A method and system for three-dimensional gray-scale direct writing manufacturing by femtosecond laser two-photon absorption

Abstract

The application relates to the field of femtosecond laser micro-nano manufacturing technology and discloses a three-dimensional gray-scale direct writing manufacturing method and system of femtosecond laser two-photon absorption. The method establishes a voxelized exposure dose field through nonlinear dose-attribute response modeling and records the dose sensitivity of each voxel; a physical information neural network is used to predict the laser propagation wavefront distortion of each voxel, and an output full-structure voxel wavefront distortion prediction field is obtained; a cumulative distortion minimization dynamic programming algorithm is used to optimize and rearrange the voxel writing sequence, so that an optimal writing sequence is obtained; laser scanning is performed according to the optimal writing sequence; and online state Bayesian estimation and a spatial light modulator wavefront pre-compensation closed-loop mechanism are used to correct the writing deviation in real time. The application can effectively suppress the accumulation of path wavefront distortion during deep voxel writing, and realize accurate coincidence of three-dimensional refractive index distribution and design targets.

Description

Technical Field

[0001] This invention relates to the field of femtosecond laser micro / nano manufacturing technology, and more specifically, to a three-dimensional grayscale direct-write manufacturing method and system for femtosecond laser two-photon absorption. Background Technology

[0002] Femtosecond laser two-photon polymerization (TPP) technology is one of the main methods for manufacturing three-dimensional micro / nano structures with submicron resolution, and it has significant application value in the field of gradient refractive index micro-optical components. By controlling the laser exposure dose, a continuously gradient three-dimensional refractive index distribution can be achieved within the photosensitive resin, thereby manufacturing functional micro-optical components such as gradient refractive index lenses and waveguide couplers.

[0003] However, in the conventional layer-by-layer writing process from shallow to deep, the laser beam must traverse the already written non-uniform refractive index layer before reaching the deep target voxel. The refractive index deviation of the written voxel forms a refractive index perturbation column along the laser propagation path, causing transversely non-uniform phase perturbation on the laser beam wavefront, resulting in focal wavefront distortion. This distortion accumulates with increasing writing depth, causing the actual exposure dose of the deep voxel to systematically deviate from the design value, and the three-dimensional refractive index accuracy to continuously degrade with increasing depth.

[0004] In existing technologies, conventional adaptive optics methods cannot directly solve the above problems: during TPP writing, the laser optical path propagates in one direction, making it impossible to insert a wavefront sensor to measure path distortion in real time; furthermore, the path distortion experienced by each voxel in the three-dimensional gradient refractive index structure depends on the three-dimensional refractive index distribution of the currently written voxel above its laser path, which is a structure-specific quantity that dynamically changes with the writing process, and cannot be replaced by voxel-by-voxel prediction with a single global measurement. Therefore, existing technologies suffer from the technical problems of decreased deep voxel writing accuracy with increasing depth and insufficient accuracy of the three-dimensional refractive index distribution. Summary of the Invention

[0005] This invention provides a three-dimensional grayscale direct writing manufacturing method and system based on femtosecond laser two-photon absorption, which solves the technical problems of continuous accumulation of path wavefront distortion and degradation of three-dimensional refractive index distribution accuracy with increasing depth during deep voxel writing in related technologies.

[0006] This invention provides a method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption, comprising the following steps: S1. Obtain the target three-dimensional refractive index distribution design map, and use the nonlinear dose-attribute response modeling method to establish the voxelized exposure dose field to obtain a three-dimensional initial exposure dose distribution map covering the entire structural space. S2 uses the three-dimensional initial exposure dose distribution map to deduce the refractive index perturbation field, and uses a physical information neural network to predict the laser propagation wavefront distortion of each voxel, outputting a voxel wavefront distortion prediction field covering the entire structure. S3. Based on the predicted field of wavefront distortion of the whole structure voxels and the dose sensitivity of each voxel, the cumulative distortion minimization dynamic programming algorithm is used to optimize and rearrange the voxel writing order to obtain the optimal writing sequence that effectively suppresses the propagation of deep errors. S4. Perform laser scanning according to the optimal writing sequence. Use online state Bayesian estimation and spatial light modulator wavefront pre-compensation closed-loop mechanism to obtain a three-dimensional grayscale structure that accurately matches the designed refractive index distribution.

[0007] Preferably, in S1, the nonlinear dose-attribute response modeling method includes two cascaded nonlinear mappings: the first mapping is a mapping from refractive index deviation to polymerization conversion rate, a comparison dataset of refractive index deviation and polymerization conversion rate is established through pre-manufacturing calibration experiments, and a monotonic mapping function is established by piecewise polynomial fitting; The second segment maps the polymerization conversion rate to the exposure dose. An S-curve is obtained by fitting the measured dataset through calibration experiments. While completing the dose mapping, the dose-refractive index sensitivity of each voxel is calculated. The sensitivity is defined as the product of the local slope of the S-curve at the target dose of the corresponding voxel and the slope of the refractive index-conversion rate mapping. The sensitivity value of each voxel and the target dose value are stored together in the three-dimensional initial exposure dose distribution map.

[0008] Preferably, in step S2, the step of extrapolating the refractive index perturbation field from the three-dimensional initial exposure dose distribution map includes: substituting the three-dimensional initial exposure dose distribution map into the dose-conversion-refractive index mapping chain calibrated in step S1, and inversely extrapolating to obtain the expected refractive index values ​​of each voxel in the whole structure after being written, and constructing a three-dimensional expected refractive index distribution map. The difference between the three-dimensional expected refractive index distribution map and the original resin refractive index is used as the three-dimensional refractive index perturbation field. The three-dimensional refractive index perturbation field quantifies the degree of deviation of each voxel from the refractive index of the uniform original resin.

[0009] Preferably, in S2, the input features of the physical information neural network are constructed with the target voxel as the center: a three-dimensional sub-tensor is extracted from the three-dimensional refractive index perturbation field with the target voxel's lateral coordinate as the center, the lateral range covering the lateral range corresponding to the objective lens entrance pupil diameter, and the depth range covering the incident surface to the target voxel depth. The network adopts an adaptive size input strategy, performs global average pooling along the depth direction to compress the perturbation cylinder into a fixed-length depth integral feature vector, retains the lateral spatial structure information, and then feeds it into a 3D convolutional encoder for spatial feature extraction. After global max pooling, it outputs a compact feature vector, which is concatenated with the depth normalization value of the target voxel and then input into a multilayer perceptron decoder. The output is a wavefront distortion prediction represented by a preset number of Zernike polynomial coefficients.

[0010] Preferably, the training of the physical information neural network adopts a composite loss function with enhanced physical constraints, including: a data loss term, which measures the mean square error between the Zernike coefficients output by the network and the standard answer calculated by the beam propagation method simulation; and a physical consistency loss term, which reconstructs the predicted Zernike coefficients into a wavefront phase diagram and calculates the focal plane intensity distribution through numerical Fresnel diffraction propagation, requiring it to be close to the focal plane intensity distribution simulated by the beam propagation method. The training dataset includes a large-scale synthetic dataset and a small-scale real-world manufacturing experimental dataset. A transfer learning approach is used, freezing the first two convolutional blocks of the encoder and fine-tuning the subsequent convolutional blocks and the fully connected decoder.

[0011] Preferably, in S2, the voxel wavefront distortion prediction field performs two functions in S3: firstly, as the basis for the block segmentation strategy, by identifying the region with the heaviest wavefront distortion burden in the whole structure, it guides the division of the corresponding depth range into finer depth blocks; Secondly, as a selection criterion for the beam search candidate set, voxels with distortion values ​​less than the preset distortion threshold are processed directly in the conventional order and are not included in the beam search optimization. Computational resources are concentrated on key voxels with distortion values ​​greater than the preset distortion threshold.

[0012] Preferably, in S3, the cumulative distortion minimization dynamic programming algorithm adopts a sequence optimization strategy based on depth block: the entire structure is divided into multiple consecutive depth blocks in the depth direction, and the writing order between blocks adopts a strict order from the deepest block to the shallowest block; When writing the k-th block, the voxels of the deeper already written blocks are all below the depth of all voxels in the k-th block and are not on the laser path of any voxel in the k-th block, thus eliminating inter-block path interference. The internal path distortion of each block only comes from the already written voxels within the same block.

[0013] Preferably, sequence optimization within each depth block includes: the write order of each layer within the block follows the deep-first principle; Voxels within the same depth layer are sorted according to a weighted comprehensive score of refractive index deviation and dose sensitivity, with voxels with higher scores being written first. For each depth block, the physical information neural network is used to evaluate the path distortion of key voxel candidate writing order schemes in real time. The candidate schemes are generated through finite beam search, and the beam width parameter of the beam search is adaptively set according to the number of voxels in the block. The scheme with the minimum total path distortion of key voxels within a block is selected as the final write sequence for that block. The optimal write sequence is obtained by splicing together the optimal sequences within all blocks in the order of deep layer priority between blocks.

[0014] Preferably, in S4, the online state Bayesian estimation and spatial light modulator wavefront pre-compensation closed-loop mechanism are executed cyclically at the monomer granularity. The writing cycle for each voxel includes the following steps in sequence: predicting the wavefront distortion of the current target voxel, calculating the spatial light modulator phase compensation, performing laser writing, measuring the two-photon excitation fluorescence signal, performing Bayesian state update, and correcting the prediction of subsequent voxels based on the updated state, covering all voxels in the entire structure until the optimal writing sequence is completed.

[0015] Preferably, in S4, the online state Bayesian estimation includes: simultaneously acquiring the two-photon excited fluorescence backscattering signal in real time through a single-photon counting module while writing each voxel; An integrated Kalman filter is used to perform Bayesian online estimation of the writing state. The state vector is defined as the aggregation conversion rate vector of the voxels already written above the laser path of the currently written voxel. The prediction step uses the dose-attribute model in the nonlinear dose-attribute response modeling method to predict the polymerization conversion rate of the next voxel. The observation step weights and fuses the measured two-photon excitation fluorescence signal with the predicted signal to obtain a posterior estimate of the actual polymerization conversion rate of the current voxel, thereby updating the actual refractive index estimate of the corresponding voxel.

[0016] Preferably, the acquisition of the two-photon excited fluorescence backscattering signal further includes: the photoinitiator generates fluorescence under two-photon excitation, the fluorescence signal intensity decreases monotonically with the increase of polymerization conversion rate, and a quantitative mapping between fluorescence signal intensity and polymerization conversion rate is established through pre-calibration; During the calibration phase, the background of the resin matrix is ​​subtracted by measuring the background of the unexposed area to ensure that the two-photon excited fluorescence signal reflects the fluorescence change caused by the consumption of photoinitiator.

[0017] Preferably, in S4, the spatial light modulator wavefront pre-compensation closed-loop mechanism includes: for each target voxel to be written, the physical information neural network is called again based on the local path state estimate updated by the integrated Kalman filter, the path distortion prediction of the corresponding voxel in the current actual writing state is calculated, the predicted Zernike coefficients are converted into a spatial light modulator phase map, and a conjugate phase with the opposite sign to the expected path distortion is applied. When the deviation between the posterior estimate of the actual polymerization conversion rate of a voxel and the target conversion rate exceeds a preset threshold, and the deviation direction is consistent in multiple written voxels in the same laser path direction column, the expected dose of subsequent voxels that have not yet been written in that column is adjusted in the opposite direction. The adjustment amount is determined by back-calculation using a dose-attribute nonlinear model based on the magnitude of the deviation and the dose sensitivity of each voxel.

[0018] Preferably, in the reverse adjustment of the expected dose of subsequent voxels that have not yet been written in the column, the dose sensitivity is high for voxels whose target dose falls in the range of the maximum slope of the S-curve, and the adjustment step size is reduced to avoid overcompensation. For voxels whose target dose falls within the saturation range of the S-curve, their dose sensitivity is low, and the step size is adjusted to amplify the effect; the adjustment is achieved by modifying the laser power command or dwell time parameter of subsequent voxels.

[0019] Preferably, a femtosecond laser two-photon absorption three-dimensional grayscale direct writing manufacturing system is used to perform the steps in the above-described femtosecond laser two-photon absorption three-dimensional grayscale direct writing manufacturing method, including: The dose field establishment module is used to obtain the target three-dimensional refractive index distribution design map. It uses a nonlinear dose-attribute response modeling method to establish a voxelized exposure dose field and obtain a three-dimensional initial exposure dose distribution map covering the entire structural space. The wavefront distortion prediction module is used to deduce the refractive index perturbation field from the three-dimensional initial exposure dose distribution map, and to predict the wavefront distortion of laser propagation of each voxel using a physical information neural network, outputting a voxel wavefront distortion prediction field covering the entire structure. The write sequence optimization module is used to optimize and rearrange the voxel writing order based on the predicted field of the full structure voxel wavefront distortion and the dose sensitivity of each voxel, using a dynamic programming algorithm that minimizes cumulative distortion, to obtain the optimal write sequence that effectively suppresses the propagation of deep errors. The closed-loop write execution module is used to perform laser scanning according to the optimal write sequence. It adopts an online state Bayesian estimation and spatial light modulator wavefront pre-compensation closed-loop mechanism to obtain a three-dimensional grayscale structure that accurately matches the designed refractive index distribution.

[0020] The beneficial effects of this invention are as follows: The voxel writing order is globally optimized and rearranged by using a dynamic programming algorithm to minimize cumulative distortion. A strategy of deep block partitioning and deep-layer priority writing between blocks is adopted to eliminate path interference between blocks from a mechanism perspective. This ensures that the path distortion within each deep block only comes from the written voxels within the same block, and controls the cumulative amount of path distortion within the block within the dynamic range of the spatial light modulator phase compensation. This solves the problem of deep voxel path distortion exceeding the compensation capacity in conventional layer-by-layer writing. By using a physical information neural network to quickly predict structure-specific wavefront distortion, and combining it with an integrated Kalman filter for online Bayesian estimation of the actual writing state, the spatial light modulator is driven to perform voxel-by-voxel wavefront pre-compensation. Furthermore, the cumulative effect of material response model errors is corrected through a dose compensation channel, thereby achieving coordinated closed-loop control of two error sources: path distortion and material response deviation. This ensures that the three-dimensional refractive index distribution accurately matches the design target. Attached Figure Description

[0021] Figure 1 This is a flowchart of a three-dimensional grayscale direct writing manufacturing method using femtosecond laser two-photon absorption according to the present invention; Figure 2 This invention provides a flowchart of a three-dimensional grayscale direct-write manufacturing method using femtosecond laser two-photon absorption. Figure 1 ; Figure 3 This invention provides a flowchart of a three-dimensional grayscale direct-write manufacturing method using femtosecond laser two-photon absorption. Figure 2 . Detailed Implementation

[0022] The subject matter described herein will now be discussed with reference to exemplary embodiments. It should be understood that these embodiments are discussed only to enable those skilled in the art to better understand and implement the subject matter described herein, and changes may be made to the function and arrangement of the elements discussed without departing from the scope of this specification. Various processes or components may be omitted, substituted, or added as needed in the examples. Furthermore, some features described in the examples may be combined in other examples.

[0023] At least one embodiment of the present invention discloses a method for three-dimensional grayscale direct writing fabrication using femtosecond laser two-photon absorption, such as... Figures 1 to 3 As shown, it includes the following steps: S1. Obtain the target three-dimensional refractive index distribution design map, and use the nonlinear dose-attribute response modeling method to establish the voxelized exposure dose field to obtain a three-dimensional initial exposure dose distribution map covering the entire structural space. Target three-dimensional refractive index distribution design diagram This is the starting point of the manufacturing process. Generated by optical design software based on the optical functional goals of the component, it defines the required refractive index value for each spatial location within the component to be manufactured in the form of three-dimensional coordinate-refractive index pairs. The original design is usually given in the form of a continuous distribution function, which must first be converted into a discrete voxel representation suitable for two-photon writing. Voxel discretization uses the minimum resolved volume determined by the objective lens's numerical aperture as the reference unit. The lateral voxel side length is approximately the effective exposure width of the laser focus in the corresponding direction, and the axial voxel height is approximately half the two-photon excitation depth of focus. Both together determine the three-dimensional density of the voxel grid and the total number of voxels. For each voxel location... The target refractive index is obtained by sampling from the continuous distribution function. And calculate the refractive index relative to the original photosensitive resin. refractive index deviation This serves as input for subsequent material response modeling.

[0024] From the target refractive index deviation To the required laser exposure dose The conversion requires two cascaded nonlinear mappings. The first mapping is the mapping from refractive index deviation to polymerization conversion rate: the degree to which monomers are converted into polymer networks (conversion rate) during the two-photon polymerization of photosensitive resin. There is an approximately linear relationship between the refractive index and the change in resin refractive index. However, as the conversion rate approaches saturation, the sensitivity of the refractive index increment to the conversion rate gradually decreases, exhibiting a nonlinear characteristic. This mapping was established through pre-manufacturing calibration experiments: a set of uniformly exposed test samples at a single depth were prepared, the exposure dose was systematically changed in a stepwise manner, the actual polymerization conversion rate of each sample was measured by Fourier transform infrared spectroscopy (FTIR), and the change in refractive index was measured using a phase-shifting interferometer to establish the model. - Compare with the dataset, and then establish a piecewise polynomial fitting. The monotonic mapping function. The second mapping is the mapping from polymerization conversion rate to exposure dose: during two-photon absorption, the effective two-photon dose D within the voxel is converted into the polymerization initiation radical concentration through an integral dose accumulation mechanism jointly determined by the photoinitiator concentration, laser peak intensity, and pulse repetition rate, and then competes with the oxygen inhibition concentration to determine the final conversion rate. This mapping is also established through calibration experiments, based on actual measurements. - The dataset was fitted to obtain an S-shaped (sigmoid) curve, which has the steepest slope near the dose threshold and gradually saturates in the high dose range. Its parameters (threshold dose, slope coefficient, saturation plateau value) vary with resin batch and manufacturing environment, and need to be recalibrated before each batch is used.

[0025] Through the above two mappings, the target of each voxel is... Gradually transform into a goal Then convert it into the target exposure dose. Simultaneously with dose mapping, the dose-refractive index sensitivity is calculated for each voxel: sensitivity is defined as the product of the local slope of the S-curve and the slope of the refractive index-conversion mapping at the target dose for that voxel, reflecting the magnitude of the refractive index deviation caused by a unit dose error at that voxel. For voxels with moderate refractive index deviations, their target dose falls within the range with the steepest S-curve slope, resulting in the highest sensitivity and the greatest impact of a unit dose error on the refractive index. For voxels with large refractive index deviations, their target dose falls within the higher saturation range of the S-curve, resulting in relatively lower sensitivity. The sensitivity values ​​of each voxel, along with the target dose values, are stored together in the 3D initial exposure dose distribution map. This serves as the basis for prioritizing accuracy control in step S3 (sequence optimization) and as a reference for the reverse calculation of compensation amounts in step S4 (dose compensation channel). After completing dose mapping for all voxels, the three-dimensional initial exposure dose distribution map is generated. A complete description of the exposure dose that each voxel should receive under ideal conditions (no path distortion) and its corresponding dose sensitivity is provided as input for step S2.

[0026] S2 uses the three-dimensional initial exposure dose distribution map to deduce the refractive index perturbation field, and uses a physical information neural network to predict the laser propagation wavefront distortion of each voxel, outputting a voxel wavefront distortion prediction field covering the entire structure. S1 output three-dimensional initial exposure dose distribution map Containing dose information for all locations within the entire structure under ideal writing conditions, and substituting this into the dose-conversion-refractive index mapping chain calibrated in S1, the expected refractive index values ​​of each voxel in the entire structure after writing can be derived in reverse, thereby constructing a three-dimensional expected refractive index distribution map. The graph shows the refractive index of the original resin. difference field This is a three-dimensional refractive index perturbation field, which quantifies the degree of refractive index deviation of each voxel relative to the uniform original resin. It is the basic data for analyzing the optical effects of laser propagation path.

[0027] In a conventional layer-by-layer writing sequence from shallow to deep, when the laser is focused on a depth of... When the target voxel is located, the beam originates from the incident surface ( Propagated along the depth direction to traversing all depths The refractive index deviations of these written voxels. A three-dimensional refractive index perturbation column is formed. As the laser beam passes through this perturbation column, each time it encounters a refractive index deviation of... A thin layer (thickness equal to the voxel axial height) This will accumulate a phase increment at that point. This phase increment can be expressed as:

[0028] in The wavelength of the laser. This represents the refractive index deviation of the thin layer. This is the axial height of the voxel. Because... In the horizontal The directional distribution is non-uniform. The phase accumulation of light rays passing through the perturbed column from different lateral positions is different, which means that the wavefront of the laser beam has been subjected to a laterally non-uniform phase perturbation distribution before reaching the focal point of the target voxel, causing focal wavefront distortion. This distortion is structurally specific: its lateral distribution is entirely determined by the non-uniform refractive index distribution above the laser path of the target voxel, and is a dynamic quantity unique to each target voxel and dependent on the current 3D writing state.

[0029] Accurate prediction of this wavefront distortion theoretically requires a layer-by-layer numerical solution to the paraxial wave equation (i.e., beam propagation method, BPM). However, for three-dimensional structures containing thousands or even tens of thousands of voxels, performing a complete BPM simulation for each voxel would require computation time far exceeding the time budget for real-time manufacturing, making it impractical in engineering. (With a lateral range...) ,depth voxel size approximately Taking a typical structure as an example, the number of BPM simulation grid points is approximately 1.6 million. A single simulation on a GPU takes several seconds to tens of seconds, while the number of voxels in the entire structure can reach tens of thousands. The total time for voxel-by-voxel BPM simulation will reach hundreds to thousands of hours, far exceeding the manufacturing time budget. To address this, this step designs and trains a Physics-Informed Neural Network (PINN) to achieve rapid prediction of structure-specific wavefront distortions.

[0030] The input features of this PINN are based on the target voxel. Constructing around the center: from a three-dimensional refractive index perturbation field Extract from the middle Centered on the horizontal range, covering the horizontal and depth range corresponding to the entrance pupil diameter of the objective lens. The three-dimensional subtensor is used. The physical basis of this truncation method is that the contribution of refractive index perturbation on the laser path to wavefront distortion in TPP writing has the characteristic of "depth integral", that is, phase accumulation along the propagation direction is the dominant effect, while lateral inhomogeneity determines the spatial distribution of wavefront distortion. Therefore, only the refractive index perturbation column directly above the laser path of the target voxel has a substantial contribution to its wavefront distortion, and the refractive index distribution outside the path can be ignored. Since the input subtensor size corresponding to target voxels at different depths is different, the network adopts an adaptive size input strategy: global average pooling is performed along the depth direction to compress the perturbation column at any depth into a fixed-length depth integral feature vector, while retaining the lateral spatial structure information. Then, it is fed into a three-dimensional convolutional encoder for spatial feature extraction. The encoder is composed of multiple three-dimensional convolutional layers and batch normalization layers stacked alternately. The number of feature maps is increased layer by layer in the channel dimension to capture the multi-scale lateral inhomogeneity features of refractive index perturbation. After global max pooling, a compact feature vector of fixed dimensions is output. The feature vector is concatenated with the depth-normalized value of the target voxel and then input into a multilayer perceptron decoder consisting of fully connected layers. The final output is in the form of Zernike polynomial coefficients. The wavefront distortion prediction, which is represented by the wavefront, covers up to the 5th radial order and includes aberration terms that have the most significant impact on the intensity distribution of the two-photon focus, such as defocus, primary coma, primary astigmatism, and primary spherical aberration.

[0031] The network is trained using a composite loss function with enhanced physical constraints. The data loss term measures the root mean square error between the network's output Zernike coefficients and the standard answer calculated by BPM simulation. The physical consistency loss term reconstructs the predicted Zernike coefficients into a wavefront phase map, calculating the corresponding focal plane intensity distribution through numerical Fresnel diffraction propagation, aiming to make it as close as possible to the focal plane intensity distribution in the BPM simulation. Introducing focal plane intensity distribution constraints, rather than just wavefront phase constraints, is a specific design for TPP manufacturing scenarios: the aggregation threshold effect of TPP means that the peak shape of the focal intensity distribution directly determines the actual aggregation volume and conversion rate of voxels. Therefore, constraining the focal plane intensity distribution is closer to the actual manufacturing results than constraining only the wavefront phase, guiding the network to prioritize the prediction accuracy of aberration terms that have the greatest impact on manufacturing precision. The training dataset consists of two parts: a large-scale synthetic dataset, which generates diverse three-dimensional refractive index distributions through random parameterization, and obtains standard wavefront distortion labels for each voxel through BPM simulation. Taking the typical structure scale mentioned above as an example, a single BPM simulation takes about 5 to 30 seconds (GPU execution), and the total computation time for generating 100,000 training samples is about 500 to 3000 GPU hours. This can be completed in parallel by a computing cluster and is a one-time offline computation that does not affect the real-time performance of manufacturing. The small-scale real-world manufacturing experimental dataset is obtained through offline interferometric measurements of actual written samples. The three-dimensional refractive index distribution of the written samples is measured using a Mach-Zehnder interferometer. The deviation field between the measured actual refractive index distribution and the design value is substituted into the forward BPM simulation to infer the actual path wavefront distortion of each voxel during writing, which serves as the calibration label under real manufacturing conditions. The specific method of transfer learning is as follows: the first two convolutional blocks of the encoder are frozen (responsible for extracting low-level refractive index perturbation spatial features, with minimal difference between synthetic and real data), and only the subsequent convolutional blocks of the encoder and the fully connected decoder are fine-tuned. The default size of the real dataset is 500 to 2000 samples, and the default number of fine-tuning rounds is 50. After training, PINN's wavefront distortion inference time for each voxel is approximately 1 to 3 milliseconds (executed on a GPU), which is 3 to 4 orders of magnitude shorter than BPM simulation, meeting real-time requirements.

[0032] Run the PINN process on each voxel of the entire structure one by one, and output the result using S1. Assuming the current expected writing state (i.e., writing is performed in the usual shallow-to-deep order, with all voxels above each voxel already written according to the design before each voxel is written), the predicted wavefront distortion field of the full-structure voxels is obtained. Each element This describes the expected wavefront distortion during voxel writing in a conventional writing sequence. The prediction field performs two specific functions in step S3: first, as the basis for the block segmentation strategy, it identifies the regions with the heaviest wavefront distortion burden in the entire structure (typically locations with greater depth and a high concentration of high-refractive-index-biased voxels above them), guiding the division of the depth range containing these regions into finer depth blocks to reduce path distortion accumulation within the blocks; second, as the basis for selecting the beam search candidate set, for... For voxels with relatively small distortion values ​​(indicating that their path distortion is not significant under normal order, and the benefit of order adjustment is limited), they are processed directly in the normal order and are not included in the bundle search optimization. This concentrates computational resources on key voxels with larger distortion values, thereby improving the efficiency of sequence optimization.

[0033] S3. Based on the predicted field of wavefront distortion of the whole structure voxels and the dose sensitivity of each voxel, the cumulative distortion minimization dynamic programming algorithm is used to optimize and rearrange the voxel writing order to obtain the optimal writing sequence that effectively suppresses the propagation of deep errors. The input to step S3 consists of two parts: the predicted full-structure voxel wavefront distortion field output from S2. (Used for block-based strategy decision-making and selection of key optimization targets) and the PINN model trained by S2 (used for real-time path distortion evaluation of candidate write sequences). Their functions are clearly defined: It provides a global macro view to guide the formulation of optimization strategies; the PINN model provides sequence-by-sequence micro evaluation capabilities to support the comparison and selection of specific candidate solutions.

[0034] The physical mechanism by which the writing order affects path distortion can be analyzed as follows: when voxels... When written, above its laser path (depth) Same as The number of voxels that have been written and the refractive index deviation value together determine the magnitude of path distortion. If in voxels... Before it is written, the voxels above its path have not yet been written, so the path contains only uniform original resin, and the refractive index deviation field The path distortion is zero along the entire path. This analysis shows that if each voxel is written to when there are no voxels already written above its laser path, the path distortion of the entire structure can be reduced to near zero, corresponding to the writing sequence that proceeds along the depth direction from the end away from the incident surface to the end near the incident surface.

[0035] However, a purely "voxel-by-voxel depth-first" strategy faces significant mechanical efficiency challenges in engineering practice. The lateral scanning of a TPP system is performed by a galvanometer mirror at kilohertz speeds, while the switching of axial focusing depth relies on the Z-axis stepping of the piezoelectric-driven objective or the stage. After Z-axis stepping, the system must wait for the mechanical vibration to fully decay (settling time) before writing to avoid focus position jitter caused by vibration affecting voxel positioning accuracy. For piezoelectric objectives, the default settling time is approximately 0.5 to 2 milliseconds, while for the stage it is approximately 10 to 50 milliseconds. If strictly adhering to the voxel-by-voxel depth-first order, switching the Z-axis depth after writing each voxel would result in a cumulative settling time that would increase the total manufacturing time by one to two orders of magnitude, which is unacceptable in engineering. In addition, the potential scattering effect of deep voxels on subsequent shallow voxels must be considered: when the laser passes through the written polymer voxels to reach the shallow target voxel, the refractive index difference between the polymer voxels and the unpolymerized resin will cause scattering, and the scattering intensity increases with the increase of the refractive index difference and the density of the written voxels; in GRIN structures with a large refractive index modulation range, this scattering effect cannot be ignored and needs to be controlled within an acceptable range through a reasonable block strategy.

[0036] To achieve a reasonable balance between optical quality and manufacturing efficiency, this step proposes a dynamic programming sequence optimization strategy based on depth partitioning. The entire structure is uniformly divided into depth sections. A continuous depth block, The default value is the total structural depth (micrometers) divided by the depth range of a single block (default value is 5 to 10 micrometers). This value should be as large as possible while ensuring an acceptable number of Z-axis steps between blocks, in order to reduce inter-layer path interference within each block. For depth regions in the S2 prediction field with heavy wavefront distortion burdens, the blocks can be further refined based on the default value to prioritize the manufacturing accuracy of these regions. The writing order between blocks follows a strict sequence from the deepest block to the shallowest block, i.e., the block furthest from the incident surface is written completely first. block, then write the first one in sequence. Block to the first Block. In writing the first... When the block is larger, the deeper first To the All blocks have been written, but the voxels of these written blocks are all located in the first... Below the depth of all voxels in the block (i.e., downstream of the laser propagation direction), not in the... On the laser path of any voxel, therefore for the first Block writing does not contribute to path distortion. This mechanism fundamentally eliminates inter-block path interference, and the internal path distortion of each block originates only from the written voxels within the same block.

[0037] Intra-block dynamic programming performs fine-grained sequence optimization for a finite number of layers within each depth block. The writing order of each layer within the block follows a depth-first principle, ensuring that all voxels above the path (deeper layers within the same block) have been written when each layer is written, thus making the refractive index state upon which PINN's path distortion prediction for that layer's voxels known and reliable. Given the determined inter-layer order, the lateral writing paths of voxels within the same depth layer are further optimized. It is important to note that voxels within the same depth layer do not lie on each other's laser paths (lasers propagate along the z-axis, and voxels in the same layer do not obstruct each other in the lateral direction). Therefore, the writing order within the same layer does not affect the path distortion between voxels in the same layer; its optimization effect is reflected in its impact on subsequent voxels in shallower layers below that layer: when a shallower voxel is written, its laser path above it includes all written voxels in the current layer. The more accurate the refractive index state of the current layer's voxels, the more reliable the PINN path distortion prediction for the shallower voxels. Based on this mechanism, the optimization of the lateral writing order within the same layer comprehensively considers two priorities: First, voxels with larger refractive index deviations are written first, because these voxels contribute more to the path distortion of shallower voxels, and writing them accurately first can make subsequent PINN predictions more accurate; second, voxels with higher dose sensitivity recorded in S1 are written first, because these voxels (medium-deviation voxels whose target dose falls in the range of the largest slope of the S-curve) are most sensitive to dose error, and prioritizing their writing accuracy can effectively control the upper limit of refractive index error of the entire structure. In addition, voxels with high refractive index deviations have larger polymerization shrinkage, and writing them first can allow their shrinkage stress to be partially relaxed before the writing of adjacent voxels, reducing the interference of stress on the polymerization behavior of adjacent voxels. Combining the above two dimensions, voxels in each depth layer are sorted according to a weighted comprehensive score of refractive index deviation and dose sensitivity, and voxels with higher scores are written first, while also taking into account the lateral scanning path efficiency of the galvanometer, avoiding too many inefficient lateral round trips due to priority ranking.

[0038] For each depth block, the PINN trained by S2 is used to perform real-time path distortion evaluation on the key voxel candidate writing order schemes selected by the S2 prediction field (generated through a finite beam search). The total path distortion experienced by the key voxels within the block under each scheme is calculated, and the scheme with the minimum total distortion is selected as the final writing sequence for that block. The beam width parameter of the beam search is adaptively set according to the number of voxels within the block: when the number of voxels within the block is less than 500, the default value of the beam width is 20 to approximate the global optimum; when the number of voxels within the block is between 500 and 2000, the default value of the beam width is 8; when the number of voxels within the block exceeds 2000, the default value of the beam width is 3 to maintain computational efficiency. The reference value of the beam width can be calculated as follows: divide 90 by the square root of the number of voxels within the block, and then round down to obtain the reference value of the beam width B. This calculation method matches the default value within the above three intervals and can be used as a basis for parameter selection for non-standard scale structures. The evaluation method for the total path distortion within the block is as follows: for candidate sequences ( (Total number of key voxels within the block), run PINN to evaluate each voxel. In already written The path distortion over time is calculated, and the total distortion score is obtained by summing the results. Due to the fast inference speed of PINN (approximately 1 to 3 milliseconds per iteration), evaluating hundreds to thousands of candidate sequences is feasible within the time budget. All... The optimal internal sequence of each block is concatenated according to the deep-priority order between blocks to obtain the optimal write sequence covering the entire structure. This sequence achieves mechanism-based elimination of path distortion at the inter-block level and minimizes path distortion under constraints at the intra-block level, serving as the core input for step S4.

[0039] S4, laser scanning is performed according to the optimal writing sequence. A closed-loop mechanism of online state Bayesian estimation and spatial light modulator wavefront pre-compensation is adopted to obtain a three-dimensional grayscale structure that precisely matches the designed refractive index distribution. The optimal write sequence output by S3 During actual laser scanning, although sequence optimization has significantly reduced path distortion from a mechanistic perspective, two residual error sources still exist that require closed-loop mechanisms. First, sequence optimization is based on the ideal writing state predicted by the dose-property model in S1. However, the actual polymerization conversion rate of each voxel during actual writing may deviate from the predicted value due to factors such as local material inhomogeneities and environmental fluctuations. This causes the actual refractive index perturbation field to deviate from the theoretical prediction, resulting in a difference between the actual path distortion of the remaining voxels and the prediction in S2. Second, voxels in the deep sub-layers within the block still exhibit limited intra-block path distortion during writing (originating from previously written deep voxels in the same block), which needs to be corrected through SLM wavefront pre-compensation. The closed-loop mechanism addresses these two error sources collaboratively from two dimensions: state estimation and wavefront pre-compensation. The two have a clear division of labor: SLM wavefront pre-compensation addresses the wavefront phase error caused by path distortion by applying a conjugate phase to restore the focal wavefront to an ideal plane wave; the dose compensation channel addresses the material response model error. When the actual polymerization conversion rate systematically deviates from the predicted value, it indicates that there is a deviation in the current dose-property model parameters. It is necessary to correct the cumulative effect of the model error by adjusting the dose command of subsequent voxels, rather than just correcting the path distortion.

[0040] In terms of state estimation, while writing each voxel, the system simultaneously acquires the two-photon excited fluorescence (TPEF) backscattered signal returning from the focal region in real time through a single-photon counting module configured in the system's back-collecting optical path. The availability of the TPEF signal is based on the following physical principle: photoinitiators (such as 7-DEAC, which have high two-photon cross-sections) generate fluorescence under two-photon excitation. As the polymerization reaction proceeds, the photoinitiator is consumed, and the fluorescence signal intensity decreases accordingly. This decreasing trend has a monotonic correspondence with the polymerization conversion rate, and a quantitative mapping can be established through pre-calibration. Under typical TPP writing conditions (laser peak power of approximately 10 to 50 mW, repetition rate of 80 MHz, and monomer residence time of approximately 2 to 10 ms), the number of TPEF photons that can be collected during monomer exposure is approximately several hundred to several thousand, and the signal-to-noise ratio is sufficient to support the statistical estimation of the polymerization state. It should be noted that the organic-inorganic hybrid resin matrix may have an autofluorescence background, which needs to be subtracted during the calibration stage by measuring the background of the unexposed areas to ensure that the TPEF signal reflects the fluorescence change caused by the consumption of photoinitiator rather than the matrix background.

[0041] An integrated Kalman filter (EnKF) is used to perform Bayesian online estimation of the write state. The state vector of the EnKF is defined as the current write voxel. Above the laser path (depth) ,same The local path state is defined as the polymerization conversion rate vector of the voxels already written (column S1). The physical basis for this localization is that the refractive index state of voxels outside the path has no direct impact on the path distortion prediction of the current voxel and therefore does not need to be included in the state vector. Furthermore, the number of voxels written above the path is typically only tens to hundreds (depending on the current writing depth and voxel axial height), making the state vector dimension controllable; 50 to 100 ensemble members are sufficient to ensure the statistical convergence of the filter estimation. The prediction step uses the dose-attribute model in S1 to predict the polymerization conversion rate of the next voxel with the currently set laser parameters. The observation step weighted and fused the measured TPEF signal with the predicted signal to obtain a posterior estimate of the actual polymerization conversion rate of the current voxel. This updates the actual refractive index estimate of the voxel. The default number of integrated members is 50 to 100; for a larger refractive index modulation range (…),… For the structure, it is recommended to take an upper limit of 100 to ensure sufficient sampling of the material's nonlinear response.

[0042] In the wavefront pre-compensation dimension, for each target voxel to be written, the system re-calls PINN in S2 based on the latest local path state estimate (continuously updated by EnKF) to calculate the path distortion prediction of the voxel under the current actual writing state using the updated actual refractive index perturbation field. This uses a real-time updated state estimate, rather than the theoretical prediction based on the design value in S2. When the actual refractive index deviation accumulates to a certain extent (e.g., the actual refractive index deviation from the design value in a certain region exceeds 0.003), the difference between the PINN prediction based on the real state and the prediction based on the design value will have a significant impact on the SLM compensation amount. Real-time state-driven re-inference can effectively correct this difference and avoid systematic deviation of the compensation amount. The prediction is then converted into an SLM phase map: a phase distribution is applied to the pixel surface of the SLM.

[0043] in for The Zernike coefficient, For the nth Zernike polynomial, The normalized radial coordinates of the SLM pupil plane. Here are the azimuth coordinates of the SLM pupil plane. The function of this conjugate phase is: the laser beam obtains a pre-distortion wavefront at the SLM with the opposite sign to the expected path distortion. When this wavefront subsequently passes through the written area on the path, the pre-distortion and the phase delay introduced by the path refractive index perturbation cancel each other out, making the synthesized wavefront reaching the target voxel focus close to an ideal plane wave, thereby restoring the actual exposure dose reaching the focus to the design value. The phase update delay of the liquid crystal SLM is typically on the order of milliseconds, matching the typical exposure dwell time of a single voxel in two-photon writing, meeting the timing requirements of real-time voxel-by-voxel updates.

[0044] For cases where the actual polymerization conversion rate revealed by Bayesian estimation systematically deviates from the predicted value, a closed-loop mechanism provides a dose compensation channel to handle this. If a voxel... Posterior estimate of actual polymerization conversion rate Compared with the target conversion rate predicted by S1 The deviations between them exceed a preset threshold, and the deviations occur in the same direction. If multiple voxels in a column (i.e., a column along the same laser path direction, referring to a group of voxels sharing the same transverse coordinate and arranged along the depth direction) have already been written, it is determined that there is a systematic deviation in the current dose-attribute model parameters. The expected dose of subsequent voxels in that column that have not yet been written is then adjusted in the opposite direction. The adjustment amount is determined by inverse calculation using a dose-attribute nonlinear model based on the magnitude of the deviation and the dose sensitivity of each voxel recorded in S1: for voxels with high dose sensitivity (target dose falling within the range of maximum slope of the S-curve), the unit dose adjustment has the greatest effect on refractive index correction, and the adjustment step size should be correspondingly reduced to avoid overcompensation; for voxels with low dose sensitivity (target dose falling within the saturation range), the adjustment step size can be appropriately increased. This adjustment is achieved by modifying the laser power command or residence time parameter of subsequent voxels to offset the systematic influence on subsequent writing caused by errors in the material response model.

[0045] The entire closed-loop writing process proceeds continuously in a single-voxel loop, following the steps of "predicting wavefront distortion, calculating SLM compensation, performing writing, measuring TPEF, Bayesian state update, and updating subsequent predictions," covering all voxels in the entire structure until the written sequence is completed. Execution complete. After the full structure is written, the finished product undergoes post-processing (usually solvent development and heat treatment) to obtain a three-dimensional grayscale structure whose three-dimensional refractive index distribution precisely matches the design target.

[0046] In one embodiment of the invention, it is applied to the manufacturing of a compact gradient refractive index coupled microlens used in augmented reality near-eye display systems. This microlens is a cylindrical structure with a diameter of approximately 1.2 mm. The internal refractive index is distributed along a specific gradient in the radial and axial directions, causing parallel light of different wavelengths passing through it to converge to the same focal point, achieving dispersion and achromatic aberration functions. The manufacturing material is an organic-inorganic hybrid photosensitive resin with an unpolymerized refractive index... The maximum polymerizable refractive index is The effective refractive index modulation range covers all target values ​​required for this design. The following provides an example of application data from the manufacturing process.

[0047] Table 1 shows the design parameters and initial exposure dose calculation results for some target voxels (S1 output example). (Voxel coordinates) The value represents the depth from the incident surface, and the refractive index deviation. Target conversion rate Both the initial exposure dose D (in relative units) and the initial exposure dose D are calculated from two nonlinear mappings in S1. Dose sensitivity Defined as the product (in relative units) of the local slope of the S-curve at the target dose and the slope of the refractive index-conversion mapping, it reflects the magnitude of the refractive index deviation caused by a unit dose error. The voxel with the highest sensitivity corresponds to a moderate deviation range of approximately 0.5 to 0.6 in the target conversion rate.

[0048] Table 1. Design parameters and initial exposure dose calculation results for some target voxels.

[0049] As can be seen from Table 1, The target conversion rate of the voxel was 0.52, falling within the range of the steepest slope of the S-curve, indicating the highest dose sensitivity. In the intra-block horizontal write order optimization of S3, accuracy should be given priority. The target conversion rate of the voxel was 0.91, falling within the saturation range, and the dose sensitivity was lowest. It has a relatively high tolerance for dosage errors.

[0050] Table 2 shows the writing status and compensation results of some voxels during the execution of the optimal writing sequence (S4 output example). In this example, the total structure depth is 40 μm, divided into 4 depth blocks according to the S3 strategy (single block depth range 10 μm, conforming to the upper limit of the default value of 5 to 10 μm): the first block covers a depth of 30 to 40 μm, the second block covers a depth of 20 to 30 μm, the third block covers a depth of 10 to 20 μm, and the fourth block covers a depth of 0 to 10 μm. The blocks are executed in a deep-priority order. Within each block, each layer is written in a deep-priority order, and within the same layer, the writing is sorted according to the comprehensive score of refractive index deviation and dose sensitivity.

[0051] Write sequence number 1 to the deepest layer of the first block ( voxels Above its laser path ( At the time of writing, no voxels had been written (blocks 2 to 4 had not yet started writing, and voxels with an internal depth of less than 40 μm in block 1 had not yet been written), the path distortion prediction value was zero, and no SLM compensation was required. The voxel corresponding to sequence number 2 was written. Similarly, the path distortion becomes zero. Write sequence number 3 to the second deepest layer in the first block ( (This example uses an intermediate layer, not listed separately in the table.) After writing, proceed to... voxels of the first (shallowest) layer At this time, within the first block to The voxels of the layer have been written, but these voxels are all located in downstream of the voxel's laser path (laser from) Incident, first passing through And then to ), not On the laser path of the voxel, the path distortion remains zero. Writing sequence number 4 corresponds to the deepest layer of the second block ( After completing the second initial layer (i.e., the second deep layer), proceed to the second deep layer. voxels At this time, the first block ( to All data has been written, but the first voxel is located in... Downstream of the voxel's laser path, no path distortion occurs; within the second block Above the layer ( That is, the data already written in the second block. (Laminotype) located in Above the laser path of the voxel constitutes the source of intra-block path distortion. PINN predicts the principal aberration to be on the order of approximately 8 to 12 nm. After SLM pre-compensation, the actual refractive index deviation is effectively suppressed. Write sequence number 5 to the 4th block. layer voxels At this time, the first to third pieces ( to All voxels have been written, but they are all located in Downstream of the voxel's laser path, no path distortion occurs; within block 4 Above the layer ( That is, the data already written in the 4th block. The layer voxels constitute the source of path distortion within the block. PINN predicts that the principal aberration is on the order of 3 to 5 nm (because the depth of a single block is only 10 μm, the accumulation of path distortion within the block is small). After SLM pre-compensation, the actual refractive index deviation is effectively suppressed.

[0052] Table 2. Partial voxel writing status and compensation results during the execution of the optimal write sequence.

[0053] As shown in Table 2, for voxels (numbers 1 to 3) with no written voxels above the path in the writing sequence, the predicted path distortion value is zero, requiring no SLM compensation, and the measured refractive index deviation approaches zero within the measurement accuracy range. For voxels with path distortion within a finite block (numbers 4 and 5), after SLM pre-compensation guided by PINN prediction, the actual refractive index deviation is effectively suppressed and kept at a low level; and because the single block depth is only 10 μm, the path accumulation within the block is much smaller than that of conventional full-depth writing, and the principal aberration is significantly lower than that without sequence optimization. Compared with the traditional layer-by-layer writing strategy from shallow to deep, under the same experimental conditions, the deepest voxel ( During writing, all the refractive index perturbations in the shallow layer accumulated above the laser path. Estimated using an average refractive index deviation of approximately 0.03 above the path, a path length of approximately 40 μm, and a laser wavelength of 800 nm, the accumulated phase difference is approximately... The principal aberrations corresponding to transverse non-uniform wavefront distortion can exceed 80 nm, and the refractive index deviation can reach +0.008 to +0.015. This method eliminates inter-block path distortion through sequence optimization and controls intra-block residual distortion through SLM closed-loop compensation. The overall refractive index accuracy is substantially and systematically improved, effectively meeting the stringent requirements of AR near-eye display micro-optical elements for three-dimensional refractive index distribution accuracy.

[0054] The embodiments of the present invention have been described above. However, the embodiments are not limited to the specific implementation methods described above. The specific implementation methods described above are merely illustrative and not restrictive. Those skilled in the art can make more equivalent embodiments under the guidance of the present embodiments, and all of them are within the protection scope of the present embodiments.

Claims

1. A method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption, characterized in that, Includes the following steps: S1. Obtain the target three-dimensional refractive index distribution design map, and use the nonlinear dose-attribute response modeling method to establish the voxelized exposure dose field to obtain a three-dimensional initial exposure dose distribution map covering the entire structural space. S2 uses the three-dimensional initial exposure dose distribution map to deduce the refractive index perturbation field, and uses a physical information neural network to predict the laser propagation wavefront distortion of each voxel, outputting a voxel wavefront distortion prediction field covering the entire structure. S3. Based on the predicted field of wavefront distortion of the whole structure voxels and the dose sensitivity of each voxel, the cumulative distortion minimization dynamic programming algorithm is used to optimize and rearrange the voxel writing order to obtain the optimal writing sequence that effectively suppresses the propagation of deep errors. S4. Perform laser scanning according to the optimal writing sequence. Use online state Bayesian estimation and spatial light modulator wavefront pre-compensation closed-loop mechanism to obtain a three-dimensional grayscale structure that accurately matches the designed refractive index distribution.

2. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 1, characterized in that, In S1, the nonlinear dose-attribute response modeling method includes two cascaded nonlinear mappings: The first segment is a mapping from refractive index deviation to polymerization conversion rate. A comparison dataset of refractive index deviation and polymerization conversion rate is established through pre-manufacturing calibration experiments, and a monotonic mapping function is established by piecewise polynomial fitting. The second segment maps the polymerization conversion rate to the exposure dose. An S-curve is obtained by fitting the measured dataset through calibration experiments. While completing the dose mapping, the dose-refractive index sensitivity of each voxel is calculated. The sensitivity is defined as the product of the local slope of the S-curve at the target dose of the corresponding voxel and the slope of the refractive index-conversion rate mapping. The sensitivity value of each voxel and the target dose value are stored together in the three-dimensional initial exposure dose distribution map.

3. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 1, characterized in that, In S2, the step of deriving the refractive index perturbation field from the three-dimensional initial exposure dose distribution map includes: substituting the three-dimensional initial exposure dose distribution map into the dose-conversion-refractive index mapping chain calibrated in S1, and inversely deriving the expected refractive index values ​​of each voxel in the whole structure after being written, and constructing a three-dimensional expected refractive index distribution map. The difference between the three-dimensional expected refractive index distribution map and the original resin refractive index is used as the three-dimensional refractive index perturbation field. The three-dimensional refractive index perturbation field quantifies the degree of deviation of each voxel from the refractive index of the uniform original resin.

4. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 1, characterized in that, In S2, the input features of the physical information neural network are constructed with the target voxel as the center: a three-dimensional sub-tensor is extracted from the three-dimensional refractive index perturbation field with the target voxel's lateral coordinate as the center, the lateral range covering the lateral range corresponding to the objective lens entrance pupil diameter, and the depth range covering the incident surface to the target voxel depth. The network adopts an adaptive size input strategy, performs global average pooling along the depth direction to compress the perturbation cylinder into a fixed-length depth integral feature vector, retains the lateral spatial structure information, and then feeds it into a 3D convolutional encoder for spatial feature extraction. After global max pooling, it outputs a compact feature vector, which is concatenated with the depth normalization value of the target voxel and then input into a multilayer perceptron decoder. The output is a wavefront distortion prediction represented by a preset number of Zernike polynomial coefficients.

5. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 4, characterized in that, The training of the physical information neural network adopts a composite loss function with enhanced physical constraints, including: a data loss term, which measures the mean square error between the Zernike coefficients output by the network and the standard answer calculated by the beam propagation method simulation; and a physical consistency loss term, which reconstructs the predicted Zernike coefficients into a wavefront phase diagram and calculates the focal plane intensity distribution through numerical Fresnel diffraction propagation, requiring it to be close to the focal plane intensity distribution simulated by the beam propagation method. The training dataset includes a large-scale synthetic dataset and a small-scale real-world manufacturing experimental dataset. A transfer learning approach is used, freezing the first two convolutional blocks of the encoder and fine-tuning the subsequent convolutional blocks and the fully connected decoder.

6. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 1, characterized in that, In S2, the voxel wavefront distortion prediction field in S3 performs two functions: Firstly, as the basis for the segmentation strategy, by identifying the region with the heaviest wavefront distortion burden in the entire structure, the corresponding depth range is divided into finer depth blocks. Secondly, as a selection criterion for the beam search candidate set, voxels with distortion values ​​less than the preset distortion threshold are processed directly in the conventional order and are not included in the beam search optimization. Computational resources are concentrated on key voxels with distortion values ​​greater than the preset distortion threshold.

7. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 1, characterized in that, In S3, the cumulative distortion minimization dynamic programming algorithm adopts a sequence optimization strategy based on depth block: the entire structure is divided into multiple continuous depth blocks in the depth direction, and the writing order between blocks adopts a strict order from the deepest block to the shallowest block; When writing the k-th block, the voxels of the deeper already written blocks are all below the depth of all voxels in the k-th block and are not on the laser path of any voxel in the k-th block, thus eliminating inter-block path interference. The internal path distortion of each block only comes from the already written voxels within the same block.

8. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 7, characterized in that, Sequence optimization within each depth block includes: the write order of each layer within the block follows the deep-first principle; Voxels within the same depth layer are sorted according to a weighted comprehensive score of refractive index deviation and dose sensitivity, with voxels with higher scores being written first. For each depth block, the physical information neural network is used to evaluate the path distortion of key voxel candidate writing order schemes in real time. The candidate schemes are generated through finite beam search, and the beam width parameter of the beam search is adaptively set according to the number of voxels in the block. The scheme with the minimum total path distortion of key voxels within a block is selected as the final write sequence for that block. The optimal write sequence is obtained by splicing together the optimal sequences within all blocks in the order of deep layer priority between blocks.

9. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 1, characterized in that, In S4, the online state Bayesian estimation and spatial light modulator wavefront pre-compensation closed-loop mechanism are executed cyclically at the unit particle level. The writing cycle for each voxel includes the following steps in sequence: predicting the wavefront distortion of the current target voxel, calculating the spatial light modulator phase compensation, performing laser writing, measuring the two-photon excitation fluorescence signal, performing Bayesian state update, and correcting the prediction of subsequent voxels based on the updated state, covering all voxels in the entire structure until the optimal writing sequence is completed.

10. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 1, characterized in that, In S4, the online state Bayesian estimation includes: simultaneously writing each voxel, acquiring the two-photon excited fluorescence backscattering signal in real time through a single-photon counting module; An integrated Kalman filter is used to perform Bayesian online estimation of the writing state. The state vector is defined as the aggregation conversion rate vector of the voxels already written above the laser path of the currently written voxel. The prediction step uses the dose-attribute model in the nonlinear dose-attribute response modeling method to predict the polymerization conversion rate of the next voxel. The observation step weights and fuses the measured two-photon excitation fluorescence signal with the predicted signal to obtain a posterior estimate of the actual polymerization conversion rate of the current voxel, thereby updating the actual refractive index estimate of the corresponding voxel.

11. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 10, characterized in that, The acquisition of the two-photon excited fluorescence backscattering signal also includes: the photoinitiator generates fluorescence under two-photon excitation, the fluorescence signal intensity decreases monotonically with the increase of polymerization conversion rate, and a quantitative mapping between fluorescence signal intensity and polymerization conversion rate is established through pre-calibration; During the calibration phase, the background of the resin matrix is ​​subtracted by measuring the background of the unexposed area to ensure that the two-photon excited fluorescence signal reflects the fluorescence change caused by the consumption of photoinitiator.

12. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 1, characterized in that, In S4, the spatial light modulator wavefront pre-compensation closed-loop mechanism includes: for each target voxel to be written, the physical information neural network is called again according to the local path state estimate updated by the integrated Kalman filter, the path distortion prediction of the corresponding voxel in the current actual writing state is calculated, the predicted Zernike coefficients are converted into a spatial light modulator phase map, and a conjugate phase with the opposite sign to the expected path distortion is applied. When the deviation between the posterior estimate of the actual polymerization conversion rate of a voxel and the target conversion rate exceeds a preset threshold, and the deviation direction is consistent in multiple written voxels in the same laser path direction column, the expected dose of subsequent voxels that have not yet been written in that column is adjusted in the opposite direction. The adjustment amount is determined by back-calculation using a dose-attribute nonlinear model based on the magnitude of the deviation and the dose sensitivity of each voxel.

13. The method for manufacturing three-dimensional grayscale direct writing using femtosecond laser two-photon absorption according to claim 12, characterized in that, In the reverse adjustment of the expected dose of subsequent voxels that have not yet been written in the column, the dose sensitivity of voxels whose target dose falls in the range of the maximum slope of the S-curve is high, and the adjustment step size is reduced to avoid overcompensation. For voxels whose target dose falls within the saturation range of the S-curve, their dose sensitivity is low, and the step size is adjusted to amplify the effect; the adjustment is achieved by modifying the laser power command or dwell time parameter of subsequent voxels.

14. A three-dimensional grayscale direct-write manufacturing system based on femtosecond laser two-photon absorption, used to perform the steps in the three-dimensional grayscale direct-write manufacturing method based on femtosecond laser two-photon absorption as described in any one of claims 1-13, characterized in that, include: The dose field establishment module is used to obtain the target three-dimensional refractive index distribution design map. It uses a nonlinear dose-attribute response modeling method to establish a voxelized exposure dose field and obtain a three-dimensional initial exposure dose distribution map covering the entire structural space. The wavefront distortion prediction module is used to deduce the refractive index perturbation field from the three-dimensional initial exposure dose distribution map, and to predict the wavefront distortion of laser propagation of each voxel using a physical information neural network, outputting a voxel wavefront distortion prediction field covering the entire structure. The write sequence optimization module is used to optimize and rearrange the voxel writing order based on the predicted field of the full structure voxel wavefront distortion and the dose sensitivity of each voxel, using a dynamic programming algorithm that minimizes cumulative distortion, to obtain the optimal write sequence that effectively suppresses the propagation of deep errors. The closed-loop write execution module is used to perform laser scanning according to the optimal write sequence. It adopts an online state Bayesian estimation and spatial light modulator wavefront pre-compensation closed-loop mechanism to obtain a three-dimensional grayscale structure that accurately matches the designed refractive index distribution.

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