Coated optical element laser damage threshold evaluation method based on fuzzy comprehensive evaluation

Abstract

The present application relates to the technical field of laser damage evaluation, and discloses a coated optical element laser damage threshold evaluation method based on fuzzy comprehensive evaluation, comprising the following steps: the method collects the measured values of the internal defect density, residual stress, film layer absorption rate and surface root mean square roughness of the coated optical element and performs consistency verification; based on the comment set, the membership function corresponding to each factor is established, the membership is calculated by substituting the measured values to generate a fuzzy relation matrix; based on the analytic hierarchy process, a judgment matrix is constructed, and a normalized feature vector is extracted as a weight vector; the product of the weight vector and the fuzzy relation matrix is calculated to obtain a comprehensive evaluation vector, and the grade result and the quantitative numerical result are output according to the vector, the relative error is calculated by obtaining the actual damage threshold of the sample, and the model parameters are modified when the error is out of limit. The present application realizes non-destructive evaluation of multi-factor fusion and has closed-loop optimization capability, effectively improving the accuracy of threshold prediction.

Description

Technical Field

[0001] This invention relates to the field of laser damage assessment technology, specifically to a method for assessing the laser damage threshold of coated optical components based on fuzzy comprehensive evaluation. Background Technology

[0002] In high-power laser systems, coated optical elements are the core components for beam transmission and control, and their resistance to laser damage directly affects the system's output energy density and operational lifespan. Currently, the commonly used laser-induced damage threshold testing method mainly involves applying progressively stronger laser pulses to the component under test, combining this with optical microscopy or plasma flash signals to determine the damage state, and then calculating the critical damage energy density.

[0003] This traditional destructive testing method inevitably leads to irreversible physical damage to the component surface, such as craters, cracks, or film peeling, rendering the test sample unusable. Limited by this, the test can only rely on sampling inspection mechanisms, failing to meet the requirements for full testing of batch products, and cannot be directly applied to online quality monitoring during the coating process. Furthermore, existing testing methods are essentially post-verification models, only outputting isolated threshold results, failing to establish a quantitative mapping relationship between multiple physical factors such as internal defect density, residual stress level, film absorptivity, and surface root-mean-square roughness and the final damage threshold. Because it ignores the coupling effect of multiple factors, this method struggles to accurately predict the component's damage resistance after coating, resulting in large fluctuations in damage thresholds within the same batch, and failing to provide clear feedback guidance for optimizing the underlying thin film preparation process.

[0004] Furthermore, some existing evaluation schemes attempt to introduce artificial neural networks or multiple regression models for threshold prediction. However, these data-driven models are highly dependent on large-scale destructive experimental data, making sample acquisition extremely costly. The internal computational logic of such models is essentially a black box, with feature weights lacking clear physical meaning and interpretability, making it difficult to effectively interface with process control nodes in actual engineering. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a laser damage threshold assessment method for coated optical components based on fuzzy comprehensive evaluation. This method solves the problems that existing laser damage threshold testing for coated optical components cannot achieve online full inspection due to its destructive nature, and that single-factor evaluation ignores the coupling effect of multiple physical parameters, resulting in low prediction accuracy and a lack of process feedback mechanism.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation, comprising the following steps: Measured values ​​of multiple laser-induced damage threshold influencing factors for coated optical components were collected and their consistency verified. These factors included internal defect density, residual stress, film absorptivity, and root mean square surface roughness. An influencing factor set composed of each laser-induced damage threshold influencing factor and a comment set composed of preset evaluation levels were constructed, and a membership function corresponding to each laser-induced damage threshold influencing factor was established. The measured values ​​were substituted into the corresponding membership functions to calculate the membership degree of each laser-induced damage threshold influencing factor to each preset evaluation level, forming a single-factor evaluation vector. These single-factor evaluation vectors were combined to generate a fuzzy relation matrix. A judgment matrix was constructed for the influencing factor set based on the analytic hierarchy process (AHP). When the judgment matrix passed the consistency check, normalized eigenvectors were extracted as weight vectors. The product of the weight vectors and the fuzzy relation matrix was calculated to obtain a comprehensive evaluation vector. Based on the comprehensive evaluation vector, the grade output result and the quantitative value output result were output.

[0007] During the consistency verification process, multiple measured values ​​of the same laser-induced damage threshold influencing factor are collected at various locations on the surface of the coated optical element. The relative differences between the measured values ​​of the same influencing factor at these different locations are calculated. If all relative differences are less than their respective preset relative difference ratio thresholds, the consistency verification is considered successful; otherwise, the evaluation process is terminated.

[0008] When constructing the evaluation set, it was divided into five preset evaluation levels: extremely high, high, medium, low, and extremely low. The laser wavelength and pulse width parameters of the target testing environment were extracted, and corresponding continuous physical energy density threshold intervals were set for each preset evaluation level based on these parameters. When establishing the membership functions, a historical experimental database containing a preset number of samples was retrieved. This database records the measured data of each influencing factor and the corresponding damage threshold data. Frequency statistics were used to calculate the distribution frequency of the measured data within the corresponding intervals of each preset evaluation level. Based on the distribution frequency, triangular or Gaussian distribution membership functions were fitted to each influencing factor for each preset evaluation level.

[0009] The triangular distribution membership function includes typical threshold parameters corresponding to the preset evaluation level, as well as transition boundaries on the lower and upper limits. When the measured value is less than or equal to the transition boundary on the lower limit or greater than or equal to the transition boundary on the upper limit, the output membership value is zero; when the measured value is equal to the typical threshold parameter, the output membership value is one; when the measured value is between the transition boundary on the lower limit and the typical threshold parameter, or between the typical threshold parameter and the transition boundary on the upper limit, the membership value between zero and one is calculated and output according to the corresponding increasing or decreasing linear function, respectively.

[0010] In the weight vector extraction stage, the relative importance of each laser-induced damage threshold influencing factor is quantified pairwise using integer scaling values, and arranged to form a judgment matrix. The largest eigenvalue of the judgment matrix and the corresponding initial eigenvector are calculated, and the consistency ratio is calculated using the largest eigenvalue. If the consistency ratio is strictly less than 0.1, the judgment matrix passes the consistency test, and the initial eigenvector is normalized to generate the weight vector.

[0011] When outputting the grade results, the evaluation system executes sorting and maximum value search instructions to locate the column index of the element with the largest value in the comprehensive evaluation vector. Based on the column index, it searches for the corresponding preset evaluation grade in the comment set as the grade output result. When outputting the quantitative numerical results, it extracts the center value parameters corresponding to each preset evaluation grade to form a center value vector. It then performs a centroid weighted summation operation to calculate the product of each element in the comprehensive evaluation vector and the corresponding center value parameter in the center value vector. All products are then summed, and the total sum is used as the quantitative numerical output result.

[0012] This method also includes a model error correction mechanism. Gradually increasing laser pulses are applied to the sampled elements, and the critical laser energy density value at which physical damage occurs is recorded as the actual damage threshold of the sample. The absolute difference between the quantized numerical output result and the actual damage threshold is calculated. The absolute difference is divided by the actual damage threshold, and the ratio is converted into a percentage to determine the relative error. When the relative error exceeds a preset error percentage threshold, the parameters or weight vector of the membership function are corrected. The correction operations include: supplementing the acquired actual damage threshold and corresponding measured data into the historical experimental database; re-performing the frequency statistical distribution calculation; and adjusting and updating the typical threshold parameter boundaries of each preset evaluation level in the membership function in reverse; or constructing a cost function whose objective is to minimize the sum of squared residuals between the actual damage threshold and the quantized numerical output result, solving the cost function using the least squares algorithm, and redistributing the values ​​of each component in the weight vector using the solution.

[0013] The core principle of this invention lies in establishing a fuzzy mathematical mapping structure between multi-source non-destructive feature data and the critical energy of physical damage. Consistency checks are used to eliminate measurement interference from local anomalies on the optical surface, ensuring the overall reliability of the feature data. By fitting the membership function using a frequency statistical method based on historical real damage data, the four-dimensional discrete detection physical quantity is transformed into a continuous fuzzy evaluation space, overcoming the quantization error introduced by single-parameter judgment. The analytic hierarchy process (AHP) is combined to quantify the independent weight contributions of multiple physical factors, and a centroid weighted summation algorithm is applied to achieve reverse analysis from the fuzzy state to the precise physical energy density. Based on this, a closed-loop feedback architecture targeting the true damage threshold is constructed. The least squares approximation principle is used to reorganize the model parameter matrix, enabling the evaluation system to self-adapt to deviations in thin film preparation processes and continuously optimize the accuracy of non-destructive threshold prediction.

[0014] This invention provides a method for evaluating the laser damage threshold of coated optical components based on fuzzy comprehensive evaluation. It has the following beneficial effects: 1. This invention collects internal defect density, residual stress, film absorptivity, and root mean square roughness of coated optical components as feature data, and constructs fuzzy relation matrices and weight vectors using membership functions and hierarchical analysis. This scheme transforms multi-source discrete physical detection quantities into a multi-dimensional joint comprehensive evaluation system, achieving damage threshold assessment without applying destructive laser pulses to optical components. It effectively overcomes the problem of large prediction errors in traditional single-factor evaluation methods and is suitable for full inspection and online process monitoring of optical components.

[0015] 2. Based on the computationally generated comprehensive evaluation vector, this invention combines maximum value search positioning with centroid weighted summation of preset center value parameters to simultaneously output discrete evaluation level results and continuous physical quantitative numerical results. This dual-dimensional output mechanism facilitates rapid classification and judgment by the engineering side. At the same time, since the boundary parameters of the underlying membership function are established based on the frequency statistical distribution of the corresponding historical experimental database, the evaluation model can be quickly reconstructed by updating the database samples, thereby adapting to the threshold evaluation requirements of different laser working parameters and various thin film preparation processes.

[0016] 3. This invention constructs a closed-loop error correction architecture based on actual measured data feedback. By obtaining the actual damage threshold of the sample component after destructive testing, the relative error between the actual damage threshold and the system's quantitative numerical output is calculated. When the error exceeds the preset conditions, the system uses the least squares method to solve the cost function and redistribute the weight vector components, or adjusts the typical threshold parameter boundary in the membership function in the opposite direction. This self-correction mechanism enables the evaluation model to automatically compensate for the prediction deviation caused by the fluctuation of the underlying production process, thereby achieving continuous improvement in model accuracy. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the method flow of the present invention; Figure 2 This is a schematic diagram of the method flow of the present invention; Figure 3 This is a schematic diagram comparing and verifying different evaluation methods of the present invention with actual destructive test results. Detailed Implementation

[0018] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0019] This invention presents a laser damage threshold assessment method for coated optical components based on fuzzy comprehensive evaluation, which operates within a laser damage threshold assessment system. The system mainly comprises a data acquisition hardware suite, a computer processing unit, and an output terminal.

[0020] The data acquisition hardware group is used to extract non-destructive characterization parameters of the coated optical elements. Specifically, it includes: a dark field scattering microscopy system for acquiring the density of defects inside the film, a two-beam interferometer for measuring residual stress, a laser calorimeter (or photothermal co-path interferometer) for acquiring the film absorptivity, and a white light interferometer (or atomic force microscope) for extracting surface micromorphological features.

[0021] The aforementioned data acquisition hardware group communicates with the computer processing device through wired or wireless data communication interfaces (such as USB, Ethernet port, etc.) to transmit the acquired measured data to the computer processing device.

[0022] The computer processing device can be an electronic device such as a personal computer (PC), an industrial control computer, a server, or a cloud computing platform. The computer processing device internally includes at least a processor (CPU) and a memory. The memory stores computer programs, preset physical energy density threshold parameters, and a historical experimental database; the processor is used to call the programs and data in the memory to execute the core algorithm steps in this embodiment of the invention, such as consistency verification, membership calculation, fuzzy relation matrix generation, weight vector allocation, and fuzzy comprehensive evaluation.

[0023] In addition, the system includes an output terminal (such as a monitor) connected to a computer processing device to visually present the final laser-induced damage threshold level results and quantitative estimates. During the model closed-loop correction phase, the system can also be connected to an external destructive laser testing platform to provide actual damage thresholds as feedback signals.

[0024] Based on the above hardware application environment, refer to the appendix. Figure 1 This invention provides a method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation, which may include the following steps: Multiple laser-induced damage threshold influencing factors for coated optical components were collected using non-destructive characterization methods. These factors included internal defect density, residual stress, film absorptivity, and root-mean-square surface roughness. The consistency of the measured values ​​for each collected laser-induced damage threshold influencing factor was evaluated. Subsequent evaluation procedures were performed only when all measured values ​​met their respective preset difference threshold conditions. The evaluation process was terminated if any measured value for a laser-induced damage threshold influencing factor failed to meet its preset difference threshold condition.

[0025] A set of influencing factors and a set of evaluation criteria were constructed. The set of influencing factors consisted of the collected data on internal defect density, residual stress, film absorptivity, and root mean square surface roughness. The set of evaluation criteria consisted of multiple evaluation levels based on a predefined laser-induced damage threshold.

[0026] Membership functions corresponding to various laser-induced damage threshold influencing factors are established. Based on the measured values ​​of each laser-induced damage threshold influencing factor and its corresponding membership function, the membership degree of each factor to each evaluation level in the evaluation set is calculated, forming a single-factor evaluation vector for each factor. By combining the single-factor evaluation vectors of all factors, a fuzzy relation matrix is ​​generated.

[0027] The weight vector is determined using the analytic hierarchy process (AHP). A judgment matrix is ​​constructed based on the relative importance of each laser-induced damage threshold influencing factor according to expert evaluation. The eigenvectors of the judgment matrix are calculated, and, provided they pass the consistency ratio test, the normalized eigenvectors are used as the weight vectors of each laser-induced damage threshold influencing factor in the overall evaluation.

[0028] Fuzzy comprehensive evaluation is performed based on the fuzzy relation matrix and weight vector. The product of the weight vector and the fuzzy relation matrix is ​​calculated to obtain the comprehensive evaluation vector containing the membership results corresponding to each level.

[0029] The final evaluation result is output by performing defuzzification processing on the comprehensive evaluation vector. The evaluation result includes a grade output and a quantitative numerical output. The grade output is based on the maximum membership principle, using the evaluation grade corresponding to the element with the largest value in the comprehensive evaluation vector as the final laser-induced damage threshold grade. The quantitative numerical output is calculated by weighted summation of the pre-defined center values ​​corresponding to each evaluation grade and the corresponding elements in the comprehensive evaluation vector.

[0030] Perform model validation and closed-loop correction steps. Conduct laser damage tests on sampled coated optical components to obtain their actual damage threshold. Calculate the relative error between the quantized numerical output and the actual damage threshold. If the relative error exceeds a preset error threshold, adjust the threshold parameter in the membership function or the eigenvector values ​​in the weight vector in reverse order based on the actual damage threshold to update the evaluation model parameters.

[0031] See attached document Figure 1 The specific implementation steps for collecting multiple laser-induced damage threshold influencing factors of coated optical components through non-destructive characterization methods and performing consistency verification are as follows: A dark-field scattering microscopy system was used as the detection equipment. A controlled light source illuminated the surface of the coated optical element, and a dark-field detector collected the scattered light signals generated by nodules, pinholes, and impurity particles inside or on the surface of the film. A detection sensitivity threshold was set to filter background scattering noise; the sensitivity threshold was set to a detection diameter greater than or equal to 0.5 mm. Defects of size m. Multiple detection areas of preset size are randomly selected within the light-transmitting aperture range on the surface of the coated optical element. The number of defects meeting the sensitivity threshold condition within each detection area is counted. The average number of defects across multiple detection areas is calculated, and this average value is determined as the defect density within the film layer. Its unit is units / cm 2 Calculate the relative difference in the density of defects within the membrane layer between multiple detection areas. If the relative difference is less than 20%, proceed to the next influencing factor measurement stage; if the relative difference is greater than or equal to 20%, terminate the evaluation process.

[0032] Substrate curvature parameters were obtained using interferometric measurement equipment such as a two-beam interferometer. The radius of curvature of the substrate in its initial state before coating and the radius of curvature after deformation due to film stress were both obtained. The change in substrate curvature before and after coating was calculated. Based on the change in curvature, the residual stress was calculated using the Stoney method formula. ; in, This represents the calculated residual stress value; Indicates the Young's modulus of the substrate; Indicates the Poisson's ratio of the substrate; Indicates the physical thickness of the substrate; Indicates the physical thickness of the film; This indicates the change in substrate curvature before and after coating. Curvature measurement and calculation steps are repeated at multiple different locations on the surface of the coated optical element to obtain residual stress values ​​at multiple locations. The relative difference in residual stress values ​​between each location is calculated. If the relative difference is less than 10%, the process proceeds to the next measurement stage; if the relative difference is greater than or equal to 10%, the evaluation process terminates.

[0033] Measurements are performed using a laser calorimeter or a photothermal co-channel interferometer. By irradiating the film region of the coated optical element with a test laser, the accumulated heat signal or the thermally induced refractive index change signal caused by the absorption of light energy by the film layer is measured, and then the film absorptivity is calculated. The unit is ppm. Multiple measurement points are selected on the surface of the coated optical element for measurement. The relative difference in film absorptivity measured at each measurement point is calculated. If the relative difference is less than 0.5%, the process proceeds to the next measurement stage. If the relative difference is greater than or equal to 0.5%, a physical or chemical cleaning procedure is performed to remove adhering substances from the element surface, and the film absorptivity at each measurement point is remeasured after cleaning and drying. If the remeasured relative difference is still greater than or equal to 0.5%, the evaluation process is terminated.

[0034] The microscopic morphology of the component surface is acquired using a white light interferometer or atomic force microscope. Three-dimensional surface morphology data is obtained within a preset scanning field of view. The acquired 3D morphology data undergoes surface profile compensation and datum plane removal processing to eliminate interference from low-frequency substrate surface profiles on the calculation of high-frequency surface roughness. The root mean square roughness of the corresponding measurement area is calculated based on the processed 3D morphology data. The unit is nm. The above measurements are performed at multiple different locations on the surface of the coated optical element. It is determined whether the root mean square roughness (RMS) measurement values ​​at all locations are less than 0.5 nm, and simultaneously whether the relative difference between the RMS roughness measurement values ​​at each location is less than 0.5%. When both the measurement values ​​at each location and their relative differences meet the above conditions, the RMS roughness acquisition is confirmed as complete, and the subsequent fuzzy relation generation step begins; if any condition is not met, the evaluation process terminates.

[0035] See attached document Figure 1 After completing the collection and verification steps of each non-destructive feature parameter, the construction of the influencing factor set and fuzzy comment set is performed.

[0036] A set of influencing factors is established. The values ​​of the internal defect density, residual stress, film absorptivity, and root mean square roughness of the surface, all verified through testing, are extracted as feature elements to form the influencing factor set. In a computer processing device, this influencing factor set is configured and stored as an input evaluation vector containing four real numbers, serving as the input data for subsequent fuzzy mathematical operations.

[0037] A fuzzy evaluation set is constructed. The fuzzy evaluation set consists of five discrete evaluation level elements, which are labeled as extremely high, high, medium, low, and extremely low in descending order of laser damage resistance. For each evaluation level, a corresponding continuous physical energy density threshold range is defined.

[0038] The boundary values ​​for the physical energy density threshold range are configured. The rules for dividing the boundary values ​​are based on the optical parameters of the working environment of the target coated optical element, including the laser wavelength and laser pulse width. In an embodiment of optical parameters with a wavelength of 193 nanometers and a pulse width of 10 nanoseconds, the threshold ranges for each evaluation level are set as follows: the lower limit of the energy density for the extremely high level is set to 7 joules per square centimeter; the energy density range for the high level is set to 5 joules per square centimeter to 7 joules per square centimeter; the energy density range for the medium level is set to 3 joules per square centimeter to 5 joules per square centimeter; the energy density range for the low level is set to 1 joule per square centimeter to 3 joules per square centimeter; and the upper limit of the energy density for the extremely low level is set to 1 joule per square centimeter. The endpoint values ​​of each range are stored in the system as preset configuration parameters, providing a numerical mapping benchmark for deblurring calculations in the subsequent algorithm process.

[0039] See attached document Figure 1 After obtaining the set of influencing factors and the set of fuzzy comments, a quantitative mapping model between each influencing factor and each evaluation level is constructed based on historical sample data to generate a fuzzy relationship matrix.

[0040] Obtain a historical experimental database containing a preset sample size of 50 or more groups. This database records measured non-destructive characteristic parameters of multiple optical components fabricated using the same coating process, along with damage threshold data obtained from actual destructive laser testing of the corresponding components. Process the data in the historical experimental database using frequency statistics. Calculate the distribution frequency of each non-destructive characteristic parameter value within the corresponding interval of each evaluation level in the fuzzy evaluation set. Based on the calculated distribution frequency data, assign trapezoidal or Gaussian membership functions to each characteristic element in the influencing factor set, and extract the typical threshold parameters corresponding to each evaluation level.

[0041] Taking the defect density inside the membrane as an example, a trapezoidal distribution is used to construct its membership function for a specific evaluation level. Let the typical threshold parameter sequence corresponding to each evaluation level in the evaluation set be... The input value of the measured internal defect density of the film layer is then... Corresponding to the rating levels The formula for calculating membership degree is as follows: ; in, This represents the density of defects inside the input film layer. Belongs to the rating levels Membership degree; Represented as the first Typical threshold parameters fitted to each evaluation level; Indicates the first The typical threshold parameters for each evaluation level serve as the transition boundary on the lower limit side of the current evaluation level. Indicates the first The typical threshold parameters for each evaluation level serve as the transition boundary on the upper limit side of the current evaluation level. This indicates an OR condition. The formula is limited to the condition when the input value is in the range of OR. and When the time interval is between, the calculation of the increasing linear function is performed. and A decreasing linear function is performed between these points.

[0042] The measured values ​​of internal defect density, residual stress, film absorptivity, and root mean square roughness of the surface were collected and used as input variables, respectively, and substituted into the membership functions corresponding to each parameter for calculation. For any feature parameter, the set of membership values ​​belonging to all five evaluation levels was calculated. The five values ​​in the set were arranged in order of evaluation level to form a horizontal vector, and the values ​​of the horizontal vector were normalized to obtain the single-factor evaluation vector corresponding to the feature parameter.

[0043] After calculating the four feature parameters, four single-factor evaluation vectors are extracted. These four vectors are then arranged in a row-wise order to generate a 4x5 matrix, which serves as the fuzzy relation matrix. The 20 matrix elements of this fuzzy relation matrix constitute the basic data input for the subsequent comprehensive evaluation stage.

[0044] See attached document Figure 1 After generating the fuzzy relation matrix corresponding to each influencing factor, the analytic hierarchy process is used to calculate the proportional coefficients of each influencing factor participating in the comprehensive calculation.

[0045] To quantify the relative contributions of each laser-induced damage threshold influencing factor in the overall evaluation model, the analytic hierarchy process (AHP) was used to calculate the weight vector. Based on a pre-defined relative importance scaling rule, any two laser-induced damage threshold influencing factors in the influencing factor set were compared pairwise. Integer scale values ​​from 1 to 9 were used to quantify the difference in importance of one feature factor relative to another. All the quantified comparison results were arranged into a 4x4 judgment matrix. The main diagonal elements of the judgment matrix were set to 1, and the off-diagonal elements represented the relative importance ratio of the corresponding row feature factor to the column feature factor in influencing laser damage resistance.

[0046] The generated judgment matrix undergoes eigenvalue decomposition. The largest eigenvalue corresponding to the judgment matrix is ​​extracted, and its corresponding eigenvector is calculated. The obtained eigenvector is then normalized so that the sum of the values ​​of all components in the normalized vector equals 1. The normalized output vector is the initial weight vector, containing four real components, each corresponding to a weight coefficient for the internal defect density, residual stress, film absorbance, and root mean square roughness of the surface.

[0047] A matrix consistency check is performed on the judgment matrix to determine whether the input scaling values ​​used to construct the matrix satisfy the logical self-consistency condition. A consistency index is calculated using the difference between the largest eigenvalue and the matrix order, and combined with a preset average random consistency index of the same order, a consistency ratio is calculated. The pass condition for the consistency check is that the consistency ratio is strictly less than 0.1.

[0048] The system executes a conditional judgment command and compares the calculated consistency ratio with a preset value of 0.1. If the consistency ratio is less than 0.1, the judgment matrix passes the consistency check, and the currently calculated initial weight vector is confirmed as the final output weight vector, which is then sent to the subsequent comprehensive evaluation module. If the consistency ratio is greater than or equal to 0.1, the judgment matrix has a logical contradiction and fails the check. The system then abandons the currently calculated initial weight vector and re-executes the loop of pairwise comparisons, modifying judgment matrix elements, recalculating eigenvectors, and re-executing the consistency check until the output consistency ratio is less than 0.1.

[0049] See attached document Figure 1 After obtaining the fuzzy relation matrix and weight vector, a comprehensive matrix operation is performed and the evaluation result is output.

[0050] Extract the calculated weight vector and the generated fuzzy relation matrix. Using the matrix operation module configured in the computer device, perform fuzzy operator multiplication of the weight vector and the fuzzy relation matrix. The weight vector is a row vector containing 4 elements, and the fuzzy relation matrix is ​​a 4x5 matrix structure. After performing the multiplication, the output is a row vector containing 5 elements, which is the comprehensive evaluation vector.

[0051] Each element in the comprehensive evaluation vector represents the overall membership degree of the tested optical component's resistance to laser damage, indicating its belonging to the corresponding evaluation level. element The specific calculation formula is as follows: ; in, This represents the corresponding number in the comprehensive evaluation vector. The overall membership value of each evaluation level. The value of is an integer ranging from 1 to 5; This indicates the weight vector corresponding to the first... The weighted components of the factors influencing the laser-induced damage threshold. The value of is an integer ranging from 1 to 4; Represents the fuzzy relation matrix in which the th Line 1 The value of the matrix element in column 1, i.e., the value of the first column. The impact factor on the first The algorithm calculates the single-factor membership degree of each evaluation level. The algorithm logic guarantees that each... The numerical range is between 0 and 1.

[0052] Based on the calculated comprehensive evaluation vector, defuzzification data processing is performed, and the level determination result is output. The five comprehensive membership values ​​contained in the comprehensive evaluation vector are read, and sorted by size and searched for the maximum value to locate the vector column index of the element with the largest value. The corresponding evaluation level is then searched in the comment set based on this column index, and the found evaluation level is used as the final output fuzzy laser-induced damage threshold level of the tested optical element.

[0053] Numerical mapping processing is performed based on the calculated comprehensive evaluation vector to output quantified numerical results. The center value vector corresponding to each pre-set evaluation level is extracted. This vector contains five center value parameters corresponding to the physical energy density threshold ranges of each evaluation level. A centroid-weighted summation operation is performed to obtain the corresponding quantified predicted value. The calculation formula is as follows: ; in, This represents the final quantitative estimate of the laser-induced damage threshold output by the system, expressed in joules per square centimeter. Represents the corresponding first in the comprehensive evaluation vector A comprehensive membership degree value; Indicates the preset corresponding number The system calculates the center value parameter for each evaluation level. After completing the above summation calculation, the system transmits the corresponding fuzzy level string and the quantitative prediction value to the display terminal or process control database for recording and presentation.

[0054] See attached document Figure 1 After outputting the evaluation results, the parameters are adjusted and the model is updated by comparing the measured data.

[0055] A predetermined number of sample elements (1 to 2 pieces) are selected from the current production batch of coated optical elements. A destructive laser testing procedure is then performed on the selected sample elements, applying progressively increasing laser pulses to their surface and monitoring the process using optical inspection equipment until physical damage occurs on the element surface. The critical laser energy density value at which physical damage is determined is recorded, and this value is used as the actual damage threshold for the sample element.

[0056] Retrieve the quantitative predicted value output by the sample component after performing non-destructive feature parameter acquisition and comprehensive evaluation calculation. Extract the quantitative predicted value and the actual damage threshold, and perform error calculation processing to obtain the relative error value. The specific formula for calculating the relative error value is as follows: ; in, This represents the percentage of the calculated relative error. This represents the quantitative estimate output by the system for this sample component; This indicates the actual damage threshold obtained from the destructive testing of the sample component.

[0057] The system's preset error tolerance threshold is extracted; in this embodiment, the error tolerance threshold is set to 10%. A comparison command is executed to compare the calculated relative error value with the error tolerance threshold. When the relative error value is less than or equal to the error tolerance threshold, it is determined that the model parameters built into the current system match the production process of the current batch, the correction process is terminated, and the current membership function parameters and weight vector configuration are maintained.

[0058] When the relative error value exceeds the error tolerance threshold, it is determined that the current model has a prediction deviation caused by fluctuations in process parameters, triggering the model parameter correction module to perform closed-loop optimization. The model parameter correction module extracts the actual damage threshold as the target feedback quantity and executes at least one of the following two fine-tuning calculation strategies: The first correction strategy involves adjusting the membership function parameter configuration. The actual damage thresholds and corresponding non-destructive characteristic parameters are supplemented into the historical experimental database. Based on the updated database sample set, the frequency statistical distribution is recalculated, and the typical threshold parameter boundaries of each evaluation level in the membership function are adjusted and updated in reverse to reduce the difference between the model's predicted value and the target feedback quantity.

[0059] The second correction strategy involves fine-tuning the weight vector allocation. A cost function is constructed with the objective of minimizing the sum of squared residuals between the actual damage threshold and the quantitatively predicted value. The least squares algorithm is used to solve this objective cost function, and the weight coefficients corresponding to the internal defect density, residual stress, film absorptivity, and root mean square surface roughness are reassigned based on the optimal solution output.

[0060] After completing the above fine-tuning calculations, the updated membership degree typical threshold parameters and / or weight vector values ​​are extracted, written to the computer storage device to overwrite the original old model parameters, and the updated model parameters are applied to the online laser-induced damage threshold evaluation calculation process of subsequent coated optical elements prepared in the same batch and using the same process.

[0061] See attached document Figure 2 This embodiment takes the laser-induced damage threshold assessment process of a batch of high-reflectivity film samples as an example to illustrate the specific data acquisition and calculation process.

[0062] Non-destructive physical acquisition and data statistics of characteristic parameters were performed. For selected high-reflectivity film samples, a dark-field scattering microscopy system was used to acquire the defect density within the film. The optical magnification of the dark-field scattering microscopy system was configured to 200x, and the system's detection sensitivity parameters were set to identify defect targets with a diameter greater than or equal to 0.5 μm. Five independent detection areas were randomly selected on the surface of the high-reflectivity film sample, and the physical area of ​​each detection area was set to 1 mm². 2 The number of defects in each detection area was counted and the arithmetic mean was calculated. The system recorded the internal defect density of the high-reflectivity film sample as 12 defects / cm². 2 .

[0063] The residual stress of the substrate was measured using a two-beam interferometry method. The difference in physical deformation of the radius of curvature of the high-reflectivity film sample substrate before and after the coating process was measured. Substituting the difference in physical deformation of the radius of curvature and the physical thickness parameters of the substrate and the film into the Stoney formula, the residual stress of the high-reflectivity film sample was calculated to be -85 MPa. This negative value indicates that the film is currently under compressive stress.

[0064] Laser calorimetry was used to acquire the film absorptivity. The temperature rise data generated after the high-reflectivity film sample absorbed the test laser was captured using a calorimetric chamber. The absorptivity of the high-reflectivity film sample was calculated to be 45 ± 10 ppm using the heat balance equation. Subsequently, a white light interferometer was used to acquire the root mean square roughness of the surface. The scanning field of view of the white light interferometer was configured to be 50 μm × 50 μm. The acquired raw topography data underwent filtering compensation to remove the tilted reference surface. Based on the processed topography data, the root mean square roughness of the high-reflectivity film sample was measured to be 0.2 nm.

[0065] Membership functions are constructed and fuzzy relation matrices are generated. The historical experimental database stored in the system is accessed, containing non-destructive measured values ​​and corresponding destructive standard laser damage thresholds for 100 samples prepared using the same high-reflectivity film process. Frequency statistics are used to fit the acquired parameters to extremely high... ,high ,middle ,Low extremely low Trapezoidal membership functions for five evaluation levels.

[0066] The measured internal defect density of the film layer was 12 defects / cm². 2 Substituting these values ​​into the corresponding defect density trapezoidal membership function, the single-factor evaluation vectors for the five evaluation levels are calculated as [0.0, 0.1, 0.7, 0.2, 0.0].

[0067] Substituting the measured residual stress of -85 MPa into the corresponding residual stress trapezoidal membership function, the single-factor evaluation vector is calculated as [0.0, 0.2, 0.6, 0.2, 0.0]. Substituting the measured film absorbance of 45 ppm into the corresponding absorbance trapezoidal membership function, the single-factor evaluation vector is calculated as [0.0, 0.1, 0.5, 0.4, 0.0]. Substituting the measured root mean square surface roughness of 0.2 nm into the corresponding roughness trapezoidal membership function, the single-factor evaluation vector is calculated as [0.2, 0.6, 0.2, 0.0, 0.0]. The system combines these four row vectors sequentially to generate a 4-row, 5-column fuzzy relation matrix. .

[0068] Perform weight vector allocation calculation based on the analytic hierarchy process (AHP). The system receives quantitative scoring data from three domain experts who perform pairwise importance comparisons on the four influencing factors mentioned above. A 4x4 judgment matrix is ​​constructed based on the scoring data. The eigenvectors and consistency ratio of this judgment matrix are calculated, and the calculated consistency ratio is... Since 0.06 < 0.1, the system determines that the judgment matrix passes the consistency check. The system extracts the normalized feature vector as the final weight vector. The four values ​​correspond to the calculation weights of defect density, residual stress, absorption rate, and roughness, respectively.

[0069] Perform fuzzy comprehensive evaluation and output the evaluation results. The system calls the matrix multiplication module to calculate the weight vector. With fuzzy relation matrix The product of these elements yields a comprehensive evaluation vector containing five elements. After multiplication and summation operations, the final output is the comprehensive evaluation vector. .

[0070] Execute deblurring instructions to generate a threshold determination conclusion. The system iterates through and searches the comprehensive evaluation vector. All values ​​were extracted, with the highest membership degree being 0.57. The index of this highest value in the vector was located, corresponding to the third of the five evaluation levels. Based on the index location result, the system sends a qualitative evaluation command to the output terminal, indicating that the laser-induced damage threshold level of the high-reflectivity film sample is medium. Simultaneously, the system retrieves the preset threshold range parameter corresponding to this medium level and sends a quantitative evaluation command to the output terminal, indicating that the estimated laser-induced damage threshold range of the high-reflectivity film sample is between 3 J / cm². 2 Up to 5J / cm 2 between.

[0071] Specific application example: Batch full inspection and online evaluation of 193nm high reflectivity film This embodiment takes the batch production of a 193nm wavelength high-reflectivity film for a certain lithography equipment as an example. This batch produces 10 high-reflectivity film optical elements. In order to predict their resistance to laser damage without damaging the elements, the system employs the evaluation method of this invention.

[0072] For sample number 1 in the batch, the system first performs consistency verification and data acquisition. A two-beam interferometer is used to obtain the change in substrate curvature before and after coating. The system directly calls the Stoney formula from the aforementioned specific embodiment to calculate the residual stress. : ; The residual stress at this location was calculated. MPa (compressive stress). Using a dark-field scattering microscopy system, laser calorimeter, and white-light interferometer, the internal defect density of the film layer in this sample was measured. pcs / cm 2， Membrane absorption rate ppm, root mean square surface roughness nm.

[0073] The system substitutes the measured values ​​into the trained membership function to generate a 4-row, 5-column fuzzy relation matrix. Extract the weight vector obtained from expert evaluation. The system calls the comprehensive evaluation formula from the aforementioned specific embodiments to calculate the first... The overall membership degree of each evaluation level ; Calculate the comprehensive evaluation vector .

[0074] The maximum membership degree is 0.57, corresponding to a medium level. The system extracts medium-level (3-5 J / cm³) samples. 2 and the center value vector of each level [8,6,4,2,0.5], perform quantization numerical output calculation: J / cm 2 The estimated damage threshold for this component is 3.98 J / cm². 2 .

[0075] To verify the authenticity and high accuracy of the solution, 10 components were randomly selected from the batch. After completing the non-destructive prediction of this invention, conventional destructive testing (ISO21254) was then performed on them to obtain the true results. Meanwhile, the traditional single-factor empirical formula method (which only relies on defect density for fitting and prediction) is introduced as a comparison benchmark.

[0076] See attached document Figure 3 , attached Figure 3 The results of laser-induced damage threshold verification comparisons for 10 high-reflectivity film samples are presented. The horizontal axis represents the sample number within the batch (1 to 10), and the vertical axis represents the laser-induced damage threshold (unit: J / cm). 2 The diagram contains three grayscale data lines distinguished by different line types and marker symbols: Solid lines and triangle markings (actual destructive measurements): represent the true baseline values ​​measured after the component was damaged by a laser.

[0077] Dashed lines and square markers (multi-factor comprehensive prediction value of the present invention): represent the quantitative prediction value calculated using the method of the present invention under zero-damage conditions.

[0078] Dotted lines and circular markers (traditional single-factor predictions): represent traditional prediction methods that only consider defect density.

[0079] As clearly shown in the figure, because the single-factor prediction method ignores the coupled effects of stress, absorption, and roughness, its prediction results (dotted lines) fluctuate wildly and deviate significantly from the actual values ​​(errors are generally between 20% and 40%). In contrast, the prediction results (dashed lines) of this invention closely match the actual measured values ​​(solid lines), and through a closed-loop correction mechanism, the relative errors are strictly controlled within 10%. This demonstrates the beneficial effect of this invention in achieving zero-destruction full inspection while improving prediction accuracy.

Claims

1. A method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation, characterized in that, Includes the following steps: Measured values ​​of multiple laser-induced damage threshold influencing factors of coated optical components were collected and their consistency was verified. The laser-induced damage threshold influencing factors include internal defect density of the film, residual stress, film absorptivity, and root mean square surface roughness. Construct a set of influencing factors consisting of each of the laser-induced damage threshold influencing factors, a set of comments consisting of preset evaluation levels, and establish a membership function corresponding to each of the laser-induced damage threshold influencing factors; Substitute each of the measured values ​​into the corresponding membership function to calculate the membership degree of each of the laser-induced damage threshold influence factors to each of the preset evaluation levels, form a single-factor evaluation vector, and combine each of the single-factor evaluation vectors to generate a fuzzy relation matrix. Based on the analytic hierarchy process, a judgment matrix is ​​constructed for the set of influencing factors. When the judgment matrix passes the consistency test, the normalized feature vector is extracted as the weight vector. The comprehensive evaluation vector is obtained by multiplying the weight vector and the fuzzy relation matrix, and the level output result and the quantitative value output result are output based on the comprehensive evaluation vector.

2. The method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation according to claim 1, characterized in that, The steps for performing consistency verification include: Multiple measured values ​​of the same laser-induced damage threshold influencing factor were collected at multiple different locations on the surface of the coated optical element. Calculate the relative differences between the measured values ​​of the same laser-induced damage threshold influencing factor at the multiple different locations; When all the relative difference values ​​are less than their respective preset relative difference ratio thresholds, the consistency check is confirmed to be passed; otherwise, the evaluation process is terminated.

3. The method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation according to claim 1, characterized in that, The steps for constructing a set of comments consisting of preset evaluation levels include: The evaluation set is divided into five preset evaluation levels: extremely high, high, medium, low, and extremely low. Extract the laser wavelength and laser pulse width parameters of the target test environment, and set corresponding continuous physical energy density threshold ranges for each preset evaluation level based on the laser wavelength and laser pulse width parameters.

4. The method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation according to claim 3, characterized in that, The steps for establishing the membership functions corresponding to the laser-induced damage threshold influencing factors include: Retrieve a historical experimental database containing a preset number of samples. The historical experimental database records the measured data of each of the laser-induced damage threshold influencing factors, as well as the corresponding damage threshold data. The frequency distribution frequency of the measured data within the intervals corresponding to each preset evaluation level is calculated using frequency statistics. Based on the distribution frequency, a triangular distribution membership function or a Gaussian distribution membership function corresponding to each of the laser-induced damage threshold influence factors is fitted and established for each of the preset evaluation levels.

5. The method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation according to claim 4, characterized in that, The triangular distribution membership function includes typical threshold parameters corresponding to the preset evaluation level, as well as transition boundaries on the lower and upper limits. The steps for calculating the membership degree of each laser-induced damage threshold influence factor to each preset evaluation level include: When the measured value is less than or equal to the transition boundary on the lower limit side, or greater than or equal to the transition boundary on the upper limit side, the membership degree is output as zero. When the measured value is equal to the typical threshold parameter, the membership degree is output as a value of one. When the measured value is located between the transition boundary on the lower limit side and the typical threshold parameter, or between the typical threshold parameter and the transition boundary on the upper limit side, the membership degree between zero and one is calculated and output according to the corresponding increasing linear function or decreasing linear function, respectively.

6. The method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation according to claim 1, characterized in that, The step of extracting the normalized feature vector as the weight vector includes: The relative importance of each laser-induced damage threshold influencing factor is quantified using integer scaling values ​​and arranged to form the judgment matrix. Calculate the largest eigenvalue of the judgment matrix and the corresponding initial eigenvector, and use the largest eigenvalue to calculate the consistency ratio; If the consistency ratio is strictly less than 0.1, the judgment matrix is ​​determined to pass the consistency test, and the initial feature vector is normalized to generate the weight vector.

7. The method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation according to claim 1, characterized in that, The steps for outputting the level result based on the comprehensive evaluation vector include: Execute the size sorting and maximum value search instructions to locate the vector column index value containing the element with the largest value in the comprehensive evaluation vector; The corresponding preset evaluation level is searched in the comment set according to the column index value, and the found preset evaluation level is output as the level result.

8. The method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation according to claim 1, characterized in that, The steps for outputting the quantized numerical output result based on the comprehensive evaluation vector include: Extract the center value parameters corresponding to each preset evaluation level, and arrange them sequentially to form a center value vector; Perform a weighted summation operation to calculate the product of each element in the comprehensive evaluation vector with the corresponding center value parameter in the center value vector; Perform a cumulative summation calculation on all products, and output the obtained total summation value as the quantized numerical result.

9. The method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation according to claim 5, characterized in that, Also includes: Obtain the actual damage threshold of the sample. When the relative error between the quantized numerical output result and the actual damage threshold of the sample is greater than a preset error percentage threshold, correct the parameters of the membership function or the weight vector. The modification of the parameters of the membership function or the weight vector includes performing any of the following operations: The actual damage threshold of the obtained sample and the corresponding measured data are added to the historical experimental database, the frequency statistical distribution calculation is re-executed, and the typical threshold parameter boundary of each preset evaluation level in the membership function is adjusted and updated in reverse. A cost function is constructed, the objective of which is to minimize the sum of squared residuals between the actual damage threshold of the sample and the quantized numerical output result. The cost function is solved using the least squares algorithm, and the solution is used to redistribute the values ​​of each component in the weight vector.

10. The method for evaluating the laser damage threshold of coated optical elements based on fuzzy comprehensive evaluation according to claim 9, characterized in that, The steps for calculating the relative error include: A progressively stronger laser pulse is applied to the sampled element to obtain the critical laser energy density value at which physical damage occurs, and the critical laser energy density value is recorded as the actual damage threshold of the sample. Calculate the absolute difference between the quantified numerical output and the actual damage threshold of the sample; The absolute difference is divided by the actual damage threshold of the sample, and the obtained ratio is converted into a percentage to determine the relative error.

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