sin( AOIHi (2)

[0064] d Hi =| λ target / (4× n H ×cos( AOI Hi ))|(3)

[0065] n 0×sin( AOI i )= n L ×sin( AOI Li (4)

[0066] d Li =| λ target / (4× n L ×cos( AOI Li ))|(5)

[0067] - Calculate the optimal film thickness spacing according to formula (6) Interval Coarse In the formula, Indicates rounding down;

[0068] Interval Coarse =10 log10(λtarget)-2 (6)

[0069] -Based on the feature matrix of optical thin films, Interval Coarse To optimize the film thickness, the spacing is optimized, and the beam incident angle is optimized as follows: AOI The optimal film thickness at a thickness of 1 yields the highest reflectivity at the operating wavelength, including the optimized film thickness of the H material layer. D Hmin L-material layer optimized film thickness D Lmin ;Will D Hmin and D Lmin As the initial lower limit for optimizing the film thickness of the H material layer and the L material layer;

[0070] S2.3 Calculate the initial optimization upper limit:

[0071] -makei =N, calculate the upper limit coefficient of H material layer thickness optimization according to formulas (2) and (3). d HN The optimized thickness range for layer H is [0.65×]. d HN 1.35× d HN ];

[0072] - Calculate the upper limit coefficient for the thickness optimization of the L material layer according to formulas (4) and (5). d LN The optimized thickness range for layer L is [0.65×]. d LN 1.35× d LN ];

[0073] -Based on the feature matrix of optical thin films, Interval Coarse To optimize the beam incident angle for film thickness spacing, the beam incident angle is as follows: AOI N The optimal film thickness, which yields the highest reflectivity at the operating wavelength, is obtained by optimizing the film thickness of the H material layer. D Hmax L-material layer optimized film thickness D Lmax ,Will D Hmax and D Lmax As the initial upper limit for optimizing the film thickness of the H and L material layers;

[0074] S2.4. Obtain the optimized range of the initial film thickness of the H material layer as [ D Hmin , D Hmax The initial film thickness optimization range for the L material layer is []. D Lmin , D Lmax ];

[0075] Step S3: Within the initial film thickness optimization range, calculate the optimal film thickness for different beam incident angles:

[0076] S3.1 Order i =1;

[0077] S3.2 Optimizes the beam incident angle in three steps. AOI i Film thickness at time:

[0078] - Step 1 (Coarse Optimization): Let the optimization range of the H material layer thickness be [ D Hmin, D Hmax The optimized range for the film thickness of material L is []. D Lmin , D Lmax The film thickness optimization interval is: Interval Coarse The optimized film thickness D of the H material layer under the optimized film thickness interval was obtained. H-Coarse-i L material layer optimized film thickness D L-Coarse-i ;

[0079] - Step 2 (Fine Optimization): Set the H material layer thickness optimization range to [D] H-Coarse-i - Interval Coarse D H-Coarse-i + Interval Coarse The optimized range for the film thickness of material L is [D]. L-Coarse-i - Interval Coarse D L-Coarse-i + Interval Coarse ], film thickness optimization spacing Interval Fine No greater than 0.5× Interval Coarse The optimized film thickness D of the H material layer under the optimized film thickness interval was obtained. H-Fine-i L material layer optimized film thickness D L-Fine-i ;

[0080] - Step 3 (Ultra-fine Optimization): Set the thickness optimization range of the H material layer to [D]. H-Fine-i - Interval Fine D H-Fine-i + Interval Fine The optimized range for the film thickness of material L is [D]. L-Fine-i - Interval Fine D L-Fine-i + Interval Fine ], film thickness optimization spacing Interval UltraFine No greater than 0.1× Interval Coarse The optimized film thickness D of the H material layer under the optimized film thickness interval was obtained. H-UltraFine-i L material layer optimized film thickness D L-UltraFine-i The highest reflectivity of the operating wavelength R i ;

[0081] S3.3. Order D Hmin = DH-UltraFine-i , D Lmin = D L-UltraFine-i Update and optimize the lower limit of the range;

[0082] S3.4. Let i = i + 1, and repeat steps S3.2 and S3.3 until i = N.

[0083] Step S4: Generate film thickness distribution curves and working wavelength reflectance distribution curves:

[0084] S4.1 Plot the film thickness distribution curve: based on the sampling point location P i Lateral distance from the major axis r i The horizontal axis represents the optimized film thickness of the H material layer. D H-UltraFine-i And L material layer optimized film thickness D L-UltraFine-i Plot the film thickness distribution curves of material H and material L layers on the ordinate.

[0085] S4.2 Plot the reflectance distribution curve: based on the sampling point location P i The x-axis represents the highest reflectivity at the operating wavelength. R i Plot the reflectivity distribution curve at the working wavelength using the vertical axis.

[0086] The reflectivity at the aforementioned working wavelength can also be calculated using the Fresnel formula.

[0087] Example 1: Calculation of film thickness distribution in Mo / Si multilayer film system

[0088] This embodiment uses a Mo / Si multilayer ellipsoidal mirror with a working wavelength of 13.5 nm in an extreme ultraviolet lithography light source system as an example to illustrate the method for calculating the thin film thickness distribution on the surface of the ellipsoidal mirror of the present invention. The mirror is required to have high reflectivity for light with a wavelength of 13.5 nm at different incident angles on its surface.

[0089] Step S1: Read the geometric parameters of the ellipsoidal mirror and calculate the incident angle distribution curve of the beam.

[0090] S1.1 Read the geometric parameters of the ellipsoidal mirror: semi-major axis length L MajorAxis =400mm, semi-center axis and semi-minor axis length L MinorAxis =300mm, component diameter D =250mm, Number of sampling points N =6. Use position P 1 (r1=0 mm)P 2 (r2=25mm) P 3 (r3=50 mm) P 4 (r4=75 mm) P 5 (r5=100 mm) P 6 (r6=125 mm);

[0091] S1.2 Calculate the incident angle of the beam: Calculate all sampling positions according to formula (1) P i ( i The incident angles of the beams at different sampling positions are obtained by calculating the incident angles of the beams at positions 1, 2, ..., 6. AOI 1 (0.00°) AOI 2 (4.20°) AOI 3 (8.36°) AOI 4 (12.43°) AOI 5 (16.38°) AOI 6 (20.18°).

[0092] (1)

[0093] in, Sampling location P i The vector to the point of incidence of the light ray. Sampling location P i The normal vector at that point.

[0094] ;

[0095] ;

[0096] Step S2: Calculate the initial film thickness optimization range based on the beam incident angle range;

[0097] S2.1 Reading film system and material parameters: Reading the operating wavelength of the ellipsoidal mirror λ target (13.5 nm), polarization state (average component) of the incident beam, film structure (substrate | (LBH)) 50 L|air), and substrate and film material parameters. A silicon wafer was used as the substrate, with a refractive index of 13.5 nm. n s The values ​​are 0.999057632-0.001715709i; Si is used as the material for the L layer, and Si has a refractive index of 13.5 nm. n LThe values ​​are 0.999057632-0.001715709i; Mo is used as the material for the H layer, and Mo has a refractive index of 13.5 nm. n H The value is 0.923951321-0.006422472i; the B material layer is not used, meaning the thickness of the B layer is... d B =0;

[0098] S2.2. Calculate the initial lower limit of optimization:

[0099] -make i =1, and the lower limit coefficient for the thickness optimization of the H material layer is obtained by calculating according to formulas (2) and (3). d H1 The value is 3.38, and the optimized range for the thickness of the H layer is [2.20, 4.56].

[0100] - The lower limit coefficient for the thickness optimization of the L material layer is calculated according to formulas (4) and (5). d L1 The value is 3.65, and the optimized range for the film thickness of the L layer is [2.37, 4.93].

[0101] n 0×sin( AOI i ) = n H ×sin( AOI Hi (2)

[0102] d Hi =| λ target / (4× n H ×cos( AOI Hi ))|(3)

[0103] n 0×sin( AOI i ) = n L ×sin( AOI Li (4)

[0104] d Li =| λ target / (4× n L ×cos( AOI Li ))|(5)

[0105] - Calculate the optimal film thickness interval according to formula (6), where, This indicates rounding down to the nearest integer, after calculation. Interval Coarse It is 0.1 nm;

[0106] Interval Coarse =10 log10(λtarget)-2 (6)

[0107] -Based on the optical thin film feature matrix, with a film thickness interval of 0.1 nm, the beam incident angle is optimized as follows: AOI The optimal film thickness for achieving the highest reflectivity at the operating wavelength is 1: H material layer optimized film thickness. D Hmin Optimize film thickness for 2.7 nm, L material layer D Lmin The thickness is 4.2 nm; 2.7 nm and 4.2 nm are used as the lower limits for optimizing the film thickness of the H material layer and the L material layer;

[0108] S2.3 Calculate the initial optimization upper limit:

[0109] -make i =6, calculate the upper limit coefficient of H material layer thickness optimization according to formula (2) and (3). d H6 The thickness was 3.59 nm, and the optimized range of the H layer thickness was [2.33, 4.85].

[0110] -Calculate the upper limit coefficient for the thickness optimization of the L material layer according to formulas (4) and (5). d L6 The thickness was 3.92 nm, and the optimized range of the L layer thickness was [2.55, 5.30].

[0111] -Based on the optical thin film feature matrix, with a film thickness interval of 0.1 nm, the beam incident angle is optimized as follows: AOI The optimal film thickness for achieving the highest reflectivity at the working wavelength is 6: Optimal film thickness for the H material layer. D Hmax Optimize film thickness for 2.9 nm, L material layer D Lmax The thickness is set at 4.5 nm, with 2.9 nm and 4.5 nm as the upper limits for the film thickness optimization of the H material layer and the L material layer;

[0112] S2.4 Determine the initial optimization range:

[0113] The initial thickness optimization range for the H material layer is [D Hmin , D Hmax = [2.7, 2.9], the initial film thickness optimization range of the L material layer is [ D Lmin , D Lmax = [4.2, 4.5].

[0114] Step S3: Within the initial film thickness optimization range, calculate the optimal film thickness under different beam incident angles;

[0115] S3.1 Order i =1;

[0116] S3.2. Optimize the beam incident angle in three steps. AOI i Film thickness at time:

[0117] - Step 1 (Coarse Optimization): Let the optimization range of the H material layer thickness be [ D Hmin , D Hmax The optimized range for the film thickness of material L is []. D Lmin , D Lmax The film thickness optimization interval was 0.1 nm, and the optimized film thickness D of the H material layer under this optimized interval was obtained. H-Coarse-i L material layer optimized film thickness D L-Coarse-i ;

[0118] Step 2 (Fine Optimization): Set the thickness optimization range of the H material layer to [D]. H-Coarse-i -0.1, D H-Coarse-i +0.1], the optimized range for the film thickness of the L material layer is [D L-Coarse-i -0.1, D L-Coarse-i +0.1], film thickness optimization spacing Interval Fine The optimized film thickness D of the H material layer was obtained at an optimized spacing of 0.02 nm. H-Fine-i L material layer optimized film thickness D L-Fine-i ;

[0119] - Step 3 (Ultra-fine Optimization): Set the thickness optimization range of the H material layer to [D]. H-Fine-i -0.02, D H-Fine-i +0.02], the optimized range for the film thickness of the L material layer is [D L-Fine-i -0.02, D L-Fine-i +0.02], film thickness optimization interval Interval UltraFine The optimized film thickness D of the H material layer was obtained with an optimal spacing of 0.01 nm.H-UltraFine-i L material layer optimized film thickness D L-UltraFine-i The highest reflectivity of the operating wavelength R i ;

[0120] S3.3 Order D Hmin = D H-UltraFine-i , D Lmin = D L-UltraFine-i Update and optimize the lower limit of the range;

[0121] S3.4 Let i = i + 1, and repeat steps S3.2 and S3.3 until i = N.

[0122] Table 1. Parameters and results of coarse optimization, fine optimization and ultra-fine optimization stages for each sampling point in Example 1

[0123]

[0124] Step S4: Draw the film thickness distribution curve and the target wavelength reflectance distribution curve.

[0125] S4.1 Plotting the film thickness distribution curves: Using the horizontal distance from the sampling point location to the major axis [0 mm, 25 mm, 50 mm, 75 mm, 100 mm, 125 mm] as the abscissa, and the optimized film thicknesses of the H material layer [2.72 nm, 2.72 nm, 2.74 nm, 2.78 nm, 2.84 nm, 2.92 nm] and the optimized film thicknesses of the L material layer [4.18 nm, 4.2 nm, 4.24 nm, 4.3 nm, 4.38 nm, 4.48 nm] as the ordinates, plot the film thickness distribution curves for the H material layer and the L material layer respectively. Figure 2 );

[0126] S4.2 Plot the reflectance distribution curve: Using the horizontal distance of the sampling point from the major axis [0 mm, 25 mm, 50 mm, 75 mm, 100 mm, 125 mm] as the abscissa, the highest reflectance at the working wavelength... R i Using [74.29%, 74.13%, 73.64%, 72.80%, 71.52%, 69.75%] as the ordinate, plot the reflectivity distribution curve at the working wavelength. Figure 3 ).

[0127] Example 2: Calculation of film thickness distribution in Mo / C / Si multilayer film system

[0128] This embodiment uses a Mo / C / Si multilayer ellipsoidal reflector with a working wavelength of 13.5 nm as an example to illustrate the method for calculating the thin film thickness distribution on the surface of the ellipsoidal reflector of the present invention. The reflector is required to have high reflectivity for light with a wavelength of 13.5 nm at different incident angles on its surface.

[0129] Step S1: Read the geometric parameters of the ellipsoidal mirror and calculate the incident angle distribution curve of the beam;

[0130] S1.1 Read the geometric parameters of the ellipsoidal mirror: semi-major axis length L MajorAxis =380mm, semi-central axis and semi-minor axis length L MinorAxis =280mm, component diameter D =200mm, Number of sampling points N =6. Use position P 1 (0 mm) P 2 (20 mm) P 3 (40 mm) P 4 (60 mm) P 5 (80 mm) P 6 (100 mm);

[0131] S1.2 Calculate all sampling locations according to formula (1) P i ( i The incident angles of the beams at different sampling positions are obtained by calculating the incident angles of the beams at positions 1, 2, ..., 6. AOI 1 (0.00°) AOI 2 (3.75°) AOI 3 (7.47°) AOI 4 (11.12°) AOI 5 (14.69°) AOI 6 (18.14°).

[0132] (1)

[0133] in Sampling location P i The vector to the point of incidence of the light ray. Sampling location P i The normal vector at that point.

[0134] ;

[0135] ;

[0136] Step S2: Calculate the initial film thickness optimization range based on the beam incident angle range;

[0137] S2.1 Read the operating wavelength of the ellipsoidal mirror λ target (13.5 nm), polarization state (average component) of the incident beam, film structure (substrate | (LBH)) 50 L|air), and substrate and film material parameters. A silicon wafer was used as the substrate, with a refractive index of 13.5 nm. n s The values ​​are 0.999057632-0.001715709i; Si is used as the material for the L layer, and Si has a refractive index of 13.5 nm. n L The values ​​are 0.999057632-0.001715709i; Mo is used as the material for the H layer, and Mo has a refractive index of 13.5 nm. n H The values ​​are 0.923951321-0.006422472i; C is used as the material for layer B, and the refractive index of C at 13.5 nm is... n B The thickness is 0.961543873-0.006923922i. d B =0.2 nm;

[0138] S2.2 Calculate the initial lower limit of optimization:

[0139] -make i =1, and the lower limit coefficient for the thickness optimization of the H material layer is obtained by calculating according to formulas (2) and (3). d H1 The value is 3.38, and the optimized range for the thickness of the H layer is [2.20, 4.56].

[0140] - The lower limit coefficient for the thickness optimization of the L material layer is calculated according to formulas (4) and (5). d L1 The value is 3.65, and the optimized range for the film thickness of the L layer is [2.37, 4.93].

[0141] n 0×sin( AOI i )= n H ×sin( AOI Hi (2)

[0142] d Hi =| λ target / (4×n H ×cos( AOI Hi ))|(3)

[0143] n 0×sin( AOI i ) = n L ×sin( AOI Li (4)

[0144] d Li =| λ target / (4× n L ×cos( AOI Li ))|(5)

[0145] - Calculate the optimal film thickness interval according to formula (6), where, This indicates rounding down to the nearest integer, after calculation. Interval Coarse It is 0.1 nm;

[0146] Interval Coarse =10 log10(λtarget)-2 (6)

[0147] -Based on the optical thin film feature matrix, with a film thickness interval of 0.1 nm, the beam incident angle is optimized as follows: AOI The optimal film thickness for achieving the highest reflectivity at the operating wavelength is 1: H material layer optimized film thickness. D Hmin Optimize film thickness for 2.5 nm, L material layer D Lmin The thickness is 4.2 nm; 2.5 nm and 4.2 nm are used as the lower limits for optimizing the film thickness of the H material layer and the L material layer;

[0148] S2.3 Calculate the initial optimization upper limit:

[0149] -make i =6, calculate the upper limit coefficient of H material layer thickness optimization according to formula (2) and (3). d H6 The thickness was 3.55 nm, and the optimized range of the H layer thickness was [2.31, 4.79].

[0150] -Calculate the upper limit coefficient for the thickness optimization of the L material layer according to formulas (4) and (5). d L6 The thickness was 3.87 nm, and the optimized range of the L layer thickness was [2.52, 5.23].

[0151] -Based on the optical thin film feature matrix, with a film thickness interval of 0.1 nm, the beam incident angle is optimized as follows: AOI Film thickness at 6, H material layer optimized film thickness D Hmax Optimize film thickness for 2.8nm, L-material layer D Lmax The thickness is set at 4.3 nm, with 2.8 nm and 4.3 nm as the upper limits for the film thickness optimization of the H material layer and the L material layer;

[0152] S2.4 The initial film thickness optimization range of the H material layer is obtained as [ D Hmin , D Hmax = [2.5, 2.8], the optimized range of the initial film thickness of the L material layer is = [ D Lmin , D Lmax = [4.2, 4.3].

[0153] Step S3: Within the initial film thickness optimization range, calculate the optimal film thickness under different beam incident angles;

[0154] S3.1 Order i =1;

[0155] S3.2 Optimizes the beam incident angle in three steps. AOI i Film thickness at time:

[0156] - Step 1 (Coarse Optimization): Let the optimization range of the H material layer thickness be [ D Hmin , D Hmax The optimized range for the film thickness of material L is []. D Lmin , D Lmax The film thickness optimization interval was 0.1 nm, and the optimized film thickness D of the H material layer under this optimized interval was obtained. H-Coarse-i L material layer optimized film thickness D L-Coarse-i ;

[0157] Step 2 (Fine Optimization): Set the thickness optimization range of the H material layer to [D]. H-Coarse-i -0.1, D H-Coarse-i +0.1], the optimized range for the film thickness of the L material layer is [DL-Coarse-i -0.1, D L-Coarse-i +0.1], film thickness optimization spacing Interval Fine The optimized film thickness D of the H material layer was obtained at an optimized spacing of 0.02 nm. H-Fine-i L material layer optimized film thickness D L-Fine-i ;

[0158] - Step 3 (Ultra-fine Optimization): Set the thickness optimization range of the H material layer to [D]. H-Fine-i -0.02, D H-Fine-i +0.02], the optimized range for the film thickness of the L material layer is [D L-Fine-i -0.02, D L-Fine-i +0.02], film thickness optimization interval Interval UltraFine The optimized film thickness D of the H material layer was obtained with an optimal spacing of 0.01 nm. H-UltraFine-i L material layer optimized film thickness D L-UltraFine-i The highest reflectivity of the operating wavelength R i ;

[0159] S3.3 Order D Hmin = D H-UltraFine-i , D Lmin = D L-UltraFine-i Update and optimize the lower limit of the range;

[0160] S3.4 Let i = i + 1, and repeat steps S3.2 and S3.3 until i = N.

[0161] Table 2. Parameters and results of coarse optimization, fine optimization and ultra-fine optimization stages for each sampling point in Example 2.

[0162]

[0163] Step S4: Generate film thickness distribution curve and working wavelength reflectivity distribution curve.

[0164] S4.1 Plot the film thickness distribution curves: Using the horizontal distance of the sampling point from the major axis [0 mm, 20 mm, 40 mm, 60 mm, 80 mm, 100 mm] as the abscissa, the optimized film thickness of material H [2.61 nm, 2.65 nm, 2.63 nm, 2.64 nm, 2.75 nm, 2.79 nm] and material L [4.09 nm, 4.07 nm, 4.13 nm, 4.2 nm, 4.21 nm, 4.31 nm] as the ordinate, and the fixed film thickness of material B [0.2 nm, 0.2 nm, 0.2 nm, 0.2 nm, 0.2 nm, 0.2 nm] as the ordinate, plot the film thickness distribution curves for material H, material L, and material B. Figure 4 );

[0165] S4.2 Plot the reflectance distribution curve: Using the horizontal distance of the sampling point from the major axis [0 mm, 20 mm, 40 mm, 60 mm, 80 mm, 100 mm] as the abscissa, the highest reflectance at the working wavelength... R i Plot the reflectivity distribution curve at the working wavelength using [74.24%, 74.10%, 73.72%, 73.05%, 72.04%, 70.68%] as the ordinate. Figure 5 ).

[0166] The specific embodiments described herein are for illustrative purposes only and do not constitute any limitation on the scope of protection of the claims. Those skilled in the art, based on an understanding of the inventive concept, can easily make equivalent substitutions, conventional improvements, or adaptive adjustments to the technical solutions; such derivatives should still be considered within the scope of protection defined by the claims of this invention.

Claims

1. A method for calculating the thickness distribution of a thin film on the surface of an ellipsoidal reflector, characterized in that, The method includes the following steps: Step S1. Obtain the incident angle distribution of the beam: Obtain multiple sampling points P distributed radially on the surface of the ellipsoidal mirror. i Corresponding beam incident angle AOI i Where i = 1, 2, 3...N, N is the number of sampling points, and the incident angle of the beam changes monotonically along the radial direction; Step S2. Determine the initial film thickness optimization range: Among the multiple sampling points, the sampling point with the smallest incident angle of the beam, i.e., the first sampling point P1, and the sampling point with the largest incident angle of the beam, i.e., the Nth sampling point P, are selected. N Based on the preset membrane structure, material parameters, and operating wavelength λ, target Given the incident beam polarization state, the optimized film thickness corresponding to the first sampling point and the Nth sampling point is calculated respectively, and these are determined as the lower limit D of the film thickness optimization range. Ymin and upper limit value D Ymax This allows us to construct an initial film thickness optimization space that contains the potential optimal film thickness for all sampling points; where Y represents a high-refractive-index material layer or a low-refractive-index material layer. Step S3. Dynamically and progressively optimize the film thickness at each sampling point: Starting from the first sampling point P1, the following optimization operations are performed on each sampling point in sequence according to the increasing incident angle of the beam: Within the current film thickness optimization range of the current sampling point, a scanning calculation is performed with a preset optimization step size to obtain the film thickness combination that maximizes the reflectivity of the sampling point at the working wavelength, which is taken as the optimal film thickness of the current sampling point. The optimal film thickness is used as the lower limit of the film thickness optimization range for the next sampling point, while the upper limit remains unchanged, thereby dynamically updating the film thickness optimization range for the next sampling point. Repeat the above steps until all N sampling points have been optimized, and the optimal film thickness D for each sampling point is obtained. Y-UltraFine-i and the corresponding operating wavelength reflectivity R i ; Step S4. Generate and output film thickness and reflectivity distribution curves: Using the sampling point location as the abscissa and the optimal film thickness and working wavelength reflectivity as the ordinate, generate and output the film thickness distribution curve and the working wavelength reflectivity distribution curve, respectively. The optimization operation described in step S3 also includes performing a three-level precision-advancing optimization sub-step for each sampling point: Level 1, coarse optimization sub-step: Within the current film thickness optimization range of the current sampling point, at the first optimization interval Interval... Coarse Scanning optimization is performed to obtain the coarsely optimized film thickness D. Y-Coarse-i ; The second level, the fine-tuning sub-step: Using the coarse-optimized film thickness as the center, construct a reduced fine-tuning range [D]. Y-Coarse-i -Interval Coarse D Y-Coarse-i +Interval Coarse ], with the second optimized interval Interval Fine Scanning optimization was performed to obtain finely optimized film thickness D. Y-Fine-i Among them, Interval Fine No greater than 0.5 × Interval Coarse ; The third level, ultrafine optimization sub-step: Using the optimized film thickness as the center, construct a reduced ultrafine optimization range [D]. Y-Fine-i -Interval Fine D Y-Fine-i +Interval Fine ], with the third optimized interval Interval UltraFine The scanning step size is optimized to obtain the ultrafine optimized film thickness, i.e., the optimal film thickness D. Y-UltraFine-i And the reflectivity R at the operating wavelength corresponding to this film thickness combination. i Among them, Interval UltraFine No greater than 0.1 × Interval Coarse .

2. The method for calculating the thin film thickness distribution on the surface of an ellipsoidal reflector according to claim 1, characterized in that, The incident angle AOI of the beam in step S1 i Obtain it through the following methods: Read the geometric parameters of the ellipsoidal mirror, including at least the semi-major axis length L. MajorAxis Length L of the semi-central axis and semi-minor axis MinorAxis The component aperture D and the lateral distance r of each sampling point from the major axis i ; Calculate the incident angle (AOI) of the beam at each sampling point. i The formula is as follows: In the formula, For sampling point P i The vector to the point of incidence of the light ray. For sampling point P i The normal vector at that point.

3. The method for calculating the thin film thickness distribution on the surface of an ellipsoidal reflector according to claim 1, characterized in that, Step S2, which involves calculating the optimized film thickness corresponding to the first sampling point and the Nth sampling point, specifically includes: The angle of refraction (AOI) of the light beam inside the film was calculated using Snell's law. Yi The formula is as follows: n0 × sin(AOI i )=n Y ×sin(AOI Yi ) Where n0 is the refractive index of air, n Y Let Y be the refractive index of material Y at the working wavelength; Based on the quarter-wavelength film thickness formula, the thickness coefficient d of each tunable film layer corresponding to the first sampling point and the Nth sampling point is calculated respectively. Yi And based on this, the initial coarse optimization range for each tunable film layer is set [0.65×d]. Yi 1.35×d Yi The formula is as follows: d Yi =|λ target / (4×n Y ×cos(AOI Yi ))| Within the initial coarse optimization range, at the first optimization interval Interval Coarse Using the step size, reflectivity scanning optimization is performed using the optical thin film feature matrix method to obtain the optimized film thickness corresponding to the first sampling point and the Nth sampling point, which are respectively used as the lower limit and upper limit of the film thickness optimization range.

4. The method for calculating the thin film thickness distribution on the surface of an ellipsoidal reflector according to claim 3, characterized in that, First optimization interval Interval Coarse According to the operating wavelength λ target The order of magnitude is adaptively determined, as shown in the following formula: Interval Coarse =10 ⌊log10(λtarget)-2⌋ In the formula, ⌊⋅⌋ represents rounding down.

5. A system for calculating the thickness distribution of a thin film on the surface of an ellipsoidal reflector, used to implement the method as described in claim 1, characterized in that, include: The parameter input module is used to receive user-inputted geometric parameters of the ellipsoidal reflector, membrane structure parameters, material parameters, and operating wavelength information. An incident angle distribution calculation module, connected to the parameter input module, is used to calculate the beam incident angle AOIi corresponding to each sampling point according to the geometric parameters, the preset ellipsoid equation and vector operation rules, and generate a beam incident angle sequence distributed radially. The initial optimization range determination module is connected to the incident angle distribution calculation module. It is used to calculate the optimized film thickness corresponding to the minimum and maximum incident angles based on the sampling points corresponding to the minimum and maximum incident angles in the incident angle sequence of the beam, combined with the film structure, material parameters and working wavelength, and set them as the lower limit and upper limit of the film thickness optimization range, respectively, so as to construct an initial film thickness optimization space covering the entire angle range. Dynamic progressive optimization module: connected to the initial optimization range determination module and the incident angle distribution calculation module, used to calculate the final optimized film thickness and corresponding working wavelength reflectivity of each sampling point in order of increasing incident angle of the beam; Visualization output module: Connected to the dynamic progressive optimization module, it is used to automatically generate and display the film thickness distribution curve and the working wavelength reflectance distribution curve based on the lateral distance of each sampling point from the major axis, the final optimized film thickness, and the corresponding working wavelength reflectance.

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