A GLV multi-beam direct writing path planning method and system for holographic anti-counterfeiting

Abstract

The application provides a GLV multi-beam direct writing path planning method and system for holographic anti-counterfeiting, and the method comprises the following steps: acquiring model analysis depth information and discretizing the model analysis depth information into an initial feature matrix; evaluating a thermal diffusion cumulative amount to establish a physical threshold model, performing truncation and energy compensation on a dense area exceeding the threshold to generate a thermal equilibrium distribution matrix; extracting residual energy features of a splicing overlap area, constructing a semi-variance function to generate a spatial variation convolution kernel for smoothing operation to generate a reference exposure control sequence; establishing and solving a compensation model related to power, speed and depth to generate a control sequence snapshot; and collecting an instantaneous mechanical speed matching snapshot in real time to drive direct writing. The application effectively improves the machining precision and restoration degree of the holographic anti-counterfeiting topography.

Description

Technical Field

[0001] This invention belongs to the field of laser printing technology, specifically relating to a GLV multi-beam direct writing path planning method and system for holographic anti-counterfeiting. Background Technology

[0002] Holographic anti-counterfeiting, due to its complex optical diffraction properties and difficulty in counterfeiting, has been widely used in fields such as document anti-counterfeiting, trademark protection, and high-value product authentication. Holographic anti-counterfeiting patterns are typically composed of subwavelength micro / nano structures, and the morphological characteristics of these structures directly determine the final optical reproduction effect. To achieve efficient and large-area micro / nano structure fabrication, multi-beam direct-writing technology based on grating gate arrays has been used in the processing flow. This technology can simultaneously control multiple laser beams for parallel exposure, greatly improving processing efficiency. However, in the actual holographic anti-counterfeiting morphology processing, the processing accuracy and the three-dimensional reproduction degree of the final morphology often fall short of expectations, leading to a deterioration in the holographic diffraction effect and a decrease in anti-counterfeiting security.

[0003] The problems of low processing accuracy and morphology reproduction are mainly caused by the energy effects of multiple laser beams during the exposure process and the platform's motion. During multi-beam parallel scanning, the photoresist absorbs laser energy, resulting not only in localized photochemical reactions but also significant thermal release. When multiple laser beams are closely aligned or undergo continuous high-density exposure, heat is rapidly transferred and superimposed between adjacent exposure points. This nonlinear thermal diffusion process causes the actual absorbed energy in local areas to far exceed the set value, leading to overdevelopment of the photoresist. Furthermore, during large-area direct writing on the processing platform, fluctuations in the platform's mechanical speed are inevitable. These speed fluctuations directly disrupt the preset exposure dose balance, causing distortion in the spatial distribution of exposure energy, ultimately resulting in the actual processed micro / nano structures deviating from the design model in depth and contour. Summary of the Invention

[0004] This invention provides a GLV multi-beam direct writing path planning method and system for holographic anti-counterfeiting, in order to solve the above-mentioned technical problems.

[0005] In a first aspect, the present invention provides a holographic anti-counterfeiting GLV multi-beam direct-write path planning method, the method comprising the following steps: A holographic anti-counterfeiting model is obtained, and the continuous depth information of the model surface in the holographic anti-counterfeiting model is analyzed by a non-uniform sampling algorithm. The depth information is then discretized into an initial feature matrix that adapts to the characteristics of the multi-beam physical array of the processing platform in a preset two-dimensional spatial reference system. By evaluating the expected thermal diffusion accumulation of each exposed pixel in the initial feature matrix region by region, a physical threshold model for multi-beam adjacent thermal superposition is established. When the expected thermal diffusion accumulation in the densely exposed region of the initial feature matrix exceeds the physical threshold in the physical threshold model, the duty cycle of the exposed pixels representing non-critical morphology in the densely exposed region is truncated, and the energy reference of the adjacent working pixels is updated based on the principle of energy conservation to generate a thermal balance distribution matrix. The residual energy characteristics of the two sides of the overlapping area of ​​the multi-beam scanning adjacent bands in the thermal equilibrium distribution matrix are extracted, and a semivariance function reflecting the thermal diffusion trend is constructed based on the spatial autocorrelation evaluation logic. Based on the semivariance function, a spatial variation convolution kernel is generated within a preset sliding window. The spatial variation convolution kernel is then used to perform a smoothing operation on the exposure data sequence in the splicing overlap area with the optimal unbiased estimation, thereby generating a benchmark exposure control sequence that eliminates energy aggregation variation. A compensation model for the laser control power, mechanical motion speed, and target morphology depth of the associated processing platform is established. The equations of the compensation model are solved in advance for different mechanical speeds of the processing platform. The reference exposure control sequence is fused with the compensation state obtained from the equation solution to generate multiple control sequence snapshots with corresponding compensation states. The instantaneous mechanical speed of the processing platform is acquired in real time, a control sequence snapshot corresponding to the instantaneous mechanical speed is matched, and the control sequence snapshot is output to drive the multi-beam array of the processing platform to complete the direct writing of the holographic anti-counterfeiting morphology.

[0006] Optionally, the step of acquiring the holographic anti-counterfeiting model, analyzing the continuous depth information of the model surface in the holographic anti-counterfeiting model through a non-uniform sampling algorithm, and discretizing the depth information into an initial feature matrix adapted to the multi-beam physical array characteristics of the processing platform in a preset two-dimensional spatial reference frame includes the following steps: Obtain the holographic anti-counterfeiting model, extract the surface mesh data from the holographic anti-counterfeiting model, and calculate the curvature gradient vector of the surface mesh data in three-dimensional space; The preset two-dimensional spatial reference frame is divided into an initial reference grid that matches the characteristics of the multi-beam physical array of the processing platform; The curvature gradient vector is mapped onto each grid node of the initial reference grid, and the sampling density of each grid node is adjusted by a non-uniform sampling algorithm based on the mapped curvature gradient vector. In grid node regions where the sampling density is greater than or equal to a preset density threshold, high-frequency interpolation is used to extract the depth information of the holographic anti-counterfeiting model; in grid node regions where the sampling density is less than the density threshold, low-frequency interpolation is used to extract the depth information of the holographic anti-counterfeiting model. The extracted depth information is quantized and encoded, and the quantized and encoded depth information is discretized into an initial feature matrix adapted to the characteristics of a multi-beam physical array.

[0007] Optionally, the step of mapping the curvature gradient vector onto each grid node of the initial reference grid, and adjusting the sampling density of each grid node using a non-uniform sampling algorithm based on the mapped curvature gradient vector, includes the following steps: Set low-frequency change thresholds and high-frequency abrupt change thresholds for the curvature gradient vector; Traverse each grid node in the initial baseline grid and extract the magnitude of the curvature gradient vector corresponding to each grid node; Mark the grid nodes containing curvature gradient vectors whose magnitudes are below the low-frequency change threshold as smooth feature nodes; The grid nodes containing curvature gradient vectors with magnitudes higher than the high-frequency mutation threshold are marked as steep feature nodes. The grid nodes containing curvature gradient vectors whose magnitudes fall between the low-frequency change threshold and the high-frequency abrupt change threshold are marked as transition feature nodes. By using a non-uniform sampling algorithm, steep feature nodes are assigned the highest sampling density weight, smooth feature nodes are assigned the lowest sampling density weight, and transitional feature nodes are assigned the sampling density weight of linear interpolation, thus completing the sampling density adjustment of each grid node.

[0008] Optionally, the step of extracting the depth information of the holographic anti-counterfeiting model using high-frequency interpolation in grid node regions with sampling density greater than or equal to a preset density threshold, and using low-frequency interpolation in grid node regions with sampling density less than a density threshold, includes the following steps: A high-frequency polynomial fitting surface is constructed in the grid node region where steep feature nodes are located, based on the weight of the highest sampling density. High-frequency polynomial fitting surfaces are used to capture phase abrupt changes in holographic anti-counterfeiting models and extract the corresponding high-frequency depth information. A low-order smooth surface is constructed in the grid node region where the smooth feature node is located, based on the lowest sampling density weight; Redundant grid data in the holographic anti-counterfeiting model is filtered out using a low-order smooth surface, and the corresponding low-frequency depth information is extracted. High-frequency depth information and low-frequency depth information are smoothly fused using spline functions in the grid node regions where transition feature nodes are located to ensure the global continuity of extracted depth information.

[0009] Optionally, when the expected thermal diffusion accumulation in the densely exposed region of the initial feature matrix exceeds the physical threshold in the physical threshold model, the duty cycle of the exposed pixels representing non-critical morphology within the densely exposed region is truncated, and the initial feature matrix is ​​updated based on the energy conservation principle by compensating the energy reference of adjacent working pixels upwards to generate a thermal equilibrium distribution matrix, including the following steps: Locate densely exposed regions in the initial feature matrix where the expected cumulative thermal diffusion exceeds a physical threshold. The edge detection operator is used to perform convolution operation on the pixels in the densely exposed area to obtain the convolution operation result; Based on the convolution operation results, the working pixels representing key contour shapes and the exposure pixels representing non-key shapes are separated; The duty cycle of the control time window for the exposure pixels is truncated to generate a control correction sequence containing a forced sleep command. The exposure energy integral of the duty cycle cutoff loss is calculated based on the principle of energy conservation, and the exposure energy integral is superimposed on the energy reference of the adjacent working pixels according to the inverse weight of spatial distance. The forced sleep state after executing the control correction sequence and the superimposed energy benchmark are attached to each pixel as state markers, the initial feature matrix is ​​updated and a thermal equilibrium distribution matrix is ​​generated.

[0010] Optionally, the step of extracting the residual energy features of the edges on both sides of the overlapping area of ​​adjacent multi-beam scan zones in the thermal equilibrium distribution matrix, and constructing a semivariance function reflecting the thermal diffusion trend based on spatial autocorrelation evaluation logic, includes the following steps: Delineate the boundary of the splicing overlap area between adjacent bands of multi-beam scanning in a two-dimensional spatial reference frame; Extract the first residual energy feature sequence located on the left edge of the splicing overlap region from the thermal equilibrium distribution matrix, and extract the second residual energy feature sequence located on the right edge of the splicing overlap region. Use the first residual energy feature sequence and the second residual energy feature sequence as residual energy features. Based on the spatial autocorrelation assessment logic, the energy variance of the first residual energy feature sequence and the second residual energy feature sequence at different spatial lag distances is calculated. Curve fitting was performed on the energy variance to extract the nugget effect constant, the partial sill value, and the range parameter. Substitute the nugget effect constant, the partial sill value, and the range parameter into the preset spherical function model, and use the spherical function model to construct a variogram skeleton representing the degree of correlation in energy space. By mapping the skeleton of the variogram to the coordinate matrix of the spliced ​​overlapping area, a semivariogram function reflecting the thermal diffusion trend is constructed.

[0011] Optionally, the step of generating a spatial variation convolution kernel within a preset sliding window based on the semivariogram function, and using the spatial variation convolution kernel to perform a smoothing operation on the exposure data sequence in the splicing overlap area to achieve optimal unbiased estimation, thereby generating a benchmark exposure control sequence that eliminates energy aggregation variation, includes the following steps: Initialize a sliding window with a preset size within the overlapping area of ​​the stitching, and advance the sliding window pixel by pixel along the stitching path; At the current position of the sliding window, input each discrete coordinate point within the sliding window into the semivariance function, and solve to obtain the spatial covariance matrix; Invert the spatial covariance matrix and calculate the optimal weight coefficients in conjunction with unbiased constraints; Arrange the optimal weight coefficients into a two-dimensional matrix to generate the spatial mutated convolution kernel corresponding to the current sliding window position; The spatial variation convolution kernel is used to perform discrete convolution multiplication and addition operations on the exposure data sequence within the sliding window to achieve the smoothing operation of the optimal unbiased estimation and obtain the smoothing operation result. Collect and reconstruct the smoothing results of each sliding window position, and output a baseline exposure control sequence that eliminates energy aggregation variations.

[0012] Optionally, the step of establishing a compensation model for the laser control power, mechanical motion speed, and target morphology depth of the associated processing platform, pre-solving the equations of the compensation model for different mechanical speeds of the processing platform, and fusing the reference exposure control sequence with the compensation states obtained from the equation solution to generate multiple corresponding compensation state control sequence snapshots includes the following steps: A state equation is constructed as a compensation model, with the laser control power of the processing platform as the dependent variable and the mechanical motion speed of the processing platform and the depth of the target shape as the independent variables. Extract the historical speed fluctuation extremes of the processing platform and set the speed discretization step size; A set of velocity assumptions containing a finite number of mechanical velocities is constructed based on historical velocity fluctuation extremes and velocity discretization step sizes. Substitute each mechanical velocity in the velocity assumption set into the compensation model in turn to calculate and solve, and obtain the preset laser power compensation vector corresponding to each mechanical velocity; The reference exposure control sequence is fused with the preset laser power compensation vector to generate multiple control sequence snapshots corresponding to the compensation state.

[0013] In a second aspect, the present invention also provides a GLV multi-beam direct-write path planning system for holographic anti-counterfeiting, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the GLV multi-beam direct-write path planning method for holographic anti-counterfeiting as described in any one of the first aspects.

[0014] Thirdly, the present invention also provides a computer-readable storage medium storing instructions that, when executed by a processor, cause the processor to perform the GLV multi-beam direct-write path planning method for holographic anti-counterfeiting according to any one of the first aspects.

[0015] The beneficial effects of this invention are: This invention provides a GLV multi-beam direct-write path planning method for holographic anti-counterfeiting, effectively solving the problems of low processing accuracy and low shape restoration in existing holographic anti-counterfeiting technologies. This invention acquires an anti-counterfeiting model and discretizes continuous depth information into an initial feature matrix using a non-uniform sampling algorithm. By establishing a physical threshold model for adjacent thermal superposition of multi-beams, it rigorously evaluates the expected thermal diffusion accumulation in densely exposed areas. When the limit is exceeded, it performs duty cycle truncation and energy compensation based on energy conservation of adjacent pixels to generate a thermal balance distribution matrix. This step fundamentally suppresses local thermal accumulation and overexposure caused by the compact arrangement of multi-beams. Simultaneously, for the overlapping area of ​​adjacent bands in multi-beam scanning, this invention extracts residual energy features and constructs a semi-variance function reflecting the thermal diffusion trend. Then, it generates a spatial variation convolution kernel for optimal unbiased estimation smoothing, thereby eliminating energy aggregation variation in the splicing area and ensuring shape uniformity during large-area continuous processing. On the other hand, by establishing a compensation model that correlates laser power, mechanical speed and target depth, multiple control sequence snapshots corresponding to the compensation state are generated in advance, and instantaneous mechanical speed is collected in real time during the processing for matching. This adjustment mechanism effectively offsets the interference of mechanical speed fluctuations on the exposure dose, and significantly improves the processing accuracy and reproduction of holographic anti-counterfeiting three-dimensional micro-nano morphology. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a GLV multi-beam direct-write path planning method for holographic anti-counterfeiting in one embodiment of this application.

[0017] Figure 2 This is a schematic diagram of the process of generating an initial feature matrix by parsing depth information in one embodiment of this application. Detailed Implementation

[0018] The technical solutions of the embodiments of this application will be clearly described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application are within the scope of protection of this application.

[0019] The terms "first," "second," etc., used in the specification and claims of this application are used to distinguish similar objects and not to describe a specific order or sequence. It should be understood that such use of data can be interchanged where appropriate so that embodiments of this application can be implemented in orders other than those illustrated or described herein, and the objects distinguished by "first," "second," etc., are generally of the same class and the number of objects is not limited; for example, a first object can be one or more. Furthermore, in the specification and claims, "and / or" indicates at least one of the connected objects, and the character " / " generally indicates that the preceding and following objects are in an "or" relationship.

[0020] Figure 1 This is a flowchart illustrating a GLV multi-beam direct-write path planning method for holographic anti-counterfeiting in one embodiment. It should be understood that, although... Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order in which these steps are executed, and they can be performed in other orders. Figure 1 At least some steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily executed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed alternately or in turn with other steps or at least a portion of the sub-steps or stages of other steps. For example Figure 1 As shown, the GLV multi-beam direct-write path planning method for holographic anti-counterfeiting disclosed in this invention specifically includes the following steps: S101. Obtain the holographic anti-counterfeiting model, analyze the continuous depth information of the model surface in the holographic anti-counterfeiting model through a non-uniform sampling algorithm, and discretize the depth information into an initial feature matrix that adapts to the characteristics of the multi-beam physical array of the processing platform in a preset two-dimensional spatial reference system.

[0021] The three-dimensional visual effect of holographic anti-counterfeiting patterns relies on the continuously undulating three-dimensional morphology of the material surface. When converting this continuously changing morphology into processing instructions that can be recognized by multi-beam laser processing equipment, dimensionality reduction and discretization are necessary. The introduction of a non-uniform sampling algorithm primarily addresses the contradiction between the inconsistent processing accuracy requirements of complex microstructures and flat areas in the anti-counterfeiting pattern. In practice, a holographic anti-counterfeiting model containing the ideal three-dimensional microstructure of the holographic pattern is first imported into the computer processing module. A two-dimensional spatial reference system is then established, with its grid resolution strictly corresponding to the pixel spacing of the multi-beam physical array on the processing platform. When applying the non-uniform sampling algorithm to analyze the continuous depth information of the model surface, the sampling density is increased in areas with drastic changes in pattern morphology to accurately capture subtle high-frequency phase changes, while the sampling density is reduced in areas with gentle morphology to minimize redundant data processing. The depth information extracted from each location through the above sampling process is converted into discrete values ​​adapted to the modulation levels of each independent beam channel of the multi-beam array. Finally, all the discretized depth values ​​are arranged according to the coordinates of the two-dimensional spatial reference system and combined to form a two-dimensional matrix structure, namely the initial feature matrix. Each element in the matrix corresponds precisely to the ideal shape processing depth parameter that a specific laser beam in the multi-beam array needs to perform under specific physical coordinates.

[0022] S102. By evaluating the expected thermal diffusion accumulation of each exposed pixel in the initial feature matrix region by region, a physical threshold model for multi-beam adjacent thermal superposition is established.

[0023] In the case of multiple laser beams simultaneously irradiating a photosensitive material for dense exposure, photon energy is converted into heat energy, which is then conducted laterally within the material. When multiple adjacent laser beams simultaneously perform high-power exposure, the resulting heat diffusion areas overlap and accumulate spatially, causing the actual exposure area to be much larger than the ideal focused spot of a single laser beam, thus blurring the fine outline of the holographic anti-counterfeiting pattern. To address this phenomenon, it is crucial to evaluate the expected cumulative heat diffusion for each exposed pixel in the initial feature matrix region by region. In practice, the initial feature matrix is ​​divided into multiple evaluation blocks according to the scanning width of the multi-beam array. For each exposed pixel within each evaluation block, the required theoretical laser exposure energy is calculated based on the ideal processing depth parameters assigned in the initial feature matrix. Subsequently, combining the physical properties of the photosensitive material, such as thermal conductivity and specific heat capacity, the heat diffused from the pixel to its neighboring pixels under the theoretical exposure energy is calculated using the partial differential equation of heat conduction. The expected cumulative heat diffusion at that location is obtained by linearly summing the diffused heat received by each pixel from all its neighboring pixels. Based on the critical thermal limit of morphological distortion caused by effective photochemical reaction of materials, a physical threshold model for the thermal superposition of multiple beams is set to determine whether thermal accumulation exceeds the limit.

[0024] S103. When the expected thermal diffusion accumulation of the densely exposed region in the initial feature matrix exceeds the physical threshold in the physical threshold model, the duty cycle of the exposed pixels representing non-critical morphology in the densely exposed region is truncated, and the energy reference of the adjacent working pixels is compensated upward based on the principle of energy conservation to update the initial feature matrix and generate a thermal balance distribution matrix.

[0025] Within densely exposed areas, there are often working pixels that form the key contours of the anti-counterfeiting pattern, as well as non-critical shape exposure pixels that only serve a filling function. When the expected heat diffusion accumulation in a certain area exceeds the physical threshold, without intervention, the heat accumulation will lead to severe thermal melting or even material ablation. Therefore, a selective energy reduction and transfer strategy is required. In practice, once an area with an expected heat diffusion accumulation exceeding the limit is located, the key shape pixels and non-key shape pixels are first distinguished using an image edge extraction algorithm. For the exposure pixels representing non-critical shapes, the time ratio of the controlled laser beam is forcibly shortened, that is, the duty cycle is truncated, thereby directly reducing the total heat input to that area. However, simply reducing energy will cause the actual processing depth in some areas to fail to reach the ideal depth designed for the anti-counterfeiting model. Therefore, based on the principle of energy conservation, the total amount of exposure energy reduced due to the duty cycle truncation is calculated, and the total amount of energy reduced is converted into the corresponding laser power increment. According to the inverse weighting rule that the closer the spatial distance, the more is allocated, the more is distributed and superimposed on the energy reference of the adjacent working pixels representing the key contour shape. This energy redistribution mechanism, which involves the ebb and flow of energy, avoids both the distortion of the shape caused by excessive local heat accumulation and ensures that the overall processing depth of the region meets the standards. Ultimately, it updates the initial feature matrix and generates a thermal equilibrium distribution matrix.

[0026] S104. Extract the residual energy features of the two sides of the overlapping area of ​​the multi-beam scan adjacent zones in the thermal equilibrium distribution matrix, and construct a semivariance function reflecting the thermal diffusion trend based on the spatial autocorrelation evaluation logic.

[0027] The extraction of residual energy features and the construction of a semivariance function are primarily used to accurately quantify the heat diffusion patterns at the edges of adjacent scan strips. Due to limitations in array physical size, multi-beam direct-write equipment must employ multi-strip splicing scanning when processing large-area holographic anti-counterfeiting patterns. In the overlapping area of ​​adjacent strips, two consecutive scans can lead to complex secondary superposition of heat, easily resulting in splicing gaps or protrusions. Drawing upon the semivariance theory used in geostatistics to describe the spatial distribution correlation of mineral resources, the problem of assessing the variability of heat diffusion can be effectively solved. In the specific implementation, the boundary of the splicing overlap area of ​​adjacent multi-beam scan strips is delineated in a two-dimensional spatial reference frame. Residual energy data sequences from the left and right edges of the splicing overlap area are extracted from the heat balance distribution matrix generated in the previous step. Using spatial autocorrelation assessment logic, the energy distribution variance of these two residual energy sequences at different spatial distance intervals is calculated. As the spatial lag distance changes, the energy distribution variance exhibits a specific trend, reflecting the attenuation pattern of heat diffusion from high-energy areas to low-energy areas. By mathematically fitting a series of calculated energy variance scatter points, parameters reflecting spatial variability are extracted, and a semivariogram function reflecting the trend of heat diffusion is constructed. This semivariogram function can accurately describe the degree to which the thermal state of a point at a splicing edge is affected by the thermal state of other surrounding points at a specific spatial distance.

[0028] S105. Based on the semivariogram function, a spatial variation convolution kernel is generated within a preset sliding window. The spatial variation convolution kernel is then used to perform a smoothing operation on the exposure data sequence in the splicing overlap area to achieve the best unbiased estimation, thereby generating a baseline exposure control sequence that eliminates energy aggregation variation.

[0029] Conventional image smoothing filtering algorithms typically assign fixed weights, failing to adapt to the non-uniformity of energy distribution in complex thermal diffusion environments. Introducing a spatial variogram kernel essentially applies the Kriging interpolation concept from geostatistics to the optimization of laser exposure data. Specifically, a sliding window of a pre-defined size is initialized within the overlapping area of ​​the stitching, and this window advances pixel by pixel along the stitching path of the multi-beam scan. Each time the sliding window moves to a new position, the discrete coordinates within the window's coverage area are input into a pre-constructed semivariogram function to obtain the spatial covariance matrix describing the local thermal correlation. The spatial covariance matrix is ​​inverted, and combined with the unbiased constraint that the sum of all weights must equal one, the optimal weight coefficient matrix for the current local window characteristics is calculated. This optimal weight coefficient matrix is ​​then used as the spatial variogram kernel, and discrete convolution multiplication and addition operations are performed with the exposure data sequence within the current sliding window. This method dynamically and precisely adjusts the exposure control values ​​of each pixel based on the degree of thermal correlation revealed by the semivariogram function, effectively smoothing out energy abrupt changes at the stitching edges. The smoothing results of all sliding window positions are collected and recombined to finally generate a baseline exposure control sequence that eliminates energy aggregation variations, ensuring a natural transition in the morphology of the stitched area.

[0030] S106. Establish a compensation model for the laser control power, mechanical motion speed, and target morphology depth of the associated processing platform. Solve the equations of the compensation model in advance for different mechanical speeds of the processing platform. Fuse the reference exposure control sequence with the compensation state obtained from the equation solution to generate multiple control sequence snapshots with corresponding compensation states.

[0031] In multi-beam direct writing, the actual processing depth of the material surface is determined by both the laser control power and the mechanical scanning speed. Due to the inherent hysteresis and friction of the mechanical transmission mechanism, the movement speed of the processing platform inevitably fluctuates slightly. If the laser power is kept constant, a slower mechanical speed will lead to overexposure and a darker morphology, while a faster speed will lead to underexposure and a lighter morphology. Therefore, it is crucial to construct a compensation model with the laser control power of the processing platform as the dependent variable and the mechanical movement speed and the target morphology depth as independent variables. In practice, the maximum and minimum mechanical speeds of the processing platform in previous operation records are first extracted, and a small speed interval step is set to construct a set of speed assumptions containing multiple discrete mechanical speed states. Each assumed speed in the set of speed assumptions is then substituted into the compensation model for solution, calculating the precise laser power compensation value required to maintain the target morphology depth at the corresponding speed. Subsequently, the smoothed reference exposure control sequence is fused with the calculated laser power compensation values ​​at various speeds. For each assumed mechanical speed, a snapshot of the control sequence containing precise compensation parameters is generated, pre-planning control strategies to cope with speed fluctuations, which greatly reduces the workload of real-time computation.

[0032] S107. Real-time acquisition of the instantaneous mechanical speed of the processing platform, matching the control sequence snapshot corresponding to the instantaneous mechanical speed, and outputting the control sequence snapshot to drive the multi-beam array of the processing platform to complete the direct writing of the holographic anti-counterfeiting morphology.

[0033] All the complex calculations and model building involved in the initial stages ultimately need to be translated into the physical movements of the multi-beam array through a high-precision real-time synchronization mechanism. The direct-write process is extremely sensitive to time delays; even the slightest lag can lead to misalignment or deformation of the anti-counterfeiting pattern's microstructure. To address this, a high-precision grating ruler or laser interferometer mounted on the motion axis of the processing platform is used to acquire the platform's instantaneous mechanical speed in real time at an extremely high sampling frequency. Upon receiving the instantaneous mechanical speed signal, the control module quickly compares it with multiple control sequence snapshots pre-generated and stored in a high-speed cache from the previous step. A fast matching algorithm identifies the control sequence snapshot that best matches the current instantaneous mechanical speed. Once a match is successful, the control module immediately outputs the data from that snapshot. The output data, after digital-to-analog conversion, directly drives the multi-beam array on the processing platform. Each independent laser modulator in the array precisely adjusts its beam's on / off state, duty cycle, and laser power according to the instructions in the snapshot, with a response speed at the microsecond or even nanosecond level. The aforementioned process of real-time acquisition, instant matching, and precise driving is continuously repeated to ensure that the multi-beam array can still complete the perfect direct writing of the holographic anti-counterfeiting morphology with high quality even under dynamically changing mechanical motion.

[0034] In one embodiment, reference is made to Figure 2 The process involves acquiring a holographic anti-counterfeiting model, analyzing the continuous depth information of the model surface using a non-uniform sampling algorithm, and discretizing the depth information into an initial feature matrix adapted to the multi-beam physical array characteristics of the processing platform within a preset two-dimensional spatial reference frame. The steps include: S201. Obtain the holographic anti-counterfeiting model, extract the surface mesh data from the holographic anti-counterfeiting model, and calculate the curvature gradient vector of the surface mesh data in three-dimensional space; S202. Divide the preset two-dimensional spatial reference frame into an initial reference grid that matches the characteristics of the multi-beam physical array of the processing platform; S203. Map the curvature gradient vector to each grid node of the initial reference grid, and adjust the sampling density of each grid node according to the mapped curvature gradient vector using a non-uniform sampling algorithm. S204. High-frequency interpolation is used to extract the depth information of the holographic anti-counterfeiting model in grid node regions where the sampling density is greater than or equal to a preset density threshold, and low-frequency interpolation is used to extract the depth information of the holographic anti-counterfeiting model in grid node regions where the sampling density is less than the density threshold. S205. Quantize and encode the extracted depth information, and discretize the quantized and encoded depth information into an initial feature matrix that adapts to the characteristics of the multi-beam physical array.

[0035] In this embodiment, the 3D model is typically composed of a large number of polygonal patches. Extracting surface mesh data aims to obtain the geometric basis of the 3D topography. Given the numerous nanoscale abrupt changes in anti-counterfeiting patterns, conventional uniform depth extraction would lose crucial details. Therefore, a curvature gradient vector is introduced as an indicator of topography complexity. Curvature reflects the degree of curvature of a surface at a point, while the gradient indicates the direction and magnitude of the most drastic change in curvature. Specifically, each vertex in the surface mesh data is traversed, and the normal curvature in each direction passing through that vertex is calculated. In one embodiment, the principal curvature of the vertex is calculated based on the difference in normal vectors between adjacent patches around the vertex, thus obtaining the curvature gradient vector. The calculation formula is: In the formula, This represents the magnitude of the curvature gradient vector. The principal curvature of the surface in the first principal direction. The principal curvature of the surface in the second principal direction represents the curvature of the surface. and The above formula represents the locally orthogonal parameterized coordinate axes in the three-dimensional space where the surface mesh data is located. It can accurately quantify the degree of undulation on the surface of the holographic anti-counterfeiting model; a larger value indicates a more complex anti-counterfeiting micro / nano structure within the region.

[0036] The multi-beam physical array of the processing platform contains hundreds or thousands of independently controlled micromirrors or grating valves, with fixed physical spacing between each emitting pixel. To ensure that the resolved depth information can directly drive the hardware channel, the two-dimensional spatial reference frame needs to be divided into an initial reference grid that strictly corresponds to the physical spacing. The partitioning process is essentially an inverse mapping from physical spatial resolution to digital space. A Cartesian coordinate system is established, and based on the optical scaling factor of the multi-beam physical array, the effective processing spot size formed by the array pixels on the photosensitive material surface and the center distance between adjacent spots are calculated. In one embodiment, intersecting grid lines are divided on the two-dimensional plane according to the calculated center distance to generate the initial reference grid. The coordinate calculation formula for the nodes of the initial reference grid is as follows: In the formula, Represents the first in the initial reference grid Line number Two-dimensional physical coordinates of the grid nodes. This represents the effective horizontal beam spacing of the multi-beam physical array mapped onto the processing plane. This represents the effective beam spacing in the vertical direction mapped from the multi-beam physical array to the processing plane. After the above meshing, the virtual reference frame possesses the same spatial resolution characteristics as the actual array, and all subsequent extraction and processing of depth information for the anti-counterfeiting model strictly adheres to the mesh nodes.

[0037] The calculated curvature gradient vector is spatially aligned with the initial reference grid, ensuring each grid node receives a corresponding topographic change rate attribute. Conventional uniform sampling generates massive amounts of redundant data in flat areas, while insufficient sampling rates can lead to distortion in complex anti-spoofing feature areas. A non-uniform sampling algorithm adaptively adjusts the sampling density of each grid node based on the mapped curvature gradient vector. Specifically, denser sampling points are allocated to areas with more dramatic topographic changes, while sparser sampling points are allocated to areas with gentler topographic changes. In one implementation, the sampling density adjustment is based on the magnitude of the curvature gradient vector. The adjustment formula is: In the formula, This indicates the target sampling density of the grid nodes after adjustment. This represents the preset minimum allowable sampling density. This represents the highest sampling density supported by the multi-beam array hardware. This represents the minimum reference value of the global curvature gradient of the anti-counterfeiting model. This represents the maximum reference value of the global curvature gradient of the anti-counterfeiting model. The algorithm transforms complex geometric features into quantifiable digital density indicators through mathematical mapping, ensuring sufficient geometric information is retained in high-frequency abrupt change regions such as diffraction gratings, while simultaneously reducing the amount of data in the background region, achieving an optimal balance between processing accuracy and speed.

[0038] Regions with sampling densities greater than or equal to a preset density threshold concentrate the core optical features of the anti-counterfeiting pattern, exhibiting abrupt undulations in their morphology; while regions with lower sampling densities are mostly background or slowly changing contours. For high-density regions, high-frequency interpolation algorithms, such as high-order polynomial or spline curve fitting, are used to closely fit complex surface mesh data and accurately extract local microscopic depth variations. Conversely, low-density regions employ low-frequency interpolation algorithms, utilizing less surrounding node information to quickly estimate depth, filtering out minor surface noise and smoothing the overall morphology. In one implementation, the high-frequency interpolation process for extracting depth information relies on multiple closely spaced sampling points. The calculation formula is: In the formula, This represents the depth information of the target mesh nodes extracted through high-frequency interpolation. This represents the order of a higher-order polynomial. These represent the interpolation coefficients obtained by solving the fitting equations for local surface mesh data. Using the aforementioned frequency-band interpolation extraction method, the high-frequency phase features with significant anti-counterfeiting capabilities in the holographic anti-counterfeiting model can be perfectly reproduced. Simultaneously, low-frequency fluctuations introduced by modeling errors in smooth areas are filtered out, ensuring that the final extracted depth data accurately reflects the design intent while meeting the smoothness requirements of physical processing.

[0039] The depth information extracted through interpolation is a continuous floating-point value, while the digital-to-analog converter of the processing platform can only recognize discrete digital step signals. Therefore, the depth information must be quantized and encoded. The quantization process maps the continuous depth values ​​to a finite number of discrete energy levels based on the exposure response curve of the photosensitive material and the power modulation level of the laser. After quantization and encoding, the data from each grid node are arranged according to the coordinates of the two-dimensional spatial reference system and loaded into a two-dimensional array adapted to the characteristics of a multi-beam physical array, thereby generating an initial feature matrix. In one implementation, the quantization encoding combines the device's digital saturation upper limit and the maximum depth of the target shape. The quantization conversion formula is as follows: In the formula, This represents the discrete digital exposure command value generated after quantization encoding; the operator... This indicates the floor function. This represents the maximum pre-set design depth in the holographic anti-counterfeiting model. This represents the number of bits in the underlying digital-to-analog converter of the multi-beam physical array. Through the conversion process, the continuous three-dimensional topographic depth is accurately translated into an initial feature matrix that can be directly read by the physical array. Each data point in the matrix represents the laser energy pulse requirement at a specific spatial location.

[0040] In one implementation, mapping the curvature gradient vector onto each grid node of the initial reference grid, and adjusting the sampling density of each grid node using a non-uniform sampling algorithm based on the mapped curvature gradient vector, includes the following steps: Set low-frequency change thresholds and high-frequency abrupt change thresholds for the curvature gradient vector; Traverse each grid node in the initial baseline grid and extract the magnitude of the curvature gradient vector corresponding to each grid node; Mark the grid nodes containing curvature gradient vectors whose magnitudes are below the low-frequency change threshold as smooth feature nodes; The grid nodes containing curvature gradient vectors with magnitudes higher than the high-frequency mutation threshold are marked as steep feature nodes. The grid nodes containing curvature gradient vectors whose magnitudes fall between the low-frequency change threshold and the high-frequency abrupt change threshold are marked as transition feature nodes. By using a non-uniform sampling algorithm, steep feature nodes are assigned the highest sampling density weight, smooth feature nodes are assigned the lowest sampling density weight, and transitional feature nodes are assigned the sampling density weight of linear interpolation, thus completing the sampling density adjustment of each grid node.

[0041] In this embodiment, when processing complex holographic anti-counterfeiting patterns, the degree of undulation varies greatly in different regions. Without a unified benchmark, it is impossible to accurately separate the core micro / nano structure from the simplifiable flat background. The geometrical abrupt changes in the three-dimensional morphology can be quantified into comparable mathematical boundaries. Setting thresholds requires a comprehensive evaluation of the statistical distribution characteristics of the global curvature gradient of the holographic anti-counterfeiting model. In specific implementation, the average state and dispersion of the curvature gradient of the entire anti-counterfeiting model surface data are first statistically analyzed. Based on this, an adjustment factor is introduced to determine the boundary value. The low-frequency change threshold is used to delineate the region of visual approximate plane, while the high-frequency abrupt change threshold is used to lock in rapidly changing microscopic steps such as diffraction fringes. In one embodiment, the boundary is set based on the statistical mean and standard deviation of the global data. The calculation formula is as follows: Additional settings: In the formula, Represents the threshold for low-frequency changes. Represents the high-frequency mutation threshold. This represents the statistical mean of the curvature gradients corresponding to all grid nodes on the surface of the holographic anti-counterfeiting model. The statistical standard deviation of the curvature gradient. This represents the first adjustment coefficient for flat regions. This represents the second regulatory coefficient of the mutation region.

[0042] The initial reference mesh covers the entire projection area of ​​the holographic anti-counterfeiting model, and each node within the mesh corresponds to a basic coordinate point for future laser direct writing. The traversal operation must be strictly performed according to the preset row and column progression order to ensure that no node containing shape information is missed. The process of extracting the modulus value strips away the directional attributes of the surface curvature, retaining only the magnitude attribute representing the severity of curvature, thereby greatly reducing the computational complexity of subsequent classification operations. In one implementation, a two-dimensional indexing mechanism is established to scan the mesh row by row, read the pre-mapped vector data stored in memory, and then perform the modulus value calculation. The calculation logic formula for extracting the modulus value is expressed as: In the formula, This represents the magnitude scalar of the extracted curvature gradient vector. This indicates that the mapping to the initial reference mesh in the previous step... Line number Curvature gradient vector entity on column node, operator This represents the calculation of the Euclidean norm for a geometric vector containing multidimensional components. After a complete and thorough traversal and extraction operation, the complex topographic undulations within the entire two-dimensional reference frame are transformed into a set of purely scalar data.

[0043] Anti-counterfeiting patterns contain numerous flat, specular reflection areas or background transition areas with extremely slight undulations, requiring no high-resolution reconstruction in terms of optical performance. Selecting and marking grid nodes containing curvature gradient vectors with modulus values ​​below a low-frequency change threshold as smooth feature nodes essentially isolates areas that do not require high-fidelity processing at the digital level. Assigning specific labels is equivalent to giving these nodes a low-priority tag, indicating that subsequent sampling algorithms do not need to consume excessive computational resources in these areas. In one implementation, a logical comparison operator is used to compare each extracted modulus value with a set low-frequency boundary. The logical determination formula for performing classification labeling is as follows: The judgment condition is In the formula, The status flag bit representing the smooth feature node is active high when the condition is met. Once a node meets the logical judgment condition, a fixed category attribute value is added to the current node coordinates in the data matrix. Holographic anti-counterfeiting effects highly depend on nanoscale surface grating stripes, abrupt steps, and complex microlens arrays, which exhibit significant curvature jumps in geometric features. Selecting and marking grid nodes containing curvature gradient vectors with modulus values ​​higher than the high-frequency abrupt threshold as steep feature nodes is significant for accurately locating the high-frequency detail distribution area that plays a decisive role in anti-counterfeiting performance. Applying steep feature marking is equivalent to opening a high-priority green channel for critical areas in the processing chain, warning subsequent processing to utilize the densest laser beams for meticulous finishing. In one implementation, the extracted modulus value is compared with the set high-frequency abrupt threshold, performing strict numerical filtering. The corresponding classification marking logic judgment formula is: The conditions for its establishment are In the formula, This represents the status flag of a steeply shaped node. A high-level signal is triggered when the value exceeds the high-frequency limit. This core status attribute is recorded and permanently stored for grid nodes that meet the conditions.

[0044] On the other hand, between extremely flat and extremely steep features, there often exists a three-dimensional structure exhibiting a gradual transition. If the processing resolution is directly switched between these two extreme features, the discrete distribution of the laser beam will etch obvious artificial step marks on the material surface, disrupting the visual continuity and aesthetics of the anti-counterfeiting pattern. Marking and establishing the grid nodes containing curvature gradient vectors with modulus values ​​between the low-frequency change threshold and the high-frequency abrupt change threshold as transition feature nodes effectively fills the control gap between the high and low frequency regions. The transition marking indicates that this region requires a compromise processing strategy that considers both characteristics. In one implementation, a dual-boundary logic judgment is performed to lock the aforementioned buffer nodes. The classification marking logic judgment formula is expressed as: The prerequisite for determining its validity is In the formula, This represents the status flag of the transition feature node. For nodes whose values ​​fall within this range, a neutral transition label is added to the attribute list. Establishing these transition nodes creates a reasonable spatial range for the subsequent introduction of gradual sampling density interpolation, allowing the data density to smoothly and gradually decrease from a high-frequency dense state to a low-frequency sparse state, thus ensuring a natural and smooth pattern outline after physical direct writing.

[0045] Based on three pre-assigned state identifiers, specific numerical weights are mapped to ultimately complete the adaptive sampling planning layout of the two-dimensional spatial grid. A non-uniform sampling algorithm is used to precisely assign different sampling density weights to nodes of corresponding categories. Steep feature nodes are assigned the highest sampling density weight to ensure dense beam control points to capture high-frequency abrupt changes; smooth feature nodes are assigned the lowest weight to promote sparse distribution of control points to filter redundancy; and transitional feature nodes are assigned linear interpolation weights to achieve gradual changes in lattice density. In one implementation, different density allocation subroutines are called based on the node state identifier. For steep feature nodes, the sampling density is set to be equal to the highest sampling density supported by the multi-beam array hardware described above. The sampling density of smooth feature nodes is set to be equal to the minimum allowed sampling density. For transition feature nodes, linear interpolation is used to assign intermediate weights. The formula for calculating the sampling density of the transition region is: In the formula, The linear interpolation sampling density weights are the final assigned weights for the transition feature nodes. After the calculation and allocation of each weight, each grid node has specific density index parameters to guide the subsequent interpolation extraction depth, thus completely completing the task of adaptive density adjustment configuration of the non-uniform sampling algorithm at the spatial level.

[0046] In one embodiment, extracting the depth information of the holographic anti-counterfeiting model using high-frequency interpolation in grid node regions with sampling density greater than or equal to a preset density threshold, and extracting the depth information of the holographic anti-counterfeiting model using low-frequency interpolation in grid node regions with sampling density less than the density threshold, includes the following steps: A high-frequency polynomial fitting surface is constructed in the grid node region where steep feature nodes are located, based on the weight of the highest sampling density. High-frequency polynomial fitting surfaces are used to capture phase abrupt changes in holographic anti-counterfeiting models and extract the corresponding high-frequency depth information. A low-order smooth surface is constructed in the grid node region where the smooth feature node is located, based on the lowest sampling density weight; Redundant grid data in the holographic anti-counterfeiting model is filtered out using a low-order smooth surface, and the corresponding low-frequency depth information is extracted. High-frequency depth information and low-frequency depth information are smoothly fused using spline functions in the grid node regions where transition feature nodes are located to ensure the global continuity of extracted depth information.

[0047] In this embodiment, the grid region where the steep feature nodes are located often contains the core high-frequency information of the holographic anti-counterfeiting pattern, namely, the nanoscale phase transition structure. Conventional linear or low-order interpolation methods are prone to excessive smoothing of sharp edges due to insufficient fitting ability when dealing with such drastically fluctuating data points, which severely weakens the final diffraction efficiency and optical anti-counterfeiting performance of the holographic pattern. Introducing high-frequency polynomial fitting can provide sufficient degrees of freedom to infinitely approximate the real complex curvature changes. In the specific implementation, the local grid region where the steep feature nodes are located is taken as the calculation core, and the three-dimensional coordinate set of the dense original surface grid data in this region is extracted. The calculation nodes are selected in the above coordinate set according to the highest sampling density weight, and the polynomial coefficients are solved using the least squares method to minimize the sum of squared errors between the fitted surface and the real model grid. In one embodiment, the mathematical expression of the constructed high-frequency polynomial fitted surface has been presented above, namely the formula: Using this mathematical model, the originally discrete and irregular three-dimensional surface mesh is transformed into a continuously differentiable high-dimensional spatial function surface in locally steep regions.

[0048] Phase abrupt changes in holographic anti-counterfeiting models are key to achieving light wave interference and diffraction, and generating a unique stereoscopic visual experience. Physically, these manifest as steep steps or sharp grooves ranging from a few nanometers to hundreds of nanometers. Using high-frequency polynomials to fit surfaces is essentially a process of precisely sampling and measuring continuous surfaces at specific discrete coordinate points using analytical geometry. Because high-frequency surfaces possess excellent local morphology fitting, they can accurately reflect the abrupt changes in microstructure at each grid node position in a two-dimensional reference system. In one implementation, substituting the initial reference grid node coordinates corresponding to the multi-beam physical array into the aforementioned high-frequency polynomial fitting surface equation allows for the capture and extraction of high-frequency depth information. The specific formula for the calculation process is expressed as follows: In the formula, Represents the captured and extracted high-frequency depth information entity values ​​for a specific mesh node; operator This represents the mathematical operation process of substituting independent variables into the equation of a high-frequency polynomial fitted surface. This represents the horizontal index number of the target mesh node in the two-dimensional spatial reference frame. This represents the vertical index number of the target grid node. Indicates the effective beam spacing in the horizontal direction. This represents the effective spacing between light spots in the vertical direction. Through substitution calculations, the dramatic topographical fluctuations of the holographic anti-counterfeiting model in steep regions are faithfully converted into numerical sequences on the corresponding processing grid, ensuring accurate analysis of micro- and nano-scale features.

[0049] The grid regions where smooth feature nodes are located mostly correspond to mirrored backgrounds or large gradient color blocks in anti-counterfeiting patterns. These regions are extremely insensitive to morphological changes in optical performance, and there is no need to excessively consume the processing resolution of multi-beam lasers. If high-order fitting is still applied to flat regions, it will not only lead to a serious waste of memory and computing resources due to data oversampling, but may even introduce false high-frequency oscillations in flat regions due to the Runge phenomenon inherent in high-order polynomials. Adopting a low-order smooth surface construction strategy can effectively avoid the above drawbacks. In specific implementation, relying on the minimum sampling density weight given in the previous steps, only extremely sparse control nodes are selected as support points in a vast smooth grid region. In one implementation, a bilinear or biquadratic low-order surface model is selected as the fitting basis. The mathematical formula for constructing a low-order smooth surface is: In the formula, This represents the completed low-order smooth surface function model. , , , These all represent the low-order smooth surface coefficient parameters obtained by solving the sparse control point matrix. and This represents locally orthogonal parametric coordinates. By applying a low-order model, the spatial span of the physical morphology is significantly stretched, effectively smoothing out minor, unnecessary undulations and forming a macroscopically highly flat and smooth three-dimensional digital transition surface.

[0050] The redundant mesh data in the model largely originates from overly subdivided triangle patches automatically generated by 3D modeling software during export. These densely packed vertex coordinates offer no valuable optical gain in smooth areas and instead interfere with the path planning continuity of the processing platform. Low-order smooth surfaces, acting like digital low-pass filters, can completely filter out minute high-frequency noise points attached to the base anti-counterfeiting surface. The process involves selectively substituting coordinates onto the low-order smooth surface according to the initial baseline mesh arrangement. In one implementation, substituting the coordinates of mesh nodes identified as having smooth features into the low-order smooth surface equation yields the filtered, clean depth values. The corresponding low-frequency depth information extraction formula is: In the formula, The operator represents the low-frequency depth information entity value corresponding to the smooth feature nodes extracted after filtering redundant grid data. This represents the algebraic operation process of substituting coordinate variables into a low-order smooth surface model. This represents the horizontal sort number of the extracted node in the initial baseline grid. Represents the column number, Indicates the lateral physical spacing of the light spot. This indicates the longitudinal physical spacing of the laser spot. The entire extraction mechanism ensures that the data instructions in the flat area meet the channel requirements of the multi-beam array while avoiding unnecessary high-frequency fluctuations, thus guaranteeing that laser direct writing maintains a stable, low-power, and uniform processing state in this area.

[0051] At the boundary between steep and gentle feature regions, due to the use of different orders of fitted surfaces and different sampling densities on both sides, directly physically splicing the depth information of the two will inevitably result in numerical abrupt changes and geometric steps at the boundary edge. If this discontinuity is directly etched onto the material by a multi-beam laser array, it will lead to severe optical scattering defects. Introducing a spline function smoothing fusion mechanism can perfectly bridge the gaps between data from different frequency bands. Spline functions possess the excellent mathematical property of maintaining the continuity of higher-order derivatives across multiple intervals. In specific implementation, within the region marked as a transition feature node, depth information from the boundaries of adjacent high-frequency regions and adjacent low-frequency regions is simultaneously introduced as boundary constraints for spline fusion. In one implementation, weighted fusion is performed based on the linear interpolation sampling density weights of the transition region obtained above. The depth fusion calculation formula is as follows: In the formula, This represents the global continuous depth information generated after smooth fusion using spline functions. Represents the sampling density weights based on the aforementioned linear interpolation. The normalized spline smoothing weight coefficients are obtained as follows: Represents high-frequency depth information. This represents low-frequency depth information. After smooth fusion processing, the transition region data can perfectly transition the complex micro-nano mutation structure to a smooth, flat surface with a natural and smooth curve, ensuring the absolute continuity and smoothness of the final generated three-dimensional morphology throughout the entire two-dimensional spatial reference frame from the algorithm's underlying layer.

[0052] In one implementation, when the expected thermal diffusion accumulation in the densely exposed region of the initial feature matrix exceeds the physical threshold in the physical threshold model, the duty cycle of the exposed pixels representing non-critical topography within the densely exposed region is truncated, and the initial feature matrix is ​​updated by compensating the energy reference of adjacent working pixels upward based on the principle of energy conservation, and a thermal equilibrium distribution matrix is ​​generated, including the following steps: Locate densely exposed regions in the initial feature matrix where the expected cumulative thermal diffusion exceeds a physical threshold. The edge detection operator is used to perform convolution operation on the pixels in the densely exposed area to obtain the convolution operation result; Based on the convolution operation results, the working pixels representing key contour shapes and the exposure pixels representing non-key shapes are separated; The duty cycle of the control time window for the exposure pixels is truncated to generate a control correction sequence containing a forced sleep command. The exposure energy integral of the duty cycle cutoff loss is calculated based on the principle of energy conservation, and the exposure energy integral is superimposed on the energy reference of the adjacent working pixels according to the inverse weight of spatial distance. The forced sleep state after executing the control correction sequence and the superimposed energy benchmark are attached to each pixel as state markers, the initial feature matrix is ​​updated and a thermal equilibrium distribution matrix is ​​generated.

[0053] In this embodiment, when multiple laser beams are simultaneously applied to the surface of the photosensitive substrate, the thermal energy in local areas overlaps, causing the actual photosensitive area to far exceed the preset theoretical spot size. To curb the interference of thermal proximity effect, the risk range must be delineated at the macroscopic data level. Specifically, the operation is based on the initial feature matrix generated earlier, reading the expected thermal state data stored at each node position row by row and column by column. The extracted data is sent to a comparator for numerical comparison with a physical limit scale. The physical limit scale maps the equivalent parameter of the highest critical temperature at which the material can maintain a linear photochemical reaction. When it is determined that the values ​​of certain grid nodes exceed the safety limit, the set of adjacent and exceeding pixels is classified as a dense exposure area. In one embodiment, mathematical inequalities are applied to complete the positioning process. The positioning discrimination formula is expressed as follows: The premise for the determination is In the formula, This represents a status flag variable indicating whether a pixel belongs to a densely exposed area. The two-dimensional coordinates in the initial characteristic matrix are... and The expected cumulative thermal diffusion value corresponding to the exposed pixel. This represents the critical physical threshold constant set in the physical threshold model. Once the decision condition is met, the state flag variable is set to the active level.

[0054] The high-risk area contains the skeleton structure that constitutes the anti-counterfeiting features of the holographic pattern, as well as internal pixels that only serve as solid fillers. The skeleton structure determines the sharpness of the final pattern, while the internal filler pixels, surrounded by other elements, are prone to heat accumulation, making them ideal for energy reduction. Applying edge detection operators to the analysis of exposure data can effectively distinguish data nodes of different properties. In the specific implementation stage, a convolution template matrix of a preset size is slid within the defined spatial data block. The template contains specific weight coefficients used to calculate the gradient difference between the energy setpoints of the center pixel and its neighboring pixels. When the sliding center aligns with the boundary position, the summation operation produces an extreme value response. In one implementation, a classical operator is used to perform two-dimensional convolution. The calculation formula is: In the formula, The operator represents the gradient magnitude result obtained after convolution. This represents the discrete convolution operation. This represents the matrix of exposure pixel parameters input within a densely exposed area. Represents the template for the horizontal differential convolution kernel. This represents a vertically differentiable convolution kernel template. By applying a convolution operation, the differences in data parameters are transformed into significant mathematical gradient features, which fully activates and highlights the hidden topographic boundaries at the digital level.

[0055] The gradient magnitude results implicitly indicate the degree of spatial variation in morphology within local regions. Based on the difference in numerical values, data nodes within high-risk areas can be divided into two. Higher values ​​indicate transition zones where parameters abruptly change, which are the key physical boundaries maintaining the clarity of grating fringes or microlens steps; lower values ​​suggest a flat interior region where parameters remain stable. The process of classification and separation involves setting a reasonable criterion to filter the data. In one implementation, a comparison logic based on a dynamic threshold is constructed to complete the classification. The separation determination formula is described as: if... Then the corresponding grid position will be marked as the working pixel. ;like Then it is marked as the exposure pixel. In the formula, This represents the gradient magnitude result obtained from the pre-convolution operation. This represents the gradient separation boundary constant set based on the degree of local data dispersion. The attribute identifier represents the set of working pixels that have been separated to indicate the key contour shape. This represents the attribute identifier of the separated set of exposure pixels indicating non-critical features. After the above classification and archiving, data points that were originally in the same high-risk area are precisely assigned completely different processing identities. Nodes belonging to working pixels will maintain full power output to sculpt sharp features, while nodes belonging to exposure pixels become the hosts that receive energy reduction instructions.

[0056] For the internal filling data points selected in the previous stage, allowing the laser to output full power according to the initial command would cause severe thermal melting. Duty cycle truncation technology aims to forcibly reduce energy injection in the time domain. Specifically, it involves applying a time-dimensional shield to the locked host node. Within the effective emission period originally allocated to that node, a segment of the emission channel is forcibly inserted to shut off, turning the originally continuous beam irradiation into intermittent pulses, thereby significantly reducing the total heat energy deposited in the photosensitive material area. In one implementation, the truncation ratio is quantitatively calculated based on the expected thermal diffusion overscalar, and a control correction sequence is generated. The formula for calculating the truncation time window is as follows: In the formula, This represents the length of the forced sleep truncation time calculated for the exposed pixels. This represents the fundamental time constant of a single scan cycle of a multi-beam physical array. This represents the expected cumulative amount of heat diffusion for the corresponding grid node. This represents the critical physical threshold constant. Based on the calculated sleep time, the original data waveform is reconstructed, generating a control correction sequence that includes level inversion. Through duty cycle truncation intervention, the exposure of non-critical areas is effectively cooled, preventing heat conduction from damaging the surrounding delicate anti-counterfeiting structure.

[0057] While simple reduction eliminates the risk of heat buildup, it leads to insufficient overall processing depth in the area, resulting in decreased contrast of the anti-counterfeiting pattern after development. To compensate for this deficiency, the deducted energy must be transferred to the surrounding key nodes responsible for outlining the shape. The process first requires converting the dormant pulses cut off in the temporal domain into an equivalent exposure energy integral. Then, following the principle that the closer the distance, the greater the impact, the integral is decomposed and superimposed with inverse weights onto the adjacent nodes responsible for contour engraving. In one implementation, the mathematical formula for solving the integral and performing the weighted transfer is expressed as: In the formula, This represents the new energy baseline value obtained by adjacent working pixels after superimposed energy compensation. This represents the initial energy reference value set for the working pixel. The parameter representing the constant optical power intensity when the channel is operating at full load. Represents the length of the cutoff time. Represents the basic proportionality coefficient for energy transfer. This represents the spatial physical distance between the exposure pixels and the receiving compensation pixels. Through a conservation allocation mechanism, heat accumulation traps are avoided at the microscopic level, while the overall development depth of the structure is maintained at the macroscopic level, achieving a dual balance between preventing heat loss and preserving depth in processing quality.

[0058] In the preliminary steps, the latest state of both internal nodes forced into hibernation and skeleton nodes receiving transferred energy exists only in temporary variables. Modifications must be permanently embedded into the original control graph to drive downstream hardware. During update operations, precise addressing is performed using a two-dimensional spatial coordinate system, overwriting outdated data from each original node. Timing codes containing hibernation commands are bound to the corresponding locations, and compensated power parameters replace the old values. In one implementation, a state loading function is constructed to complete the matrix update. The matrix update logic is: if the value falls within the working pixel range, execution is performed. If the value falls within the exposure pixel range, then execute... In the formula, This represents the integrated data packet corresponding to the two-dimensional coordinates of the node in the updated heat balance distribution matrix. This indicates that the device is in continuous operation. This represents a new energy benchmark after superimposed compensation energy. This represents the forced sleep state flag indicating the execution control correction sequence. This represents the remaining effective exposure energy parameters after truncation. By completely replacing the curing operation, the data array, which was at risk of thermal runaway, has been transformed into a high-quality control source that combines contour sharpening and automatic thermal energy balancing.

[0059] In one implementation, calculating the exposure energy integral of the duty cycle cutoff loss based on the principle of energy conservation, and then superimposing the exposure energy integral onto the energy reference of adjacent working pixels with an inverse weighting according to spatial distance, includes the following steps: The discrete pulse count value is calculated based on the time discretization clock cycle and the duty cycle is truncated to reduce the discrete pulse count value. The discrete pulse count value is converted into a numerical exposure energy integral and the exposure energy integral is equally decomposed into multiple discrete unit energy tokens to build a token pool to be allocated. Obtain the digital saturation threshold of the underlying digital-to-analog converter of the multi-beam physical array, and perform a logical subtraction operation between the digital saturation threshold and the current energy reference of the adjacent working pixels to obtain the maximum allocable digital margin to prevent overflow of the adjacent working pixels. By combining the two-dimensional logical coordinate distance between adjacent working pixels and exposure pixels, an addressing weight is constructed with the maximum allocable digital margin as the numerator and the two-dimensional logical coordinate distance as the denominator. The addressing weights are then sorted in descending order to generate a token receiving priority sequence for adjacent working pixels. According to the order of the token receiving priority sequence, unit energy tokens are drawn one by one from the token pool to be allocated and accumulated to the energy reference of the corresponding adjacent working pixel using logical addition. At the same time, after each accumulation operation, the maximum allocable digital surplus of the adjacent working pixel that received the unit energy token is decremented in real time. When the maximum allocable digital margin of any adjacent working pixel is determined to decrease to logic zero, the anti-saturation routing logic is triggered. The adjacent working pixel that generates logic zero is permanently removed from the token receiving priority sequence, and the remaining unit energy tokens in the token pool to be allocated continue to be iteratively allocated downwards according to the token receiving priority sequence after removal, until the token pool to be allocated is exhausted, thus completing the logical anti-overflow superposition of exposure energy points.

[0060] In this embodiment, the underlying controller of the processing platform uses a high-frequency discrete clock cycle as the reference pulse to drive the multi-beam array. When a duty cycle truncation operation is performed on the exposed pixels, it essentially deprives several clock beats that were originally in the luminous state of being removed. Calculating the count of the reduced discrete pulses and mapping it equivalently to a numerical exposure energy integral is the key to digitizing the physical action. To facilitate subsequent multi-threaded allocation, the token bucket concept commonly used in computer network traffic shaping is introduced, equally dividing the large and indivisible exposure energy integral and constructing a token pool to be allocated composed of multiple minimum control units. In one embodiment, the total number of discrete tokens is derived based on the time segments that are cut off. The specific mathematical formula for generating the token pool is expressed as follows: In the formula, Represents the total number of unit energy tokens in the token pool to be allocated, operator This indicates the floor function. This represents the calculated truncation time length for the exposed pixels. Represents the discrete clock cycle of the underlying hardware time. The parameter representing the constant optical power intensity at full load of the channel. Represents the minimum energy value contained in a single discrete unit of energy token.

[0061] Each light-emitting channel in the underlying layer of the multi-beam physical array is controlled by a dedicated digital-to-analog converter (DAC). Any digital conversion hardware has a digital saturation threshold that represents the maximum output power limit. If compensation energy is blindly injected into adjacent working pixels, causing the total value to exceed this hardware limit, not only will a deeper holographic anti-counterfeiting morphology not be produced, but severe thermal damage spots will also occur due to energy overflow. Therefore, obtaining the digital saturation threshold of the underlying hardware and calculating the remaining space in advance is crucial. During the calculation, the energy reference parameters already assigned to adjacent working pixels in the initial feature matrix are retrieved. Then, a logical subtraction operator is activated to compare the difference between the digital saturation threshold and the current energy reference, thereby obtaining an accurate measure of how much compensation energy the adjacent working pixel can still safely process. In one implementation, the logical difference calculation formula for performing the spatial calculation is described as follows: In the formula, This represents the calculated maximum allocatable digital margin to prevent overflow between adjacent working pixels. This represents the digital saturation threshold parameter that is fixed in the underlying digital-to-analog converter hardware of the multi-beam physical array. This represents the initial energy reference value set for the previously calibrated adjacent working pixels.

[0062] Within a vast, dense microgrid, multiple adjacent working pixels simultaneously surround the truncation point. Using equal allocation or random assignment strategies can easily lead to weak compensation at distant nodes and instantaneous overcrowding at nearby nodes. By combining the two-dimensional logical coordinate distance between adjacent working pixels and the exposure pixel experiencing energy reduction, a composite addressing weight is constructed, with the maximum allocable digital margin as the numerator and the two-dimensional logical coordinate distance as the denominator. This balances energy demand and spatial decay effects. Nodes with larger margins and closer distances receive higher weight scores. After calculating the scores of all candidate nodes, the addressing weights are sorted in descending order to generate a token receiving priority sequence that guides precise energy allocation. In one implementation, the mathematical formula for calculating the composite weight is: In the formula, This represents the constructed integrated addressing weight value. This represents the maximum distributable numerical margin calculated in the preceding steps, while the denominator fully represents the two-dimensional logical coordinate distance. and These represent the horizontal and vertical grid coordinates of adjacent working pixels in a two-dimensional spatial reference system. and These represent the horizontal and vertical grid coordinates of the exposed pixels that are truncated in the reference frame. The allocation task is performed according to this descending order, ensuring that nodes that urgently need energy and are spatially adjacent receive the first priority for replenishment, while also preventing disorderly preemption that could cause shape distortion through a logical queuing mechanism.

[0063] With a clear priority list, energy allocation is no longer a crude, overall accumulation, but rather a refined, step-by-step drip irrigation. The processor extracts tiny unit energy tokens from the token pool according to the order of token reception priority. Each extracted token is accumulated into the energy base of its highest-priority adjacent working pixel using a hardware logic adder. Simultaneously, to maintain the dynamic accuracy of the safety red line, a deduction and refresh operation must be performed on the maximum allocatable digital reserve of the receiving node after each successful accumulation. In one implementation, the mathematical iterative logic formula for performing a single unit energy token transfer and dynamic reserve deduction is as follows: And trigger synchronously In the formula, This represents the temporary energy baseline value generated after a single token accumulation for the adjacent working pixel. This represents the energy value of a single discrete unit energy token that was previously set and extracted. This represents the current maximum allocatable number balance updated after the decrement operation. This represents the numerical balance recorded before the self-reduction operation. The dual-parallel mechanism of distributing, calculating, and deducting energy in real time ensures that every microscopic energy flow is closely monitored, completely avoiding the disaster of microstructure edge thermal melting caused by blind mass injection.

[0064] During the continuous unit token dripping process, some nearby working pixels with high initial energy will inevitably quickly absorb compensation energy and reach their hardware capacity limit. When the comparison and determination module in the processor detects that the maximum allocable digital margin of any adjacent working pixel has been reduced to a logical absolute zero, it means that the node has completely lost the ability to absorb additional compensation. If tokens are continued to be issued to it, it will directly trigger a hardware error in the digital-to-analog converter or cause severe overexposure. At this time, the anti-saturation routing logic is immediately activated, and the node with the overflow risk of generating logical zero is permanently removed from the current token receiving priority sequence. Then, the remaining energy quota in the token pool to be allocated continues to be iteratively allocated according to the new sequence after removal and reorganization. In one implementation, the mathematical determination and update operation of triggering the anti-saturation routing logic is expressed as: when it detects Execution is triggered when established. In the formula, This represents the maximum allocatable numerical reserve that is updated in real-time during the preceding steps. A value of zero indicates that the reserve has been exhausted. This represents the set of newly generated token receiving priority sequences after removing saturated nodes. The operator represents the set of priority sequences of the old tokens before the removal operation. This represents the subtraction and removal operation in a set. This represents the identifier of the adjacent working pixel entity that triggered the saturation alarm and needs to be permanently removed.

[0065] In one embodiment, extracting the residual energy features of the edges on both sides of the overlapping area of ​​adjacent multi-beam scan zones in the thermal equilibrium distribution matrix, and constructing a semivariance function reflecting the thermal diffusion trend based on spatial autocorrelation evaluation logic includes the following steps: Delineate the boundary of the splicing overlap area between adjacent bands of multi-beam scanning in a two-dimensional spatial reference frame; Extract the first residual energy feature sequence located on the left edge of the splicing overlap region from the thermal equilibrium distribution matrix, and extract the second residual energy feature sequence located on the right edge of the splicing overlap region. Use the first residual energy feature sequence and the second residual energy feature sequence as residual energy features. Based on the spatial autocorrelation assessment logic, the energy variance of the first residual energy feature sequence and the second residual energy feature sequence at different spatial lag distances is calculated. Curve fitting was performed on the energy variance to extract the nugget effect constant, the partial sill value, and the range parameter. Substitute the nugget effect constant, the partial sill value, and the range parameter into the preset spherical function model, and use the spherical function model to construct a variogram skeleton representing the degree of correlation in energy space. By mapping the skeleton of the variogram to the coordinate matrix of the spliced ​​overlapping area, a semivariogram function reflecting the thermal diffusion trend is constructed.

[0066] In this embodiment, since the width of a single physical scan of the processing platform is limited by the inherent physical size of the multi-beam array, when dealing with large-sized anti-counterfeiting patterns, the system must drive the platform to perform reciprocating splicing of multiple strips. If the edges of adjacent strips are absolutely tangent, even slight mechanical vibrations can cause gaps that are missed; if they overlap directly, double exposure will occur, leading to thermal runaway. Therefore, it is particularly necessary to artificially delineate an intersection zone with a specific width in the two-dimensional spatial reference frame as a buffer and correction area. When implementing this step, it is necessary to combine the total number of channels of the multi-beam physical array, the optical scaling ratio, and the positioning accuracy tolerance of the platform guide rail to calculate the minimum number of logical pixel columns that can cover up mechanical splicing errors. Subsequently, based on the spatial arrangement order of the scanned strips, the start and end coordinate lines of the overlapping area are accurately located in the constructed two-dimensional coordinate network. In one embodiment, assuming that the number of grid columns covered by a single scan of the multi-beam array is a fixed constant, and the pixel overlap span set between adjacent strips is known, the formula for calculating the lateral coordinate interval of the boundary of the splicing overlap area can be expressed as: And the corresponding right boundary is calculated as follows: In the formula, This represents the horizontal logical coordinate index number of the left boundary of the splicing overlap area in a two-dimensional spatial reference frame. This represents the horizontal logical coordinate index number of the right boundary of the splicing overlap area. This represents the sequence number of the currently planned stitching and scanning strip. The total width parameter represents the number of grid columns covered by a single complete scan of a multi-beam physical array. This represents the span parameter of the number of overlapping pixel columns, which is preset to mask mechanical errors.

[0067] When multiple beams expose adjacent strips, the laser energy from the edges of previously scanned strips spreads to the unprocessed area via thermal conduction, forming an invisible residual heat field. If this heat is not taken into account, unpredictable overexposure of the morphology will occur during subsequent overlapping scans. Extracting the first residual energy feature sequence located at the left edge of the overlapping area and the second residual energy feature sequence located at the right edge of the overlapping area from the thermal balance distribution matrix generated in the preceding steps aims to capture the true thermal substrate conditions on both sides. The thermal balance distribution matrix not only records the ideal exposure command but also, due to the previous duty cycle truncation and energy redistribution, its edge data is highly nonlinear. In one implementation, the direct memory access mechanism of the microprocessor is used to read the data parameters of the corresponding column across the stride according to the aforementioned defined boundary coordinate index. The mathematical expression of the specific extraction action is as follows: the first residual energy feature sequence is defined as... The second residual energy characteristic sequence is defined as In the formula, This represents the extracted residual energy feature sequence values ​​distributed vertically along the left boundary. This represents the extracted second residual energy feature sequence value distributed along the right boundary. This is the updated comprehensive matrix model containing global thermal equilibrium data generated previously. This represents the column index number of the data node in the vertical direction. and These are the left and right lateral coordinates of the overlapping area.

[0068] The core idea of ​​spatial autocorrelation-based evaluation logic is that the closer two nodes are in space, the higher the similarity of their residual energy states; as the distance increases, this mutual influence gradually weakens or even disappears. Calculating the energy variance of the first and second residual energy feature sequences at different spatial lag distances can transform the implicit correlation of heat distribution into an intuitive mathematical indicator. In implementation, the algorithm not only examines the energy differences between adjacent pixels within the same edge sequence but also cross-compares the energy fluctuations of the left and right sequences at different longitudinal misalignment distances. In one implementation, all set lag distance intervals are traversed, and a variogram calculation model is used to obtain the semivariogram values ​​of discrete points. The corresponding calculation formula is expressed as: In the formula, This represents the numerical value of the energy variance assessment calculated at a specific spatial lag distance. This represents the spatial lag distance variable between set pixel nodes. This represents the total number of pixel data pairs that can be matched and participate in the calculation when the hysteresis distance is a specific value. and These represent the values ​​of the first and second residual energy feature sequences being compared at their corresponding index positions.

[0069] The previously calculated energy variance only represents empirical values ​​at specific sampling distances, and is subject to unavoidable computational fluctuations and local noise interference. Curve fitting of the energy variance aims to use a smooth mathematical curve to penetrate these discrete points and reconstruct the most fundamental variation trajectory of thermal energy distribution. Extracting the nugget effect constant quantifies the unpredictable random energy fluctuations at the microscopic level caused by internal material impurities or extremely small power fluctuations in the laser; extracting the partial sill value characterizes the upper limit of the spatial structural variation amplitude caused by the thermal conduction physical mechanism itself; and extracting the range parameter directly defines the maximum spatial radiation radius where thermal energy can have a substantial impact. In one implementation, a weighted least squares fitting algorithm is used to approximate and optimize the discrete points, constructing an objective equation to minimize the fitting error and solve for the three key parameters. The objective formula for fitting optimization is as follows: In the formula, The sum of squared residuals represents the evaluation function value during curve fitting; we need to find its minimum value. This represents the distance confidence weight parameter assigned to the quantity based on the data. This represents the discrete energy variance value calculated in the preceding steps. This represents a theoretical model of the fitted function containing the parameters to be determined. This represents the extracted nugget effect constant, characterizing microscopic random fluctuations. This represents the partial sill value extracted to characterize the upper limit of structural variance. These represent the range parameters extracted to characterize the maximum radiation range of thermal energy. By accurately separating these three core constants, the complex and chaotic thermal energy diffusion phenomenon has been successfully deconstructed into a structured data dictionary with clear physical guidance, allowing subsequent function modeling to break free from the blindness of empiricism.

[0070] The spherical function model is introduced into this scheme because it exhibits excellent linear growth characteristics near the origin, and then smoothly transitions to a horizontal sill state after exceeding a certain threshold. This mathematical performance aligns with the microscopic mechanism of heat transfer attenuation in high-energy continuous lasers within polymer photosensitive materials with certain heat dissipation boundary conditions. Substituting the nugget effect constant, the partial sill value, and the range parameter into this spherical function model allows for the construction of a complete variogram skeleton describing the attenuation of energy correlation between any two points in space with distance. In one implementation, a piecewise algebraic equation assembly operation is performed based on the pre-defined parameters. When the hysteresis distance is within the range, the core formula for constructing the model skeleton can be expressed as: In the formula, This represents the calculated values ​​of the completed variogram skeleton used to characterize the degree of correlation in energy space. These skeleton values ​​are only calculated based on the variable lag distance. Less than or equal to range parameter The above formula is used to solve the problem. When the lag distance exceeds the range of this range parameter, the correlation degree no longer decreases with distance, and the skeleton value remains constant. With constant sum.

[0071] The variogram skeleton generated in the preliminary step is essentially a one-dimensional theoretical relation with only a scalar lag distance as the single independent variable. However, the actual overlapping region of a multi-beam array is a vast two-dimensional pixel array network, where the relative positions between any two pixel nodes encompass physical spans in both the horizontal and vertical directions. Mapping the variogram skeleton to the coordinate matrix of the overlapping region involves converting the absolute coordinate differences of all nodes into actual physical Euclidean distances that meet the input requirements of the one-dimensional skeleton, thereby constructing a semi-variance function that reflects the thermal diffusion trend. This semi-variance function not only possesses the smooth attenuation characteristics of a spherical model but also has two-dimensional analytical capabilities for specific mesh topologies. In one implementation, the Euclidean distance is calculated by traversing every discrete coordinate point within the overlapping region before the mapping is performed. The coordinate mapping derivation formula is as follows: In the formula, The operator represents the output parameters of the final generated semivariogram function with two-dimensional spatial addressing capability. This represents the invocation of the pre-constructed mutation function skeleton for parameter passing and solution operations. and Represents the horizontal and vertical index numbers of the reference starting pixel node in the two-dimensional spatial reference frame. and This represents the horizontal and vertical index numbers of the target evaluation pixel node in the spatial network. Indicates the lateral physical spacing of the light spot. This indicates the longitudinal physical spacing of the light spot.

[0072] In one implementation, a spatial variation convolution kernel is generated within a preset sliding window based on a semivariance function, and the exposure data sequence within the splicing overlap area is smoothed using the spatial variation convolution kernel to perform optimal unbiased estimation, generating a baseline exposure control sequence that eliminates energy aggregation variation. This includes the following steps: Initialize a sliding window with a preset size within the overlapping area of ​​the stitching, and advance the sliding window pixel by pixel along the stitching path; At the current position of the sliding window, input each discrete coordinate point within the sliding window into the semivariance function, and solve to obtain the spatial covariance matrix; Invert the spatial covariance matrix and calculate the optimal weight coefficients in conjunction with unbiased constraints; Arrange the optimal weight coefficients into a two-dimensional matrix to generate the spatial mutated convolution kernel corresponding to the current sliding window position; The spatial variation convolution kernel is used to perform discrete convolution multiplication and addition operations on the exposure data sequence within the sliding window to achieve the smoothing operation of the optimal unbiased estimation and obtain the smoothing operation result. Collect and reconstruct the smoothing results of each sliding window position, and output a baseline exposure control sequence that eliminates energy aggregation variations.

[0073] In this embodiment, performing a global covariance matrix inversion operation on the entire wide overlapping area would cause microprocessor overload and memory overflow due to the huge matrix dimension, severely slowing down the real-time direct-write processing cycle. A sliding window mechanism is introduced to degrade the macroscopic global smoothing into a series of microscopic local serial operations, balancing the accuracy of spatial correlation assessment with hardware execution performance. When implementing this operation, a discrete rectangular selection area with fixed length and width is first defined at the starting endpoint of the overlapping area. The size of the selection area must just cover the maximum influence radius where heat conduction can generate effective interference. Then, a fixed movement step size is set, causing the discrete rectangular selection area to be translated and scanned pixel-by-pixel along a preset multi-beam array mechanical splicing path in a two-dimensional spatial reference frame. In one embodiment, the spatial dimensions of the sliding window and the formula for the center anchor point are established. The coordinates of the window center node are expressed as: And the window coverage boundary is: , In the formula, This represents the entity representing the center anchor point of the sliding window at its current position. The horizontal grid index representing the center anchor point. Represents a vertical grid index. This represents the horizontal radius of the sliding window in pixels. This represents the number of pixels covering the vertical radius of the sliding window. and Represents the coordinates of any internal node within the window's coverage area.

[0074] The semivariance function constructed in the previous steps describes the divergence of energy differences with increasing distance. However, in the weight allocation system of multi-beam direct-write path planning, a more direct indicator is needed to characterize the positive correlation of thermal energy accumulation between spatial nodes. The spatial covariance matrix perfectly meets this requirement. During the simulation, at the current position of the sliding window, the relative position information of all discrete coordinate points within the window is extracted and substituted into the pre-mapped semivariance function to calculate the variance values ​​between each pair of nodes. Subsequently, the difference inversion operation is performed using the total structural variation sill value and the obtained semivariance values ​​to convert the divergence attribute into a correlation attribute. In one implementation, the mathematical calculation logic formula for generating local covariance elements based on the semivariance results can be expressed as: In the formula, This represents the value of the covariance element between two specific nodes in the spatial covariance matrix generated by the solution. This represents the nugget effect constant extracted in the preceding sequence. The two values ​​represent the partial sill values ​​extracted in the preceding sequence, and their sum represents the theoretical upper limit of the variogram at infinity. This represents the variance evaluation result parameter output by calling the semivariance function when the input coordinates are called.

[0075] In the multi-beam laser exposure compensation process, it is not only required to assign different smoothing weights according to the proximity of heat conduction, but also to ensure that the total energy reconstructed after weight allocation cannot increase or decrease out of thin air, otherwise it will destroy the macroscopic development depth of the holographic anti-counterfeiting morphology. This requirement conforms to the unbiased constraint condition in the optimal unbiased estimation, that is, the sum of the weight coefficients assigned to all reference nodes within the local window must be strictly equal to one. In the implementation calculation stage, the Lagrange multiplier method is introduced to forcibly bind the unbiased constraint condition to the objective equation for finding the minimum value of the estimated variance. Subsequently, the algebraic inversion operation is performed on the previously generated spatial covariance matrix, and it is multiplied by the vector array containing Lagrange multipliers. In one implementation, the core formula of the composite matrix equation system for solving the optimal weight coefficients is as follows: In the formula, This represents the output column vector containing all optimal weight coefficients and Lagrange multipliers. This represents the array of inverse matrices obtained by performing an inversion operation on the spatial covariance matrix after extending the unbiased boundary conditions. It represents the distance vector consisting of the covariance elements and constraint constants between the central node to be evaluated and each reference node within the window.

[0076] The previous step, by solving a system of higher-order matrix equations, only yielded an optimal weight coefficient array in the form of a one-dimensional column vector. This vector lacks the intuitive directional sense of the spatial grid. The underlying exposure data sequence of the multi-beam array is arranged in a two-dimensional matrix, and performing filtering and smoothing requires the use of a mask template of the same dimension. Therefore, the calculated one-dimensional weight coefficients must be rearranged and combined. During the transformation, the coefficient values ​​in the one-dimensional column vector are backfilled into the corresponding two-dimensional grid positions, strictly following the traversal order when the coordinate points inside the sliding window were substituted into the semivariance function. In one implementation, after removing the Lagrange multipliers at the end of the column vector, the formula for performing the spatial mapping transformation is expressed as: In the formula, The numerical values ​​of the elements inside the spatially mutated convolution kernel that represent the arrangement and possess physical orientation attributes. This indicates the operation of extracting specific weighted elements from a one-dimensional result column vector based on the index number within the square brackets. This represents the horizontal relative local index of the transformation target within the convolution kernel, with values ​​ranging from zero to the total window width minus one. Represents a vertical relative local index. This represents the number of pixels representing the vertical coverage radius of the sliding window as defined above.

[0077] Conventional image smoothing algorithms typically employ fixed-weight operators, which can easily lead to blurring and distortion of high-frequency anti-spoofing features. However, the spatial mutation convolution kernel deployed here uses weights dynamically calculated based on the true thermal diffusion semivariogram function, achieving a perfect balance between suppressing edge thermal abrupt changes and preserving skeleton sharpness. The computation is straightforward: the generated spatial mutation convolution kernel is used to perform point-to-point discrete convolution multiplication and addition operations with the exposure data sequence within the current coverage area of ​​the sliding window. The mask center is aligned with the window anchor point, and the surrounding weights are multiplied by the original exposure commands at their corresponding positions, then the sum is calculated. In one implementation, the mathematical formula for performing the optimal unbiased estimation smoothing operation to obtain the new value of the center node can be expressed as: In the formula, This represents the new exposure parameter result corresponding to the center node position of the sliding window after smoothing. Represents spatially mutated convolution kernel elements. This represents the initial feature exposure parameters extracted from the original input data sequence based on specific global absolute coordinate indices. and This represents the horizontal and vertical coverage radius of the window.

[0078] As the sliding window continuously advances pixel by pixel along the preset stitching path, the system repeatedly performs the entire set of actions—covariance matrix calculation, parameter mapping, and convolution multiplication and addition—at the microscopic level. Each location point generates an optimized smoothing result. These results are scattered across various temporary addresses in the memory buffer, lacking a macroscopic array structure. A collection and reassembly operation must be performed to reassemble the scattered data according to the original absolute spatial two-dimensional coordinate rules. During implementation, a blank register matrix is ​​established that is completely equivalent to the physical size of the stitching overlap area. Whenever the sliding window completes a smoothing calculation for the center node, the result is immediately written to the corresponding coordinate node in the register matrix. In one implementation, after the sliding window has traversed the set overlap area boundary, the register matrix data is extracted and the original thermal equilibrium state is overwritten. The assignment logic for the reassembly loading is expressed as follows: In the formula, The overall matrix representing the baseline exposure control sequence for eliminating energy aggregation variations in the final unified output, and the operators. This means that, according to the spatial mapping rules, all the independent smoothed result lattices generated on the right are batch-assigned and reconstructed into the contiguous storage space of the matrix on the left. The horizontal coordinate range covered by the instruction assignment is strictly anchored within the boundary of the splicing overlap area. This indicates that the coverage action extends through all available columns in the vertical direction.

[0079] In one embodiment, a compensation model is established for the laser control power, mechanical movement speed, and target morphology depth of the associated processing platform. The compensation model is pre-solved for different mechanical speeds of the processing platform. The reference exposure control sequence is then fused with the compensation states obtained from the equation solution to generate multiple corresponding compensation state control sequence snapshots. This includes the following steps: A state equation is constructed as a compensation model, with the laser control power of the processing platform as the dependent variable and the mechanical motion speed of the processing platform and the depth of the target shape as the independent variables. Extract the historical speed fluctuation extremes of the processing platform and set the speed discretization step size; A set of velocity assumptions containing a finite number of mechanical velocities is constructed based on historical velocity fluctuation extremes and velocity discretization step sizes. Substitute each mechanical velocity in the velocity assumption set into the compensation model in turn to calculate and solve, and obtain the preset laser power compensation vector corresponding to each mechanical velocity; The reference exposure control sequence is fused with the preset laser power compensation vector to generate multiple control sequence snapshots corresponding to the compensation state.

[0080] In this embodiment, during the direct writing process of holographic anti-counterfeiting images, the final depth of the micro-grooves formed on the surface of the photosensitive material is essentially determined by the total energy of photons received in the local area. When the laser output power remains constant, a slight decrease in the mechanical movement speed of the processing platform will cause the light spot to remain at the same point for a longer time, resulting in overexposure and deepening of the grooves; conversely, an increase in speed will lead to insufficient exposure and shallower grooves. Constructing the state equation is to transform this nonlinear interference caused by the unavoidable hysteresis and friction of mechanical components into a deterministic mathematical model that can be dynamically offset by adjusting the laser power. Setting the laser control power as the dependent variable and the mechanical movement speed and target morphology depth as independent variables can directly guide the precise output of the underlying digital-to-analog converter under different operating conditions. In one embodiment, the above compensation model is constructed by combining the photolithography and development photosensitivity characteristics of polymer materials. The core calculation formula of the state equation is expressed as: In the formula, The parameters representing the dependent variable of the laser control power of the processing platform obtained from the solution are: The numerical value of the input target topography depth independent variable. This represents the value of the mechanical motion speed of the machining platform at the current moment. This represents the inherent photolithography and development energy conversion constant of the photosensitive material.

[0081] Any ultra-precision mechanical guideway, in its long-term reciprocating motion, will experience periodic or random speed jitter caused by factors such as lubrication, temperature, and servo motor feedback delay. If the limits of this jitter are not understood, pre-calculated compensation data may be incomplete or generate significant useless redundancy. By extracting historical speed fluctuation extremes from the machining platform's historical operation, the worst-case operating condition boundaries of mechanical fluctuations can be precisely defined, ensuring that any future transient anomalies do not escape database control. Furthermore, since the continuous physical quantity of speed has an infinite number of possibilities, microprocessors cannot exhaustively calculate them; therefore, a speed discretization step size must be set. The step size directly determines the balance between the smoothness of the final holographic shape and memory consumption. In one implementation, extreme values ​​are extracted from the log files of the servo motor encoder over the past hundreds of working cycles, and the step size is determined by combining this with the array clock frequency. The relevant parameter calculation and extraction formulas are as follows: In the formula, This represents the total amplitude parameter of the extracted mechanical velocity limit fluctuation. This represents the historical extreme value of the highest mechanical motion speed fluctuation of the processing platform recorded in the log. This represents the historical lowest extreme value of mechanical motion speed fluctuation. The speed discretization step size is also independently set. The setting is based on ensuring that the morphological depth error caused by adjacent step sizes does not exceed one-tenth of the holographic diffraction optical wavelength.

[0082] Having the maximum speed, minimum speed, and discrete step size, we possess the necessary and sufficient conditions to enumerate all typical operating conditions. Constructing a speed hypothesis set containing a finite number of mechanical speeds based on historical speed fluctuation extremes and speed discretization step sizes removes the computationally intensive floating-point calculation work from the real-time process of direct-write processing, moving it to the preparation stage and greatly reducing the concurrent burden on the microprocessor during high-speed motion. Starting from the minimum extreme value, the set discrete step size is successively added until the calculated value reaches or exceeds the boundary of the maximum extreme value. The discrete values ​​from all paths together form a monotonically increasing hypothesis array. In one implementation, a one-dimensional array pointer in computer memory is used to automatically fill the set. The recursive mathematical formula for constructing the speed hypothesis set can be expressed as: In the formula, The first value generated by recursive calculation in the representative velocity hypothesis set An assumed numerical value for discrete mechanical velocity. This is the starting point of the historical lowest mechanical velocity extreme value obtained above. To set the complete velocity discretization step size constant for the preceding steps, The non-negative integer index of the recursive sequence, with values ​​increasing from zero. ,in This represents the total amplitude of the speed limit fluctuation.

[0083] Substituting each mechanical velocity from the set of velocity assumptions into the compensation model for calculation is equivalent to having the central processing unit simulate countless exposure processes under different jitter conditions in a very short time. Due to the large number of array channels and varying target depths, the system must calculate the required power for each luminous pixel individually for each specific assumed velocity. Therefore, what is obtained is not a single numerical value, but a preset laser power compensation vector containing multi-channel data. In one implementation, the target topography parameters within the reference grid are traversed, and a loop of calculation instructions is executed to substitute the parameters into the equations. The core derivation formula for obtaining the compensation vector at a specific velocity is: In the formula, Represents the first in the set of velocity assumptions The two-dimensional preset laser power compensation vector elements obtained by solving the mechanical velocity calculation. The numerical value of the preceding target topography depth independent variable represents the coordinate node in the two-dimensional spatial reference frame of the multi-beam physical array. Represents the current proposal to be replaced. An assumed value for mechanical speed, is the photolithography development energy conversion constant.

[0084] The baseline exposure control sequence generated in the preceding steps has eliminated the risk of thermal splicing abrupt changes between adjacent stripes through mutated function convolution, while the preset laser power compensation vector overcomes the problem of underexposure and overexposure caused by mechanical axial fluctuations. Fusion of the baseline exposure control sequence and the preset laser power compensation vector essentially involves the final mathematical superposition of static spatial thermal balance optimization and dynamic temporal velocity following optimization. The fusion generates multiple snapshots of control sequences corresponding to the compensation states. Each snapshot is pre-loaded into a high-speed static random access memory (SRAM) of a field-programmable gate array (FPGA). In one implementation, the safety parameters of each dimension are multiplied and assembled bitwise to solidify into the final underlying data format.

[0085] The present invention also discloses a GLV multi-beam direct-write path planning system for holographic anti-counterfeiting, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the GLV multi-beam direct-write path planning method for holographic anti-counterfeiting as described in any of the above.

[0086] The processor can be a central processing unit (CPU). Of course, depending on the actual use, it can also be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), off-the-shelf programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or any conventional processor, etc., and this application does not limit it.

[0087] The memory can be an internal storage unit of a computer device, such as a hard disk or RAM, or an external storage device, such as a plug-in hard disk, smart memory card (SMC), secure digital card (SD), or flash memory card (FC) provided on the computer device. Furthermore, the memory can be a combination of internal storage units and external storage devices of a computer device. The memory is used to store computer programs and other programs and data required by the computer device. The memory can also be used to temporarily store data that has been output or will be output. This application does not limit this.

[0088] The present invention also discloses a computer-readable storage medium storing instructions that, when executed by a processor, cause the processor to perform the GLV multi-beam direct-write path planning method for holographic anti-counterfeiting described in any of the above embodiments.

[0089] The computer program can be stored in a machine-readable medium. The computer program includes computer program code, which can be in the form of source code, object code, executable file, or certain middleware. The machine-readable medium includes any entity or device capable of carrying computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the machine-readable medium includes, but is not limited to, the above-mentioned components.

[0090] The GLV multi-beam direct-write path planning method for holographic anti-counterfeiting described in the above embodiments is stored in the computer-readable storage medium and loaded and executed on the processor to facilitate the storage and application of the above method.

[0091] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of protection of this application is limited to these examples; within the framework of this application, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of different aspects of one or more embodiments of this application as described above, which are not provided in detail for the sake of brevity.

[0092] One or more embodiments in this application are intended to cover all such substitutions, modifications, and variations that fall within the broad scope of this application. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of one or more embodiments in this application should be included within the protection scope of this application.

Claims

1. A GLV multi-beam direct-write path planning method for holographic anti-counterfeiting, characterized in that, Includes the following steps: A holographic anti-counterfeiting model is obtained, and the continuous depth information of the model surface in the holographic anti-counterfeiting model is analyzed by a non-uniform sampling algorithm. The depth information is then discretized into an initial feature matrix that adapts to the characteristics of the multi-beam physical array of the processing platform in a preset two-dimensional spatial reference system. By evaluating the expected thermal diffusion accumulation of each exposed pixel in the initial feature matrix region by region, a physical threshold model for multi-beam adjacent thermal superposition is established. When the expected thermal diffusion accumulation in the densely exposed region of the initial feature matrix exceeds the physical threshold in the physical threshold model, the duty cycle of the exposed pixels representing non-critical morphology in the densely exposed region is truncated, and the energy reference of the adjacent working pixels is updated based on the principle of energy conservation to generate a thermal balance distribution matrix. The residual energy characteristics of the two sides of the overlapping area of ​​the multi-beam scanning adjacent bands in the thermal equilibrium distribution matrix are extracted, and a semivariance function reflecting the thermal diffusion trend is constructed based on the spatial autocorrelation evaluation logic. Based on the semivariance function, a spatial variation convolution kernel is generated within a preset sliding window. The spatial variation convolution kernel is then used to perform a smoothing operation on the exposure data sequence in the splicing overlap area with the optimal unbiased estimation, thereby generating a benchmark exposure control sequence that eliminates energy aggregation variation. A compensation model for the laser control power, mechanical motion speed, and target morphology depth of the associated processing platform is established. The equations of the compensation model are solved in advance for different mechanical speeds of the processing platform. The reference exposure control sequence is fused with the compensation state obtained from the equation solution to generate multiple control sequence snapshots with corresponding compensation states. The instantaneous mechanical speed of the processing platform is acquired in real time, a control sequence snapshot corresponding to the instantaneous mechanical speed is matched, and the control sequence snapshot is output to drive the multi-beam array of the processing platform to complete the direct writing of the holographic anti-counterfeiting morphology.

2. The GLV multi-beam direct-write path planning method for holographic anti-counterfeiting according to claim 1, characterized in that, The process of acquiring the holographic anti-counterfeiting model, analyzing the continuous depth information of the model surface through a non-uniform sampling algorithm, and discretizing the depth information into an initial feature matrix adapted to the multi-beam physical array characteristics of the processing platform in a preset two-dimensional spatial reference frame includes the following steps: Obtain the holographic anti-counterfeiting model, extract the surface mesh data from the holographic anti-counterfeiting model, and calculate the curvature gradient vector of the surface mesh data in three-dimensional space; The preset two-dimensional spatial reference frame is divided into an initial reference grid that matches the characteristics of the multi-beam physical array of the processing platform; The curvature gradient vector is mapped to each grid node of the initial reference grid, and the sampling density of each grid node is adjusted by a non-uniform sampling algorithm based on the mapped curvature gradient vector. In grid node regions where the sampling density is greater than or equal to a preset density threshold, high-frequency interpolation is used to extract the depth information of the holographic anti-counterfeiting model; in grid node regions where the sampling density is less than the density threshold, low-frequency interpolation is used to extract the depth information of the holographic anti-counterfeiting model. The extracted depth information is quantized and encoded, and the quantized and encoded depth information is discretized into an initial feature matrix adapted to the characteristics of a multi-beam physical array.

3. The GLV multi-beam direct-write path planning method for holographic anti-counterfeiting according to claim 2, characterized in that, The process of mapping the curvature gradient vector onto each grid node of the initial reference grid, and adjusting the sampling density of each grid node using a non-uniform sampling algorithm based on the mapped curvature gradient vector, includes the following steps: Set low-frequency change thresholds and high-frequency abrupt change thresholds for the curvature gradient vector; Traverse each grid node in the initial baseline grid and extract the magnitude of the curvature gradient vector corresponding to each grid node; Mark the grid nodes containing curvature gradient vectors whose magnitudes are below the low-frequency change threshold as smooth feature nodes; The grid nodes containing curvature gradient vectors with magnitudes higher than the high-frequency mutation threshold are marked as steep feature nodes. The grid nodes containing curvature gradient vectors whose modulus values ​​are between the low-frequency change threshold and the high-frequency abrupt change threshold are marked as transition feature nodes. By using a non-uniform sampling algorithm, steep feature nodes are assigned the highest sampling density weight, smooth feature nodes are assigned the lowest sampling density weight, and transitional feature nodes are assigned the sampling density weight of linear interpolation, thus completing the sampling density adjustment of each grid node.

4. The GLV multi-beam direct-write path planning method for holographic anti-counterfeiting according to claim 3, characterized in that, The process of extracting depth information of the holographic anti-counterfeiting model using high-frequency interpolation in grid node regions with sampling density greater than or equal to a preset density threshold, and using low-frequency interpolation in grid node regions with sampling density less than a density threshold, includes the following steps: A high-frequency polynomial fitting surface is constructed in the grid node region where steep feature nodes are located, based on the weight of the highest sampling density. High-frequency polynomial fitting surfaces are used to capture phase abrupt changes in holographic anti-counterfeiting models and extract the corresponding high-frequency depth information. A low-order smooth surface is constructed in the grid node region where the smooth feature node is located, based on the lowest sampling density weight; Redundant grid data in the holographic anti-counterfeiting model is filtered out using a low-order smooth surface, and the corresponding low-frequency depth information is extracted. High-frequency depth information and low-frequency depth information are smoothly fused using spline functions in the grid node regions where transition feature nodes are located to ensure the global continuity of extracted depth information.

5. The GLV multi-beam direct-write path planning method for holographic anti-counterfeiting according to claim 1, characterized in that, When the expected thermal diffusion accumulation in the densely exposed region of the initial feature matrix exceeds the physical threshold in the physical threshold model, the duty cycle of the exposed pixels representing non-critical morphology within the densely exposed region is truncated, and the initial feature matrix is ​​updated by compensating the energy reference of adjacent working pixels upward based on the principle of energy conservation, and a thermal equilibrium distribution matrix is ​​generated. This includes the following steps: Locate densely exposed regions in the initial feature matrix where the expected cumulative thermal diffusion exceeds a physical threshold. The edge detection operator is used to perform convolution operation on the pixels in the densely exposed area to obtain the convolution operation result; Based on the convolution operation results, the working pixels representing key contour shapes and the exposure pixels representing non-key shapes are separated; The duty cycle of the control time window for the exposure pixels is truncated to generate a control correction sequence containing a forced sleep command. The exposure energy integral of the duty cycle cutoff loss is calculated based on the principle of energy conservation, and the exposure energy integral is superimposed on the energy reference of the adjacent working pixels according to the inverse weight of spatial distance. The forced sleep state after executing the control correction sequence and the superimposed energy benchmark are attached to each pixel as state markers, the initial feature matrix is ​​updated and a thermal equilibrium distribution matrix is ​​generated.

6. The GLV multi-beam direct-write path planning method for holographic anti-counterfeiting according to claim 1, characterized in that, The steps for extracting residual energy features from the edges of the overlapping regions of adjacent multi-beam scan zones in the thermal equilibrium distribution matrix and constructing a semivariance function reflecting the thermal diffusion trend based on spatial autocorrelation evaluation logic include the following: Delineate the boundary of the splicing overlap area between adjacent bands of multi-beam scanning in a two-dimensional spatial reference frame; Extract the first residual energy feature sequence located on the left edge of the splicing overlap region from the thermal equilibrium distribution matrix, and extract the second residual energy feature sequence located on the right edge of the splicing overlap region. Use the first residual energy feature sequence and the second residual energy feature sequence as residual energy features. Based on the spatial autocorrelation assessment logic, the energy variance of the first residual energy feature sequence and the second residual energy feature sequence at different spatial lag distances is calculated. Curve fitting was performed on the energy variance to extract the nugget effect constant, the partial sill value, and the range parameter. Substitute the nugget effect constant, the partial sill value, and the range parameter into the preset spherical function model, and use the spherical function model to construct a variogram skeleton representing the degree of correlation in energy space. By mapping the skeleton of the variogram to the coordinate matrix of the spliced ​​overlapping area, a semivariogram function reflecting the thermal diffusion trend is constructed.

7. The GLV multi-beam direct-write path planning method for holographic anti-counterfeiting according to claim 6, characterized in that, The process of generating a spatial variation convolution kernel within a preset sliding window based on the semivariogram function, and then using the spatial variation convolution kernel to perform a smoothing operation on the exposure data sequence within the splicing overlap area with the optimal unbiased estimation to generate a benchmark exposure control sequence that eliminates energy aggregation variation, includes the following steps: Initialize a sliding window with a preset size within the overlapping area of ​​the stitching, and advance the sliding window pixel by pixel along the stitching path; At the current position of the sliding window, input each discrete coordinate point within the sliding window into the semivariance function, and solve to obtain the spatial covariance matrix; Invert the spatial covariance matrix and calculate the optimal weight coefficients in conjunction with unbiased constraints; Arrange the optimal weight coefficients into a two-dimensional matrix to generate the spatial mutated convolution kernel corresponding to the current sliding window position; The spatial variation convolution kernel is used to perform discrete convolution multiplication and addition operations on the exposure data sequence within the sliding window to achieve the smoothing operation of the optimal unbiased estimation and obtain the smoothing operation result. Collect and reconstruct the smoothing results of each sliding window position, and output a baseline exposure control sequence that eliminates energy aggregation variations.

8. The GLV multi-beam direct-write path planning method for holographic anti-counterfeiting according to claim 1, characterized in that, The process of establishing a compensation model for the laser control power, mechanical movement speed, and target morphology depth of the associated processing platform, and solving the equations of the compensation model in advance for different mechanical speeds of the processing platform, and fusing the reference exposure control sequence with the compensation states obtained from the equation solution to generate multiple control sequence snapshots corresponding to the compensation states, includes the following steps: A state equation is constructed as a compensation model, with the laser control power of the processing platform as the dependent variable and the mechanical motion speed of the processing platform and the depth of the target shape as the independent variables. Extract the historical speed fluctuation extremes of the processing platform and set the speed discretization step size; A set of velocity assumptions containing a finite number of mechanical velocities is constructed based on historical velocity fluctuation extremes and velocity discretization step sizes. Substitute each mechanical velocity in the velocity assumption set into the compensation model in turn to calculate and solve, and obtain the preset laser power compensation vector corresponding to each mechanical velocity; The reference exposure control sequence is fused with the preset laser power compensation vector to generate multiple control sequence snapshots corresponding to the compensation state.

9. A GLV multi-beam direct-write path planning system for holographic anti-counterfeiting, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the GLV multi-beam direct-write path planning method for holographic anti-counterfeiting as described in any one of claims 1 to 8.

10. A computer-readable storage medium storing instructions thereon, characterized in that, When executed by the processor, the instruction causes the processor to be configured to perform the GLV multi-beam direct-write path planning method for holographic anti-counterfeiting according to any one of claims 1 to 8.

Images