A method and system for hologram generation for circular arc chamfer cutting

Abstract

This invention discloses a hologram generation method and system for chamfering of circular arcs. The method includes: completing parameter configuration, initializing the input light field, and setting the focal point and constraint surfaces. For the focal point and constraint surfaces to be optimized in the current round, the original focal point light field distribution is first obtained through Fourier transform, and then the input light field matrix is ​​expanded according to simulation and DOE accuracy. The actual light field of each constraint surface is calculated along the positive optical axis from the farthest point, compared with the ideal intensity to generate a weighted correction matrix and determine convergence, and then the closer constraint surfaces are processed in turn. The corrected light field of each constraint surface is propagated back along the optical axis to the original focal point, and the inverse Fourier transform is used to obtain the inverse input light field. After averaging, the phase is extracted and combined with the original amplitude to generate a new input light field. This process is repeated iteratively until the light field calculation of all preset focal points is completed, and the final DOE phase distribution is output. This meets the fine requirements of circular arc chamfering.

Description

Technical Field

[0001] This invention belongs to the field of laser processing and computational optics, and more specifically, relates to a method and system for generating holograms for chamfering cutting. Background Technology

[0002] In the field of laser cutting, Airy beams are widely used in the precision machining of glass chamfers due to their non-diffraction properties and self-healing capabilities. However, Airy beams have significant drawbacks when practically applied to glass chamfer cutting: during free-space propagation, they self-bend, propagating along a fixed parabolic trajectory, resulting in an asymmetrical light field distribution. This characteristic leads to insufficient energy proportion in the main lobe of the Airy beam, with a large amount of energy dispersed in the side lobes. Consequently, the effective energy acting on the processing area per unit time is limited when cutting glass chamfers, severely impacting processing efficiency, especially when processing high-strength glass materials, where the inefficiency is even more pronounced.

[0003] Traditional machining methods have long faced numerous limitations in chamfering. The physical contact between the tool and the workpiece generates machining stress, which can easily cause cracks or breakage in brittle materials such as glass. Furthermore, tools wear out quickly with prolonged use, requiring frequent replacements to maintain machining accuracy, increasing production costs and reducing efficiency. Moreover, the precision of machining is limited by the manufacturing precision of the tool itself and factors such as vibrations during operation, making it difficult to meet the demands of high-precision chamfering.

[0004] With the development of laser processing technology, non-contact cutting has gradually become an important alternative to mechanical processing, and hologram generation technology is the core means to achieve precise control of the laser light field. However, most existing hologram generation methods are designed for planar or simple curved surface cutting scenarios. For rounded corner cutting with complex paths, it is difficult to achieve precise control of the light field. Conventional light field control methods usually use a single constraint surface for iterative optimization. This approach makes the light field prone to focus shift during propagation, especially in critical areas such as rounded corners, where uneven energy distribution directly affects cutting accuracy.

[0005] Meanwhile, existing technologies lack a systematic grouping strategy when dealing with multiple constrained surfaces. The correction of optical field deviations on each constrained surface is independent and lacks coordination, resulting in low efficiency in optical field optimization. Furthermore, during the optical field initialization phase, the parameter configuration does not match the physical quantities of the actual cutting scenario well, often causing discrepancies between the digitally simulated optical field and the actual physical optical field, further reducing the processing quality of the rounded chamfer. These problems mean that existing technologies cannot effectively solve the processing efficiency problem caused by insufficient main lobe energy of the Airy beam in glass rounded chamfer cutting, and also struggle to balance the accuracy of the cutting path and the stability of the optical field energy. This fails to meet the requirements of high-precision and high-efficiency processing and limits its application in cutting arbitrary curved surfaces. Summary of the Invention

[0006] This invention aims to address the problems of insufficient main lobe energy and low efficiency when using Airy beams for glass chamfering, overcoming the limitations of traditional machining methods such as limited precision and high cost, as well as the insufficient precision and low optimization efficiency of existing hologram generation methods in complex path cutting. Through a multi-constraint surface grouping strategy, precise parameter configuration, and light field initialization, precise light field control is achieved, improving main lobe energy and efficiency, ensuring stable focusing and uniform energy, meeting the requirements of high-precision and high-efficiency processing, and extending to arbitrary curved surface cutting.

[0007] To address the aforementioned deficiencies or improvement needs of existing technologies, as a first aspect of this invention, the present invention provides a hologram generation method for chamfer cutting of circular arcs, comprising: S1. Complete parameter configuration, input light field initialization, and focus and constraint surface settings; S2. For the focus and constraint surface that need to be optimized in the current round, firstly, the light field distribution at the original focus is obtained by performing Fourier transform on each polarization direction of the current input light field, and then the input light field matrix is ​​expanded according to the simulation accuracy and DOE accuracy. S3. Calculate the actual light field distribution of each constraint surface along the positive direction of the optical axis, starting from the farthest point. By comparing it with the ideal intensity distribution, generate a weighted correction matrix and complete the convergence judgment. When the constraint surface at a far distance meets the convergence condition, start to perform the same operation on the constraint surface that is closer to the original focal point, and so on to complete the calculation of the light field distribution of all constraint surfaces. S4. Propagate the corrected light fields of each constraint surface in S3 in the reverse direction along the optical axis to the original focal point, and obtain the reverse input light field through inverse Fourier transform; after averaging, extract the phase information and combine it with the original amplitude to generate a new input light field; S5. Repeat the iterative process of S3 and S4 until the light field of all preset focal points has been calculated, and output the final optimized DOE phase distribution value.

[0008] Furthermore, the parameters in S1 include: simulation field size. Simulation accuracy , DOE accuracy ,wavelength Polarization state, incident light radius Focal spot radius DOE size, input light size, constraint spacing and lateral displacement angle .

[0009] Furthermore, the specific process for setting the focus and constraint surface in S1 is as follows: Group the constraint surfaces according to their distance from the original focal point, from farthest to closest. Using the original focal point as the center, select one constraint surface along the optical axis in both the positive and negative directions, with each constraint spacing equal to one constraint interval. Determine the focal radius using the following formula. The focus is on the constraint surface. Lateral offset on the surface; thus, each constraint surface generates strength constraints based on the focal point distribution. : In the formula, For the current constrained surface, the optical field geometry is denoted as ; For the next set of constrained surfaces, the optical field geometry is denoted as .

[0010] Furthermore, the calculation method for the actual light field distribution of each constraint surface in S3 is as follows: In the frequency domain, a lens can be equivalent to a phase modulation factor, the expression of which is: in, The frequency domain phase modulation transfer function of the lens; Wavelength; The focal length of the lens; Frequency domain coordinates; It is the imaginary unit; multiplying the initial frequency domain optical field by the lens modulation factor yields the frequency domain optical field distribution after lens modulation; Let the distance between the farthest constraint surface and the lens be... According to the angular spectrum propagation theory, the propagation factor of the light field in the frequency domain is: in, Let be the frequency domain phase modulation function for the propagation of the light field; multiply the frequency domain light field modulated by the lens by this propagation factor to obtain the frequency domain light field propagating to the farthest constraint surface; perform an inverse Fourier transform on the above frequency domain light field to convert it back to the spatial domain, and the actual light field distribution on the constraint surface farthest from the focal point in front of the lens focal point can be obtained.

[0011] Furthermore, the method for calculating the weighted correction matrix in S3 is as follows: Suppose that along the optical axis there is There are several constraint surfaces, numbered as follows: , No. The spatial coordinates of the constraint surfaces are: Since the constraint surface only constrains the amplitude, the optical field deviation only needs to be calculated based on the amplitude deviation. No. The amplitude deviation of each constrained surface is defined as: The amplitude deviation distribution; For constraint surfaces The ideal amplitude distribution; For constraint surfaces The actual amplitude distribution; For the identification index of the constraint surface; For spatial coordinates; its physical meaning is the difference between the actual amplitude and the ideal amplitude, reflecting the deviation requirement of the amplitude constraint of the constraint surface; Weighted correction matrix To address the amplitude constraint deviations of each constraint surface, a correction is needed by mapping the propagation operator to a preset focus. The formula is as follows: In the formula, The number of light field groups involved in the correction; For light field deviation Corrected weights; The sequence number of the light field group; propagation operator Describing the light field from the constraint surface Propagation to the focal point can be represented in the frequency domain as: in, For constraint surfaces Distance from the preset focus; Wavelength; Let be the normalized spatial frequency of the light field in the frequency domain. The propagation operator inverse operation is used to "reverse propagate" the amplitude deviation of the constraint surface back to the focal point, thereby realizing a closed loop for optical field correction based on amplitude constraints.

[0012] Furthermore, the convergence determination method in S3 is as follows: The convergence of the model is quantitatively scored by combining two dimensions: the objective function and the iteration difference. Let the objective function be... The sum of squares of the weighted deviations of each constraint surface and the difference of the objective function between two adjacent iterations are... ; in accordance with Compared with the preset accuracy threshold The degree of proximity is determined by the logic that "the closer to the threshold, the higher the score." Mapped to relative ratings: In the formula, For objective function The final output is a relative score; Preset precision threshold; For sensitivity, the control score follows The rate of decay as it increases; It is a non-linear adjustment factor that determines the "steepness" of the scoring curve; like Meets the change threshold The score increases with continuous iteration; a basic score is given for each instance that meets the requirements, and a low score is given for each instance that does not meet the requirements. In the formula, For the current based Calculated score; For the last time based on Calculated score; The base score is the minimum score guaranteed when the conditions are met in a single iteration. For continuous compliance counter; For a single consecutive reward point; This is the maximum consecutive reward cap; This is the lowest score when the condition is not met; Retain coefficients for historical ratings; Set weights for the objective function and iterative difference. , The overall convergence score of the model is obtained by weighted summation: In the formula, For the overall score; by The model is compared with the set score to determine whether it has converged.

[0013] Furthermore, the specific calculation method for the objective function and the iteration difference is as follows: objective function The calculation method is as follows: in, For the first Weights of group bias; For the first The deviation distribution of the group of light fields; The number of light field groups involved in the deviation calculation; The difference between the objective functions of two adjacent iterations is The calculation method is as follows: in, For the first The total deviation of the next iteration; For the first The total deviation of each iteration.

[0014] Furthermore, the calculation process for the new input light field in S4 is as follows: Let the input light field involved in the calculation be... Each light field has a complex amplitude distribution, that is: in, For the first Each light field component; Amplitude; For phase, ; The arithmetic mean of the complex amplitudes of all light fields is used to obtain the average complex amplitude. : in, This represents the total number of light field components; This is an index of the light field components; the average value includes the average amplitude. and average phase ; From the average complex amplitude Extracting the phase component This serves as the basis for subsequent processing; Based on simulation accuracy and physical precision Determine the reduction factor : Average phase Multiply by the scaling factor to get the fit. Precision phase : New input light field It is composed of the selected amplitude and the scaled phase: in, The amplitude of the input light field remains constant during modulation, while only the phase is scaled. It is the imaginary unit.

[0015] As a second aspect of the present invention, the present invention provides a hologram generation system for chamfering cutting of circular arcs, comprising: The parameter and initial setting unit is used to complete parameter configuration, input light field initialization, and focal point and constraint surface setting. The optical field transformation and expansion unit is used to optimize the focal point and constraint surface in the current round. First, it performs Fourier transform on each polarization direction of the current input optical field to obtain the optical field distribution at the original focal point. Then, it expands the input optical field matrix according to the simulation accuracy and DOE accuracy. The constrained surface forward optimization unit is used to calculate the actual light field distribution of each constrained surface starting from the farthest point along the positive optical axis. By comparing it with the ideal intensity distribution, a weighted correction matrix is ​​generated and convergence is determined. When the constrained surface at a far distance meets the convergence condition, the same operation is performed on the constrained surface closer to the original focal point, and so on, to complete the calculation of the light field distribution of all constrained surfaces. A new optical field unit is generated in reverse, which is used to propagate the corrected optical fields of each constraint surface in the forward optimization unit of the constraint surface in reverse along the optical axis to the original focal point, and obtain the reverse input optical field through inverse Fourier transform; after averaging, the phase information is extracted and combined with the original amplitude to generate a new input optical field; The iterative output phase value unit is used to repeat the iterative process of the constraint surface forward optimization unit and the reverse generation of new light field unit until the light field of all preset focal points is calculated and the final optimized DOE phase distribution value is output.

[0016] As a third aspect of the invention, the invention provides a computer-readable storage medium having a computer program stored thereon, the computer program being executed by a processor of any step of the hologram generation method for chamfer cutting.

[0017] In summary, compared with the prior art, the above-described technical solutions conceived by this invention can achieve the following beneficial effects: 1. The hologram generation method for chamfering of the present invention groups constraint surfaces according to their distance from the original focal point in ascending order. Constraint surfaces are selected at intervals along the positive and negative directions of the optical axis. The optical field geometry of the next set of constraint surfaces is determined by combining the current constraint surface's optical field geometry, the constraint interval, and the lateral displacement angle, thus achieving an orderly setting of constraint surfaces. This feature enables the optical field to form a multi-dimensional constraint framework along the propagation path, allowing for precise layer-by-layer optical field control. This ensures that the strength constraints of each constraint surface match the path requirements of the chamfering, providing a clear target boundary for subsequent iterative optimization of the optical field and improving the accuracy of the optical field focusing position.

[0018] 2. The hologram generation method for chamfering of the present invention generates intensity constraints based on the focal point distribution on each constraint surface, and achieves iterative optimization by combining optical field deviation calculation and correction superposition. This feature allows the actual optical field to gradually approach the ideal optical field. By quantifying the deviation and making targeted corrections, the amplitude and phase distribution of the optical field are adapted to the energy and path requirements of chamfering, ensuring the coordinated operation of multi-focal optical fields, improving cutting accuracy, and meeting the fine requirements of chamfering processing.

[0019] 3. The hologram generation method for circular arc chamfer cutting of the present invention converts optical field deviations into correctable physical quantities through inverse modulation, and then obtains the total correction amount by weighted superposition, thereby achieving integrated optimization of multiple sets of optical field deviations. This feature can transform optical field deviations of different constraint surfaces into unified correction parameters, balance the optimization needs of each constraint surface through weight allocation, prioritize the correction of deviations in key areas, and ensure that the deviations at each position of the optical field can be effectively controlled during propagation. This provides a precise correction basis for generating an optical field that conforms to the circular arc chamfer cutting path, improving the targeting of optical field optimization. Attached Figure Description

[0020] Figure 1 This is a flowchart of a hologram generation method for chamfering cutting according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the optical path according to an embodiment of the present invention; Figure 3 This is a system unit diagram of an embodiment of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0022] Example 1 Please refer to Figure 1 This embodiment 1 provides a hologram generation method for chamfering of circular arcs, including: S1. Complete parameter configuration, input light field initialization, and focus and constraint surface settings; S2. For the focus and constraint surface that need to be optimized in the current round, firstly, the light field distribution at the original focus is obtained by performing Fourier transform on each polarization direction of the current input light field, and then the input light field matrix is ​​expanded according to the simulation accuracy and DOE accuracy. S3. Calculate the actual light field distribution of each constraint surface along the positive direction of the optical axis, starting from the farthest point. By comparing it with the ideal intensity distribution, generate a weighted correction matrix and complete the convergence judgment. When the constraint surface at a far distance meets the convergence condition, start to perform the same operation on the constraint surface that is closer to the original focal point, and so on to complete the calculation of the light field distribution of all constraint surfaces. S4. Propagate the corrected light fields of each constraint surface in S3 in the reverse direction along the optical axis to the original focal point, and obtain the reverse input light field through inverse Fourier transform; after averaging, extract the phase information and combine it with the original amplitude to generate a new input light field; S5. Repeat the iterative process of S3 and S4 until the light field of all preset focal points has been calculated, and output the final optimized DOE phase distribution value.

[0023] This embodiment 1 further elaborates on the above steps.

[0024] (1) Parameters and initial settings Please refer to Figure 2 , Figure 2 A schematic diagram of the optical path in Embodiment 1 is provided. With the support of the hologram generation method with rounded chamfer cutting, the laser can form an arc-shaped focal distribution after passing through the DOE and the lens.

[0025] The initial process of this embodiment 1 mainly includes three parts: parameter configuration, input light field initialization, and focal point and constraint surface setting.

[0026] In a preferred embodiment, during the parameter configuration phase, several key parameters need to be determined, including: the size of the simulation field. Simulation accuracy , DOE accuracy ,wavelength Polarization state, incident light radius Focal spot radius DOE size, input light size, constraint spacing and lateral displacement angle .

[0027] The input light field initialization is completed based on the above parameters, providing an initial state for subsequent light field manipulation.

[0028] When setting the focal spot and constraint surfaces, first group the constraint surfaces according to their distance from the original focal spot, from farthest to nearest. Using the original focal spot as the center, select a constraint surface along the positive and negative optical axes, at every other constraint interval. Determine the focal spot radius corresponding to the constraint surface. After the lateral offset, each constraint surface generates intensity constraints based on the distribution of the focal points. The optical field geometry of the current constraint surface, combined with the constraint spacing and lateral displacement angle, yields the optical field geometry of the next set of constraint surfaces, thus achieving an orderly arrangement of constraint surfaces.

[0029] In a preferred embodiment, the specific process for setting the focus and constraint surface is as follows: Group the constraint surfaces according to their distance from the original focal point, from farthest to closest. Using the original focal point as the center, select one constraint surface along the optical axis in both the positive and negative directions, with each constraint spacing equal to one constraint interval. Determine the focal radius using the following formula. The focus is on the constraint surface. Lateral offset on the surface; thus, each constraint surface generates strength constraints based on the focal point distribution. : In the formula, For the current constrained surface, the optical field geometry is denoted as ; For the next set of constrained surfaces, the optical field geometry is denoted as .

[0030] (2) Light field transformation and expansion For the focal points and constraints that need to be optimized in the current round, the processing should be carried out step by step in combination with the characteristics of the light field and the accuracy requirements, so as to ensure that the light field control can accurately adapt to the needs of rounded chamfer cutting.

[0031] First, the focal point and constraint surface corresponding to the current round are selected as the optimization targets. Given the known number of focal points, a Fourier transform is performed on the light field in each polarization direction of the current input light field. This step, by transforming the light field from the spatial domain to the frequency domain, more clearly presents the spectral characteristics of the light field, thus accurately obtaining the light field distribution at the original focal point. This distribution contains the amplitude and phase information of the light field at the focal point, providing an initial reference for the light field characteristics for subsequent optimization. This ensures that the optimization direction always remains consistent with the light field requirements of the target focal point, avoiding deviation from the energy and path requirements needed for the chamfered cut.

[0032] Next, the input light field is expanded. Using interpolation, the input light field matrix is ​​adjusted based on the simulation accuracy and the DOE accuracy. The expansion factor is determined by the ratio of DOE accuracy to simulation accuracy, ultimately yielding the expanded input light field. The core of this operation is to compensate for the accuracy difference between digital simulation and physical devices, ensuring that the matrix size of the input light field matches the physical accuracy of the DOE. This expansion reduces the loss of light field information caused by accuracy mismatch, allowing the light field to more accurately adapt to the characteristics of actual optical components during subsequent DOE modulation. This lays a solid foundation for generating holograms that meet the requirements of chamfered cutting, ensuring the stability and accuracy of the light field during the cutting process.

[0033] (3) Forward optimization of constraint surfaces The processing starts with the constraint surface furthest away along the positive direction of the optical axis, calculates the actual light field distribution of each constraint surface in turn, generates a weighted correction matrix by comparing it with the ideal intensity distribution, and judges the convergence. After the far-distance constraint surface meets the convergence condition, the closer constraint surfaces are processed step by step until the light field distribution of all constraint surfaces is calculated.

[0034] When calculating the actual light field distribution, the spatial domain light field distribution is obtained by combining the lens frequency domain phase modulation factor and the light field propagation factor with the inverse Fourier transform. This approach can accurately reproduce the true propagation state of the light field under different constraint surfaces, providing a reliable basis for subsequent deviation analysis and ensuring that the light field characteristics match the path requirements of the circular arc chamfer cutting.

[0035] In a preferred embodiment, the actual light field distribution of each constraint surface is calculated as follows: In the frequency domain, a lens can be equivalent to a phase modulation factor, the expression of which is: in, The frequency domain phase modulation transfer function of the lens; Wavelength; The focal length of the lens; Frequency domain coordinates; It is the imaginary unit; multiplying the initial frequency domain optical field by the lens modulation factor yields the frequency domain optical field distribution after lens modulation; Let the distance between the farthest constraint surface and the lens be... According to the angular spectrum propagation theory, the propagation factor of the light field in the frequency domain is: in, Let be the frequency domain phase modulation function for the propagation of the light field; multiply the frequency domain light field modulated by the lens by this propagation factor to obtain the frequency domain light field propagating to the farthest constraint surface; perform an inverse Fourier transform on the above frequency domain light field to convert it back to the spatial domain, and the actual light field distribution on the constraint surface farthest from the focal point in front of the lens focal point can be obtained.

[0036] When generating the weighted correction matrix, the light field deviations of all constraint surfaces are taken into account and mapped to the correction requirements of the preset focus through a propagation operator. This allows for the overall optimization needs of each constraint surface to be coordinated, making the correction direction more closely match the light field control target at the focus, improving the integrity and specificity of the light field optimization, and avoiding the impact of local deviations on the overall cutting effect.

[0037] In a preferred embodiment, the weighted correction matrix is ​​calculated as follows: Suppose that along the optical axis there is There are several constraint surfaces, numbered as follows: , No. The spatial coordinates of the constraint surfaces are: Since the constraint surface only constrains the amplitude, the optical field deviation only needs to be calculated based on the amplitude deviation. No. The amplitude deviation of each constrained surface is defined as: The amplitude deviation distribution; For constraint surfaces The ideal amplitude distribution; For constraint surfaces The actual amplitude distribution; For the identification index of the constraint surface; For spatial coordinates; its physical meaning is the difference between the actual amplitude and the ideal amplitude, reflecting the deviation requirement of the amplitude constraint of the constraint surface; Weighted correction matrix To address the amplitude constraint deviations of each constraint surface, a correction is needed by mapping the propagation operator to a preset focus. The formula is as follows: In the formula, The number of light field groups involved in the correction; For light field deviation Corrected weights; The sequence number of the light field group; propagation operator Describing the light field from the constraint surface Propagation to the focal point can be represented in the frequency domain as: in, For constraint surfaces Distance from the preset focus; Wavelength; Let be the normalized spatial frequency of the light field in the frequency domain. The propagation operator inverse operation is used to "reverse propagate" the amplitude deviation of the constraint surface back to the focal point, thereby realizing a closed loop for optical field correction based on amplitude constraints.

[0038] Specifically, after the constraint surface completes the amplitude deviation correction, the logic for replacing the amplitude is as follows: the actual effective amplitude of the constraint surface is... The amplitude constraint of the constraint surface is corrected by the "amplitude replacement", and then the back propagation process is performed based on the replaced amplitude to promote the iterative optimization of the light field.

[0039] Convergence is assessed by quantifying and weighting the scores from two dimensions: the objective function and the iteration difference. This multi-dimensional evaluation comprehensively reflects the convergence state of the light field optimization, ensuring that the light field deviation is controlled within a preset range and that the iteration process is stable. It avoids over-correction or insufficient convergence, providing a strict convergence standard for generating high-precision holograms, and ultimately guaranteeing the accuracy and efficiency of the rounded bevel cutting.

[0040] In a preferred embodiment, the convergence determination method is as follows: The convergence of the model is quantitatively scored by combining two dimensions: the objective function and the iteration difference. Let the objective function be... The sum of squares of the weighted deviations of each constraint surface and the difference of the objective function between two adjacent iterations are... ; in accordance with Compared with the preset accuracy threshold The degree of proximity is determined by the logic that "the closer to the threshold, the higher the score." Mapped to relative ratings: In the formula, For objective function The final output is a relative score; Preset precision threshold; For sensitivity, the control score follows The rate of decay as it increases; It is a non-linear adjustment factor that determines the "steepness" of the scoring curve; like Meets the change threshold The score increases with continuous iteration; a basic score is given for each instance that meets the requirements, and a low score is given for each instance that does not meet the requirements. In the formula, For the current based Calculated score; For the last time based on Calculated score; The base score is the minimum score guaranteed when the conditions are met in a single iteration. For continuous compliance counter; For a single consecutive reward point; This is the maximum consecutive reward cap; This is the lowest score when the condition is not met; Retain coefficients for historical ratings; Set weights for the objective function and iterative difference. , The overall convergence score of the model is obtained by weighted summation: In the formula, For the overall score; by The model is compared with the set score to determine whether it has converged.

[0041] In a preferred embodiment, the specific calculation methods for the objective function, iterative difference, and modified matrix norm are as follows: objective function The calculation method is as follows: in, For the first Weights of group bias; For the first The deviation distribution of the group of light fields; The number of light field groups involved in the deviation calculation; The difference between the objective functions of two adjacent iterations is The calculation method is as follows: in, For the first The total deviation of the next iteration; For the first The total deviation of each iteration.

[0042] (4) Reverse generation of new light field First, calculate the light field distribution of all foci and constraint surfaces after the original focal point. Replace the actual amplitude of the current constraint surface with the product of the corrected weight matrix and the desired light field intensity distribution to obtain the input light field for backpropagation. Calculate the light field distribution after the original focal point sequentially from farthest to nearest.

[0043] Next, based on diffraction theory, the light field distribution of all focal points and constraint surfaces after the original focal point is propagated back to the original focal point along the reverse light path. The light field distribution of the current focal point and constraint surface light field propagated back to the original focal point is calculated, and the number of iterations is increased.

[0044] Then, based on the light field distribution obtained from backpropagation, the corresponding number of reverse input light fields are obtained through inverse Fourier transform.

[0045] Next, the corrected light fields of each constraint surface from the previous steps are propagated back along the optical axis to the original focal point, and the inverse Fourier transform is used to obtain the inverse input light field. These inverse input light fields are averaged to extract phase information, and then combined with the original amplitude to generate a new input light field.

[0046] In a preferred embodiment, the calculation process for the new input light field is as follows: Let the input light field involved in the calculation be... Each light field has a complex amplitude distribution, that is: in, For the first Each light field component; Amplitude; For phase, ; The arithmetic mean of the complex amplitudes of all light fields is used to obtain the average complex amplitude. : in, This represents the total number of light field components; This is an index of the light field components; the average value includes the average amplitude. and average phase ; From the average complex amplitude Extracting the phase component This serves as the basis for subsequent processing; Based on simulation accuracy and physical precision Determine the reduction factor : Average phase Multiply by the scaling factor to get the fit. Precision phase : New input light field It is composed of the selected amplitude and the scaled phase: in, The amplitude of the input light field remains constant during modulation, while only the phase is scaled. It is the imaginary unit.

[0047] This process integrates the correction information of each constraint surface through backpropagation, providing a new starting point for the iterative optimization of the light field and ensuring that the light field manipulation can continue to advance in a direction that meets the cutting requirements.

[0048] (5) Iteratively output phase value During the iteration process, the optical field optimization calculation and backpropagation operation are repeatedly performed until the optical field calculation of all preset focal points is completed, and finally the optimized DOE phase distribution value is output.

[0049] Each iteration begins with optical field optimization calculations, starting from the farthest constraint surface along the positive optical axis. The actual optical field distribution of each constraint surface is obtained sequentially, compared with the ideal intensity distribution, and a weighted correction matrix is ​​generated. Convergence is then assessed through multi-dimensional evaluation. Closer constraint surfaces are processed only after the distant constraint surfaces meet the requirements. This step continuously corrects optical field deviations, ensuring that the optical field characteristics of each constraint surface gradually conform to the requirements of rounded chamfer cutting.

[0050] Then, backpropagation is performed, propagating the corrected optical fields of each constraint surface back along the optical axis to the original focal point. The inverse Fourier transform yields the inverse input optical field, which is then averaged to extract phase information and combined with the original amplitude to generate a new input optical field. This operation integrates the optimization results of each constraint surface and feeds them back to the initial optical field, providing an adjusted starting point for the next iteration and forming a closed loop for optical field manipulation.

[0051] Through this iterative process, the optimization effect is continuously accumulated, and the deviation between the actual distribution of the light field and the ideal state is gradually reduced until the light field of all preset focal points meets the expected requirements. At this point, the output DOE phase distribution value can accurately control the light field and meet the accuracy and efficiency requirements of circular bevel cutting.

[0052] Example 2 Please refer to Figure 3 This embodiment 2 provides a hologram generation system for chamfering cutting of arcs, including: The parameter and initial setting unit is used to complete parameter configuration, input light field initialization, and focal point and constraint surface setting. The optical field transformation and expansion unit is used to optimize the focal point and constraint surface in the current round. First, it performs Fourier transform on each polarization direction of the current input optical field to obtain the optical field distribution at the original focal point. Then, it expands the input optical field matrix according to the simulation accuracy and DOE accuracy. The constrained surface forward optimization unit is used to calculate the actual light field distribution of each constrained surface starting from the farthest point along the positive optical axis. By comparing it with the ideal intensity distribution, a weighted correction matrix is ​​generated and convergence is determined. When the constrained surface at a far distance meets the convergence condition, the same operation is performed on the constrained surface closer to the original focal point, and so on, to complete the calculation of the light field distribution of all constrained surfaces. A new optical field unit is generated in reverse to propagate the corrected constraint surface optical fields in S3 in reverse along the optical axis to the original focal point. The reverse input optical field is obtained through inverse Fourier transform. After averaging, the phase information is extracted and combined with the original amplitude to generate a new input optical field. The iterative output phase value unit is used to repeat the iteration process of S3 and S4 until the light field of all preset focal points is calculated and the final optimized DOE phase distribution value is output.

[0053] Example 3 This embodiment 3 also provides a computer-readable storage medium storing a computer program that, when executed by a processor, can implement any step of a hologram generation method for chamfer cutting.

[0054] The computer-readable storage medium may include various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0055] For a description of the computer-readable storage medium provided in this application, please refer to the above method embodiments; further details will not be repeated here.

[0056] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for generating holograms for chamfering of circular arcs, characterized in that, include: S1. Complete parameter configuration, input light field initialization, and focus and constraint surface settings; S2. For the focus and constraint surface that need to be optimized in the current round, firstly, the light field distribution at the original focus is obtained by performing Fourier transform on each polarization direction of the current input light field, and then the input light field matrix is ​​expanded according to the simulation accuracy and DOE accuracy. S3. Calculate the actual light field distribution of each constraint surface along the positive direction of the optical axis, starting from the farthest point. By comparing it with the ideal intensity distribution, generate a weighted correction matrix and complete the convergence judgment. When the constraint surface at a far distance meets the convergence condition, start to perform the same operation on the constraint surface that is closer to the original focal point, and so on to complete the calculation of the light field distribution of all constraint surfaces. S4. Propagate the corrected light fields of each constraint surface in S3 in the opposite direction along the optical axis to the original focal point, and obtain the reverse input light field through inverse Fourier transform; After averaging the light, the phase information is extracted and combined with the original amplitude to generate a new input light field. S5. Repeat the iterative process of S3 and S4 until the light field of all preset focal points has been calculated, and output the final optimized DOE phase distribution value; The parameters in S1 include: simulation field size. Simulation accuracy , DOE accuracy ,wavelength Polarization state, incident light radius Focal spot radius DOE size, input light size, constraint spacing and lateral displacement angle ; The specific process for setting the focus and constraint surface in S1 is as follows: Group the constraint surfaces according to their distance from the original focal point, from farthest to closest. Using the original focal point as the center, select one constraint surface along the optical axis in both the positive and negative directions, with each constraint spacing equal to one constraint interval. Determine the focal radius using the following formula. The focus is on the constraint surface. Lateral offset on the surface; thus, each constraint surface generates strength constraints based on the focal point distribution. : wherein is the light field geometry of the current set of constraints; is the light field geometry of the next set of constraints; The method for calculating the weighted correction matrix in S3 is as follows: Suppose that along the optical axis there is There are several constraint surfaces, numbered as follows: , No. The spatial coordinates of the constraint surfaces are: Since the constraint surface only constrains the amplitude, the optical field deviation only needs to be calculated based on the amplitude deviation. No. The amplitude deviation of each constrained surface is defined as: The amplitude deviation distribution; For constraint surfaces The ideal amplitude distribution; For constraint surfaces The actual amplitude distribution; For the identification index of the constraint surface; For spatial coordinates; its physical meaning is the difference between the actual amplitude and the ideal amplitude, reflecting the deviation requirement of the amplitude constraint of the constraint surface; Weighted correction matrix To address the amplitude constraint deviations of each constraint surface, a correction is needed by mapping the propagation operator to a preset focus. The formula is as follows: In the formula, The number of light field groups involved in the correction; For light field deviation Corrected weights; The sequence number of the light field group; propagation operator Describing the light field from the constraint surface Propagation to the focal point can be represented in the frequency domain as: in, For constraint surfaces Distance from the preset focus; Wavelength; Let be the normalized spatial frequency of the light field in the frequency domain. The propagation operator inverse operation is used to "reverse propagate" the amplitude deviation of the constraint surface back to the focal point, thereby realizing a closed loop for optical field correction based on amplitude constraints.

2. The hologram generation method for chamfering cutting according to claim 1, characterized in that, The method for calculating the actual light field distribution of each constraint surface in S3 is as follows: In the frequency domain, a lens can be equivalent to a phase modulation factor, the expression of which is: in, The frequency domain phase modulation transfer function of the lens; Wavelength; The focal length of the lens; Frequency domain coordinates; It is the imaginary unit; multiplying the initial frequency domain optical field by the lens modulation factor yields the frequency domain optical field distribution after lens modulation; Let the distance between the farthest constraint plane and the lens be According to the angular spectrum propagation theory, the propagation factor of the light field in the frequency domain is in, Let be the frequency domain phase modulation function for the propagation of the light field; multiply the frequency domain light field modulated by the lens by this propagation factor to obtain the frequency domain light field propagating to the farthest constraint surface; perform an inverse Fourier transform on the above frequency domain light field to convert it back to the spatial domain, and the actual light field distribution on the constraint surface farthest from the focal point in front of the lens focal point can be obtained.

3. The hologram generation method for chamfering cutting according to claim 1, characterized in that, The convergence determination method in S3 is as follows: The convergence of the model is quantitatively scored by combining two dimensions: the objective function and the iteration difference. Let the objective function be... The sum of squares of the weighted deviations of each constraint surface and the difference of the objective function between two adjacent iterations are... ; in accordance with Compared with the preset accuracy threshold The degree of proximity is determined by the logic that "the closer to the threshold, the higher the score." Mapped to relative ratings: In the formula, For objective function The final output is a relative score; Preset precision threshold; For sensitivity, the control score follows The rate of decay as it increases; It is a non-linear adjustment factor that determines the "steepness" of the scoring curve; If Satisfies change threshold , continuous iteration score improvement; single satisfaction has basic score, no satisfaction score is low; In the formula, For the current based Calculated score; For the last time based on Calculated score; The base score is the minimum score guaranteed when the conditions are met in a single iteration. For continuous compliance counter; For a single consecutive reward point; This is the maximum consecutive reward cap; This is the lowest score when the condition is not met; Retain coefficients for historical ratings; Set weights for the objective function and iterative difference. , The overall convergence score of the model is obtained by weighted summation: In the formula, is the total score; whether the model is converged is determined by comparing the total score with the set score value. and the set score value.

4. The method for generating a hologram for circular-arc chamfer cutting according to claim 3, wherein, The specific calculation method for the objective function and the iteration difference is as follows: Objective function The calculation method is as follows: in, For the first Weights of group bias; For the first The deviation distribution of the group of light fields; The number of light field groups involved in the deviation calculation; The difference between the objective functions of two adjacent iterations is The calculation method is as follows: wherein is the total bias for the th iteration; is the total bias for the th iteration.

5. The method for generating a hologram for circular-arc chamfer cutting according to claim 1, wherein, The calculation process for the new input light field in S4 is as follows: Let the input light field participating in the computation be Each light field is a complex amplitude distribution, i.e. in, For the first Each light field component; Amplitude; For phase, ; The arithmetic mean of the complex amplitudes of all light fields is used to obtain the average complex amplitude. : in, This represents the total number of light field components; This is an index of the light field components; the average value includes the average amplitude. and average phase ; extracting a phase portion from the average complex amplitude as a basis phase distribution for subsequent processing as a basis phase distribution for subsequent processing According to the simulation accuracy and the physical accuracy , the reduction factor is determined: Average phase Multiply by the scaling factor to get the fit. Precision phase : New input light field It is composed of the selected amplitude and the scaled phase: wherein, is the amplitude of the input optical field, the amplitude remains unchanged during the modulation, only the phase is scaled; is the imaginary unit.

6. A hologram generating system for circular arc chamfer cutting, characterized by comprising: include: The parameter and initial setting unit is used to complete parameter configuration, input light field initialization, and focal point and constraint surface setting. The optical field transformation and expansion unit is used to optimize the focal point and constraint surface in the current round. First, it performs Fourier transform on each polarization direction of the current input optical field to obtain the optical field distribution at the original focal point. Then, it expands the input optical field matrix according to the simulation accuracy and DOE accuracy. The constrained surface forward optimization unit is used to calculate the actual light field distribution of each constrained surface starting from the farthest point along the positive optical axis. By comparing it with the ideal intensity distribution, a weighted correction matrix is ​​generated and convergence is determined. When the constrained surface at a far distance meets the convergence condition, the same operation is performed on the constrained surface closer to the original focal point, and so on, to complete the calculation of the light field distribution of all constrained surfaces. A new optical field unit is generated in reverse, which is used to propagate the corrected optical fields of each constraint surface in the forward optimization unit of the constraint surface in reverse along the optical axis to the original focal point, and obtain the reverse input optical field through inverse Fourier transform; After averaging the light, the phase information is extracted and combined with the original amplitude to generate a new input light field. The iterative output phase value unit is used to repeat the iterative process of the constraint surface forward optimization unit and the reverse generation of new light field unit until the light field of all preset focal points has been calculated, and the final optimized DOE phase distribution value is output; The parameters mentioned above, along with those in the initial setting unit, include: simulation field size. Simulation accuracy , DOE accuracy ,wavelength Polarization state, incident light radius Focal spot radius DOE size, input light size, constraint spacing and lateral displacement angle ; The specific process for setting the parameters and the focus and constraint surfaces in the initial setting unit is as follows: The constraint surfaces are grouped according to the distance from the original focal point, and one constraint surface is selected for each constraint interval along the optical axis in the positive direction and the reverse direction with the original focal point as the center, and the focal point radius is determined according to the following formula The transverse offset of the focal point on the constraint surface ; and then the intensity constraint of each constraint surface is generated according to the focal point distribution : wherein is the light field geometry of the current set of constraints; is the light field geometry of the next set of constraints; The method for calculating the weighted correction matrix in the constrained surface forward optimization unit is as follows: Suppose that along the optical axis there is There are several constraint surfaces, numbered as follows: , No. The spatial coordinates of the constraint surfaces are: Since the constraint surface only constrains the amplitude, the optical field deviation only needs to be calculated based on the amplitude deviation. No. The amplitude deviation of each constrained surface is defined as: The amplitude deviation distribution; For constraint surfaces The ideal amplitude distribution; For constraint surfaces The actual amplitude distribution; For the identification index of the constraint surface; For spatial coordinates; its physical meaning is the difference between the actual amplitude and the ideal amplitude, reflecting the deviation requirement of the amplitude constraint of the constraint surface; Weighted correction matrix The amplitude constraint deviation of each constraint surface needs to be mapped to the correction requirement of the preset focal point through the propagation operator, and the formula is: In the formula, The number of light field groups involved in the correction; For light field deviation Corrected weights; The sequence number of the light field group; propagation operator Describing the light field from the constraint surface Propagation to the focal point can be represented in the frequency domain as: in, For constraint surfaces Distance from the preset focus; Wavelength; Let be the normalized spatial frequency of the light field in the frequency domain. The propagation operator inverse operation is used to "reverse propagate" the amplitude deviation of the constraint surface back to the focal point, thereby realizing a closed loop for optical field correction based on amplitude constraints.

7. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program is executed by a processor to implement the hologram generation method for circular-arc chamfer cutting according to any one of claims 1-5.

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