A method and system for designing a progressive multifocal lens based on linear solution-nonlinear correction with residual field compensation

Abstract

The application provides a linear solution-nonlinear correction progressive multifocal lens design method and system based on residual field compensation, and belongs to the technical field of optical element design. The method comprises the following steps: scanning the curvature radius and selecting the optimal spherical base with the minimum power deviation energy; constructing a linear solver based on the linearization expansion of Euler-Lagrange equation to obtain an initial surface height; calculating the real average curvature through strict differential geometry formula, constructing a residual field feedback correction driving power field, and iterating until the error meets the standard; rotating and transforming the coordinate system according to the prescription astigmatism axis position, superimposing the toric component and adjusting the astigmatism attenuation through the proportional coefficient; adding a smoothing factor to optimize the surface processing, and combining intelligent thickness compensation to ensure that the thinnest point of the lens meets the impact resistance standard. The application solves the problems of power loss and astigmatism deviation in the high-addition and high-astigmatism scenarios, adapts to large-scale customization demand, and improves the visual effect and processing feasibility of the progressive multifocal lens.

Description

Technical Field

[0001] This invention belongs to the field of optical element design technology, specifically relating to a linear solution-nonlinear correction progressive multifocal lens design method and system based on residual field compensation. Background Technology

[0002] The core of progressive multifocal lens design lies in solving for a continuous and smooth freeform surface based on the user's prescription (including parameters such as spherical power, cylindrical power, axis, and under-illuminated power) to achieve continuous clear vision at distance, near, and intermediate distances.

[0003] In existing technologies, the design methods for progressive multifocal lenses are mainly divided into direct surface design and variational partial differential equation (PDE) design. The variational PDE method determines the optimal surface shape by solving for the extrema of the energy functional, which can better balance the overall optical power distribution and has become a commonly used technical approach in the industry. To meet the computational speed requirements of industrial production, existing designs typically linearize the nonlinear Euler-Lagrange equations. This simplification can meet basic requirements in low-power lens design, but in high-power or high-astigmatism scenarios, the surface gradient of the lens changes drastically, the linearization assumption fails, and higher-order errors become significant. The linearization model ignores higher-order gradient terms, which not only causes the actual optical power to be significantly lower than the target value but also causes unexpected distortion of iso-optical power lines, affecting visual effects. While using a fully nonlinear solver can guarantee design accuracy, it suffers from long computation time and poor numerical stability, making it difficult to meet the efficiency requirements of large-scale industrial customization.

[0004] Therefore, how to ensure design accuracy while taking into account computational efficiency, and how to fill the technological gap between rapid estimation and accurate simulation, has become a key issue that urgently needs to be addressed in the field of progressive multifocal lens design. Summary of the Invention

[0005] The purpose of this invention is to address the problems of large computational errors and low computational efficiency in solving linearized partial differential equations when dealing with high-power and high-astigmatism lenses in the prior art. This invention provides a linear solution-nonlinear correction progressive multifocal lens design method and system based on residual field compensation. It retains the efficiency of the linear solver while introducing an external nonlinear error observation and compensation loop based on rigorous differential geometry formulas. Through linear prediction and nonlinear correction, it generates high-quality progressive multifocal lenses that meet national optical standards and converge quickly.

[0006] In a first aspect, embodiments of the present invention provide a linear solution-nonlinear correction progressive multifocal lens design method based on residual field compensation, the method comprising the following steps: S1. Scan different radii of curvature, calculate the optical power deviation energy corresponding to each radius of curvature, and select the radius of curvature with the smallest optical power deviation energy as the optimal spherical substrate. S2. Based on the linearized expansion of the Euler-Lagrange equations near the optimal spherical base, a linear solver is constructed to solve the linear elliptic partial differential equations and obtain the initial surface shape sag. S3. Calculate the true average curvature of the current surface corresponding to the initial surface elevation using rigorous differential geometric formulas; S4. Calculate the deviation between the true average curvature and the target curvature, construct the residual field, feed the residual field back to the driving optical power field, correct the input of the linear solver, and iterate through multiple rounds until the key point error is less than the preset threshold. S5. Based on the astigmatic axis in the prescription astigmatism, perform a rotation transformation on the spherical base coordinate system and superimpose the complex surface component on the spherical base; calculate the equivalent astigmatism value after superposition. If it deviates from the target, scale the input astigmatism amount by a scaling factor to offset the astigmatism attenuation caused by the curvature of the freeform surface. S6. Add a smoothing factor to the linear solver, apply gradient penalty to the non-functional area of ​​the lens, perform thickness compensation, calculate the gap between the lens and the front surface, and automatically adjust the center thickness of the lens.

[0007] Furthermore, step S1 specifically includes: Scan multiple radii of curvature with different values R Calculate the radius of curvature for each curve. R Corresponding optical power deviation energy I ( R The optical power deviation energy I ( R By detecting the actual optical power of the lens at the corresponding radius of curvature and the target optical power... P target The accumulated deviation is used to determine the selected optical power deviation energy. I ( R The minimum radius of curvature is used as the optimal spherical base.

[0008] Furthermore, the specific steps of step S2 are as follows: S21. Based on the linear expansion of the Euler-Lagrange equations near the optimal spherical basis, construct a linear solver. L ( u ); S22. The initial state is equal to the target optical power. P target Driven optical power P drive To obtain the initial surface profile elevation, solve the linear elliptic partial differential equation as the input excitation. u The solution to the linear elliptic partial differential equation is as follows:

[0009] Among them, the driving optical power in the initial state P drive Equal to target optical power P target .

[0010] Further, in step S3, the formula for calculating the true average curvature of the current surface type is:

[0011] After obtaining the initial surface elevation u, the true mean curvature of the initial surface elevation u is directly calculated using rigorous differential geometric formulas. H actual , u x For surface profile elevation u right x First-order partial derivative in the direction; u y For surface profile elevation u right y First-order partial derivative in the direction; u xx For surface profile elevation u right x Second-order partial derivative in direction; u yy For surface profile elevation u right y Second-order partial derivative in direction; u xy For surface profile elevation u right x , y Mixed second-order partial derivatives in the direction.

[0012] Furthermore, the specific steps of step S4 are as follows: S41. Calculate the deviation between the true mean curvature and the target curvature, and construct the residual field:

[0013] in, This represents the deviation between the average curvature and the target curvature. S42. Optical power is driven by the input of the linear solver, which is then corrected by the residual field. P drive :

[0014] in, The driving optical power before correction. The corrected driving optical power. It is a relaxation factor.

[0015] Furthermore, in step S5, the formula for superimposing the complex surface components on the spherical substrate is:

[0016]

[0017] in, The coordinate system after rotation transformation represents the sagitta of the complex surface. , Let be the radius of curvature of the complex surface. For the new base sagitta including astigmatism, The optimal spherical base sagitta is given.

[0018] Furthermore, in step S5, if the calculated and superimposed equivalent astigmatism value deviates from the target, the specific steps for scaling the input astigmatism amount using a scaling factor to offset the astigmatism attenuation caused by the curvature of the freeform surface are as follows: S51. Based on the refractive index n of the lens material, convert the radius of curvature of the torus into the optical power in the corresponding direction:

[0019] S52. The equivalent astigmatism value is the absolute difference between the optical powers in two directions:

[0020] S53. Comparison With the target astigmatism value If the deviation exceeds the preset threshold, an adjustment will be initiated. S54. Input astigmatism amount The adjustment formula is:

[0021] in, This is a dynamic scaling factor; S55. Adjustment Then, the complex surface components are re-superimposed, and the equivalent astigmatism value is calculated. until and The deviation is less than or equal to the preset threshold.

[0022] Furthermore, in step S54, the dynamic scaling factor The adjustment rules are as follows: like < Increase Up to the first preset value; like > , reduce To the second preset value; in, The initial value is 1.

[0023] Furthermore, in step S6: The smoothing factor γ is used to balance the optical performance of the lens with the feasibility of processing. The system calculates the gap between the lens and the front surface across the entire field and automatically adjusts the lens center thickness (CT) to ensure that the thinnest point of the lens meets the impact resistance standard.

[0024] In a second aspect, embodiments of the present invention also provide a linear solution-nonlinear correction progressive multifocal lens design system based on residual field compensation, the system being used to implement the method described in the first aspect, the system comprising: The spherical substrate determination module is used to scan different radii of curvature, calculate the optical power deviation energy corresponding to each radius of curvature, and select the radius of curvature with the smallest optical power deviation energy as the optimal spherical substrate. The linear solver module is used to construct a linear solver based on the linearized expansion of the Euler-Lagrange equations near the optimal spherical base, solve the linear elliptic partial differential equations, and obtain the initial surface shape sag. The average curvature calculation module is used to calculate the true average curvature of the current surface corresponding to the initial surface elevation using rigorous differential geometry formulas. The residual calculation and feedback module is used to calculate the deviation between the true average curvature and the target curvature, construct the residual field, feed the residual field back to the driving optical power field, correct the input of the linear solver, and iterate through multiple rounds until the key point error is less than the preset threshold. The astigmatism coupling module is used to rotate and transform the spherical base coordinate system according to the astigmatism axis in the prescription astigmatism, and superimpose the complex surface component on the spherical base; calculate the equivalent astigmatism value after superposition; if it deviates from the target, the input astigmatism amount is scaled by a scaling factor to offset the astigmatism attenuation caused by the curvature of the freeform surface. The surface optimization module adds a smoothing factor to the linear solver, applies gradient penalty to the non-functional areas of the lens, performs thickness compensation, calculates the gap between the lens and the front surface, and automatically adjusts the center thickness of the lens.

[0025] As can be seen from the above technical solutions, the present invention has the following advantages: The linear solution-nonlinear correction design, employing an optimal spherical substrate and residual field feedback, retains the computational efficiency of the linear solver while utilizing rigorous differential geometry formulas to calculate the true average curvature and construct a residual field to correct optical power. This avoids higher-order errors caused by the failure of linearization assumptions, ensuring optical power accuracy even in high-intensity and high-astigmatism scenarios. Multi-round iterative feedback of the residual field compensates for higher-order gradient terms neglected by the linearization model, matching the actual optical power with the target value and eliminating unexpected distortions in iso-optical power lines, thus improving visual comfort. The linear solution-nonlinear correction framework, combining linear solution and residual compensation, avoids the time-consuming and stability issues of fully nonlinear solutions while maintaining design accuracy, adapting to the efficiency requirements of large-scale industrial customization. Coordinate rotation transformation and dynamic scaling factor adjustment offset the astigmatism attenuation caused by freeform surfaces, ensuring the accuracy of axis and degree in high-astigmatism prescriptions. Attached Figure Description

[0026] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a flowchart illustrating the linear solution-nonlinear correction progressive multifocal lens design method based on residual field compensation of the present invention.

[0028] Figure 2 This is a thermal diagram illustrating the error generated by the linear approximation of existing technology.

[0029] Figure 3 This is a thermodynamic diagram illustrating the error generated by the linear solution-nonlinear correction of this invention.

[0030] Figure 4 This is a comparative schematic diagram of the meridional optical power profile of the present invention.

[0031] Figure 5 This is a schematic diagram of the linear solution-nonlinear correction progressive multifocal lens design system based on residual field compensation according to the present invention. Detailed Implementation

[0032] The various embodiments of the invention will be described more fully in the detailed steps of the linear solution-nonlinear correction progressive multifocal lens design method based on residual field compensation, which will be described in detail below. The invention may have various embodiments, and adjustments and modifications may be made therein. However, it should be understood that there is no intention to limit the various embodiments of the invention to the specific embodiments disclosed herein, but rather the invention should be understood to cover all adjustments, equivalents, and / or alternatives falling within the spirit and scope of the various embodiments of the invention.

[0033] It should be understood that, when used in this specification, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or collections thereof. The terms "comprising," "including," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0034] The terms "one embodiment" or "some embodiments" used in this invention mean that one or more embodiments of the invention include the specific features, structures, or characteristics described in that embodiment. Therefore, the terms "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of the invention do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized.

[0035] To make the objectives, features, and advantages of this invention more apparent and understandable, specific embodiments and accompanying drawings will be used to clearly and completely describe the technical solutions protected by this invention. Obviously, the embodiments described below are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0036] Please see Figure 1 The diagram shows a flowchart of a linear solution-nonlinear correction progressive multifocal lens design method based on residual field compensation. The method includes the following steps: S1. Scan different radii of curvature, calculate the optical power deviation energy corresponding to each radius of curvature, and select the radius of curvature with the smallest optical power deviation energy as the optimal spherical substrate; S2. Based on the linearized expansion of the Euler-Lagrange equations near the optimal spherical base, a linear solver is constructed to solve the linear elliptic partial differential equations and obtain the initial surface elevation. S3. Calculate the true average curvature of the current surface corresponding to the initial surface elevation using rigorous differential geometry formulas; S4. Calculate the deviation between the true average curvature and the target curvature, construct the residual field, feed the residual field back to the driving optical power field, correct the input of the linear solver, and iterate through multiple rounds until the key point error is less than the preset threshold. S5. Based on the astigmatic axis in the prescription astigmatism, perform a rotation transformation on the spherical base coordinate system and superimpose the complex surface component on the spherical base; calculate the equivalent astigmatism value after superposition; if it deviates from the target, scale the input astigmatism amount by a scaling factor to offset the astigmatism attenuation caused by the curvature of the freeform surface. S6. Add a smoothing factor to the linear solver, apply gradient penalty to the non-functional area of ​​the lens, perform thickness compensation, calculate the gap between the lens and the front surface, and automatically adjust the center thickness of the lens.

[0037] As a refinement and extension of the specific implementation of the above embodiments, in order to fully illustrate the specific implementation process of this embodiment, another linear solution-nonlinear correction progressive multifocal lens design method based on residual field compensation is provided. This method includes the following steps: S1. Scan different radii of curvature, calculate the optical power deviation energy corresponding to each radius of curvature, and select the radius of curvature with the smallest optical power deviation energy as the optimal spherical substrate; the specific steps of S1 are as follows: Scan multiple radii of curvature with different values R Calculate the radius of curvature for each curve. R Corresponding optical power deviation energy I ( R The optical power deviation energy I ( R By detecting the actual optical power of the lens at the corresponding radius of curvature and the target optical power... P target The accumulated deviation is used to determine the selected optical power deviation energy. I ( R The minimum radius of curvature is used as the optimal spherical base.

[0038] In some embodiments, the lens design grid is initialized (using a uniform sampling grid of 1024×1024), and the target optical power field on the rear surface is calculated (+5.00D in the distance vision zone, +5.00D+2.00D=+7.00D in the near vision zone, with a continuous transition in optical power in the gradient zone). The radius of curvature is then scanned. R (Range: 50mm~100mm, step size 2mm), calculate the radius of curvature for each curve. R Corresponding optical power deviation energy I ( R ): when RWhen the focal length is 75mm, the cumulative optical power deviation in the distance zone is 0.08D. when R At 80mm, the optical power deviation energy I ( R Minimum (0.03D), select R =80mm is the optimal radius for the spherical base.

[0039] S2. Based on the linearized expansion of the Euler-Lagrange equations near the optimal spherical basis, construct a linear solver to solve the linear elliptic partial differential equations and obtain the initial surface elevation. The specific steps of step S2 are as follows: S21. Based on the linear expansion of the Euler-Lagrange equations near the optimal spherical basis, construct a linear solver. L ( u ); S22. The initial state is equal to the target optical power. P target Driven optical power P drive To obtain the initial surface profile elevation, solve the linear elliptic partial differential equation as the input excitation. u The solution to the linear elliptic partial differential equation is as follows:

[0040] Among them, the driving optical power in the initial state P drive Equal to target optical power P target .

[0041] In some embodiments, based on the Euler-Lagrange equations R Linear expansion is performed near the optimal spherical base of 80 mm to construct a linear solver. L ( u ), with the target optical power field as the driving optical power field P drive (initial P drive =Target optical power P target Solve the linear elliptic partial differential equation to obtain the initial surface elevation. u Distribution data.

[0042] S3. Calculate the true average curvature of the current surface corresponding to the initial surface elevation using rigorous differential geometry formulas; in step S3, the formula for calculating the true average curvature of the current surface is:

[0043] After obtaining the initial surface elevation u, the true mean curvature of the initial surface elevation u is directly calculated using rigorous differential geometric formulas. H actual , u x For surface profile elevation u right x First-order partial derivative in the direction; u y For surface profile elevation u right y First-order partial derivative in the direction; u xx For surface profile elevation u right x Second-order partial derivative in direction; u yy For surface profile elevation u right y Second-order partial derivative in direction; u xy For surface profile elevation u right x , y Mixed second-order partial derivatives in the direction.

[0044] In some embodiments, the true average curvature is calculated using a strict differential geometry formula (including all higher-order gradient terms) for the initial surface profile height u obtained in step S2. If the calculated optical power is +4.92D, it deviates from the target curvature corresponding to +5.00D.

[0045] S4. Calculate the deviation between the true average curvature and the target curvature, construct the residual field, feed the residual field back to the driving optical power field, correct the input of the linear solver, and iterate through multiple rounds until the key point error is less than a preset threshold; the specific steps of step S4 are as follows: S41. Calculate the deviation between the true mean curvature and the target curvature, and construct the residual field:

[0046] in, This represents the deviation between the average curvature and the target curvature. S42. Optical power is driven by the input of the linear solver, which is then corrected by the residual field. P drive :

[0047] in, The driving optical power before correction. The corrected driving optical power. It is a relaxation factor.

[0048] In some embodiments, after solving the initial surface elevation, residual field feedback iteration is performed: The deviation between the true mean curvature and the target curvature is calculated. The target curvature in the far field corresponds to an optical power of +5.00D, while the actual optical power corresponding to the true mean curvature is +4.92D. A residual field Residual(x,y) is constructed: Residual(x,y) = 5.00D - 4.92D = 0.08D. The driving optical power field is corrected by taking a relaxation factor λ = 0.3, resulting in a corrected driving optical power field of 4.944D. After repeated iterations, the residual field shrinks to 0.01D, and the keypoint error in the far field (0.01D) is lower than the preset threshold (0.05D). The iteration converges, and the actual optical power stabilizes at +4.99D.

[0049] S5. Based on the astigmatic axis in the prescription astigmatism, perform a rotation transformation on the spherical base coordinate system, and superimpose complex surface components on the spherical base; calculate the equivalent astigmatism value after superposition. If it deviates from the target, scale the input astigmatism amount using a scaling factor to offset the astigmatism attenuation caused by the curvature of the freeform surface; the formula for superimposing complex surface components on the spherical base in step S5 is:

[0050]

[0051] in, The coordinate system after rotation transformation represents the sagitta of the complex surface. , Let be the radius of curvature of the complex surface. For the new base sagitta including astigmatism, The optimal spherical base sagitta is given.

[0052] In step S5, if the calculated and superimposed equivalent astigmatism value deviates from the target, the specific steps for offsetting the astigmatism attenuation caused by the curvature of the freeform surface by scaling the input astigmatism amount using a scaling factor are as follows: S51. Based on the refractive index n of the lens material, convert the radius of curvature of the torus into the optical power in the corresponding direction:

[0053] S52. The equivalent astigmatism value is the absolute difference between the optical powers in two directions:

[0054] S53. Comparison With the target astigmatism value If the deviation exceeds the preset threshold, an adjustment will be initiated. S54. Input astigmatism amount The adjustment formula is:

[0055] in, This is a dynamic scaling factor; In step S54, the dynamic scaling factor The adjustment rules are as follows: like < Increase Up to the first preset value; like > , reduce To the second preset value; in, The initial value is 1.

[0056] S55. Adjustment Then, the complex surface components are re-superimposed, and the equivalent astigmatism value is calculated. until and The deviation is less than or equal to the preset threshold.

[0057] In some embodiments, a prescription is used with a spherical lens of +5.00D, astigmatism of -1.50D, and an axis of 90°. Based on the prescription axis of 90°, a rotation matrix is ​​applied to the optimal spherical base coordinate system (x for horizontal, y for vertical). x '= x , y '=- y Align with the principal direction of astigmatism (vertical direction); Take the refractive index of the lens material n =1.56, initial dynamic scaling factor =1, input astigmatism amount -1.50D; calculate the radius of curvature of the complex surface. =84.4mm =65.8mm, calculate the sagitta of the complex surface, superimpose it to the optimal base sagitta, and obtain the new base sagitta; Calculated using rigorous differential geometry formulas, the vertical optical power is +5.00D, the horizontal optical power is +6.38D, and the equivalent astigmatism is -1.38D. This deviates from the target astigmatism of -1.50D by 0.12D (exceeding the preset ±0.02D threshold). Because... < Increase Upgraded to version 1.09 (adjusted according to actual conditions), the input astigmatism was updated to -1.635D. The curvature radius and superposition sag of the complex surface were recalculated, and the equivalent astigmatism value was recalculated to -1.49D, with a deviation of 0.01D from the target. The equivalent astigmatism value of the superimposed surface converged to -1.49D, with an axis error of 0.5°, matching the prescription astigmatism requirements.

[0058] S6. A smoothing factor is added to the linear solver to apply gradient penalty to the non-functional areas of the lens, perform thickness compensation, calculate the gap between the lens across the entire field and the front surface, and automatically adjust the lens center thickness. In step S6: In some embodiments, the smoothing factor γ ranges from 0.01 to 0.2, and is used to balance the optical performance of the lens with the feasibility of processing. The system calculates the gap between the lens and the front surface across the entire field and automatically adjusts the lens center thickness (CT) to ensure that the thinnest point of the lens meets the impact resistance standard.

[0059] In some embodiments, a smoothing factor γ = 0.05 is selected to penalize the surface gradient of the non-functional area (within 2 mm outside the viewing area) at the lens edge in the linear solver, suppressing the gradient fluctuation in this area from 0.8D / mm to 0.3D / mm, thus preserving the optical performance of the viewing area while reducing the manufacturing difficulty. Based on the current surface data, the gap between the entire field and the front surface is calculated. When the initial center thickness CT = 2.0 mm, the thickness at the thinnest point at the edge is only 0.8 mm (which does not meet the impact resistance standard). Based on the sagitta of the lens's front surface (usually spherical) and the sagitta of its front and rear surfaces (freeform surfaces), the thickness at any position of the lens is calculated (thickness = front surface sagitta - rear surface sagitta + center thickness CT). The entire field thickness data is iterated to find the position corresponding to the minimum value (usually the non-functional area at the lens edge). If the thinnest point thickness is <1.0mm, CT is increased according to the rule ΔCT = 1.0mm - current thinnest point thickness + safety margin (0.2mm), and the entire field thickness is recalculated until the thinnest point thickness >1.0mm. After adjusting CT, the optical power of the viewing area is re-verified to ensure that thickness compensation does not affect core optical parameters. Through thickness compensation, CT is automatically adjusted to 2.5mm, the entire field gap is recalculated, and the final thickness of the thinnest point (edge ​​area) of the lens increases to 1.2mm.

[0060] It should be noted that, Figure 2 This is a schematic diagram of the error generated by linear approximation in the prior art. Figure 3 The error heatmap generated in this embodiment of the invention, compared with the large area error of >0.20D generated by the traditional linear method, this embodiment converges the maximum residual of the effective view area to within the range of 0.05D, which meets the GB 10810.2-2006 standard. Figure 4 This is a schematic diagram comparing the optical power profile of the meridian. The optical power curve of this embodiment highly coincides with the target curve, eliminating the oscillation and insufficient degree phenomenon in the linear solution.

[0061] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0062] Please see Figure 5 The figure shows a linear solution-nonlinear correction progressive multifocal lens design system based on residual field compensation. The system includes: The spherical substrate determination module is used to scan different radii of curvature, calculate the optical power deviation energy corresponding to each radius of curvature, and select the radius of curvature with the smallest optical power deviation energy as the optimal spherical substrate. The linear solver module is used to construct a linear solver based on the linearized expansion of the Euler-Lagrange equations near the optimal spherical base, solve the linear elliptic partial differential equations, and obtain the initial surface shape sag. The average curvature calculation module is used to calculate the true average curvature of the current surface corresponding to the initial surface elevation using rigorous differential geometry formulas. The residual calculation and feedback module is used to calculate the deviation between the true average curvature and the target curvature, construct the residual field, feed the residual field back to the driving optical power field, correct the input of the linear solver, and iterate through multiple rounds until the key point error is less than the preset threshold. The astigmatism coupling module is used to rotate and transform the spherical base coordinate system according to the astigmatism axis in the prescription astigmatism, and superimpose the complex surface component on the spherical base; calculate the equivalent astigmatism value after superposition; if it deviates from the target, the input astigmatism amount is scaled by a scaling factor to offset the astigmatism attenuation caused by the curvature of the freeform surface. The surface optimization module adds a smoothing factor to the linear solver, applies gradient penalty to the non-functional areas of the lens, performs thickness compensation, calculates the gap between the lens and the front surface, and automatically adjusts the center thickness of the lens.

[0063] This embodiment improves computational efficiency and accuracy through the interactive collaboration of the spherical substrate determination module, linear solution module, average curvature calculation module, residual calculation and feedback module, astigmatism coupling module, and surface optimization module.

[0064] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for manufacturing a linear solution-nonlinear correction progressive multifocal lens based on residual field compensation, characterized in that, The method includes the following steps: S1. Scan different radii of curvature, calculate the optical power deviation energy corresponding to each radius of curvature, and select the radius of curvature with the smallest optical power deviation energy as the optimal spherical substrate. S2. Based on the linearized expansion of the Euler-Lagrange equations near the optimal spherical base, a linear solver is constructed to solve the linear elliptic partial differential equations and obtain the initial surface shape sag. S3. Calculate the true average curvature of the current surface corresponding to the initial surface elevation using rigorous differential geometric formulas; S4. Calculate the deviation between the true average curvature and the target curvature, construct the residual field, feed the residual field back to the driving optical power field, correct the input of the linear solver, and iterate through multiple rounds until the key point error is less than the preset threshold. S5. Based on the astigmatic axis in the prescription astigmatism, perform a rotation transformation on the spherical base coordinate system and superimpose the complex surface component on the spherical base; calculate the equivalent astigmatism value after superposition. If it deviates from the target, scale the input astigmatism amount by a scaling factor to offset the astigmatism attenuation caused by the curvature of the freeform surface. S6. Add a smoothing factor to the linear solver, apply gradient penalty to the non-functional area of ​​the lens, perform thickness compensation, calculate the gap between the lens and the front surface, and automatically adjust the center thickness of the lens. In step S5, the formula for superimposing complex surface components on the spherical substrate is: in, The coordinate system after rotation transformation represents the sagitta of the complex surface. , Let be the radius of curvature of the complex surface. For the new base sagitta including astigmatism, The optimal spherical base sagitta; In step S5, if the calculated and superimposed equivalent astigmatism value deviates from the target, the specific steps for offsetting the astigmatism attenuation caused by the curvature of the freeform surface by scaling the input astigmatism amount using a scaling factor are as follows: S51. Based on the refractive index n of the lens material, convert the radius of curvature of the torus into the optical power in the corresponding direction: S52. The equivalent astigmatism value is the absolute difference between the optical powers in two directions: S53. Comparison With the target astigmatism value If the deviation exceeds the preset threshold, an adjustment will be initiated. S54. Input astigmatism amount The adjustment formula is: in, This is a dynamic scaling factor; S55. Adjustment Then, the complex surface components are re-superimposed, and the equivalent astigmatism value is calculated. until and The deviation is less than or equal to the preset threshold; In step S54, the dynamic scaling factor The adjustment rules are as follows: like < Increase Up to the first preset value; like > , reduce To the second preset value; in, The initial value is 1; In step S6: The smoothing factor γ is used to balance the optical performance of the lens with the feasibility of processing, and its value ranges from 0.01 to 0.

2. The gap between the lens and the front surface is calculated across the entire field and the lens center thickness CT is automatically adjusted so that the thinnest point of the lens meets the impact resistance standard. Step S6 includes: penalizing the surface gradient of the non-functional area at the edge of the lens in the linear solver by using a smoothing factor, suppressing the gradient fluctuation in this area from 0.8D / mm to 0.3D / mm; calculating the gap between the entire field and the front surface based on the current surface data; if the impact resistance standard is not met, calculating the thickness of the lens at any position based on the sag of the front surface and the current sag of the rear surface; traversing the entire field thickness data to find the position corresponding to the minimum value; if the thickness of the thinnest point is <1.0mm, increasing the lens center thickness CT according to the rule ΔCT=1.0mm-current thinnest point thickness+safety margin, recalculating the entire field thickness until the thickness of the thinnest point of the lens is >1.0mm; through thickness compensation, automatically adjusting the lens center thickness CT to 2.5mm, recalculating the entire field gap, and finally increasing the thickness of the thinnest point of the lens to 1.2mm.

2. The method for manufacturing a linearly solved, nonlinearly corrected progressive multifocal lens based on residual field compensation according to claim 1, characterized in that, The specific steps of step S1 are as follows: Scan multiple radii of curvature with different values R Calculate the radius of curvature for each curve. R Corresponding optical power deviation energy I ( R The optical power deviation energy I ( R By detecting the actual optical power of the lens at the corresponding radius of curvature and the target optical power... P target The accumulated deviation is used to determine the selected optical power deviation energy. I ( R The minimum radius of curvature is used as the optimal spherical base.

3. The method for manufacturing a linearly solved, nonlinearly corrected progressive multifocal lens based on residual field compensation according to claim 1, characterized in that, The specific steps of step S2 are as follows: S21. Based on the linear expansion of the Euler-Lagrange equations near the optimal spherical basis, construct a linear solver. L ( u ); S22. The initial state is equal to the target optical power. P target Driven optical power P drive To obtain the initial surface profile elevation, solve the linear elliptic partial differential equation as the input excitation. u The solution to the linear elliptic partial differential equation is as follows: Among them, the driving optical power in the initial state P drive Equal to target optical power P target .

4. The method for manufacturing a linearly solved, nonlinearly corrected progressive multifocal lens based on residual field compensation according to claim 3, characterized in that, In step S3, the formula for calculating the true average curvature of the current surface type is: After obtaining the initial surface elevation u, the true mean curvature of the initial surface elevation u is directly calculated using rigorous differential geometric formulas. H actual , u x For surface profile elevation u right x First-order partial derivative in the direction; u y For surface profile elevation u right y First-order partial derivative in the direction; u xx For surface profile elevation u right x Second-order partial derivative in direction; u yy For surface profile elevation u right y Second-order partial derivative in direction; u xy For surface profile elevation u right x , y Mixed second-order partial derivatives in the direction.

5. The method for manufacturing a linearly solved, nonlinearly corrected progressive multifocal lens based on residual field compensation according to claim 4, characterized in that, The specific steps of step S4 are as follows: S41. Calculate the deviation between the true mean curvature and the target curvature, and construct the residual field: in, This represents the deviation between the average curvature and the target curvature. S42. Optical power is driven by the input of the linear solver, which is then corrected by the residual field. P drive : in, The driving optical power before correction. The corrected driving optical power. It is a relaxation factor.

6. A linear solution-nonlinear correction progressive multifocal lens design system based on residual field compensation, the system being used to implement the method as described in any one of claims 1-5, characterized in that, The system includes: The spherical substrate determination module is used to scan different radii of curvature, calculate the optical power deviation energy corresponding to each radius of curvature, and select the radius of curvature with the smallest optical power deviation energy as the optimal spherical substrate. The linear solver module is used to construct a linear solver based on the linearized expansion of the Euler-Lagrange equations near the optimal spherical base, solve the linear elliptic partial differential equations, and obtain the initial surface shape sag. The average curvature calculation module is used to calculate the true average curvature of the current surface corresponding to the initial surface elevation using rigorous differential geometry formulas. The residual calculation and feedback module is used to calculate the deviation between the true average curvature and the target curvature, construct the residual field, feed the residual field back to the driving optical power field, correct the input of the linear solver, and iterate through multiple rounds until the key point error is less than the preset threshold. The astigmatism coupling module is used to rotate and transform the spherical base coordinate system according to the astigmatism axis in the prescription astigmatism, and superimpose the complex surface component on the spherical base; calculate the equivalent astigmatism value after superposition; if it deviates from the target, the input astigmatism amount is scaled by a scaling factor to offset the astigmatism attenuation caused by the curvature of the freeform surface. The surface optimization module adds a smoothing factor to the linear solver, applies gradient penalty to the non-functional areas of the lens, performs thickness compensation, calculates the gap between the lens and the front surface, and automatically adjusts the center thickness of the lens.

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