Line-distance-variable grating spectrometer performance and tolerance collaborative optimization method, spectrometer, system, terminal and medium

Abstract

The invention relates to the technical field of optical instrument design, and discloses a line-distance-variable grating spectrometer performance and tolerance collaborative optimization method, a spectrometer, a system, a terminal and a medium, and the method comprises the steps: constructing a performance evaluation function of the spectrometer; determining an optimization variable, and obtaining a target optimization result meeting requirements according to the performance evaluation function and the optimization variable; performing tolerance analysis according to the target optimization result to obtain an evaluation result; and determining a design result of the spectrometer according to the evaluation result. According to the method, a strict ray tracing method is adopted to replace an approximation formula, the calculation precision is improved, high performance is pursued, and meanwhile it is ensured that the design scheme has the high yield under existing machining and assembling tolerances.

Description

Technical Field

[0001] This application relates to the field of optical instrument design technology, and in particular to a method for synergistic optimization of performance and tolerance of a variable line spacing grating spectrometer, the spectrometer, the system, the terminal, and the medium. Background Technology

[0002] Grating spectrometers are key equipment in advanced light sources, especially free-electron laser (FEL) devices, for enabling photon energy diagnostics and precise measurement of spectral characteristics. Variable line spacing (VLS) gratings are widely used in the design of spectrometers for grazing-incidence soft X-rays and extreme ultraviolet (VUV / EUV) bands due to their advantages in eliminating aberrations.

[0003] In the design of VLS grating spectrometers, existing technologies generally employ analytical models based on Fermat's principle. This approach uses a series of theoretical formulas (such as the grating equation and focusing equation) to approximate and calculate the spectrometer's key performance indicator—resolution (λ / Δλ, where λ is the center wavelength and Δλ is the minimum resolvable wavelength difference). These formulas include core structural parameters such as the grazing incidence angle, grating line density parameters, and the lengths of the incident and exit arms. Designers typically use mature optimization algorithms (such as least squares methods and genetic algorithms) to optimize these structural parameters to achieve the spectrometer's theoretical design specifications.

[0004] The theoretical calculation formulas described above employ numerous approximations when considering key factors affecting the actual resolving power of the spectrometer. These factors include: the finite size of the entrance slit, the finite size of the exit slit or detector pixels, various optical aberrations (such as defocus, coma, spherical aberration, etc.), and grating substrate surface shape errors. This approximation results in inaccurate calculations of the spectrometer's resolving power, leading to insufficient precision in the resolving power calculation.

[0005] Therefore, existing technologies still need to be improved and developed. Summary of the Invention

[0006] The main objective of this application is to provide a method for synergistic optimization of performance and tolerance of a variable line spacing grating spectrometer, as well as the spectrometer, system, terminal, and medium, aiming to solve the problem that existing grating spectrometers employ a large number of approximations, resulting in low accuracy of the spectrometer's calculation results.

[0007] The first aspect of this application provides a method for synergistic optimization of the performance and tolerance of a variable line spacing grating spectrometer, the method comprising the following steps: Construct a performance evaluation function for the spectrometer; Determine the optimization variables, and based on the performance evaluation function and the optimization variables, obtain the target optimization result that meets the requirements; Based on the optimization results of the stated objectives, a tolerance analysis is performed to obtain the evaluation results; The design results of the spectrometer are determined based on the evaluation results.

[0008] Optionally, in one embodiment of this application, the performance evaluation function is an optimization objective function; The performance evaluation function for constructing the spectrometer specifically includes: Determine the initial optical model of the spectrometer; The resolution of the initial optical model is defined as the optimization objective function.

[0009] Optionally, in one embodiment of this application, obtaining the target optimization result that meets the requirements based on the performance evaluation function and the optimization variables specifically includes: Based on the performance evaluation function, and according to the optimization variables, the initial optimization results corresponding to the optimization variables are obtained; Determine the boundary conditions corresponding to the optimization variables. If the initial optimization result does not meet the performance requirements, update the optimization variables based on the boundary conditions until the updated optimization variables meet the performance requirements. If the initial optimization result meets the performance requirements, then the initial optimization result is taken as the target optimization result.

[0010] Optionally, in one embodiment of this application, determining the boundary conditions corresponding to the optimization variable specifically includes: The optimization variables are functionally grouped to obtain the dispersion and focusing group and the aberration balance group; The boundary conditions are obtained by setting the dispersion and focusing group and the aberration balance group.

[0011] Optionally, in one embodiment of this application, the evaluation result is the yield rate; The tolerance analysis based on the target optimization results to obtain the evaluation results specifically includes: Determine the variables and randomly generate a set of error values ​​corresponding to the variables; The error value is superimposed on the target optimization result to obtain a virtual result; The virtual results are iterated and looped to obtain multiple performance data. The yield rate is obtained based on the aforementioned performance data.

[0012] Optionally, in one embodiment of this application, determining the spectrometer design result based on the evaluation result specifically includes: If the yield rate is greater than or equal to the first preset value, then the target optimization result is taken as the design result of the spectrometer. If the yield rate is less than or equal to the second preset value, a sensitivity term is introduced into the optimization objective function or the optimization variable is adjusted until the yield rate is greater than or equal to the first preset value.

[0013] A second aspect of this application also provides a variable line spacing grating spectrometer, wherein the variable line spacing grating spectrometer is designed according to the variable line spacing grating spectrometer performance and tolerance co-optimization method as described in any of the above schemes.

[0014] A third aspect of this application also provides a system for co-optimizing the performance and tolerance of a variable line spacing grating spectrometer, wherein the system is used to implement the method for co-optimizing the performance and tolerance of a variable line spacing grating spectrometer as described in any of the above solutions; the system includes: The function building module is used to construct performance evaluation functions for the spectrometer. The iterative optimization module is used to determine the optimization variables and obtain the target optimization result that meets the requirements based on the performance evaluation function and the optimization variables. The tolerance analysis module is used to perform tolerance analysis based on the target optimization results and obtain evaluation results. The design result output module is used to determine the design result of the spectrometer based on the evaluation result.

[0015] A fourth aspect of this application also provides a terminal, wherein the terminal includes: a memory, a processor, and a variable line spacing grating spectrometer performance and tolerance co-optimization program stored in the memory and executable on the processor, wherein when the variable line spacing grating spectrometer performance and tolerance co-optimization program is executed by the processor, it implements the steps of the variable line spacing grating spectrometer performance and tolerance co-optimization method as described above.

[0016] A fifth aspect of this application also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a performance and tolerance co-optimization program for a variable line spacing grating spectrometer, and when the variable line spacing grating spectrometer performance and tolerance co-optimization program is executed by a processor, it implements the steps of the variable line spacing grating spectrometer performance and tolerance co-optimization method as described above.

[0017] Beneficial Effects: This application provides a method for performance and tolerance co-optimization of a variable-spacing grating spectrometer, as well as the spectrometer, system, terminal, and medium. This application constructs a performance evaluation function based on rigorous ray tracing to accurately calculate the spectrometer's resolution; performs performance optimization of initial structural parameters to meet theoretical performance indicators; performs Monte Carlo tolerance analysis on the optimized structure to evaluate tolerance cost and yield; and performs judgment and feedback control based on the tolerance cost evaluation results. If the tolerance cost is unacceptable, the relevant error sensitivity is controlled and re-optimized; if the tolerance cost is acceptable, the final design result is output. This application can solve the problem of a serious disconnect between theoretical performance and actual engineering performance in VLS grating spectrometer design. By constructing an iterative co-optimization framework that highly couples performance optimization and tolerance analysis, and using rigorous ray tracing to replace approximate formulas, it accurately incorporates actual factors such as aberrations, slit effects, and surface errors, thereby improving calculation accuracy. While pursuing high performance, it ensures that the design scheme has high yield and high robustness under existing processing and assembly tolerances. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of a preferred embodiment of the method for synergistic optimization of performance and tolerance of the variable line spacing grating spectrometer of this application; Figure 2 This is a flowchart illustrating the specific implementation steps of the entire execution process in a preferred embodiment of the method for synergistic optimization of performance and tolerance of a variable line spacing grating spectrometer according to this application. Figure 3 This is a schematic diagram of the optical design results in a preferred embodiment of the performance and tolerance co-optimization method for the variable line spacing grating spectrometer of this application; Figure 4 This is a schematic diagram of the tolerance allocation results in a preferred embodiment of the performance and tolerance co-optimization method for variable line spacing grating spectrometers in this application; Figure 5 This is a schematic diagram of Monte Carlo calculation results in a preferred embodiment of the method for co-optimizing the performance and tolerance of a variable line spacing grating spectrometer in this application; Figure 6 This is a structural diagram of a preferred embodiment of the performance and tolerance co-optimization system for the variable line spacing grating spectrometer of this application; Figure 7 This is a structural diagram of a preferred embodiment of the terminal of this application.

[0020] Explanation of reference numerals in the attached figures: 100. Function construction module; 200. Iterative optimization module; 300. Tolerance analysis module; 400. Design result output module. Detailed Implementation

[0021] To make the objectives, technical solutions, and effects of this application clearer and more explicit, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. The described embodiments are only possible technical implementations of this application and not all possible implementations. Based on the embodiments in this application, those skilled in the art can obtain other embodiments without creative effort, and these embodiments are also within the protection scope of this application.

[0022] First, let's introduce the terms used in the embodiments of this application: FEL, Free-Electron Laser; VUV, Vacuum Ultraviolet; ZPL, Zemax Programming Language; Zemax, Zemax Macro Language. ZEMAX, ZEMAX OpticStudio, optical simulation software; SXFEL, Soft X-ray FEL; FERMI, Free Electron Laser, is a type of FEL device; FLASH, Free-Electron Laser, another FEL device; VLS, Varied Line Spacing, VLS grating; λ / Δλ, resolution (wavelength resolution ability), where λ is the center wavelength and Δλ is the minimum resolvable wavelength difference. The larger the value, the higher the resolution. FWHM, Full Width at Half Maximum, is the width at half the height of a spectral peak. It is used to quantize resolution; the smaller the FWHM, the higher the resolution. PML, or Perfectly Matched Layer, is an absorption boundary condition used in optical simulations to reduce numerical reflection.

[0023] PBC, Periodic Boundary Condition, is suitable for simulating periodic structures such as gratings and waveguides, ensuring boundary continuity.

[0024] PEC, or Perfect Electric Conductor, simulates a metallic boundary where incident waves are completely reflected.

[0025] FSBC, Free Space Boundary Condition, simulates open boundaries and is suitable for far-field propagation analysis.

[0026] TWAV, Test Wavelength, is the wavelength specified in tolerance analysis to standardize testing (e.g., 633nm red light).

[0027] COMP, or Back Focal Compensation, compensates for defocus aberration by adjusting the detector position (back focal), thereby improving yield.

[0028] RMS (Root Mean Square) is used to quantify the spot radius or wavefront error; the smaller the RMS, the better the imaging quality.

[0029] MTF, Modulation Transfer Function, is a comprehensive indicator for evaluating the contrast and resolution of an imaging system.

[0030] In related technologies, existing optimization design methods mainly focus on achieving purely theoretical performance indicators, but it is difficult to effectively incorporate the impact of various engineering tolerances (such as the assembly position tolerance, angle tolerance, nonlinear tolerance of grating line density, detector installation tolerance, etc.) on spectrometer performance into the optimization process, thus lacking engineering feasibility.

[0031] Furthermore, due to the aforementioned drawbacks, in actual engineering implementation, the cumulative effect of various tolerances leads to a significant decrease in the actual measured resolution of the manufactured and assembled spectrometer compared to the theoretical design value. This discrepancy often reaches several times or even higher (for example, the actual measured values ​​of the grating spectrometers designed in foreign FEL devices such as FERMI, FLASH, and SXFEL are far lower than the theoretical design values), resulting in a huge gap between theoretical and actual performance. This problem has become a recognized engineering implementation challenge in the field of precision optics.

[0032] To address the issue of low accuracy in calculation results caused by extensive approximations in grating spectrometers, this application constructs a performance evaluation function based on rigorous ray tracing to accurately calculate the spectrometer's resolution; performs performance optimization of initial structural parameters to meet theoretical performance indicators; conducts Monte Carlo tolerance analysis on the optimized structure to evaluate tolerance costs and yield; and performs judgment and feedback control based on the tolerance cost evaluation results. If the tolerance cost is unacceptable, the relevant error sensitivity is controlled and re-optimized; if the tolerance cost is acceptable, the final design result is output. This application solves the problem of a severe disconnect between theoretical performance and actual engineering performance in VLS grating spectrometer design by constructing an iterative collaborative optimization framework that highly couples performance optimization and tolerance analysis. It replaces approximate formulas with rigorous ray tracing, accurately incorporating actual factors such as aberrations, slit effects, and surface errors, thereby improving calculation accuracy. While pursuing high performance, it ensures that the design scheme has high yield and high robustness under existing processing and assembly tolerances.

[0033] This invention proposes a method for the collaborative optimization of performance and tolerance in variable-spacing grating spectrometers, aimed at addressing the disconnect between theoretical and practical engineering performance in existing VLS grating spectrometer designs. The core idea is to construct an iterative collaborative optimization framework that highly couples performance optimization and tolerance analysis. This framework is based on rigorous ray tracing for performance evaluation and incorporates Monte Carlo tolerance analysis to quantify and control the impact of engineering tolerances.

[0034] The overall technical effects of this application are as follows: First, the accuracy of performance evaluation: By adopting a rigorous ray tracing method, the propagation path of light in the spectrometer can be accurately simulated, thereby achieving accurate calculation of the spectrometer's resolution under the influence of actual factors such as aberrations, slit effects, and surface errors, which is significantly higher than the approximate calculation accuracy of existing theoretical formulas.

[0035] Second, it boasts high engineering feasibility: During the optimization process, tolerance cost is incorporated as a crucial indicator into the iterations, achieving synergistic optimization of performance indicators and tolerance allocation. This method effectively controls critical error sensitivity, ensuring that the final design scheme, within reasonable machining and assembly tolerances, still meets expected performance indicators, significantly narrowing the gap between theoretical design results and engineering reality.

[0036] Third, improved design efficiency and reliability: This method provides a systematic and quantitative design process that can efficiently guide the processing accuracy of optical components and the assembly requirements of the system, providing a highly reliable design basis for photon energy diagnostic equipment in the field of advanced light sources.

[0037] The technical solutions of this application will be described in detail below with specific embodiments. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments.

[0038] The preferred embodiment of this application describes a method for synergistic optimization of the performance and tolerance of a variable-pitch grating spectrometer, such as... Figure 1 and Figure 2 As shown, the method for synergistic optimization of performance and tolerance of the variable line spacing grating spectrometer includes the following steps: In step S101, a performance evaluation function for the spectrometer is constructed.

[0039] In one possible implementation, the performance evaluation function is an optimization objective function; It should be noted that this solution mainly includes two stages: system performance optimization (high-performance design) and tolerance analysis optimization (highly feasible design), forming a closed-loop iterative process.

[0040] Specifically, in Phase One, the first step is to set the initial structure: based on relevant design parameters such as light source parameters, working distance, receiving aperture, wavelength range, and performance requirements, the initial structure (optimization starting point) of the spectrometer is set, that is, the corresponding initial optical model is established in mature optical simulation software (such as Zemax, Shadow, CODEV).

[0041] Step S101 specifically includes: Step S1011: Determine the initial optical model of the spectrometer.

[0042] Its specific implementation is as follows: K111, Requirements Analysis and Topology Selection. Input Analysis: Having obtained the design specifications, the selection decision is made based on these specifications to choose the type of spectrometer. Different topologies determine the basic direction of light and the fundamental characteristics of aberrations.

[0043] K112. Based on Gaussian optics initial parameter calculations, the radius of curvature, spacing, and angle are estimated using paraxial optics formulas to ensure the optical path is functional. Focal length and arm length are determined: Based on the working distance (WD) and receiving aperture (detector size), the focal lengths of the collimating and focusing lenses are initially determined using the magnification formula. Grating selection and incident angle setting: Based on the grating equation, combined with the center wavelength and grating density, the incident and diffraction angles are initially set. Minimum deviation angle configuration is determined: To reduce astigmatism, the initial structure is often set near the minimum deviation angle of the grating (i.e., the incident and diffraction angles are symmetrical about the grating normal).

[0044] K113. Beam height and pupil matching. Calculate the incident height of the beam on each mirror to ensure the mirrors do not block the light. Calculate the numerical aperture (NA) or F-number to ensure matching with the light source fiber / slit, avoiding energy loss.

[0045] K114. Software Modeling and Coordinate System Establishment. Define Surfaces: Establish the following in sequence: Slit (object surface) - Collimating Lens - Grating - Focusing Lens - Detector (image surface). Set Parameters: Fill the corresponding surface attribute columns with the radius of curvature, thickness (i.e., arm length), conic coefficient (usually set to 0 initially for a sphere, or -1 for a parabola), and grating line density calculated in step K112.

[0046] K115. Initial optical path verification: Enable ray tracing without any optimization. Check: whether the ray hits the center of the mirror, whether there is severe obstruction, and whether the master ray connects the slit center and the detector center. If the ray is erratic or completely unfocused, it indicates an error in the initial parameter calculation; return to step K112 to readjust. This will determine the initial optical model.

[0047] Step S1012: Define the resolution of the initial optical model as the optimization objective function.

[0048] In Phase One, the second step is to construct a performance evaluation function: using the ray tracing function of the software, the propagation path of light in the system is simulated, the aberrations and the focused spot size of different spectral lines are accurately calculated, and the resolution (λ / Δλ) is defined as the optimization target (performance evaluation function) through the linear dispersion formula.

[0049] Step S1012 is specifically implemented as follows: The core optimization objective is determined as: resolution. Physical definition: Resolution R = λ / Δλ, which is the smallest wavelength difference that can be distinguished. Mathematical transformation (linear dispersion formula): According to the Rayleigh criterion or pixel sampling theorem, Δλ depends on the linear dispersion rate (D = dλ / Δλ). x / d λ (Unit: mm / nm) and detector pixel size (p) and spot diameter (d) spot Evaluation function objective: Minimize (spot size + pixel size / linear dispersion).

[0050] Introducing imaging quality constraints (aberration control): Spot size and wavefront aberration. To achieve high resolution, the spot must be small enough, and the wavefront must be flat. Geometric aberration control: Calculate the RMS spot radius or geometric MTF, aiming to make all rays intersect at a single point as much as possible. Diffraction limit control: Calculate the RMS wavefront aberration WFE, with the objective: WFE < λ / 4 (Maresia criterion).

[0051] Establish structural and boundary constraints (boundary conditions). Optical path constraint: Ensure light is not blocked and the working distance meets requirements. Dispersion linearity constraint: The spectrometer must not only be able to separate particles, but also to separate them accurately (wavelength and position have a linear relationship).

[0052] Formulation: Construct the overall evaluation function.

[0053] MF=w1(RMS center ) 2 +w2(FWHM center ) 2 +w3 (Astigmatism) 2 +...; Here, MF stands for evaluation function, also known as the optimization objective function. It is the direct goal of optimization, a numerical value representing the performance of the system. The task of the optimization algorithm is to find a set of variables that minimizes MF. R represents resolution, the core performance indicator of the spectrometer, physically defined as R = λ / Δλ. This is the ultimate physical goal that the evaluation function aims to achieve. λ is the center wavelength, the specific wavelength targeted by the current optimization. Δλ is the minimum resolvable wavelength difference, the smallest wavelength interval between two adjacent spectral lines that the spectrometer can distinguish. The smaller Δλ is, the better the performance. SpotRadiusi / RMS_Spot_Radiusij represents the spot radius / RMS spot radius, the size of the spot formed by light focusing on the detector after passing through the system, usually quantified by the RMS (root mean square) radius. FWHM ij Half-width at half-height (WHM) is the width at half the peak of the focused spot's energy distribution. w1, w2, and w3 are weighting factors used to balance optimization priorities under different fields of view and wavelengths. Astigmatism is an aberration that indicates light rays cannot focus at the same point in the tangential and sagittal directions. Adding it to the evaluation function can control astigmatism, resulting in a more rounded and smaller spot.

[0054] In step S102, the optimization variables are determined, and the target optimization result that meets the requirements is obtained based on the performance evaluation function and the optimization variables.

[0055] Specifically, in Phase 1, the third step is to optimize the variable settings: the grazing incidence angle, grating line density parameters, and exit arm size are used as optimization variables, and necessary boundary conditions (such as grating line density limits, exit arm length limits, etc.) are set.

[0056] The fourth step is performance iterative optimization: The spectrometer's performance is optimized using built-in optimization algorithms in commercial optical design software (such as the hammer algorithm in ZEMAX) or mature open-source algorithms (such as least squares method, genetic algorithm, etc.). The optimization results are then assessed to determine if they meet the performance requirements; if so, the process proceeds to the next stage; otherwise, the optimization variables and boundary conditions are adjusted for re-optimization.

[0057] Step S102 specifically includes: based on the performance evaluation function, obtaining the initial optimization result corresponding to the optimization variable according to the optimization variable; determining the boundary conditions corresponding to the optimization variable; if the initial optimization result does not meet the performance requirements, updating the optimization variable based on the boundary conditions until the updated optimization variable meets the performance requirements; if the initial optimization result meets the performance requirements, taking the initial optimization result as the target optimization result.

[0058] Specifically, determining the boundary conditions corresponding to the optimization variables includes: grouping the optimization variables by function to obtain a dispersion and focus group and an aberration balance group; and setting the boundary conditions for the dispersion and focus group and the aberration balance group.

[0059] Step S102 is specifically implemented as follows: K121. List all physically adjustable geometric parameters of the spectrometer: Radius: Focal length of the collimating and focusing mirrors; Thickness / Distance: Distance (i.e., arm length) from the slit to the collimating mirror, from the collimating mirror to the grating, from the grating to the focusing mirror, and from the focusing mirror to the detector; Angle: Incident angle (α), diffraction angle (β), and tilt angle of the mirrors. Surface Properties: Grating density, conicity (determining whether it's a sphere or parabola), and higher-order aspherical coefficients.

[0060] K122. Filtering through physical intuition or simple differential calculations: Primary variables (coarse adjustment): Arm length / focal length: Directly determines magnification and focusing ability, has the greatest impact on spot size, and must be set as a variable. Grating line density: Directly determines dispersion rate (D), which is the core of resolution and must be set as a variable. Secondary variables (aberration correction): Aspheric / Conic coefficients: Mainly used to balance spherical aberration and coma. Grating incident angle: Affects not only dispersion but also astigmatism and blaze efficiency. Eliminate weakly correlated variables: For example, "slit width" is usually used as a fixed input condition rather than an optimization variable (unless a widened slit is designed); substrate thickness is usually fixed if it does not affect optical path to reduce weight.

[0061] K123. Variable decoupling and grouping: Group variables by function: Group A (dispersion and focusing): grating line density, detector position (emission arm length). Group B (aberration balance): conicity of the mirror, grating tilt angle (Pitch / Roll). First optimize Group A to "focus" the light, then optimize Group B to "focus the light neatly".

[0062] K124. Set physical boundary conditions. Manufacturing limitation: The grating line density cannot be infinitely large, and it is necessary to set Min < d < Max. Structural limitation: The length of the exit arm cannot be negative and cannot exceed the size of the instrument housing. Geometric limitation: The grazing incidence angle is usually between 85° and 89° (close to 90°) and cannot be set to 0°.

[0063] K131. Initialize the calculation (starting point evaluation), perform the first ray tracing based on the initial structure and variable range, and calculate the current evaluation function value.

[0064] K132. Construct the sensitivity matrix. The optimization algorithm (especially the damped least squares method / DLS) calculates the partial derivatives (Jacobian Matrix) to generate a sensitivity matrix, which tells the algorithm in which direction each variable should move (increase or decrease) and how much to move most effectively to reduce the MFV.

[0065] K133. Correct the parameters and iterate. According to the sensitivity matrix, calculate a new set of variable values. Before applying this new set of values, check whether the set boundaries are violated. If it exceeds the limit, force it back to the boundary value.

[0066] K134. Re - trace and convergence judgment. Build a model with the new parameters, perform ray tracing again, and calculate the new MFV. Case A (success): The MFV drops significantly and the aberrations are balanced. Continue to iterate. Case B (oscillation / ineffectiveness): The MFV does not decrease but increases, or gets stuck. The algorithm will automatically adjust the damping factor, which is equivalent to reducing the step size and trying more cautiously; or switch the algorithm (such as switching from the hammer algorithm to the genetic algorithm) for global search. Case C (satisfied): The MFV is less than the set threshold (such as the resolution R > 1000 and all aberration operands are zero). The iteration stops and enters phase two. Case D (failure): After 100 iterations, it still does not meet the standard. Manual intervention / automatic rollback: Prompt that this initial structure is not feasible, and return to the previous step to adjust the initial structure or relax the variable range.

[0067] In step S103, perform tolerance analysis according to the target optimization result to obtain an evaluation result.

[0068] In the second phase, the first step, Monte - Carlo tolerance analysis: Perform Monte - Carlo tolerance analysis and optimization on the optimization results that meet the performance requirements. The error parameters to be analyzed include but are not limited to: the 6 - degree - of - freedom position / angle tolerances (X, Y, Z, Pitch, Roll, Yaw) of the grating, the 6 - degree - of - freedom tolerances of the detector, the manufacturing tolerances of the grating line density parameters, and the base surface shape error, etc.

[0069] The second step is tolerance cost assessment and judgment: calculate the statistical distribution of system performance (such as resolution) and yield rate within the set tolerance range, in order to assess the tolerance cost (i.e. the processing and assembly difficulty required to achieve the engineering indicators).

[0070] The evaluation result is the yield rate.

[0071] Step S103 specifically includes: determining variables and randomly generating a set of error values ​​corresponding to the variables; superimposing the error values ​​onto the target optimization result to obtain a virtual result; iterating the virtual result to obtain multiple performance data; and obtaining the yield rate based on the multiple performance data.

[0072] Step S103 is specifically implemented as follows: K211. Define the error sources and probability distribution (input). Determine the variables: List all parameters that may cause errors: the 6 degrees of freedom of the grating (X, Y, Z, Pitch, Roll, Yaw); the 6 degrees of freedom of the detector; the grating line density (manufacturing error); and the substrate surface shape (flatness error). Define the distribution: Assume a normal distribution (Gaussian distribution).

[0073] K212, Random Sampling. Using a random number generator (RNG), a set of error values ​​is randomly selected based on the tolerance range and distribution pattern set in the first step.

[0074] K213. Superimposed Perturbations and Performance Calculation. This set of randomly selected error values ​​is superimposed onto the ideal nominal model optimized in Stage 1 to construct a virtual flawed prototype. The performance of this flawed prototype (mainly resolution λ / Δλ or spot size) is calculated using ray tracing software. Results: Prototype A's resolution is 9800 (unacceptable); Prototype B's resolution is 10200 (acceptable).

[0075] K214, Statistical Loop (Iteration). Repeat steps K212 and K213 N times. Record performance data in each loop.

[0076] K215, Statistical Analysis and Output (Results). Generating a Histogram: Plotting the distribution of these N results. Horizontal axis: Resolution (performance). Vertical axis: Frequency of occurrence (probability).

[0077] Calculate the yield rate: Calculate the percentage of prototypes whose performance is greater than or equal to the design specifications.

[0078] Specifically, extract statistical features. From the N samples in the Monte Carlo simulation, extract the mean, standard deviation, and distribution of performance indicators (such as resolution R). Calculate the yield rate and set a cutoff line, which is the minimum requirement of the design specifications. Statistically analyze how many of the N simulations result in values ​​above the cutoff line.

[0079] In step S104, the design result of the spectrometer is determined based on the evaluation result.

[0080] In Phase Two, the third step, Sensitivity Control and Re-optimization: If the tolerance cost is unacceptable (low yield): This indicates that the system is too sensitive to existing tolerances. In this case, sensitivity control needs to be applied to parameters that do not meet tolerance requirements (i.e., introducing a sensitivity term into the performance evaluation function or adjusting the optimization variables), and then returning to Phase One to re-optimize the system performance. If the tolerance cost is acceptable (high yield): Output the final design results, including structural parameters and the final tolerance allocation table.

[0081] It should be noted that, to improve the efficiency of the optimization design, the aforementioned collaborative optimization method is automated: relevant control programs (such as Zemax Programming Language, Python interfaces, etc.) are written to automatically execute ray tracing and tolerance analysis. Combined with optimization algorithms (such as the aforementioned hammer algorithm, least squares method, genetic algorithm, etc.), the structural parameters and tolerance range are iteratively adjusted so that the spectrometer's resolution remains close to the theoretical optimum while considering tolerances. After multiple iterations and convergence, the optimal structural parameters and tolerance limits are output to guide actual manufacturing and assembly.

[0082] Step S104 specifically includes: if the yield rate is greater than or equal to a first preset value, then the target optimization result is used as the design result of the spectrometer; if the yield rate is less than or equal to a second preset value, then a sensitivity term is introduced into the optimization objective function or the optimization variable is adjusted until the yield rate is greater than or equal to the first preset value.

[0083] Step S104 is specifically implemented as follows: K221. Establish the correlation between yield rate and manufacturing cost. 99% yield rate - requires extremely high precision machining (expensive). 50% yield rate - half are scrap, significant material waste (high hidden costs). 95% yield rate - the industry's typical acceptance standard (costs controllable).

[0084] K222, Binary Decision. YES (Pass): Proceed to the output stage. NO (Fail): Proceed to sensitivity control and re-optimization.

[0085] K231. Sensitivity Source Tracing. Using Monte Carlo data, sensitivity analysis is performed to calculate the correlation coefficient or contribution of each error source (such as grating roll angle, scribing density) to performance degradation (such as reduced resolution).

[0086] K232. Develop control strategies. Strategy A (Direct Control): If a parameter is highly sensitive but not critical, directly add a "sensitivity penalty term" to the evaluation function. Strategy B (Structural Adjustment): If the structure itself is too sensitive (e.g., a large grazing incidence angle causes a sharp increase in aberrations), adjust the optimization variables or boundary conditions.

[0087] K233, Rollback and Iteration. Feedback the modified evaluation function and adjusted variable ranges back to Phase 1. Re-execute steps 1-4 of Phase 1 (rebuild the model and re-optimize).

[0088] K234. Convergence check. Repeat the cycle from stage one to stage two. The cycle ends when the yield rate calculated in stage two meets the target, or when performance and yield rate reach Pareto optimality (cannot be improved simultaneously).

[0089] The effects of this invention will be described in detail below using a specific VLS grating spectrometer design example: Using the above scheme, the design of the grating spectrometer, the core diagnostic equipment required for the free-electron laser device, was completed. Its main optical design parameters and ray tracing diagram are shown below. (See attached image) Figure 3 (Optical design results) Figure 4 (Tolerance calculation results) and Figure 5 (Monte-Carlo calculation results): Table 1: Grating Design Parameters

[0090] Table 2: Tolerance Allocation Results

[0091] The results show that the resolution of the 100% misaligned system is better than 3000, meaning that after considering the tolerance effects, the theoretical design value of the spectrometer's resolution is 3000. These results demonstrate that the present invention has the following advantages: Achieve high-precision performance calculation ( Figure 3 As shown): Figure 3 (a) in the diagram is a schematic diagram of ray tracing. Figure 3(b) shows the ray tracing results at a center wavelength of 10 nm (4000 bandwidth input). Rigorous ray tracing can replace approximate formulas, using the actual spot size as the core basis for evaluating resolution, thus accurately incorporating the effects of various aberrations such as defocus, coma, and spherical aberration, as well as engineering factors such as light source size and detector pixels, into the design evaluation.

[0092] A synergistic balance between tolerance and performance Figure 4 and Figure 5 (As shown): For the symbols of the grating and camera guide rail assembly errors (X, Y, Z, Pitch, Roll, Yaw) in Table 2, please refer to [the table / reference needed]. Figure 4 , Figure 4 (a) in the diagram is a schematic diagram of grating assembly error. Figure 4 (b) in the table is a schematic diagram of the camera guide rail assembly error; in Table 2, N0, N1, and N2 represent the line density error of the variable line spacing grating. The expression for the variable line spacing grating is as follows: N = N0 + N1 * Y + N2 * Y2. Figure 5 In the model, the resolution of 100% misaligned systems is better than 3000. Statistical results provided by Monte Carlo analysis allow designers to visually observe the impact of engineering tolerances on performance distribution. The sensitivity control mechanism during the iteration process ensures that optimization is no longer simply about pursuing the theoretically perfect performance point, but rather about finding the most stable and robust design region within the tolerance fluctuation range.

[0093] The optimization results have clear engineering guidance: the final output tolerance allocation results (such as...) Figure 3 The tolerance allocation table shown provides quantitative and achievable accuracy requirements for grating fabrication, detector and optical component installation and debugging. For example, it gives clear numerical requirements for the positional tolerances of the grating in the Y and Z directions and the pitch angle tolerance, which greatly improves the efficiency and success rate of engineering implementation.

[0094] In the embodiments of this application, a precise performance evaluation method based on rigorous ray tracing is innovatively adopted as the performance evaluation benchmark in the optimization process, rather than an approximate theoretical formula, thereby achieving high-precision calculation of actual resolution (considering all aberrations, slits, surface errors, etc.).

[0095] An iterative collaborative optimization framework for performance and tolerance: This innovatively proposes a bidirectional iterative optimization process that links system performance optimization with Monte Carlo tolerance analysis optimization. This makes tolerance cost (engineering feasibility) a core constraint in design optimization, effectively avoiding the design trap of theoretically high performance but being impractical in engineering.

[0096] The introduction of error sensitivity control mechanism: When the tolerance analysis results are not ideal, the control of error-sensitive parameters is innovatively used as a feedback loop and integrated into the next round of performance optimization to guide the design to evolve towards a direction that is less sensitive to tolerances (high robustness).

[0097] The above-mentioned VLS grating spectrometer design method is the first of its kind in the field of advanced light sources.

[0098] It is understood that this invention can be implemented on any optical design software platform that supports rigorous ray tracing and integrated optimization algorithms, such as: Implementation using commercial software (preferred): Utilize commercial optical design software such as ZEMAX or Code V, and programmatically implement the above performance evaluation function and Monte Carlo iterative control logic through their built-in macro language (such as ZPL) or secondary development interface.

[0099] Based on open source / custom code implementation: Using programming languages ​​such as Python and C++, combined with optical propagation theory (such as Fresnel diffraction or rigorous ray tracing), custom spectrometer performance models and Monte Carlo simulation programs are written, and mature optimization libraries (such as SciPy, MCMC) are used to achieve co-optimization.

[0100] Algorithm replacement or combination: The optimization algorithm can be replaced from the traditional least squares algorithm to a global optimization algorithm (such as genetic algorithm, particle swarm optimization, etc.) to ensure that the optimal solution is found in a wider design space.

[0101] Variations of tolerance analysis methods: In addition to the Monte Carlo method, sensitivity analysis or statistical methods (such as the RSS method) can also be used for initial tolerance assessment to save calculation time, but the final engineering verification still requires the Monte Carlo method.

[0102] Extending the design objective function: In addition to resolution (λ / Δλ), other key performance indicators such as diffraction efficiency and stray light suppression capability can be integrated into the performance evaluation function through weighted methods to achieve multi-objective collaborative optimization.

[0103] Applicable to different types of dispersive elements: The core idea of ​​this solution (performance-tolerance collaborative iteration) can be extended to the design optimization of non-VLS gratings (such as spherical gratings, planar gratings) or other dispersive elements (such as blazed gratings, crystal spectrometers, etc.), and even extended to multi-grating systems, grating monochromator systems, grating pulse compression and broadening systems, etc.

[0104] Based on the above embodiments, this application also provides a variable line spacing grating spectrometer, wherein the variable line spacing grating spectrometer is designed according to the variable line spacing grating spectrometer performance and tolerance co-optimization method as described in any of the above schemes.

[0105] Next, referring to the accompanying drawings, the performance and tolerance co-optimization system of the variable line spacing grating spectrometer proposed in the embodiments of this application is applied to the performance and tolerance co-optimization method of the variable line spacing grating spectrometer described in any of the above schemes.

[0106] Figure 6 This is a structural diagram of the performance and tolerance co-optimization system of the variable line spacing grating spectrometer according to an embodiment of this application.

[0107] like Figure 6 As shown, the performance and tolerance co-optimization system of the variable line spacing grating spectrometer includes: a function construction module 100, an iterative optimization module 200, a tolerance analysis module 300, and a design result output module 400.

[0108] Specifically, the function construction module 100 is used to construct the performance evaluation function of the spectrometer; The iterative optimization module 200 is used to determine the optimization variables and obtain the target optimization result that meets the requirements based on the performance evaluation function and the optimization variables. The tolerance analysis module 300 is used to perform tolerance analysis based on the target optimization results and obtain evaluation results. The design result output module 400 is used to determine the design result of the spectrometer based on the evaluation result.

[0109] Figure 7 A structural diagram of a terminal provided in an embodiment of this application. The terminal may include: The memory 501, the processor 502, and the computer program stored on the memory 501 and capable of running on the processor 502.

[0110] When the processor 502 executes the program, it implements the method for co-optimizing the performance and tolerance of the variable line spacing grating spectrometer provided in the above embodiments.

[0111] Furthermore, the terminal also includes: Communication interface 503 is used for communication between memory 501 and processor 502.

[0112] The memory 501 is used to store computer programs that can run on the processor 502.

[0113] Memory 501 may include high-speed RAM memory, and may also include non-volatile memory, such as at least one disk storage device.

[0114] If the memory 501, processor 502, and communication interface 503 are implemented independently, then the communication interface 503, memory 501, and processor 502 can be interconnected via a bus to complete communication between them. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EIS) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 7 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0115] Optionally, in a specific implementation, if the memory 501, processor 502, and communication interface 503 are integrated on a single chip, then the memory 501, processor 502, and communication interface 503 can communicate with each other through an internal interface.

[0116] Processor 502 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of this application.

[0117] This embodiment also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method for co-optimizing the performance and tolerance of a variable-pitch grating spectrometer.

[0118] One embodiment of this application provides a computer program product, including a computer program that, when executed by a processor, implements the features described in this application. Figure 1 The corresponding embodiments provide a method for co-optimizing the performance and tolerance of a variable line spacing grating spectrometer.

[0119] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0120] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0121] Any process or method described in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of the preferred embodiments of this application includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as should be understood by those skilled in the art to which embodiments of this application pertain.

[0122] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable storage medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable storage medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable storage media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable storage medium could be paper or other suitable media on which the program can be printed, since the program can be obtained electronically by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0123] It should be understood that the various parts of this application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiments, the N steps or methods can be implemented using software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0124] Those skilled in the art will understand that all or part of the steps of the methods in the above embodiments can be implemented by a program instructing related hardware. The program can be stored in a computer-readable storage medium, and when executed, the program includes one or a combination of the steps of the method embodiments.

[0125] Furthermore, the functional units in the various embodiments of this application can be integrated into a processing module, or each unit can exist physically separately, or two or more units can be integrated into a module. The integrated module can be implemented in hardware or as a software functional module. If the integrated module is implemented as a software functional module and sold or used as an independent product, it can also be stored in a computer-readable storage medium.

[0126] The storage medium mentioned above can be a read-only memory, a disk, or an optical disk, etc. Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions, and variations to the above embodiments within the scope of this application.

[0127] It should be understood that the application of this application is not limited to the examples above. Those skilled in the art can make improvements or modifications based on the above description, and all such improvements and modifications should fall within the protection scope of the appended claims.

[0128] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of this application.

Claims

1. A method for synergistic optimization of performance and tolerance of a variable-spacing grating spectrometer, characterized in that, The method for jointly optimizing the performance and tolerance of the variable-spacing grating spectrometer includes: Construct a performance evaluation function for the spectrometer; Determine the optimization variables, and based on the performance evaluation function and the optimization variables, obtain the target optimization result that meets the requirements; Based on the optimization results of the stated objectives, a tolerance analysis is performed to obtain the evaluation results; The design results of the spectrometer are determined based on the evaluation results.

2. The method for synergistic optimization of performance and tolerance of a variable-spacing grating spectrometer according to claim 1, characterized in that, The performance evaluation function is an optimization objective function; The performance evaluation function for constructing the spectrometer specifically includes: Determine the initial optical model of the spectrometer; The resolution of the initial optical model is defined as the optimization objective function.

3. The method for synergistic optimization of performance and tolerance of a variable-spacing grating spectrometer according to claim 2, characterized in that, The step of obtaining the target optimization result that meets the requirements based on the performance evaluation function and the optimization variables specifically includes: Based on the performance evaluation function, and according to the optimization variables, the initial optimization results corresponding to the optimization variables are obtained; Determine the boundary conditions corresponding to the optimization variables. If the initial optimization result does not meet the performance requirements, update the optimization variables based on the boundary conditions until the updated optimization variables meet the performance requirements. If the initial optimization result meets the performance requirements, then the initial optimization result is taken as the target optimization result.

4. The method for synergistic optimization of performance and tolerance of a variable-spacing grating spectrometer according to claim 3, characterized in that, The determination of the boundary conditions corresponding to the optimization variables specifically includes: The optimization variables are functionally grouped to obtain the dispersion and focusing group and the aberration balance group; The boundary conditions are obtained by setting the dispersion and focusing group and the aberration balance group.

5. The method for synergistic optimization of performance and tolerance of a variable-spacing grating spectrometer according to claim 3, characterized in that, The evaluation result is the yield rate; The tolerance analysis based on the target optimization results to obtain the evaluation results specifically includes: Determine the variables and randomly generate a set of error values ​​corresponding to the variables; The error value is superimposed on the target optimization result to obtain a virtual result; The virtual results are iterated and looped to obtain multiple performance data. The yield rate is obtained based on the aforementioned performance data.

6. The method for synergistic optimization of performance and tolerance of a variable-spacing grating spectrometer according to claim 5, characterized in that, The process of determining the spectrometer design results based on the evaluation results specifically includes: If the yield rate is greater than or equal to the first preset value, then the target optimization result is taken as the design result of the spectrometer. If the yield rate is less than or equal to the second preset value, a sensitivity term is introduced into the optimization objective function or the optimization variable is adjusted until the yield rate is greater than or equal to the first preset value.

7. A variable-spacing grating spectrometer, characterized in that, The variable line spacing grating spectrometer is designed according to the performance and tolerance co-optimization method of the variable line spacing grating spectrometer as described in any one of claims 1-6.

8. A system for synergistic optimization of performance and tolerance of a variable line spacing grating spectrometer, characterized in that, The variable line spacing grating spectrometer performance and tolerance co-optimization system is used to implement the variable line spacing grating spectrometer performance and tolerance co-optimization method according to any one of claims 1-6, wherein the variable line spacing grating spectrometer performance and tolerance co-optimization system includes: The function building module is used to construct performance evaluation functions for the spectrometer. The iterative optimization module is used to determine the optimization variables and obtain the target optimization result that meets the requirements based on the performance evaluation function and the optimization variables. The tolerance analysis module is used to perform tolerance analysis based on the target optimization results and obtain evaluation results. The design result output module is used to determine the design result of the spectrometer based on the evaluation result.

9. A terminal, characterized in that, The terminal includes: a memory, a processor, and a variable line spacing grating spectrometer performance and tolerance co-optimization program stored in the memory and executable on the processor. When the variable line spacing grating spectrometer performance and tolerance co-optimization program is executed by the processor, it implements the steps of the variable line spacing grating spectrometer performance and tolerance co-optimization method as described in any one of claims 1-6.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a performance and tolerance co-optimization program for a variable line spacing grating spectrometer, which, when executed by a processor, implements the steps of the performance and tolerance co-optimization method for a variable line spacing grating spectrometer as described in any one of claims 1-6.

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