Design method for adaptively generating optical micropattern based on substrate parameters

Abstract

The invention belongs to the technical field of electrical digital data processing, and discloses a design method for adaptively generating an optical micropattern based on substrate parameters, which comprises the following steps of: acquiring a non-uniform physical parameter diagram of an actual substrate, constructing an optical residual potential field for representing optical performance deviation on the basis of the non-uniform physical parameter diagram, and then, taking a reference pattern as an initial pattern, the method comprises the following steps: carrying out iterative optimization on a micro-pattern unit in a potential field, carrying out coordination on adjustment based on potential field gradient and smoothing correction based on neighborhood influence in each step of iteration, updating the potential field in real time, and finally, after iteration convergence, carrying out spatial derivation analysis on a final residual potential field to generate manufacturing tolerance guidance information. According to the method, the non-uniformity of the substrate is used as an internal constraint of design, and a closed-loop feedback system is used, so that a design result is matched with physical reality.

Description

Technical Field

[0001] This invention relates to a design method for adaptively generating optical micropatterns based on substrate parameters, belonging to the field of electronic digital data processing technology. Background Technology

[0002] Currently, a mainstream approach to designing micropatterns for optical components involves creating an idealized substrate model in a computer, then generating a geometrically precise digital micropattern file through data processing. This file is then unidirectionally delivered to the physical manufacturing stage for execution. This approach has been adopted when the substrate is made of traditional materials with high purity and high homogeneity due to its clear process and ease of standardization. However, as application demands expand towards new functional materials such as stretchable and biodegradable materials, this approach exhibits inherent inadequacies. These new materials generally possess endogenous non-uniformity in the spatial distribution of physical parameters. When the digital file generated based on the ideal model is applied to such physical substrates, unpredictable deviations will occur between the optical performance of the manufactured component and the design objectives, making the design process dependent on physical pilot production and subsequent corrections.

[0003] To address uncertainties and deviations in the physical world, adaptive optimization techniques using closed-loop feedback systems have emerged in some other advanced manufacturing fields. For example, Chinese invention patent CN119126686A discloses an adaptive optimization method for surface mount process parameters based on automatic optical inspection feedback. This method uses an automatic optical inspection (AOI) device to inspect the circuit board after mounting and feeds back the detected mounting offsets, defects, and other results to the control system. The system then uses algorithms such as Bayesian optimization and particle swarm optimization to dynamically adjust process parameters such as the mounting height and air blowing delay of the pick-and-place machine for the production of the next circuit board. This method constructs a physical closed loop of production-inspection-feedback-adjustment, solving the problem of dynamic process drift caused by factors such as machine thermal deformation in electronic manufacturing.

[0004] However, the aforementioned real-time feedback control schemes for physical manufacturing processes cannot solve the technical problems faced by this invention. The differences are as follows: 1. Surface mount technology optimization occurs during the manufacturing execution stage, aiming to correct dynamically generated process errors in real time. In contrast, the optical performance deviation that this invention aims to address stems from the non-uniformity of the static physical parameters of the substrate material, a problem that exists in the design stage before manufacturing begins. 2. The output of surface mount technology is a series of dynamically changing equipment control parameters. However, for optical micropatterns, once their geometric definition is solidified through photolithography masks, it cannot be adjusted in real time during manufacturing. The compensation scheme must exist in the form of a pre-optimized and static digital design file. In summary, existing technical approaches inherently create a separation between design and reality, and there are constraints between computational efficiency and physical accuracy. Specifically, this manifests in: 1. The design process lacks initial input to the physical reality of the substrate, and its non-uniformity is considered as interference that downstream processes need to tolerate, rather than information that upstream design can utilize. 2. High-precision physical simulation and high-efficiency data processing are difficult to effectively reconcile within the existing technical framework. Therefore, the technical problem to be solved by this invention is how to provide an electrical digital data processing method that can take the non-uniform physical parameters of the substrate as the initial constraints of the design and directly generate an optical micro-pattern digital file that is inherently consistent with the physical reality through a computational closed loop. Summary of the Invention

[0005] This invention provides a design method for adaptively generating optical micropatterns based on substrate parameters. Its main purpose is to solve the problem that existing design methods fail to take the non-uniform physical parameters of the substrate as initial input, resulting in a disconnect between the design results and physical reality, and making it difficult to achieve a balance between computational efficiency and model accuracy.

[0006] To achieve the above objectives, this invention provides a design method for adaptively generating optical micropatterns based on substrate parameters, the method comprising the following steps: Step a: Obtain the spatial non-uniform physical parameter map of the actual substrate where the optical micro-pattern to be designed is located; Step b: Obtain the reference micropattern acting on the ideal substrate, compare the reference micropattern with the spatial non-uniform physical parameter map, and calculate an optical residual potential field characterizing the optical performance deviation based on the preset local phase approximation model that does not rely on global ray tracing. Step c: Using the reference micropattern as the initial pattern, iteratively optimize the micropattern units in the initial pattern. In each iteration: Step c1: Calculate the local gradient of the micropattern unit at the position of the optical residual potential field to obtain the first adjustment amount; Step c2: Calculate the smoothing constraint of the micropattern unit due to the geometric parameters of its neighboring micropattern units to obtain the second adjustment amount; Step c3: According to the preset synthesis rule, synthesize the first adjustment amount and the second adjustment amount into a geometric update amount, and use the geometric update amount to adjust the geometric parameters of the micropattern unit; Step c4: Update the optical residual potential field based on the adjusted pattern. Step d: When the iteration meets the preset convergence condition, stop the iteration and obtain the final micropattern; Step e involves performing spatial differentiation analysis on the final optical residual potential field corresponding to the final micropattern to generate manufacturing tolerance guidance information that indicates the sensitivity of different regions of the micropattern to manufacturing errors.

[0007] Preferably, the iterative optimization in step c further includes: in each iteration, after adjusting the geometric parameters of the micropattern unit using a geometric update amount, applying a random perturbation to the geometric parameters; and the magnitude of the random perturbation is set to decrease as the iteration proceeds.

[0008] Preferably, the reduction in the amplitude of random perturbation is based on non-uniform control of the local spatial characteristics of the optical residual potential field; the method further includes: analyzing the gradient distribution of the optical residual potential field during the iteration process to generate a scalar field C(x,y) characterizing the local complexity of the optical residual potential field; and controlling the attenuation rate α(x,y) of the amplitude of random perturbation in different regions of the micropattern according to the scalar field, the control rule following: , where α base is a preset base decay rate, and k is a preset adjustment coefficient.

[0009] Preferably, in step e, spatial derivative analysis is performed on the final optical residual potential field, specifically including: calculating the spatial second derivative of the final optical residual potential field to determine the local curvature of the potential field, and identifying regions with local curvature greater than a preset curvature threshold as critical regions that are highly sensitive to manufacturing errors, and identifying regions with local curvature not greater than the preset curvature threshold as non-critical regions that are less sensitive to manufacturing errors.

[0010] Preferably, after generating manufacturing tolerance guidance information, the method further includes: selecting at least one probe point in both critical and non-critical regions; applying a virtual perturbation that increments from zero to the geometric parameters of each probe point, and calculating the nonlinear response of the optical performance deviation caused by the virtual perturbation; and determining and outputting a quantitative tolerance threshold associated with the probe point based on the perturbation amplitude corresponding to the first time the rate of change of the response value in the nonlinear response exceeds a preset rate of change threshold.

[0011] Preferably, the preset synthesis rule in step c3 is: to perform a weighted summation of the first adjustment amount and the second adjustment amount, wherein the weight factor of the second adjustment amount is set to a function that monotonically decreases with the increase of the number of iterations.

[0012] Preferably, in step c2, calculating the smoothing constraint on the micro-pattern unit specifically includes: obtaining the parameter difference between the micro-pattern unit and all its directly adjacent micro-pattern units in at least one geometric parameter; and calculating all parameter differences according to a preset elastic potential energy function to obtain a resultant force aimed at reducing the parameter difference, which is the second adjustment amount.

[0013] Preferably, the convergence condition preset in step d is: in a preset number of consecutive iterations, the rate of change of the total energy value of the optical residual potential field is less than a preset rate of change threshold.

[0014] Preferably, the geometric parameters include at least one of the center position coordinates of the micropattern unit, a dimensional parameter characterizing its contour, and a rotation angle parameter characterizing its orientation.

[0015] Preferably, in step c4, the optical residual potential field is updated based on the adjusted pattern, using the same local phase approximation model as the optical residual potential field calculated in step b.

[0016] Compared with the prior art, the beneficial effects of the present invention are: 1. By acquiring the non-uniform physical parameter map of the actual substrate and comparing it with the reference micropattern, a two-dimensional digital scalar field, namely the optical residual potential field, is generated to characterize the optical performance deviation. The iterative optimization in the design process is not carried out on the preset ideal model, but the geometric parameters of each micropattern unit are adjusted directly and correlated with the local gradient of the unit at the location of the optical residual potential field. This approach makes the physical non-uniformity of the substrate an intrinsic constraint of the design rather than an external disturbance from the very beginning of the micropattern generation process. Therefore, the final output micropattern is not a local correction of the ideal pattern, but a native self-consistent solution generated on a specific physical substrate to achieve the target optical function.

[0017] 2. During the iterative optimization process, the adjustment of the geometric parameters of the micro-pattern unit is based not only on the local gradient of the optical residual potential field, but also on the geometric parameter state of its neighboring units, so as to maintain the local smoothness of the generated pattern. This dual mechanism of performance optimization based on local gradient and physical continuity maintenance based on neighborhood influence avoids the possible abrupt changes or discontinuities in the pattern structure that may result from simply pursuing the optimal point. This ensures that each step of the iterative convergence simultaneously meets the requirements of both optical performance convergence and physical structure realization, thus giving the entire data processing flow convergence stability.

[0018] 3. After adjusting the geometric parameters of the micropattern unit according to the optical residual potential field, a random perturbation with decreasing amplitude as the iteration proceeds can be applied. Furthermore, the decay rate of the random perturbation amplitude is non-uniformly controlled based on the local complexity characterized by the gradient distribution of the optical residual potential field. In regions with a flat potential field, the perturbation amplitude decays faster to accelerate convergence; in regions with a complex potential field, the perturbation amplitude decays slower to allow for more thorough optimization. This combination of deterministic gradient optimization and adaptive random perturbation enables the design method to break free from dependence on the initial pattern selection and overcome potential local optimum traps during the optimization process without sacrificing computational efficiency.

[0019] 4. After iterative convergence and output of the final micropattern, spatial differentiation analysis can be performed on the final optical residual potential field corresponding to the final pattern to determine the local curvature of the potential field. Regions with large potential field curvature correspond to regions where changes in the geometric parameters of the micropattern have a significant impact on optical performance, while regions with small potential field curvature have the opposite effect. Based on this, manufacturing tolerance guidance information that indicates the sensitivity of different regions of the micropattern to manufacturing errors can be generated. This process utilizes intermediate data from the design stage to provide a direct basis for the downstream physical manufacturing stage, establishing a direct information channel based on the inherent correlation of data between the two originally independent stages of design and manufacturing. Attached Figure Description

[0020] Figure 1 This is an overall flowchart of the adaptive micropattern generation method of the present invention; Figure 2 These are the optimized calibration curves for the core parameters of this invention under different materials; Figure 3 This is a schematic diagram illustrating the principle of the iterative optimization core mechanism of this invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below. Obviously, the described embodiments are only a part of the embodiments of this invention, and not all of them. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0022] The design method for adaptive generation of optical micropatterns based on substrate parameters claimed in this invention has a data processing flow that mainly includes data acquisition and mapping of physical parameters, construction and initialization of optical residual potential field data structure, iterative optimization data processing based on gradient descent and neighborhood constraints, and downstream data generation based on final potential field topography analysis. These steps are interconnected at the data level and together constitute a data processing method that takes the non-uniformity of the physical reality of the substrate as the initial constraint and aims to generate a digital definition file of a micropattern that is adapted to the physical reality.

[0023] In one application scenario, for example, designing an optical micropattern array for beam shaping on a hydrogel substrate, the hydrogel substrate, due to its material properties, exhibits random fluctuations in its refractive index and thickness spatially. To address this non-uniformity of physical parameters, the method claimed in this invention is configured to first perform step a, using an optical profilometer and a refractive index measuring device to perform a gridded scan of the actual substrate surface to be processed, obtaining a two-dimensional discrete sampling spatial non-uniform physical parameter map. This parameter map is an M×N array in data structure, where each array element records the actual physical parameter at the corresponding spatial coordinates (x, y), such as the refractive index n. real The physical state of the substrate is transformed into a structured dataset that can be directly accessed by a power-powered digital data processing system, using (x,y) and thickness t(x,y).

[0024] Next, to establish a quantitative benchmark for measuring design deviations, the system executes step b; first, a reference micropattern is acquired acting on an ideal substrate, which is set to have a uniform ideal refractive index n. ideal With ideal thickness t ideal The mathematical plane; subsequently, the system superimposes the digital definition of this reference micro-pattern onto the spatially non-uniform physical parameter map obtained in the previous step, and performs comparison calculations based on a preset local phase approximation model that does not rely on global ray tracing. In this embodiment, this model is determined as follows: In the formula, λ represents the optical phase deviation calculated at coordinates (x, y), in radians; λ is the preset operating wavelength, in nanometers; n real(x,y) represents the actual refractive index at the corresponding coordinates obtained from a spatially inhomogeneous physical parameter diagram; it is dimensionless. ideal The refractive index of the ideal substrate corresponding to the reference micropattern is dimensionless; t(x,y) is the actual thickness at the corresponding coordinates obtained from the spatially non-uniform physical parameter map, in nanometers; by performing this calculation on all micropattern unit positions, the system generates a two-dimensional digital scalar field characterizing the optical performance deviation, namely the optical residual potential field V(x,y). This potential field is also an M×N array in terms of data structure, where each element V(x,y) represents a different value. i ,y j The value of ) is the value of the corresponding position. For example, if at coordinates (10, 25), n real It is 1.51, n ideal Given a wavelength of 1.50, a wavelength of t of 1000 nm, and a working wavelength of λ of 500 nm, the optical residual potential energy V(10,25) at that point is calculated as follows: .

[0025] The subsequent step c involves iteratively optimizing the micro-pattern units within the reference micro-pattern using the reference micro-pattern as the initial pattern. In each iteration, for any micro-pattern unit in the pattern, the system executes two computational branches in parallel. The first is step c1, which calculates the local gradient ▽V of the micro-pattern unit's position in the optical residual potential field V(x,y). This gradient is a two-dimensional vector, and a vector proportional to the magnitude of this gradient but opposite in direction is determined as the first adjustment amount. The second is step c2, which calculates the smoothing constraints of the micro-pattern unit under the influence of the geometric parameters of its neighboring micro-pattern units. The specific data processing for calculating the smoothing constraints of the micro-pattern unit in step c2 is as follows: First, obtain the geometric parameters p of the current micro-pattern unit i. i The corresponding geometric parameters p of the micropattern unit j and all its directly adjacent micropattern units j j Then, the potential energy corresponding to all parameter differences is calculated based on a preset elastic potential energy function. In one feasible implementation, this elastic potential energy function E smooth Set as a quadratic potential function: In this formula, N(i) refers to the set of all directly adjacent units of the unit, and k is a preset elastic coefficient, the value of which is related to the physical size of the micropattern unit and the mechanical modulus of the substrate material; the calculated second adjustment amount is the elastic potential energy E. smooth For geometric parameter p i The negative gradient is calculated as follows: In this formula, F smooth This is the second adjustment amount, and its data structure is a variable related to the geometric parameter p. iA vector of the same dimension is used to update the geometric parameters of the micropattern unit in subsequent steps. In step c3, the system combines the first adjustment amount and the second adjustment amount into a final geometric update amount according to a preset synthesis rule. In this embodiment, the rule is set to perform a weighted summation of the two. When combining the first adjustment amount and the second adjustment amount according to the preset synthesis rule in step c3, the weighting factor w2 of the second adjustment amount is a function w2(t) that monotonically decreases with the number of iterations. A specific form of this function can be an exponential decay function. In this formula, w max The initial maximum value of the weighting factor is usually set between 0.5 and 1.0, t is the current iteration number, and the decay constant λ is a key control parameter. Its numerical calibration procedure is as follows: For a substrate with a relatively gentle change in the spatial gradient of physical parameters, a larger λ value is selected so that the weight of the smoothing constraint decreases rapidly, thereby accelerating the convergence to the optimal solution for optical performance; conversely, for a substrate with drastic fluctuations in physical parameters, a smaller λ value is selected so that the smoothing constraint maintains a higher weight in more iterations, in order to suppress the abrupt change in geometric parameters caused by fitting local high-frequency noise. The specific value of this parameter λ can be determined by an offline parameter optimization process performed on representative substrate samples; then, this geometric update amount is used to adjust the geometric parameters of the micropattern unit; finally, in step c4, based on the adjusted pattern, the system uses the same local phase approximation model as in step b to recalculate and update the entire optical residual potential field V(x,y), providing an updated data basis for the next iteration.

[0026] The termination of the iteration process is determined by step d, i.e., the iteration stops when the preset convergence condition is met. In this embodiment, the condition is determined as follows: during 10 consecutive iterations, the rate of change of the total energy value of the optical residual potential field, i.e., V(x,y), in the entire field is less than the preset rate of change threshold of 10. -6When this condition is met, the system determines that it has converged and outputs the pattern data at this time as the final micro-pattern. In the above iterative optimization process, in order to reduce the possibility of the algorithm getting stuck in a local optimum, a preferred implementation method is to introduce a random perturbation mechanism in the iterative optimization of step c. Specifically, in step c3 of each iteration, that is, after adjusting the geometric parameters of the micro-pattern unit with geometric update, a small perturbation with random direction and amplitude proportional to a global virtual temperature parameter T is applied to the geometric parameters. Furthermore, the parameter T is set to decrease nonlinearly as the iteration progresses. In the early stage of the iteration, the value of T is high, and the random perturbation makes the micro-pattern unit have a probability of crossing the local potential barrier. As the iteration progresses, the value of T gradually decreases, the perturbation weakens, and the system achieves stable convergence within the explored better solution region. This method reduces the dependence of the final design result on the initial pattern selection.

[0027] To further improve computational efficiency, the process of reducing the amplitude of random perturbations can be configured to be non-uniformly controlled based on the local spatial characteristics of the optical residual potential field. Specifically, during the iteration process, the system additionally analyzes the gradient distribution of the optical residual potential field and calculates the divergence of the gradient field. This generates a scalar field C(x,y) that characterizes the local complexity of the potential field. Accordingly, the globally uniform decay rate is replaced by a spatially non-uniform decay rate α(x,y), whose regulation rule follows: In the formula, α(x,y) is the local decay rate at coordinates (x,y); α base is a preset base decay rate; k is a preset adjustment coefficient; The absolute value of the scalar field representing the local complexity of the potential field at the corresponding coordinates is given. Thus, in regions with a flat potential field, the decay rate is faster, and the system converges more quickly. In regions with a complex potential field, the decay rate is slower, and the system undergoes a longer period of perturbation optimization, thereby distributing computational resources non-uniformly.

[0028] Once the design process is complete and the final micropattern is generated, to connect the design data with the downstream physical manufacturing process, the system executes step e, which performs spatial derivative analysis on the converged final optical residual potential field corresponding to the final micropattern. This step utilizes intermediate data from the design process to extract information about the design scheme's sensitivity to manufacturing errors. Specifically, the system calculates the spatial second derivative of the final optical residual potential field to determine the local curvature of the potential field. Regions with high curvature correspond to sharper potential well shapes, meaning that even small deviations in geometric parameters can lead to drastic changes in optical performance, indicating that these regions are sensitive to manufacturing errors. Conversely, regions with low curvature have a higher tolerance for manufacturing errors. Based on this, by setting a preset curvature threshold, the system can divide the micro-pattern into critical regions that are highly sensitive to manufacturing errors and non-critical regions that are less sensitive, and generate manufacturing tolerance guidance information.

[0029] To elevate manufacturing tolerance guidance information from qualitative zoning to quantitative calibration, a further implementation involves executing an active detection process after generating the aforementioned guidance information. The system selects at least one detection point in both critical and non-critical regions. For each detection point, a virtual perturbation δ, increasing from zero, is applied to the geometric parameters of the micro-pattern unit at that point. A local phase approximation model is used to calculate the nonlinear response ΔV(δ) of the local optical performance deviation caused by this virtual perturbation. By monitoring the response curve, the system identifies the perturbation amplitude corresponding to the first time the rate of change of the response value exceeds a preset rate of change threshold, and determines this amplitude as the quantitative tolerance threshold δ associated with that detection point. critical Finally, by spatially interpolating the quantitative tolerance thresholds obtained from all detection points, a quantitative tolerance map can be generated.

[0030] To further verify the necessity and key technical effects of the gradient optimization and smoothing constraint synergy mechanism described in this invention, the following comparative examples are provided for illustration.

[0031] Comparative Example 1: To verify the necessity of synergistic adjustment based on potential field gradient and smoothing correction based on neighborhood influence as described in this invention, this comparative example is set up. This comparative example adopts a simplified data processing flow that performs iterative optimization based solely on the optical residual potential field gradient. The only difference between this flow and the flow disclosed in the specific embodiments is that in the iterative optimization step, step c2 is completely removed, that is, the smoothing constraint (second adjustment amount) of the micropattern unit due to the geometric parameters of its neighboring micropattern units is not calculated, and the geometric parameters of the micropattern unit are adjusted only based on the first adjustment amount calculated in step c1. The experiment uses the same numerical simulation non-uniform substrate data model with a size of 10mm×10mm as in Example 2 as the input data. This model is generated by superimposing a linear gradient along the x-axis and a two-dimensional Gaussian random field with an amplitude of 5% of the peak value on an ideal planar substrate. The experiment also uses a reference micropattern designed for an ideal substrate as the initial pattern, and the goal is to generate a final micropattern that can compensate for the non-uniformity of the substrate.

[0032] After 1000 iterations of optimization, the final micropattern data file and its corresponding optical performance were evaluated. To ensure the engineering feasibility of the evaluation, two key performance indicators were introduced: Final optical performance (RMS wavefront error): This measures the root mean square error of the output wavefront. The smaller the value, the better the optical performance compensation effect. Pattern manufacturability evaluation: This is a comprehensive measure based on the maximum difference in geometric parameters between adjacent units in the final micropattern (i.e., the pattern smoothness index) and the number of GDSII acute angle violations reported after importing the generated micropattern digital file into the industry-standard Design Rule Check (DRC) software. The larger the pattern smoothness value, the more severe the geometric parameter abrupt change in the pattern in a local area. GDSII acute angle violations are directly related to features that cannot be accurately reproduced in physical manufacturing (such as photomask manufacturing) and are a direct industrial indicator for measuring manufacturability. The test results are summarized in Table 1.

[0033] Table 1: Comparison of key performance indicators under different processing methods.

[0034]

[0035] Due to the lack of a smoothing constraint mechanism, the micropattern unit will perform greedy optimization during the iteration process. In order to fit the high-frequency noise or local details in the physical parameter map of the substrate, it will produce drastic changes in geometric parameters that are unrelated to its neighborhood. Experimental results confirm that without the invention key point of smoothing correction based on neighborhood influence, even if the optimization idea of ​​gradient descent is adopted, it is impossible to obtain a technical solution that simultaneously achieves optical performance and physical feasibility.

[0036] Example 1: In a production process for an augmented reality waveguide display, the diffraction grating element is required to be fabricated on a large-area flexible thin-film substrate made of recycled polymer. This substrate material is chosen for its cost and flexibility, but its manufacturing process results in a non-uniform gradient variation in thickness and refractive index on a centimeter scale. When photolithography is performed using a standard grating digital file generated based on an ideal homogeneous substrate model, the resulting physical element exhibits deviations in diffraction angles and diffraction efficiencies in different regions, leading to distortion and uneven brightness in the final displayed image, with a yield rate below 5%. To address this problem, for each flexible substrate to be processed on the production line, step a in the specific implementation is first performed, i.e., obtaining a two-dimensional spatial non-uniform physical parameter map of the specific substrate. Subsequently, step b is performed, comparing a target reference micropattern used to generate a standard 60-degree diffraction angle under an ideal substrate with the parameter map to generate an initial optical residual potential field V(x,y). Due to the gradient variation of the substrate's physical parameters, this initial potential field exhibits variations in thickness and refractive index on a centimeter scale. The above data distribution is a complex one, tilted from one end to the other and superimposed with local undulations. This data structure quantifies the systematic optical performance deviation that would occur if the reference pattern were applied directly. After entering the iterative optimization process in step c, a synergistic relationship is formed between the first adjustment based on the local gradient and the second adjustment based on the neighborhood influence. In the early stage of iteration, due to the large overall tilt of the potential field, the gradient adjustment causes the geometric parameters of the entire micro-pattern unit to shift rapidly in the direction of compensating for the gradient. This process aims to quickly reduce the total potential energy of the system. If only this gradient adjustment is used, the local part of the pattern will produce geometric discontinuities due to local noise in the fitted potential field. At this time, as a smoothing constraint mechanism of the second adjustment, a suppression effect on drastic parameter changes is applied by calculating the difference in geometric parameters between adjacent units, thus maintaining the physical continuity of the generated pattern. This synergy between the data processing for performance optimization and the data processing for maintaining physical continuity allows the pattern data in the iterative process to both approach the optical target and maintain structural integrity.

[0037] Furthermore, this invention provides a processing method that balances computational efficiency and result accuracy by placing a computationally inefficient local phase approximation model within an iteratively updated closed-loop data stream. In each iteration, the update of the optical residual potential field relies solely on algebraic calculations that do not require ray tracing. The cumulative effect of multiple iterations causes the geometric parameters of the micropattern to approach a high-precision solution through continuous feedback and correction. Finally, when the iterative process stops according to the preset convergence condition, the final micropattern obtained no longer has the geometric definition of the original reference pattern, but rather a compensated non-uniform pattern generated to achieve the target diffraction effect on this specific non-uniform substrate. The uniform pattern, when this data file is used to guide subsequent photolithography processes, the introduced geometric non-uniformity offsets the optical effects caused by the non-uniformity of the substrate's physical parameters, resulting in uniform diffraction performance of the final manufactured physical components and increasing the yield to over 95%. The operation of this embodiment demonstrates a transformation of the design process from a static, one-way digital file generation to a dynamic, adaptive data processing process that interacts with physical reality in a closed loop. This process does not attempt to modify the physical substrate, but rather uses the actual state of the substrate as the initial data and inherent constraints of the design process, thereby generating a digital solution corresponding to that specific physical reality.

[0038] Example 2: This example uses a simulation test environment based on electrical digital data processing to verify the effectiveness of the method claimed in this invention in compensating for the non-uniformity of the substrate physical parameters, as well as the interaction between different data processing mechanisms within it. The test environment uses a numerically simulated non-uniform substrate data model with a size of 10mm×10mm. This model generates a spatial non-uniform physical parameter map with controllable non-uniformity by superimposing a linear gradient along the x-axis and a two-dimensional Gaussian random field with an amplitude of 5% of the peak value on an ideal planar substrate data, which serves as the unified input data for all test sample groups.

[0039] The experiment set up two control samples and one test sample of the method of the present invention, namely, a control group, a synergistic effect verification group, and the present invention sample group. The control group adopted the existing technology, that is, a reference micropattern designed for an ideal substrate, whose corresponding digital file was applied directly to the aforementioned non-uniform substrate data model without modification. The synergistic effect verification group adopted an incomplete data processing flow that only included the gradient optimization step of the method of the present invention and disabled the smoothing constraint step. The present invention sample group adopted the complete data processing flow disclosed in the specific implementation method, which included the synergistic effect of gradient optimization and smoothing constraint. The final performance of all sample groups was quantitatively evaluated by two indicators. The first is the final optical performance, which is measured by the root mean square error of the output wavefront. The smaller the value, the closer the optical performance is to the target. The second is the final pattern smoothness, which is measured by the maximum value of the difference in geometric parameters between adjacent units in the final micropattern. This value is related to the manufacturability of the pattern. The smaller the value, the smoother the pattern.

[0040] After the experiment was started, the system first calculated the performance index of the control group. Due to the mismatch between the reference micropattern and the non-uniform substrate, its root mean square wavefront error was measured to be 0.85π (in radians), and its pattern smoothness was set to 1.0 as the benchmark. Subsequently, the system performed 1000 iterations of optimization on the synergistic effect verification group and the sample group of the present invention, respectively. During the iteration process, the root mean square wavefront error of the synergistic effect verification group decreased, but its micropattern units produced discontinuous geometric parameter jumps in order to fit the details of the local potential field. The root mean square wavefront error of the sample group of the present invention also continued to decrease, and its geometric parameters remained within a small range of variation throughout the iteration process. After the iteration converged, data were collected on the final state of each sample group.

[0041] Table 2: A comparison of key performance indicators for each experimental sample group after iterative convergence.

[0042]

[0043] Referring to Table 2, the experimental data show that although the synergistic effect verification group reduced the root mean square wavefront error from 0.85π to 0.12π, its pattern smoothness index was 25.4, which means that the generated pattern has physical abrupt changes, affecting manufacturability. The sample group of this invention has a final root mean square wavefront error of 0.15π, which is on the same order of magnitude as the synergistic effect verification group. At the same time, its pattern smoothness index is 2.1, which is lower than that of the synergistic effect verification group and close to the baseline value of the control group. This data comparison shows that, with the participation of the smoothing constraint mechanism, the entire data processing process can optimize optical performance while suppressing the discontinuity of the pattern structure that may be caused by simple gradient descent, thereby obtaining data output that has both optical performance and physical realizability.

[0044] Example 3: This example combines Figures 1 to 3 This paper describes a design method for adaptively generating optical micropatterns based on basis parameters, such as... Figure 1 As shown, the process begins with the physical parameter acquisition and mapping step, which obtains a spatially non-uniform physical parameter map of the actual substrate, transforming the physical reality into a structured dataset. Subsequently, in the optical residual potential field construction step, based on the reference pattern and physical parameter map, and according to the local phase approximation model, the initial optical performance deviation is quantified. The core of the process is an iterative optimization loop. In each step of the loop, a first adjustment amount based on the potential field gradient is obtained through gradient calculation, and a second adjustment amount based on the neighborhood influence is obtained through smoothing constraint calculation. These two adjustment amounts are then used in the geometric parameter synthesis and adjustment step according to preset parameters. Rules are coordinated to update the geometric parameters of the micropattern units. An adaptive random perturbation mechanism, which is a key module, can be introduced to enhance the global optimization capability. Then, in the optical residual potential field update step, the potential field data is updated in real time based on the adjusted pattern until the convergence condition determination step confirms that the total energy change rate of the potential field is less than a preset threshold, at which point the iteration terminates. Finally, the process outputs two results: one is the final micropattern generation, which is a digital definition file that is natively self-consistent with a specific physical substrate; the other is the generation of manufacturing tolerance guidance information, which provides process guidance for downstream manufacturing by analyzing the curvature of the final potential field.

[0045] like Figure 2 As shown in the figure, the horizontal axis represents the gradient step size α, a key parameter in the iterative optimization, and the vertical axis represents the comprehensive cost function J, which balances optical performance and computational efficiency. The figure shows three curves corresponding to three different materials: polylactic acid film, hydrogel substrate, and flexible polymer. Each curve presents a unique minimum point, indicating that for each specific substrate material, there exists an optimal gradient step size α value that minimizes the comprehensive cost function J. This verifies the necessity and effectiveness of parameter calibration for different materials.

[0046] like Figure 3 As shown, the wavy region at the bottom of the figure represents a non-uniform substrate with non-uniform physical parameters n(x,y) and t(x,y). On this substrate, the initial dashed reference pattern adjusts its position coordinate x during iteration, driven by two main factors: first, the gradient ▽V from the upper optical residual potential field V(x,y), aimed at reducing optical performance deviations; and second, the neighborhood constraint between adjacent pattern units, aimed at maintaining the physical continuity of the pattern. After optimization, the pattern finally converges to the solid-line optimized pattern, whose positional distribution compensates for the non-uniformity of the substrate. Furthermore, the annotation box at the top of the figure further reveals two applications of the finally converged potential field V(x,y): one is through analysis of its second derivative. First, manufacturing tolerance analysis is performed to determine the sensitivity to manufacturing errors. Second, the potential field change ΔV is less than a threshold as the convergence condition for iteration.

[0047] Example 4: This example provides a specific and reproducible standardized engineering calibration procedure for systematically calibrating the control parameters in the data processing flow when applying the method claimed in this invention to a new substrate material. In one application scenario, a production line plans to use the method of this invention to generate optical micropatterns for a novel polylactic acid biodegradable film substrate. The non-uniformity of the physical parameters of this film differs from previously processed materials. Therefore, directly using common algorithm parameters, such as the gradient descent step size α, the weighting factor w1 of the first adjustment, and the weighting factor w2 of the second adjustment in the iterative optimization process, may lead to problems in the data processing. The processing converges slowly or fails to achieve the expected compensation accuracy. To address this issue, this embodiment discloses an offline parameter calibration method, which is executed on a computing platform independent of the production line. First, 10 samples are randomly selected from different batches of novel polylactic acid films, and the spatial non-uniform physical parameter map of each sample with a resolution of 1024×1024 pixels is obtained using the measuring equipment in the specific embodiment. These 10 sets of data constitute a statistically representative benchmark dataset. Next, to quantitatively evaluate the algorithm performance under different parameter combinations, a comprehensive cost function J(α,w1,w2) is defined, with the following specific form: In the formula, J is the value of the comprehensive cost function, which is dimensionless; The average final root mean square wavefront error obtained after the algorithm is run on the benchmark dataset, in radians; The average number of iterations required to reach the convergence condition; K1 and K2 are preset weight coefficients, whose numerical relationship determines the relative emphasis on optical performance and computational efficiency during the optimization process. In this embodiment, they are set to 0.7 and 0.3, respectively.

[0048] The calibration process employs a parameter space grid search strategy to find the parameter combination that minimizes the cost function J. Specifically, the system traverses and calculates within a preset parameter space, where the gradient descent step size α ranges from 0.01 to 0.2 with a step size of 0.01, the weight factor w1 for the first adjustment ranges from 0.5 to 1.0 with a step size of 0.1, and the weight factor w2 for the second adjustment ranges from 0.1 to 0.5 with a step size of 0.1. For each parameter combination (α, w1, w2) in the grid, the system automatically invokes the method of this invention, using that parameter combination as the configuration, and runs an iterative optimization process once on all 10 benchmark data samples, recording the final root mean square wavefront error and the number of convergence iterations for each sample. After traversing all parameter combinations, the system calculates the average value of the comprehensive cost function J corresponding to each combination and selects the parameter set that minimizes the J value, denoted as . This serves as the algorithm parameter set for this novel polylactic acid film material.

[0049] Meanwhile, the calibration process for the curvature threshold used to generate manufacturing tolerance guidance information is performed after the aforementioned algorithm parameter set is determined. Using this parameter set, the system runs again on 10 benchmark data samples to generate the final optical residual potential field and corresponding curvature map. On the other hand, through a finite element optical simulation model, known minute geometric perturbations are applied to one of the samples at different locations, and their actual impact on optical performance is calculated, thereby obtaining a benchmark manufacturing sensitivity distribution map. Finally, by performing statistical correlation analysis between the calculated curvature map and the benchmark sensitivity distribution map, a curvature value that can distinguish between high-sensitivity and low-sensitivity areas with 99% confidence is determined, and this value is set as the curvature threshold for the material. By executing the above calibration procedure, a set of core algorithm parameters is determined for this specific material. This set of parameters is embedded in the production line control software, ensuring that the data processing flow of the method follows this set of preset parameters when processing any new polylactic acid film, thus guaranteeing the portability of the method across different material systems and the reliability of its engineering applications.

[0050] Example 5: In an application with high requirements for the consistency of optical component performance, to ensure the adaptability of the method of the present invention to different substrates with large differences in physical parameter distribution characteristics, a data processing step for pre-analysis of input data can be added before the system performs iterative optimization. This step first calculates the local spatial gradient of the two-dimensional array representing the refractive index distribution in the obtained spatially non-uniform physical parameter map. The maximum value is then compared with a preset gradient threshold ▽n. thresholdFor comparison, this threshold is a parameter calibrated through offline experiments to characterize the applicable boundary of the local phase approximation model. If the calculated maximum gradient value is lower than the threshold, it indicates that the physical parameters of the substrate change relatively gently, and the system will call the local phase approximation model in the specific implementation for subsequent processing. If the maximum gradient value is higher than the threshold, it indicates that there is a sharp change in the physical parameters of the substrate, and the system will automatically switch to an alternative physical approximation model. This alternative model introduces an additional first-order correction term on the basis of the local phase approximation model to correct the propagation path of light at the interface of drastic parameter changes.

[0051] When the target optical function to be generated is complex, such as generating an asymmetric structured light illumination pattern, a suitable reference micropattern is difficult to obtain directly through conventional methods. In such cases, the method of this invention can adopt a two-stage iterative strategy to generate an initial pattern. In the first stage, the system uses a uniformly distributed micropattern as the initial input and performs a fixed number of coarse-grained iterative optimizations on a downsampled spatial non-uniform physical parameter map. The purpose of this stage is to quickly obtain a pattern profile that roughly matches the target optical function in the low-frequency components of space. Subsequently, in the second stage, the system upsamples the coarse-grained pattern output from the first stage and uses it as the reference micropattern. On the original full-resolution spatial non-uniform physical parameter map, it initiates a complete iterative optimization process aimed at achieving a preset convergence condition, as described in the specific implementation. In this way, an initial state generation path without external input is formed for the design problem of complex optical functions.

[0052] Example 6: This example provides a specific and reproducible standardized engineering calibration procedure for systematically calibrating the control parameters in the data processing flow when applying the method claimed in this invention to a new substrate material. In one application scenario, a production line plans to use the method of this invention to generate optical micropatterns for a novel polylactic acid biodegradable film substrate. The non-uniform statistical characteristics of the physical parameters of this film are different from those of previously processed materials. Therefore, directly using general algorithm parameters, such as the gradient descent step size α, the weighting factor w1 of the first adjustment, and the weighting factor w2 of the second adjustment in the iterative optimization process, may lead to data... The processing converges slowly or fails to achieve the expected compensation accuracy. To address this issue, this embodiment discloses an offline parameter calibration method, which is executed on a computing platform independent of the production line. First, 10 samples are randomly selected from different batches of novel polylactic acid films, and the spatial non-uniform physical parameter map of each sample with a resolution of 1024×1024 pixels is obtained using the measuring equipment in the specific embodiment. These 10 sets of data constitute a statistically representative benchmark dataset. Next, to quantitatively evaluate the algorithm performance under different parameter combinations, a comprehensive cost function J(α,w1,w2) is defined, with the following specific form: In the formula, J is the value of the comprehensive cost function, which is dimensionless; The average final root mean square wavefront error obtained after the algorithm is run on the benchmark dataset, in radians; The average number of iterations required to reach the convergence condition; K1 and K2 are preset weight coefficients, whose relative magnitudes are used to balance optical performance and computational efficiency, and are set to 0.7 and 0.3 respectively in this embodiment.

[0053] The calibration process employs a parameter space grid search strategy to find the parameter combination that minimizes the cost function J. Specifically, the system performs traversal calculations within a preset parameter space, where the gradient descent step size α ranges from 0.01 to 0.2 with a step size of 0.01, the weight factor w1 for the first adjustment ranges from 0.5 to 1.0 with a step size of 0.1, and the weight factor w2 for the second adjustment ranges from 0.1 to 0.5 with a step size of 0.1. For each parameter combination (α, w1, w2) in the grid, the system automatically invokes the method claimed in this invention, using that parameter combination as the configuration, and runs an iterative optimization process once on all 10 benchmark data samples, recording the final root mean square wavefront error and the number of convergence iterations for each sample. After traversing all parameter combinations, the system calculates the average value of the comprehensive cost function J corresponding to each combination and selects the parameter set that minimizes the J value, denoted as . The parameter set was determined as the algorithm parameter set applicable to this novel polylactic acid film material. Simultaneously, the calibration process for the curvature threshold used to generate manufacturing tolerance guidance information was performed after the aforementioned algorithm parameter set was determined. Using this parameter set, the system ran again on 10 benchmark data samples to generate the final optical residual potential field and corresponding curvature map. On the other hand, through a finite element optical simulation model, known minute geometric perturbations were applied to one of the samples at different locations, and their actual impact on optical performance was calculated, thereby obtaining a benchmark manufacturing sensitivity distribution map. Finally, by performing statistical correlation analysis between the calculated curvature map and the benchmark sensitivity distribution map, a curvature value that can distinguish between high-sensitivity and low-sensitivity areas with 99% confidence was determined, and this value was set as the curvature threshold for the material. By executing the calibration procedure, a set of core algorithm parameters was determined for this specific material. This set of parameters was embedded into the production line control software, ensuring that the data processing flow of the method follows this set of preset parameters when processing any new polylactic acid film, thus providing parameter basis for the application of this method across different material systems.

[0054] It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention.

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims

1. A design method for adaptively generating optical micropatterns based on substrate parameters, characterized in that, The method includes the following steps: Step a: Obtain the spatial non-uniform physical parameter map of the actual substrate where the optical micro-pattern to be designed is located; Step b: Obtain a reference micropattern acting on an ideal substrate, compare the reference micropattern with a spatially non-uniform physical parameter map, and calculate an optical residual potential field characterizing the optical performance deviation based on a preset local phase approximation model. Step c: Using the reference micropattern as the initial pattern, iteratively optimize the micropattern units in the initial pattern. In each iteration: Step c1: Calculate the local gradient of the micropattern unit at the position of the optical residual potential field to obtain the first adjustment amount; Step c2: Calculate the smoothing constraint of the micropattern unit due to the geometric parameters of its neighboring micropattern units to obtain the second adjustment amount; Step c3: According to the preset synthesis rule, synthesize the first adjustment amount and the second adjustment amount into a geometric update amount, and use the geometric update amount to adjust the geometric parameters of the micropattern unit; Step c4: Update the optical residual potential field based on the adjusted pattern. Step d: When the iteration meets the preset convergence condition, stop the iteration and obtain the final micropattern; Step e involves performing spatial differentiation analysis on the final optical residual potential field corresponding to the final micropattern to generate manufacturing tolerance guidance information that indicates the sensitivity of different regions of the micropattern to manufacturing errors.

2. The design method for adaptive generation of optical micropatterns based on substrate parameters according to claim 1, characterized in that, The iterative optimization in step c also includes: in each iteration, after adjusting the geometric parameters of the micropatterned unit using the geometric update amount, applying a random perturbation to the geometric parameters; and the magnitude of the random perturbation is set to decrease as the iteration proceeds.

3. The design method for adaptive generation of optical micropatterns based on substrate parameters according to claim 2, characterized in that, The reduction in the amplitude of random perturbations is based on non-uniform control of the local spatial characteristics of the optical residual potential field. The method also includes: analyzing the gradient distribution of the optical residual potential field during the iteration process to generate a scalar field C(x,y) characterizing the local complexity of the optical residual potential field; and controlling the attenuation rate α(x,y) of the amplitude of random perturbations in different regions of the micropattern based on the scalar field, with the control rule following: , where α base is a preset base decay rate, and k is a preset adjustment coefficient.

4. The design method for adaptive generation of optical micropatterns based on substrate parameters according to claim 1, characterized in that, In step e, spatial derivative analysis is performed on the final optical residual potential field. Specifically, this includes: calculating the spatial second derivative of the final optical residual potential field to determine the local curvature of the potential field, and identifying regions with local curvature greater than a preset curvature threshold as critical regions that are highly sensitive to manufacturing errors, and identifying regions with local curvature less than the preset curvature threshold as non-critical regions that are less sensitive to manufacturing errors.

5. The design method for adaptive generation of optical micropatterns based on substrate parameters according to claim 4, characterized in that, After generating manufacturing tolerance guidance information, the method further includes: selecting at least one probe point in both critical and non-critical regions; applying a virtual perturbation that increments from zero to the geometric parameters of each probe point, and calculating the nonlinear response of the optical performance deviation caused by the virtual perturbation; and determining and outputting a quantitative tolerance threshold associated with the probe point based on the perturbation amplitude corresponding to the first time the rate of change of the response value in the nonlinear response exceeds a preset rate of change threshold.

6. The design method for adaptive generation of optical micropatterns based on substrate parameters according to claim 1, characterized in that, The preset synthesis rule in step c3 is: to perform a weighted summation of the first adjustment amount and the second adjustment amount, wherein the weight factor of the second adjustment amount is set to be a function that monotonically decreases with the number of iterations.

7. The design method for adaptive generation of optical micropatterns based on substrate parameters according to claim 1, characterized in that, In step c2, the smoothing constraint on the micro-pattern unit is calculated, which specifically includes: obtaining the parameter difference between the micro-pattern unit and all its directly adjacent micro-pattern units in at least one geometric parameter; and calculating all parameter differences according to a preset elastic potential energy function to obtain a resultant force aimed at reducing the parameter difference, which is the second adjustment amount.

8. The design method for adaptive generation of optical micropatterns based on substrate parameters according to claim 1, characterized in that, The convergence condition preset in step d is: in a series of preset number of iterations, the rate of change of the total energy value of the optical residual potential field is less than the preset rate of change threshold.

9. The design method for adaptive generation of optical micropatterns based on substrate parameters according to claim 1, characterized in that, The geometric parameters include at least one of the center position coordinates of the micropattern unit, the size parameter characterizing its contour, and the rotation angle parameter characterizing its orientation.

10. The design method for adaptive generation of optical micropatterns based on substrate parameters according to claim 1, characterized in that, In step c4, the optical residual potential field is updated based on the adjusted pattern, using the same local phase approximation model as the optical residual potential field calculated in step b.

Images