A method of astigmatism control for progressive lenses and related devices

Abstract

The application discloses a stigmation control method of progressive lenses and a related device, and relates to the field of progressive multifocal lens design. The method comprises the following steps: selecting a plurality of sampling points on a first surface in the aperture of the progressive lenses; calculating the average diopter and the stigmation amplitude of each sampling point under a first optical condition and a second optical condition, respectively, and constructing a first residual control item and a second residual control item, respectively; constructing a first stigmation control optimization target according to the first residual control item, and solving a first lens design variable meeting the first stigmation control optimization target; constructing a second stigmation control optimization target according to the second residual control item, and solving the second stigmation control optimization target by taking the first surface structure determined by the first lens design variable as an optimization reference, to obtain a second lens design variable. The application can keep the average diopter distribution stable in the direction of the progressive channel while optimizing the stigmation.

Description

Technical Field

[0001] This application relates to the field of progressive multifocal lens design, and in particular to a method and apparatus for controlling astigmatism in progressive lenses. Background Technology

[0002] Progressive multifocal lenses achieve a gradual change in refractive power from the distance vision zone to the near vision zone by creating a continuously varying curvature distribution on the lens surface. According to Minkwitz's theorem, the faster the change in refractive power along the progressive path, the greater the change in astigmatism on both sides of the lens. Therefore, astigmatism is inevitable in progressive lens design, and the design goal is usually to optimize and control the amplitude, gradient, and spatial distribution of astigmatism.

[0003] In existing progressive lens design methods, astigmatism control is typically achieved through the following methods: 1. Single-stage multi-objective optimization: Refractive power and astigmatism are optimized simultaneously, but the coupling is strong and the initial value is sensitive, making it difficult to achieve astigmatism optimization while maintaining the stability of the average refractive power distribution in the asymptotic channel direction; 2. Direct optimization under wearing conditions: Astigmatism is controlled under actual wearing conditions, but the average refractive power distribution in the asymptotic channel direction is easily disrupted. There is a lack of a unified strategy for optimizing normal incidence and wearing conditions, resulting in low design stability. 3. Local empirical correction: Astigmatism can be improved by adjusting local curvature or empirically, but it lacks systematic constraints and controllability. It is easy to destroy the progressive channel refractive power target during the process of adjusting the lateral curvature.

[0004] Most of the methods described above optimize under a single optical condition, lacking a mechanism to establish consistent constraints across different optical modeling conditions (such as normal incidence and wearing conditions). During multi-condition switching or joint optimization, strong coupling remains between refractive power constraints and astigmatism control, easily leading to instability in the optimization process or introducing additional refractive power deviations while improving astigmatism. Therefore, establishing a unified and stable constraint optimization mechanism under different optical conditions has become an urgent technical problem to be solved. Summary of the Invention

[0005] The purpose of this application is to provide a method and related device for controlling astigmatism in progressive lenses, which can optimize astigmatism while maintaining a stable average refractive power distribution in the progressive channel direction, thereby improving the visual comfort and adaptability of the wearer when wearing the designed progressive lens.

[0006] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a method for controlling astigmatism in progressive lenses, comprising: Several sampling points are selected on the first surface within the aperture of the progressive lens; Under the first optical conditions, calculate the first average refractive power and the first astigmatism amplitude at each sampling point; The first residual control term is constructed based on the first average refractive power and the first astigmatism amplitude at each sampling point; The first astigmatism control optimization objective is constructed based on the first residual control term, and the first lens design variables that satisfy the first astigmatism control optimization objective are solved. The first lens design variables are used to characterize the geometry of the first surface of the progressive lens and to ensure that the progressive lens meets the preset average refractive power distribution and astigmatism control requirements under the first optical conditions. Based on the first surface geometry corresponding to the first lens design variables, and under the second optical conditions, the second average diopter and the second astigmatism amplitude value of each sampling point are calculated. A second residual control term is constructed based on the second average refractive power and the second astigmatism amplitude at each sampling point; The second astigmatism control optimization objective is constructed based on the second residual control term. The first surface geometry determined by the first lens design variables is used as the optimization benchmark to solve the second astigmatism control optimization objective and obtain the second lens design variables. This allows for the optimized control of the astigmatism distribution of the progressive lens under the second optical conditions without compromising the optical response constraints corresponding to the design objective under the first optical conditions.

[0007] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and capable of running on the processor, wherein the processor executes the computer program to implement the aforementioned progressive lens astigmatism control method.

[0008] Thirdly, this application provides a computer program product, including a computer program that, when executed by a processor, implements the aforementioned progressive lens astigmatism control method.

[0009] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a method and related apparatus for astigmatism control in progressive lenses. Several sampling points are selected on a first surface within the aperture of the progressive lens. Under first and second optical conditions, the average refractive power and astigmatism amplitude of each sampling point are calculated, and a first residual control term and a second residual control term are constructed respectively. A first astigmatism control optimization objective is constructed based on the first residual control term, and the first lens design variables satisfying the first astigmatism control optimization objective are solved. A second astigmatism control optimization objective is constructed based on the second residual control term, and the first surface geometry determined by the first lens design variables is used as the optimization benchmark to solve the second astigmatism control optimization objective, obtaining the second lens design variables. This application first constructs and solidifies refractive behavior constraints under first optical conditions during the progressive lens design process, and then performs astigmatism optimization under second optical conditions under these constraints. This effectively reduces design instability caused by multi-objective coupling, improves the accuracy and stability of the progressive lens refractive power distribution, and simultaneously improves astigmatism distribution characteristics, thereby enhancing the wearer's visual comfort and adaptability. Attached Figure Description

[0010] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0011] Figure 1 This is an application environment diagram of a progressive lens astigmatism control method according to an embodiment of this application; Figure 2 A schematic flowchart illustrating a progressive lens astigmatism control method according to an embodiment of this application; Figure 3 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0012] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0013] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0014] The astigmatism control method for progressive lenses provided in this application can be applied to, for example... Figure 1 In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up independently, integrated into server 104, or placed in the cloud or on another server. Terminal 102 can send an instruction to server 104 to randomly select several sampling points on the first surface within the progressive lens aperture. Upon receiving the instruction, server 104 selects several sampling points on the first surface within the progressive lens aperture. Under first optical conditions, it calculates the first average refractive power and the first astigmatism amplitude for each sampling point. Based on the first average refractive power and the first astigmatism amplitude for each sampling point, it constructs a first residual control term. Based on the first residual control term, it constructs a first astigmatism control optimization objective and solves for the first lens design variables that satisfy the first astigmatism control optimization objective. Under second optical conditions, it calculates the second average refractive power and the second astigmatism amplitude for each sampling point. Based on the second average refractive power and the second astigmatism amplitude for each sampling point, it constructs a second residual control term. Based on the second residual control term, it constructs a second astigmatism control optimization objective and solves for the second astigmatism control optimization objective based on the first surface geometry determined by the first lens design variables as the optimization benchmark, obtaining the second lens design variables. Server 104 can then feed back the obtained second lens design variables that satisfy the second astigmatism control optimization objective to terminal 102.

[0015] Among them, terminal 102 can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices and portable wearable devices, and server 104 can be implemented by independent servers or server clusters composed of multiple servers, or it can be a cloud server.

[0016] In one exemplary embodiment, such as Figure 2 As shown, a method for controlling astigmatism in progressive lenses is provided. This method is executed by a computer device, specifically a terminal or server, or both. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the explanation includes the following steps 201 to 207. Wherein: Step 201: Select several sampling points on the first surface within the aperture of the progressive lens. The first surface refers to any freeform surface of the progressive lens.

[0017] Sampling within the progressive lens aperture Points The sampling methods include, but are not limited to, random sampling, grid sampling, non-uniform sampling, or sampling according to preset rules; The coordinates are the local planar coordinates of the first surface of the lens (in mm). The origin of the coordinates is usually set at the center of the asymptotic channel or the geometric optical center.

[0018] Step 202: Under the first optical conditions, calculate the first average diopter and the first astigmatism amplitude for each sampling point.

[0019] Step 203: Construct a first residual control term based on the first average refractive power and the first astigmatism amplitude at each sampling point. The first residual control term is used to characterize the deviation between the optical response under the first optical condition and the design target. The optical response includes, but is not limited to, the average refractive power, the astigmatism amplitude, and their spatial distribution characteristics.

[0020] Step 204: Construct the first astigmatism control optimization objective based on the first residual control term obtained in step 203, solve for the first lens design variable that satisfies the first astigmatism control optimization objective, which is used to characterize the geometric structure of the first surface of the progressive lens, and make the progressive lens meet the preset average refractive power distribution and astigmatism control requirements under the first optical conditions.

[0021] Step 205: Based on the first surface geometry corresponding to the first lens design variable obtained in step 204, calculate the second average diopter and the second astigmatism amplitude for each sampling point under the second optical conditions.

[0022] Step 206: Based on the second average refractive power and second astigmatism amplitude value obtained for each sampling point in step 205, construct a second residual control term. The second residual control term is used to characterize the deviation between the optical response under the second optical condition and the design target.

[0023] Step 207: Construct a second astigmatism control optimization objective based on the second residual control term obtained in step 206, and use the first surface geometry determined by the first lens design variables obtained in step 204 as the optimization benchmark to solve the second astigmatism control optimization objective and obtain the second lens design variables. This is to optimize and control the astigmatism distribution of the progressive lens under the second optical conditions while keeping the optical response constraints corresponding to the design objective under the first optical conditions intact.

[0024] The aforementioned optical conditions (first optical conditions and second optical conditions) characterize the geometric state or observation conditions when light is incident on a progressive lens, and may include, but are not limited to: ① Normal incident conditions, that is, the situation where light rays are incident along the normal direction of the lens surface; ② Wearing conditions, i.e., actual usage scenarios that take into account lens wearing parameters and changes in the angle of incidence of vision; ③ Oblique incidence condition, that is, the situation where light rays are incident on the lens at a non-zero angle of incidence; ④ Multi-viewpoint conditions, i.e., optical conditions corresponding to different viewing directions; ⑤ Modeling conditions based on different pupil light distributions, i.e. optical computation conditions constructed based on different light sampling strategies.

[0025] In this embodiment, the first optical condition is used to establish the calculation conditions for the reference refractive distribution. Taking the first optical condition as the normal incidence condition where light is incident along the normal direction of the lens surface and the second optical condition as the calculation condition for simulating the actual wearing state as an example, the astigmatism control method of this application is explained. In one embodiment, the second optical condition includes changes in the lens tilt angle, wrap angle, vertex distance and line of sight incident angle.

[0026] By implementing steps 201 to 207 above, using the first surface geometry determined by the first lens design variables obtained in step 204 as the optimization benchmark, the astigmatism distribution of the progressive lens is optimized and controlled under the second optical condition. Through the above steps, the optimization under the second optical condition is carried out on the basis of inheriting the refractive response structure determined under the first optical condition, thereby avoiding the destruction of the target optical response distribution established under the first optical condition in the subsequent astigmatism optimization process, and suppressing the introduction of additional refractive error during the second optical optimization process. This establishes a stable consistency constraint mechanism between different optical conditions, realizes the synergistic optimization of optical response under different optical conditions, and improves the stability and controllability of astigmatism distribution control.

[0027] In another exemplary embodiment of this application, step 202, under the first optical conditions, calculates the first average refractive power and the first astigmatism amplitude value for each sampling point, specifically including: (a1) Under the first optical conditions, the maximum and minimum refractive power at each sampling point are calculated based on the fundamental refractive component of the second surface of the progressive lens and the equivalent refractive component of the principal curvature direction of the first surface at each sampling point.

[0028] In one exemplary embodiment, to facilitate understanding of the structural relationship of a progressive lens, a progressive lens can be understood as including a first surface and a second surface disposed opposite to each other. The first surface and the second surface correspond to the two optical surfaces of the lens, respectively. In some embodiments, the first surface may be the surface closer to the human eye, and the second surface may be the surface farther from the human eye; however, this application is not limited to this, and the naming of the first surface and the second surface is only used to distinguish different surfaces, and does not limit their corresponding positional relationship with the human eye.

[0029] The formula for calculating the fundamental refractive component of the second surface of a progressive lens is as follows: in, The basic refractive component of the second surface of the progressive lens, expressed in diopters (D). The refractive index of the progressive lens material; The radius of curvature of the second surface is in mm; the factor 1000 is used for the unit conversion between the radius of curvature (mm) and the focal length (m) in the definition of diopter.

[0030] The equivalent refractive component along the principal curvature direction of the first surface can be calculated using the local second-order curvature of the first surface elevation function. In one exemplary embodiment, this can be achieved using the first surface elevation function. Calculating sampling points using the Hessian matrix The two principal curvatures The two principal curvatures are used to characterize the degree of principal curvature of the local surface, and are then converted into equivalent refractive components in the directions of the two principal curvatures of the first surface. The formula for calculating the equivalent refractive components in the directions of the two principal curvatures of the first surface is as follows: At the sampling point Maximum refractive power With minimum diopter The calculation formula is: (a2) Calculate the first average refractive power and the first astigmatism amplitude of each sampling point based on the maximum and minimum refractive power at each sampling point.

[0031] Among them, sampling points First mean diopter for: Sampling points First astigmatism value for: The first astigmatism amplitude can be expressed in an equivalent form during numerical optimization: The unit of the first astigmatism amplitude is diopter (D), and the astigmatism amplitude is used to describe the difference in refractive power at the sampling point.

[0032] In another exemplary embodiment of this application, in step 203, a first residual control term is constructed based on the first average refractive power and the first astigmatism amplitude at each sampling point. The first residual control term is used to characterize the deviation between the optical response under the first optical condition and the design target. Specifically, it includes: (b1) Construct the first average refractive power residual term based on the first average refractive power of each sampling point, the design target average refractive power, and the radial weight related to the position of the sampling point in the lens aperture.

[0033] (b2) Construct an astigmatic residual term based on the first astigmatic amplitude, astigmatic threshold and radial weight related to the position of the sampling point in the lens aperture for each sampling point; wherein the first residual control term includes a first average refractive power residual term and an astigmatic residual term.

[0034] In another exemplary embodiment of this application, the expression for the first mean refractive power residual term is: In the formula, Indicates the first The first average refractive power residual term of each sampling point; The average refractive power residual weighting coefficient (dimensionless) is used to control the relative importance of the first average refractive power in the overall optimization objective. Indicates the relationship with the first The radial weights of each sampling point are related to its position within the lens aperture. Considering the impact of the sampling point's position within the aperture on optimization, the weights are close to 1 in the central region and close to the preset minimum weight in the edge region. ; Indicates the first sampling points The first mean refractive power; Indicates the first sampling points The design target mean refractive power, in one exemplary embodiment, varies primarily along the asymptotic channel direction (y-direction).

[0035] The first average refractive power residual term is used to characterize the deviation between the first average refractive power at the sampling point and the design target average refractive power under the first optical condition, so that the refractive power distribution in the asymptotic channel direction is close to the design target distribution. It is the core constraint term for controlling the refractive change in the asymptotic channel.

[0036] To reduce the excessive influence of the lens edge region on the optimization results, a radial weighting coefficient related to its position in the lens aperture is introduced at the sampling point: in, is the radial weighting coefficient, and is the dimensionless weighting factor, used to control the contribution ratio of different spatial regions to the residual function; , indicating sampling point The radial distance in the local plane coordinate system of the lens, in mm, satisfies... ; The effective design radius of the lens is in mm, and D is the design diameter of the lens. The preset minimum weight value satisfies .

[0037] The function is defined as: according to From the form of the function, we can derive: because ,therefore: thus, If the function only truncates in the lower bound direction, and the upper bound does not occur within the physical interval, then the radial weighting coefficient can be equivalently expressed as: Therefore, the following condition is always satisfied: When the sampling point is located in the center area of ​​the lens hour, The central region has a higher influence weight on the first residual control term; when the sampling point is close to the edge of the lens... hour, The weights of the edge regions are restricted but not zero, thereby: 1. preventing the edge regions from having an excessive dominant influence on the overall optimization results; 2. avoiding numerical divergence caused by the loss of control over the degrees of freedom of the edge region surface during the optimization process; 3. maintaining the global continuity of the lens surface; 4. improving the overall optimization convergence stability.

[0038] In another exemplary embodiment of this application, the expression for the image residual term is: In the formula, Indicates the first Astigmatism residual term for each sampling point; This represents the cylindrical lens residual weighting coefficient (dimensionless), used to control the relative importance of astigmatism constraints in the overall optimization objective; Indicates the first sampling points The first astigmatism amplitude; This represents the astigmatism threshold, also known as the cylindrical lens threshold, measured in diopters (D). It is used to limit astigmatism to within the design allowable range. This indicates that residual calculation is performed only for astigmatism exceeding a threshold, in order to reduce the impact of local astigmatism exceeding the limit on the overall optimization results. To ensure the stability of numerical optimization, this... The function can be approximated by differentiability, for example Approximate calculations can be performed using smoothed ReLU or other continuously differentiable functions.

[0039] The cylindrical lens residual term (astigmatism residual term) is used to characterize the degree of deviation of the astigmatism amplitude at the sampling point from the preset astigmatism threshold, so as to constrain the local astigmatism distribution, while keeping the optimization objective function differentiable and avoiding numerical bursts.

[0040] In another exemplary embodiment of this application, the first residual control term further includes: a surface regularization term, the expression of which is: in, For surface regularization terms; The first surface residual surface elevation function is used to characterize the first surface residual surface elevation function. Order of freedom coefficients (such as Chebyshev or polynomial coefficients). These are the regularization weights (dimensionless), which typically increase with increasing order, for example... This is to prevent higher-order terms from becoming too large.

[0041] Surface regularization terms are used to prevent the explosion of higher-order surface coefficients during optimization, maintaining global surface smoothness and optimization stability. Surface regularization terms enhance the stability of numerical optimization and can be selectively introduced in some implementations based on design requirements.

[0042] In another exemplary embodiment of this application, in step 203, the first average refractive power residual term and the astigmatic residual term under the first optical condition are spliced ​​together to obtain the first residual control term. : In another exemplary embodiment, the first residual control term may further include a surface regularization term: The design variable vector for progressive lenses is as follows: in, and To characterize the vector height function of the first surface residual surface The free coefficients control the local shape of the progressive channel and the over-prescription area.

[0043] In another exemplary embodiment of this application, in step 204, a first astigmatism control optimization objective is constructed based on the first residual control term, and the first astigmatism control optimization objective is optimized and solved to obtain a first lens design variable. The first lens design variable is used to characterize the geometric structure of the first surface of the progressive lens and to make the progressive lens meet the preset average refractive power distribution and astigmatism control requirements under the first optical conditions.

[0044] The optimization solution method can be any numerical method applicable to nonlinear optimization. In one exemplary embodiment, the optimization solution method includes a gradient-based optimization method or a nonlinear least squares method.

[0045] In one exemplary implementation, the first astigmatism control optimization objective is a scalar optimization index constructed from the first residual control term.

[0046] In one exemplary implementation, the scalar optimization metric is the norm or weighted norm of the first residual control term, for example: Among them, the first residual control term It includes the first average refractive power residual term and the astigmatism residual term under the first optical condition, and may further include a surface regularization term according to actual needs. After optimizing the first astigmatism control objective, the first lens design variable under the first optical condition is obtained. As an example, the first lens design variable can be represented in vector form, denoted as... , used to characterize the geometry of the first surface of a progressive lens.

[0047] In one exemplary implementation, to suppress the impact of abnormal residuals on the optimization results, the scalar optimization index can also be constructed using a robust loss function, such as soft-L1, Huber, or smooth ReLU functions.

[0048] In another exemplary embodiment of this application, before performing the above-mentioned residual solution under the first optical condition, an initial design variable vector can be constructed based on the design target refractive power distribution. This satisfies the preset refractive change trend in the asymptotic channel direction and serves as the initial state for optimization under the first optical condition, thereby improving the convergence stability of the first residual control optimization objective.

[0049] In another exemplary embodiment of this application, in step 205, based on the first surface geometry corresponding to the first lens design variable obtained in step 204, under the second optical conditions, the second average refractive power and the second astigmatism amplitude value of each sampling point are calculated, specifically including: (c1) Under the second optical condition, based on the local geometry of the first surface, for each pupil ray in the set of pupil rays corresponding to each sampling point, calculate the equivalent refractive power of each pupil ray in the sagittal and tangential directions.

[0050] The second optical condition is the calculation condition defined in the foregoing embodiments for simulating the actual wearing state, including but not limited to the lens tilt angle, wrap angle, vertex distance, and the change in the angle of incidence of the line of sight caused by eyeball rotation.

[0051] At the sampling point For each ray j (j=1,2,...,J) in the pupil ray set, based on the incident direction of the pupil ray under the second optical condition and the local geometry of the first surface, the equivalent refractive power in the sagittal direction and the tangential direction are calculated. In an exemplary embodiment, the equivalent refractive power in the sagittal and tangential directions can be calculated based on the projection relationship between the equivalent refractive components corresponding to the two principal curvature directions of the first surface and the pupil ray direction, for example: in, This is the equivalent refractive power of the pupil ray in the sagittal direction; This represents the equivalent refractive power of the pupillary light in the tangential direction. and Sampling points The equivalent refractive components corresponding to the two principal curvature directions of the first surface; and This is the unit vector corresponding to the principal curvature direction; and are the unit vectors of the j-th pupil ray in the sagittal and tangential planes, respectively; j represents the number of pupil rays.

[0052] (c2) The equivalent refractive power of the pupil ray in the sagittal and tangential directions is corrected by using the normal angle between the incident direction of each pupil ray and the lens surface.

[0053] Using the normal angle between the incident direction of each pupil ray and the lens surface The Coddington approximation is used to correct the equivalent refractive power to compensate for the effective refractive change caused by oblique incidence. in, This is the corrected equivalent refractive power of the pupil ray in the sagittal direction; It is the corrected equivalent refractive power of the pupil ray in the tangential direction.

[0054] (c3) Calculate the average refractive power and astigmatism amplitude corresponding to each pupil ray by using the corrected equivalent refractive power of the pupil ray in the sagittal and tangential directions.

[0055] Single pupil ray (the first) The average refractive power of the pupillary light (strips of light) With astigmatism amplitude for: (c4) Calculate the second average refractive power and the second astigmatism amplitude of each sampling point based on the average refractive power and astigmatism amplitude of each pupil light corresponding to each sampling point.

[0056] For sampling points For the corresponding line of sight, the average refractive power and astigmatism amplitude of the corresponding pupillary light beam are weighted and averaged to obtain the bundle-average refractive power (bundle-average refractive power) and astigmatism amplitude at that line of sight point. These are used as the second average refractive power and the second astigmatism amplitude, respectively. The expression is as follows: in, For light weights, =1.

[0057] In another exemplary embodiment of this application, in step 206, a second residual control term is constructed based on the second average refractive power and second astigmatism amplitude value of each sampling point obtained in step 205. The second residual control term is used to characterize the deviation between the optical response under the second optical condition and the design target, specifically including: (d1) Based on the second average refractive power of each sampling point and the design target average refractive power under the first optical condition, construct the second average refractive power residual term; the second average refractive power residual term is used to maintain the stable inheritance of the target refractive distribution established under the first optical condition under the second optical condition.

[0058] (d2) Based on the second astigmatism amplitude value of each sampling point, construct astigmatism constraint terms and astigmatism threshold constraint terms. The second residual control terms include the second average refractive power residual term, the astigmatism constraint term, and the astigmatism threshold constraint term.

[0059] In another exemplary embodiment of this application, the second average refractive power residual term can serve as a strong constraint term under the second optical condition. To ensure that the asymptotic channel maintains the refractive change trend of the design target under the second optical condition, a design target average refractive power constraint corresponding to that under the first optical condition is introduced. The expression for the second average refractive power residual term is: In the formula, Indicates the first The second average refractive power residual term for each sampling point; This represents the global weight (dimensionless), used to control the relative importance of the first optical mean refractive constraint in the entire objective function of the second optical condition optimization; Indicates the first The position of each sampling point depends on a weight, which is used to control the position of different sampling points. As an example, regarding the contribution to the residuals, under the second optical condition, due to changes in eye rotation and the angle of incidence of the line of sight, additional weights can be applied to the channel region or the distance reference gaze region. For instance, weights can be increased in the region y≈corridor / 2. The corridor refers to the narrow, vertical region on the progressive lens that connects the distance and near regions, where the power gradually increases from the distance power to the near power. It is obtained by combining the radial weighting function and the longitudinal channel weighting function, thus ensuring that the channel and transition are not destroyed; Indicates the first sampling points The design target average refractive power under the first optical condition is used as a strong constraint target.

[0060] In another exemplary embodiment of this application, the expression for the pixel constraint term is: In the formula, Indicates the first Astigmatism constraint term for each sampling point; This represents the weighting coefficient, used to control the importance of astigmatism constraints under the second optical condition; Indicates the first sampling points The second astigmatism amplitude; astigmatism constraint under the second optical condition is used to reduce non-prescription astigmatism overall.

[0061] In another exemplary embodiment of this application, the expression for the image threshold constraint term is: In the formula, Indicates the first Astigmatism threshold constraint term for each sampling point; The weighting coefficient (dimensionless) is used to control the importance of the astigmatism threshold constraint under the second optical condition. This represents the astigmatism threshold; the astigmatism threshold constraint under the second optical condition is used to ensure that the astigmatism does not exceed the design allowable range. In numerical optimization, the above... The function can be implemented using differentiable approximations, for example... Smoothed ReLU or other continuously differentiable functions.

[0062] In another exemplary embodiment of this application, in step 206, the second residual control term further includes a trust region constraint term; wherein, a trust region constraint term under the second optical condition is constructed based on the first lens design variable that satisfies the first astigmatism control optimization objective; the trust region constraint term is used to constrain the degree of deviation between the second lens design variable that satisfies the second astigmatism control optimization objective and the first lens design variable that satisfies the first astigmatism control optimization objective; the second residual control term includes a second average refractive power residual term, an astigmatism constraint term, an astigmatism threshold constraint term, and a trust region constraint term.

[0063] In another exemplary embodiment of this application, a trust region constraint term is constructed under the second optical condition based on the first lens design variable that satisfies the first astigmatism control optimization objective, so as to constrain the degree of deviation of the second lens design variable from the first lens design variable, and to make the optimization under the second optical condition take the first surface geometry determined by the first lens design variable as the optimization benchmark.

[0064] Specifically, the trust region constraint term is used to characterize the degree of deviation between the design variables of the second lens under the second optical condition and the design variables of the first lens under the first optical condition, and participates in the overall optimization as part of the second residual control term.

[0065] In one exemplary implementation, the expression for the trust region constraint term is: In the formula, This represents the vector of design variables for the second lens that satisfies the optimization objective for second astigmatism control. The Trust region constraints corresponding to each component; These are weighting coefficients (dimensionless) used to control the importance of trust region constraints; The first lens design variable vector is used to meet the first astigmatism control optimization objective. The One component; The second lens design variable vector is used to meet the optimization objective of the second astigmatism control. The Each component.

[0066] In another exemplary embodiment of this application, the second residual control term further includes an additional refractive power constraint term under the second optical condition; the additional refractive power constraint term under the second optical condition is constructed based on the second average refractive power at each sampling point, the target average refractive power of the progressive lens distance reference area, and the target additional refractive power.

[0067] Specifically, to ensure that the near-field addition of the additional refractive power under the second optical condition meets the design objectives, the near-field addition under the second optical condition is defined as the average refractive power of the distance reference line-of-sight region. : Constraint proximity bonus Approaching its target with a proximity bonus Then, under the second optical condition, an additional refractive power constraint term is added. for: in, , which is a weighting coefficient (dimensionless) used to control the importance of the second optical additional refractive power constraint; Sampling point under the second optical condition The beam-average refractive power at the corresponding line-of-sight point, i.e., the second average refractive power; In one exemplary embodiment, to use the target average refractive power of the reference area, It is the weighted average of the average refractive power of multiple sampling points within the distant reference line of sight area; An additional refractive power distribution function is applied to the target. In one exemplary embodiment, the additional refractive power of the target varies primarily along the asymptotic channel direction (y-direction), which is represented at the sampling point. The proximity bonus of a target relative to a distant reference area can be obtained from the sampling point. Mean refractive power distribution function of the target The calculation yielded: In another exemplary embodiment of this application, in step 206, the defined residual components (second average refractive power residual term, astigmatism constraint term, astigmatism threshold constraint term, trust region constraint term, and additional refractive power constraint term under the second optical condition) are concatenated to obtain a second residual control term. In one exemplary embodiment, the second residual control term... Represented as: in, This is the second mean refractive error term; Add a refractive power constraint term under the second optical condition; This is the astigmatism constraint term under the second optical condition; This is the astigmatism threshold constraint term under the second optical condition; It belongs to the trust region constraint.

[0068] In one exemplary embodiment, the second residual control item is determined according to actual needs. The additional refractive power constraint term under the second optical condition can be omitted. .

[0069] In another exemplary embodiment of this application, in step 207, a second astigmatism control optimization objective is constructed based on the second residual control term obtained in step 206. The second astigmatism control optimization objective is solved based on the first surface geometry corresponding to the first lens design variable obtained in step 204 as the optimization benchmark, yielding the second lens design variable. This achieves optimized control of the astigmatism distribution of the progressive lens under the second optical condition, while maintaining the optical response constraints (average refractive power distribution constraints) corresponding to the design objective under the first optical condition. The second optical condition includes, but is not limited to, the lens tilt angle, the wrap angle, and the change in the incident angle of the line of sight caused by eye movement. Astigmatism control includes, but is not limited to, adjusting the astigmatism magnitude, astigmatism gradient, astigmatism spatial distribution, and astigmatism axial continuity.

[0070] The optimization solution method can be any numerical method applicable to nonlinear optimization. In one exemplary embodiment, the optimization solution method includes a gradient-based optimization method or a nonlinear least squares method.

[0071] In one implementation, the second astigmatism control optimization objective is a scalar optimization index constructed from the second residual control term.

[0072] In one exemplary implementation, the scalar optimization metric is the norm or weighted norm of the second residual control term, for example: in, For at least one free surface elevation function The second lens design variable is represented in vector form. The second residual control term... It includes a second average refractive power residual term under the second optical condition, an astigmatism constraint term, and may further include at least one of an astigmatism threshold constraint term, a trust region constraint term, and an additional refractive power constraint term.

[0073] In one exemplary implementation, to suppress the impact of abnormal residuals on the optimization results, the scalar optimization index can also be constructed using a robust loss function, such as soft-L1, Huber, or smooth ReLU functions.

[0074] In this application, during the astigmatism optimization process under the second optical condition, the first surface geometry corresponding to the first lens design variable obtained in step 204 is used as the optimization benchmark. In some exemplary embodiments, using the first surface geometry as the constraint benchmark can be implemented in at least one way. For example, the first surface geometry corresponding to the first lens design variable is introduced during the calculation process under the second optical condition to calculate the second average refractive power and the second astigmatism amplitude; the first lens design variable is used as the initial state under the second optical condition to improve the convergence stability of the optimization process; and the first lens design variable vector is introduced when constructing the second residual control term. Trust region constraints are used to limit the design variable vector of the second lens. The offset range.

[0075] In this application, the first surface geometry is used as a constraint benchmark. The astigmatism optimization process under the second optical condition is restricted to the constraint space of the first surface geometry determined by the first lens design variables. The stability of the target average refractive power distribution under the first optical condition is maintained by the second average refractive power residual term. Thus, the astigmatism optimization under the second optical condition is carried out based on the refractive response structure determined under the first optical condition, thereby preventing the target optical response distribution established under the first optical condition from being destroyed in the subsequent astigmatism optimization process and suppressing the introduction of additional refractive power errors during the second optical optimization process, achieving effective decoupling between the refractive power design target and the astigmatism control target.

[0076] This application also provides an application scenario in which the aforementioned astigmatism control method for progressive lenses is applied. Specifically, the astigmatism control method for progressive lenses provided in this embodiment can be applied in the design and manufacturing process of progressive lenses. This process includes a design target determination stage, a design variable solving stage, and a lens processing and manufacturing stage. The design target determination stage is used to determine the target average refractive power distribution and astigmatism control target of the progressive lens based on user requirements; the design variable solving stage is used to solve for the lens design variables that satisfy the target average refractive power distribution and astigmatism control target; the lens processing and manufacturing stage is used to generate the surface geometry of the progressive lens based on the solved lens design variables and to process and manufacture the progressive lens. The astigmatism control method for progressive lenses provided in this embodiment belongs to the design variable solving stage.

[0077] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 3As shown, this computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The database stores astigmatism control data for progressive lenses. The I / O interfaces are used for exchanging information between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements an astigmatism control method for progressive lenses.

[0078] Those skilled in the art will understand that Figure 3 The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0079] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0080] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0081] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties. Moreover, the collection, use and processing of the relevant data are carried out in compliance with the relevant data protection laws and policies of the country where the location is located, and with the authorization granted by the owner of the corresponding device.

[0082] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium, and when executed, it can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0083] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0084] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0085] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for controlling astigmatism with progressive lenses, characterized in that, include: Several sampling points are selected on the first surface within the aperture of the progressive lens; Under the first optical conditions, calculate the first average refractive power and the first astigmatism amplitude at each sampling point; The first residual control term is constructed based on the first average refractive power and the first astigmatism amplitude at each sampling point; The first astigmatism control optimization objective is constructed based on the first residual control term, and the first lens design variables that satisfy the first astigmatism control optimization objective are solved. The first lens design variable is used to characterize the geometry of the first surface of the progressive lens and to ensure that the progressive lens meets the preset average refractive power distribution and astigmatism control requirements under the first optical conditions. Based on the first surface geometry corresponding to the first lens design variables, and under the second optical conditions, the second average diopter and the second astigmatism amplitude value of each sampling point are calculated. A second residual control term is constructed based on the second average refractive power and the second astigmatism amplitude at each sampling point; The second astigmatism control optimization objective is constructed based on the second residual control term. The first surface geometry determined by the first lens design variables is used as the optimization benchmark to solve the second astigmatism control optimization objective and obtain the second lens design variables. This allows for the optimized control of the astigmatism distribution of the progressive lens under the second optical conditions without compromising the optical response constraints corresponding to the design objective under the first optical conditions.

2. The astigmatism control method for progressive lenses according to claim 1, characterized in that, Under the first optical conditions, the first average refractive power and the first astigmatism amplitude are calculated for each sampling point, specifically including: Under the first optical condition, the maximum and minimum refractive power at each sampling point are calculated based on the fundamental refractive component of the second surface of the progressive lens and the equivalent refractive component in the principal curvature direction of the first surface at each sampling point. Calculate the first average refractive power and the first astigmatism amplitude for each sampling point based on the maximum and minimum refractive power at each sampling point.

3. The astigmatism control method for progressive lenses according to claim 1, characterized in that, The first residual control term is constructed based on the first average refractive power and the first astigmatism amplitude at each sampling point, specifically including: Based on the first average refractive power of each sampling point, the design target average refractive power, and the radial weight related to the position of the sampling point in the lens aperture, a first average refractive power residual term is constructed. Based on the first astigmatism amplitude, astigmatism threshold, and radial weight related to the position of the sampling point in the lens aperture for each sampling point, an astigmatism residual term is constructed; wherein, the first residual control term includes a first average refractive power residual term and an astigmatism residual term.

4. The astigmatism control method for progressive lenses according to claim 3, characterized in that, The first residual control term also includes: a surface regularization term; wherein, the surface regularization term is based on the first surface residual surface elevation function. The order of freedom coefficients and the regular weight coefficients are determined.

5. The astigmatism control method for progressive lenses according to claim 1, characterized in that, Based on the first surface geometry corresponding to the first lens design variables, and under the second optical conditions, the second average refractive power and the second astigmatism amplitude value at each sampling point are calculated, specifically including: Under the second optical condition, based on the local geometry of the first surface, for each pupil ray in the pupil ray set corresponding to each sampling point, the equivalent refractive power of each pupil ray in the sagittal and tangential directions is calculated. The equivalent refractive power of the pupil ray in the sagittal and tangential directions is corrected by using the normal angle between the incident direction of each pupil ray and the lens surface. Using the corrected equivalent refractive power of the pupil rays in the sagittal and tangential directions, calculate the average refractive power and astigmatism amplitude corresponding to each pupil ray; Calculate the second average refractive power and the second astigmatism value for each sampling point based on the average refractive power and astigmatism amplitude of each pupil light corresponding to each sampling point.

6. The astigmatism control method for progressive lenses according to claim 1, characterized in that, A second residual control term is constructed based on the second average refractive power and the second astigmatism amplitude at each sampling point, specifically including: Based on the second average refractive power of each sampling point and the design target average refractive power under the first optical condition, construct the second average refractive power residual term; Based on the second astigmatism amplitude value of each sampling point, astigmatism constraint term and astigmatism threshold constraint term are constructed; the second residual control term includes the second average diopter residual term, astigmatism constraint term and astigmatism threshold constraint term.

7. The astigmatism control method for progressive lenses according to claim 6, characterized in that, The second residual control term also includes a trust region constraint term; The trust region constraint term is constructed based on the first lens design variable that satisfies the first astigmatism control optimization objective; the trust region constraint term is used to constrain the deviation between the second lens design variable that satisfies the second astigmatism control optimization objective and the first lens design variable that satisfies the first astigmatism control optimization objective.

8. The astigmatism control method for progressive lenses according to claim 6 or 7, characterized in that, The second residual control term also includes an additional refractive power constraint term under the second optical condition; the additional refractive power constraint term under the second optical condition is constructed based on the second average refractive power of each sampling point, the target average refractive power of the progressive lens distance reference area, and the target additional refractive power.

9. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that the processor executes the computer program to implement the astigmatism control method for a progressive lens according to any one of claims 1-8.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the astigmatism control method for progressive lenses as described in any one of claims 1-8.

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