Improved calculation of ophthalmic lenses

Abstract

This invention relates to a method for defining a surface model for calculating at least one surface of at least one ophthalmic lens from at least a set of ordered parameters of a lens and / or from variables dependent on the ordered parameters. The method includes: providing a training dataset comprising a large set of ordered parameters; providing at least one target value for at least one characteristic of at least one lens for each set of ordered parameters in the training dataset; providing at least one surface model parameterized by model parameters; and determining optimized values ​​of model parameters of the surface model using the provided target values, for example, by optimizing the values ​​of the model parameters to minimize or maximize an objective function for the model parameters that depends at least on the model parameters and on the provided target values. If the provided target value for at least one characteristic of a lens in each set of ordered parameters is consistent with a value of the same characteristic of at least one lens that can be calculated using the surface model given the model parameter values ​​of the surface model in the corresponding set of ordered parameters, then the objective function of the model parameters for each set of ordered parameters contains at least one term having a minimum or maximum value. Furthermore, this invention also relates to a method for determining at least one surface of at least one ophthalmic lens by means of a surface model, a corresponding manufacturing method, and a corresponding computer program product and apparatus.

Description

Technical Field

[0001] This invention relates to a method for determining a surface model, a method for determining at least one surface of at least one ophthalmic lens using a surface model, and a corresponding manufacturing method. Furthermore, this invention also relates to corresponding computer program products and apparatus. Background Technology

[0002] The purpose of calculating ophthalmic lenses (e.g., spectacle lenses) is to calculate the shape of the surface of an ophthalmic lens or a pair of lenses and their orientation (i.e., orientation and position) relative to each other, so that they have specific geometric properties (e.g., predetermined thickness at certain points of the lens) and optical properties adapted to subsequent wearing conditions (e.g., adapted optically and, if necessary, physiologically to the eye or a pair of eyes viewing through the ophthalmic lens).

[0003] Examples of ophthalmic lenses are contact lenses and spectacle lenses, such as monocular lenses and contact lenses, multifocal spectacle lenses and multifocal contact lenses, and spectacle lenses with variable refractive power (e.g., progressive multifocal lenses).

[0004] For traditional eyeglass lenses, the type of fit is typically limited to the eye's refractive error, the refractive index of the material used for the lens, and the size and / or shape of the lens edge. Refractive errors can include spherical, cylindrical, and axial lenses, and, where necessary, additional power or near-refractive and / or prism prescriptions.

[0005] For so-called personalized lenses, individual parameters can be added as other parameters, such as the orientation and distance of the lens to the eye (given by the centering parameter), the distance or orientation of the axial length point to the lens and / or relative to each other, the distance of individual objects at certain viewpoints (e.g., reference points) in the lens, and the individual positions of these viewpoints in the lens.

[0006] For personalized eyeglasses, additional parameters can be added, such as visual conditions specifically defined for the eyeglasses, visual behaviors (e.g., the interaction between head turning and eye turning), biometric parameters describing the eye (e.g., including higher-order wavefront errors (e.g., the Bizenick coefficient set), pupil size and / or position in different viewing directions, eye length, curvature and position of the eye's refractive surfaces, refractive index of the medium), or other parameters specific to the intended wearer.

[0007] The surface shape of ophthalmic lenses is typically described as a freeform surface, which can be parameterized, for example, by a set of so-called sags. Other local representations (such as spline representations) or nonlocal representations (such as Zernike decompositions) are also possible. If one of the surfaces is a relatively simple surface, such as a spherical lens, then only its curvature, or so-called fundamental curve, can be specified for this purpose.

[0008] Examples of ordering parameters can be found in general standards for eyeglass lenses (see, for example, EU Regulation 93 / 42 / EEC on medical devices).

[0009] Therefore, in summary, the purpose of ophthalmic lens calculation is to calculate a set of surface parameters that can be used to manufacture an ophthalmic lens or a pair of lenses from a set of ordered parameters.

[0010] For traditional eyeglasses, this can be achieved by directly calculating surface parameters (e.g., by overlapping a specific surface defined for the product with another surface to adjust the prescription at a reference or measurement point). In individualized or personalized eyeglasses, optimization is typically used, which requires the shape and orientation of the starting surface and one or more objective functions to be optimized.

[0011] Such a starting surface can remain constant for a variety of ordering parameters, or it can be interpolated and / or extrapolated for multiple starting surfaces belonging to different sets of ordering parameters.

[0012] For example, examples of objective function-based optimization methods are illustrated in EP 1 091 233, DE 10 2012 000 390, EP 2 384 479, and EP 2177 943.

[0013] Exemplary methods using direct calculation are described in EP 0 654 692 A1 or US 4 514 061 A. An example of interpolation calculation is described in EP 2 449 420.

[0014] The drawback of conventional computational methods for ophthalmic lenses is that, as the number of ordered parameters increases, direct computation (e.g., by superposition) becomes infeasible or is accompanied by a decline in quality, or the computation time for optimization runs becomes increasingly longer because the objective function evaluated in the optimization becomes more complex.

[0015] Some methods, such as those described in EP 0 654 692 A1 or US 4 514 061 A (Winthrop), directly calculate the surface of an ophthalmic lens from a small set of parameters with low computational effort. However, these methods cannot be used to calculate commonly used ophthalmic lenses today because they can only be used to calculate defined families of surfaces based on outdated criteria (e.g., progressive multifocal lens optimization based on surface properties rather than usage characteristics).

[0016] Calculations for ophthalmic lenses, particularly the computationally intensive optimization of individualized or personalized lenses, are typically repeated every time, even if the lenses have the same or very similar ordering parameters, resulting in identical or similar surfaces. These calculations are usually performed during the manufacturing of the ophthalmic lenses (to define the surfaces to be manufactured when designing the lenses, or to verify the manufacturability of the lenses using the surface geometry). They are also used in consultations (e.g., with opticians) to clarify the optical and geometric characteristics of individualized or personalized ophthalmic lenses (e.g., the location and thickness of the zone of clear vision in progressive multifocal lenses) to future wearers. To minimize waiting times, calculations must be completed quickly in this particular application.

[0017] EP 2 449 420 discloses a method for rapidly calculating the surface of a spectacle lens by interpolating an already optimized surface in a parameter space. However, this method requires either pre-calculating the surface variations based on the parameter space, leading to high storage requirements, or repeating this process on each calculation, resulting in longer computation times. Summary of the Invention

[0018] The objective of this invention is to reduce the computational workload required to calculate ophthalmic lenses while limiting storage requirements. This enables faster and lower-cost calculation of ophthalmic lenses with lower computational power consumption.

[0019] This objective is achieved by a computer-implemented method, a corresponding apparatus and computer program product for defining a surface model, a computer-implemented method for determining at least one surface of at least one ophthalmic lens, a corresponding apparatus and computer program product, and a method and apparatus for manufacturing an ophthalmic lens.

[0020] According to the first aspect, a computer-implemented method for determining a surface model for calculating at least one surface of at least one ophthalmic lens (e.g., a contact lens or spectacle lens) is derived from a set of ordered parameters and / or variables dependent on the ordered parameters (e.g., variables derived from the ordered parameters) of at least one ophthalmic lens.

[0021] In the context of this application, "calculation of at least one surface of an ophthalmic lens" includes the calculation of a surface or at least a portion of a surface. In other words, "calculation of at least one surface of an ophthalmic lens" can be understood as the calculation of at least a portion of the surface or the calculation of the entire surface.

[0022] At least one ophthalmic lens can be a single lens. It is also possible to calculate one or both lenses in a pair of ophthalmic lenses. For example, at least one pair of ophthalmic lenses (lens pairs) can be calculated using a surface model, comprising specific lenses for a person's right and left eyes. In this case, a set of ordering parameters (ordering parameter set) can contain ordering values ​​for the two lenses of the lens pair (e.g., the left and right lenses of a pair of spectacle lenses, and ordering data for both eyes).

[0023] At least one surface calculated based on a surface model can be parameterized by at least one parameter. In this case, calculating the surface by means of a surface model includes calculating at least one parameter (surface parameter) of the surface from ordered parameters or variables (auxiliary variables) that depend on the ordered parameters (e.g., variables derived from the ordered parameters).

[0024] For example, a surface can be described by the curvature or principal curvature at at least one point (e.g., a reference point for an ophthalmic lens) and by orientation through the surface normal and, if necessary, through the principal meridional plane. Furthermore, it is feasible to describe the surface by a local representation (e.g., a spline representation or polynomial representation with corresponding coefficients) or a non-local representation (e.g., a Zernike decomposition with corresponding coefficients).

[0025] Alternatively, the surface can be directly predefined, for example, using a set of sags from a large number of grid points. In this case, calculating the surface using a surface model involves calculating the surface sags from a large number of grid points using the predefined parameters or variables (auxiliary variables) that depend on the predefined parameters (e.g., variables derived from the predefined parameters).

[0026] In one example, the arrangement of one of the surfaces of the ophthalmic lens and / or that surface relative to another surface of the ophthalmic lens is calculated using a surface model based on a set of ordered parameters. The other surface may be a predetermined surface, such as a sphere with a predetermined curvature, which may depend on the ordered parameters (e.g., in a known system of basic curves). In another example, the arrangement (i.e., orientation and / or position) of both surfaces of the ophthalmic lens and / or their relative to each other is calculated using a surface model based on a set of ordered parameters.

[0027] The calculation of at least one surface from a set of ordered parameters of an ophthalmic lens using a surface model is preferably performed directly (i.e. without iteration) or with fewer iteration steps, such as fewer than 30, 25, 15, 10, 5 or 3 iteration steps.

[0028] At least one surface of an ophthalmic lens is calculated using a surface model from a specific set of ordered parameters. Within the scope of this application, this ophthalmic lens is referred to as a lens calculated based on the surface model from the set of ordered parameters. As mentioned above, a lens calculated based on a surface model can be one of a pair of lenses. In this case, one or both lenses of the lens pair can be calculated based on the surface model. An ophthalmic lens can be, for example, a spectacle lens, such as an individualized and / or personalized spectacle lens. For example, in the case of individualized spectacle lenses, the orientation of the spectacle lens in front of the user's eye is considered in the calculation or optimization of the spectacle lens. The orientation of the spectacle lens can be characterized, for example, by tilt angle, temple angle, pupillary distance, corneal separation distance, and / or other parameters. For example, in the case of personalization, the perceptual design is adjusted to meet the individual use purpose of the glasses. Spectacle lenses can be, for example, monocular lenses, multifocal lenses, or progressive lenses.

[0029] The surface model can be a parametric model. The surface model may include at least one variable parameter. Furthermore, the surface model may have at least one constant parameter (e.g., the location of the evaluation point within the lens).

[0030] The method for determining the surface model includes the following steps:

[0031] Provide a training dataset comprising multiple sets of ordering parameters, each set containing values ​​for at least a portion of the parameters required to order at least one ophthalmic lens;

[0032] Provide at least one target value for at least one predetermined characteristic of at least one ophthalmic lens for each ordered parameter set in the training dataset;

[0033] Provide at least one surface model parameterized by model parameters, which, given model parameter values, can be used to calculate at least one surface of at least one ophthalmic lens based on an ordered parameter set and / or on variables derived from the ordered parameter set (providing an initial surface model, and, if necessary, initial parameterization of the surface model); and

[0034] Obtaining a surface model for calculating at least one surface of at least one ophthalmic lens includes:

[0035] By using the provided target values, the optimized values ​​of the model parameters for at least one surface model are determined.

[0036] Determining optimized values ​​for model parameters used for at least one surface model may include:

[0037] Optimize the values ​​of model parameters for at least one surface model (parameterization of the surface model) with the aim of minimizing or maximizing the objective function for the model parameters of at least one surface model, which depends at least on the model parameters and on the provided objective values.

[0038] If the objective value provided for at least one characteristic of at least one ophthalmic lens for each set of ordered parameters is consistent with the value of the same characteristic of at least one lens calculated or computable using the surface model given the value of the model parameters of the surface model in the corresponding set of ordered parameters, then the objective function of the model parameters of each set of ordered parameters contains at least one term having a minimum or maximum value.

[0039] If at least one lens is one of a pair of lenses, then multiple sets of ordering parameters may each contain values ​​of at least a portion of the parameters required to order the pair of lenses. At least one characteristic may include the binocular characteristics of the pair of lenses.

[0040] For example, a surface model can be used to calculate at least one pair of lenses, including lenses specific to a person's right and left eyes. In this case, the ordering parameter set contains ordering parameters for the right and left lenses, respectively. Furthermore, the characteristics for which target values ​​are provided may include at least one binocular characteristic that depends on the surface data of the left and right lenses. The target value of at least one binocular characteristic may include a value that takes into account at least one characteristic (e.g., a surface characteristic) at a first position of the first lens of the lens pair and the same characteristic at a second position of the second lens of the same lens pair in its calculation.

[0041] In addition, the initial complexity of the surface model can optionally be provided. For example, an initial number of model parameters can be predetermined.

[0042] In addition to parameterizing the surface model, the complexity of the surface model can optionally be optimized or adjusted. Optimization of the surface model complexity may include, for example, varying the number of model parameters and / or regularization.

[0043] For example, providing at least one surface model parameterized by model parameters may include providing at least two surface models with different complexities, wherein the complexity of the surface model includes one or more of the following variables:

[0044] – The type and / or quantity of ordering parameters used in the model;

[0045] –Depending on the type and / or number of variables ordered as parameters;

[0046] – The number of model parameters;

[0047] – The type and / or strength of regularization used for the objective function to optimize model parameters.

[0048] In addition, the method may also include:

[0049] Provide a validation dataset comprising multiple sets of ordering parameters, each set containing values ​​for at least a subset of parameters required to order at least one ophthalmic lens; and

[0050] To validate each set of ordered parameters in the dataset, provide at least one target value for at least one characteristic of at least one ophthalmic lens.

[0051] Obtaining a surface model for calculating at least one surface of at least one ophthalmic lens may further include:

[0052] Given previously determined optimized values ​​of the model parameters for each surface model, calculate the values ​​of the validation objective function and / or the values ​​of variables derived from the validation objective function for the provided surface models of different complexities, wherein the validation objective function depends on the provided objective values, and if the provided objective value for at least one characteristic of at least one ophthalmic lens for each ordering parameter set is consistent with the value of the same characteristic of at least one lens calculated or computable using the surface model given the optimized values ​​of the model parameters of the surface model for the corresponding ordering parameter set, then the validation objective function contains at least one term with a minimum or maximum value for each ordering parameter set in the validation dataset; and

[0053] Based on the calculated values ​​of the verification objective function and / or with the aid of the values ​​of variables derived from the verification objective function, a surface model for calculating at least one surface of at least one ophthalmic lens is selected or determined from surface models of different complexities parameterized using the optimized values ​​of the model parameters.

[0054] For the purposes of this application, the term "provide" includes "definition", "transfer", "obtain", "read", "extract from memory, database and / or table", "receive", etc.

[0055] For the purposes of this application, the term "determine" also includes "definition", "calculation", "obtaining", etc.

[0056] Ordering parameter set

[0057] To define the surface model, an ordered set of parameters is provided to calculate at least two other different ophthalmic lenses or lens pairs. Advantageously, more than 10, 100, 1000, 10000, 100000, or 1000000 ordered sets of parameters are used when defining the surface model to calculate the other ophthalmic lenses.

[0058] The ordering parameter set preferably covers a large range, preferably the entire range, of ophthalmic lenses that may be ordered later (e.g., see the refractive limits mentioned by the ophthalmic lens manufacturer, individual frame parameters when ordering spectacle lenses, other lens parameters such as freely selectable object distances, and other ordering parameters). For example, the refractive value range of the ordering parameter set could be -20 dpt to +20 dpt for spherical lenses and -8 dpt to +8 dpt for cylindrical lenses.

[0059] Here, the ordering parameter set may include one, more, or all of the ordering parameters required to order a single ophthalmic lens or a pair of ophthalmic lenses. Examples of ordering parameters can also be found in general standards for eyeglass lenses (see, for example, EU Regulation 93 / 42 / EEC on medical devices).

[0060] Therefore, the order parameter set may include at least one of the following order parameters:

[0061] - Parameters of ophthalmic lenses, such as materials (with the refractive index of the lens if necessary), the desired thickness of the lens, coatings, etc.

[0062] – Refractive values, such as spherical and / or cylindrical lenses with axial and / or additional and / or near-refractive and / or prisms with a base;

[0063] – Geometric parameters of the eyeglass frame;

[0064] –Uses of ophthalmic lenses, such as for reading, working on a computer, sports, etc.;

[0065] - Physiological parameters or characteristics of the future wearer of ophthalmic lenses;

[0066] -The biological parameters or characteristics of the future wearer's eyes, such as the position of the axial length point, the individual structure of the eye, the pupil diameter, and individual wavefront measurements;

[0067] -Preferred visual behaviors for future wearers;

[0068] – Other known parameters for the individualization and / or personalization of ophthalmic lenses. Parameters for the individualization of ophthalmic lenses may, for example, characterize the orientation of the ophthalmic lens in front of the wearer's eye. Parameters for the personalization of ophthalmic lenses may characterize adjustments to the perceptual design, for example, to meet the individual use purpose of the glasses. These parameters for the individualization and / or personalization of ophthalmic lenses may, for example, be mapped to design features, the location of reference points, progressive lengths, etc.

[0069] Variables that depend on the ordering parameters (e.g., variables derived from the ordering parameters) may include, for example, the refractive index of the material, the mechanical properties of the material, the mechanical properties of the coating, the thickness distribution of the ophthalmic lens, the expected distribution of residual astigmatism at the point of use, the expected distribution of refractive error at the point of use, etc.

[0070] The set of ordering parameters required to define the surface model may, but does not necessarily, involve ophthalmic lenses that have already been ordered, calculated, or manufactured. Depending on the implementation of the surface model, it may be advantageous if the ophthalmic lens has already been ordered, calculated, or manufactured. Therefore, it is also possible that the set of ordering parameters is only within the permissible limits of the ordering parameters. Thus, the refractive power may be within the delivery range of the ophthalmic lens, but the lens itself may never have been ordered, calculated, or manufactured.

[0071] Furthermore, redundant orders in the order dataset can be removed before finalization if necessary to reduce the number of datasets (e.g., for results of very frequent orders). Alternatively or additionally, the order dataset can be stratified for the same reasoning, while still ensuring a high degree of coverage of the order parameter range.

[0072] Characteristics and target values

[0073] Furthermore, to define the surface model for each ordered parameter set in the training dataset, at least one target value for at least one predetermined characteristic of at least one ophthalmic lens is provided. The target values ​​for different ordered parameter sets may be different or may be the same for at least a portion of the ordered parameter sets.

[0074] For the purposes of this application, the term "target value" includes the expected or required value of at least one characteristic of an ophthalmic lens (e.g., spectacle lens or contact lens). The target value may include multiple values ​​or a combination of multiple values. The target value may be extracted from a database, for example, and / or calculated using a predetermined optimization algorithm.

[0075] At least one predetermined characteristic of an ophthalmic lens can be, for example, an optical or geometric characteristic of a single ophthalmic lens or a pair of lenses comprising an ophthalmic lens. At least one predetermined characteristic can be a physical characteristic of the lens, such as sagitta, curvature, or variables derived therefrom, such as surface astigmatism, surface refractive value, etc. At least one predetermined characteristic can be an "indirect" characteristic, i.e., a characteristic associated with at least one model (e.g., an object distance model, an eye model, a usage position model, etc.). Examples of indirect characteristics include residual astigmatism, refractive error, etc.

[0076] For example, a characteristic can be one of the following:

[0077] – The sag of at least one surface and / or the derivative of the sag (e.g., in a direction perpendicular to it);

[0078] - Surface properties or surface parameters of at least one surface, such as curvature in at least one viewpoint, coefficients of a parametric function (e.g., spline function or polynomial function) describing the surface;

[0079] - At least one surface property, such as smoothness, ordinary differential property, manufacturability;

[0080] - At least one optical variable or characteristic of the surface or ophthalmic lens, such as refractive value or refractive error (preferably in the position of use), astigmatism or residual astigmatism (preferably in the position of use), vertical prism and / or horizontal prism (preferably in the position of use), higher-order imaging error (preferably in the position of use), etc. The optical variable or characteristic may be specified, for example, in the form of a power vector;

[0081] – The gradient of optical variables or properties of at least one surface or at least one ophthalmic lens, such as the gradient of (residual) astigmatism and / or refractive value or refractive error;

[0082] – The distribution and / or gradient of optical variables or properties of at least one surface or ophthalmic lens, such as the amount and / or axis of refractive error, vector components and / or astigmatism or residual astigmatism at the location of use, prism, prism substrate, distribution of prism vector components, or the distribution of variables derived therefrom. “Distribution” can be understood not only as an optical property or its gradient in the sense of a function of spatial location (e.g., (x, y) position) on the ophthalmic lens, but also as the frequency distribution of these variables in the sense of a probability distribution;

[0083] – Width of the good vision zone (e.g., the sun, in which residual astigmatism and / or refractive error is less than 1 dpt, preferably less than 0.75 dpt or 0.5 dpt);

[0084] - Geometric parameters or characteristics of ophthalmic lenses (not included in the ordering parameters), such as lens center thickness, lens edge thickness, coating thickness, lens diameter, lens mass, etc.

[0085] - Material parameters or material properties of ophthalmic lenses (not included in the ordering parameters);

[0086] – Geometric parameters of the eyeglass frame (not included in the ordering parameters);

[0087] – The manufacturability of the lens (e.g., no undercut surface);

[0088] – Binocular characteristics or characteristics of a pair of lenses including ophthalmic lenses. Binocular characteristics can be characteristics that take into account at least one characteristic (e.g., surface characteristics, geometric characteristics, optical characteristics, visual perception characteristics, etc.) at a first position of the first lens of the lens pair (e.g., a pair of spectacle lenses) and the same characteristic at a second position of the second lens of the same lens pair in its calculation. At least one binocular characteristic of a lens pair can be, for example, a deviation or difference in at least one optical variable or characteristic between the first and second lenses of the lens pair. Exemplary binocular characteristics of a lens pair are deviations or differences in the horizontal and / or vertical prisms (minus the prism difference of the prescription) at corresponding viewpoints (e.g., at at least one reference point, such as a prism reference point) between the right and left lenses of the lens pair, the difference in magnification between the left and right lenses, the difference in the fundamental curves between the left and right lenses, the position of the design point or its difference, the visual perception characteristics of the future wearer of the ophthalmic lens calculated using a surface model, etc. In addition, the parameters or characteristics of the lens pair may also include deviations in at least one geometric parameter between the first and second lenses of the lens pair, such as deviations in center thickness, edge thickness, coating thickness, anterior surface curvature, etc.

[0089] - Discomfort associated with visual quality and / or body posture in ophthalmic lens wearers, calculated using surface models;

[0090] - Visual perception characteristics of future wearers of ophthalmic lenses calculated using surface models.

[0091] Other relevant characteristics may also be considered.

[0092] The target value, for different sets of ordering parameters, can be a value (e.g., a set point) of at least one ophthalmic characteristic of the lens to be calculated or manufactured, which has already been calculated or is determined according to known methods (e.g., by minimizing or maximizing a known objective function in an iterative optimization method). It is also possible to obtain the target value using measurements from already manufactured ophthalmic lenses. The ordering parameters of the manufactured or to-be-manufactured lens are preferably at least partially known.

[0093] As a target value for at least one characteristic of at least one ophthalmic lens, for example, a measured value of at least one characteristic of a manufactured ophthalmic lens can be set, or a value determined or determinable from one or more measured values ​​of a manufactured ophthalmic lens can be determined. It is also feasible to set the set value of the ophthalmic lens to be manufactured as the target value.

[0094] For example, the target value of the average surface refractive index of an ophthalmic lens can be determined from the sagittal measurement of the lens surface (through the average curvature of the surface) based on the lens's position, provided the refractive index is known. The target value of astigmatism for the lens in the position of use (also depending on the position) can be determined based on the sagittal measurement, tilt angle, eyeglass holder angle, holder length and height (order values), and the position of the axial length point (order values ​​or model assumptions).

[0095] When defining a surface model, in addition to the ordering parameter set used for multiple ophthalmic lenses (base lenses), one or more surfaces belonging to the ordering parameter set of these lenses can also be used. The ophthalmic lenses used to define the surface model are also referred to as base lenses within the scope of this application. Base lenses can be lenses that have been calculated or optimized according to known methods and, if necessary, manufactured.

[0096] Additionally or alternatively, objective functions and / or their surface derivatives, depending on these ordered parameter sets, may be used for calculating ophthalmic lenses or base lenses according to existing techniques. The latter can be understood, for example, as the change of the objective function with varying sag. Thus, the objective value can correspond to a setpoint input into these objective functions. Here, the objective function and / or its surface derivatives are preferably such that they can be evaluated for any surface. Here, the objective function and / or its derivatives are typically evaluated based on appropriate parameterization of the ophthalmic lens surface.

[0097] If the surfaces of multiple base lenses are used to define the surface model, it is advantageous that these surfaces have already been calculated. It is also advantageous that the base lenses have already been fabricated, since their calculations have already served a purpose and can be reused to define the surface model without consuming additional computing power.

[0098] The method described herein can also be readily performed using the measuring surfaces of the ophthalmic lens (and the distances between the surfaces relative to each other) instead of the calculation surfaces. Furthermore, other properties, such as the refractive index, can also be measured.

[0099] The above explanation pertains to the characteristics and target values ​​associated with the training dataset. Of course, the same or similar methods can be used to determine or compute the characteristics and target values ​​for other ordered parameter sets (such as validation and test datasets). Here, it is not necessary to use the same characteristic with corresponding target values ​​for the training, validation, and test datasets. However, it is generally simpler to use the same target value for the same characteristic across different parameter sets.

[0100] Surface model

[0101] The surface model can be any model, such as a machine learning-based model. For example, machine learning algorithms are described in the following literature: Jeremy Watt, Reza Borhani, Aggelos Katsaggelos: Machine learning Refined: Foundations, Algorithms, and Applications, Cambridge University Press, 2020.

[0102] A surface model can be described by appropriately defined model parameters, which, together with at least some or preferably all ordered parameters and / or variables derived therefrom, are used to calculate one or more surfaces of an ophthalmic lens.

[0103] If one or more ordering parameters can be meaningfully mapped to one or more real numbers, it is advantageous to construct the surface model such that the surface generated by the surface model is a continuous or even continuously differentiable function of the ordering parameters, to ensure the design continuity of the ophthalmic lens with respect to these ordering parameters.

[0104] The surface model defined by the model parameters can be implemented as a regression model or include a regression model. The regression model takes at least some, or preferably all, ordered parameters and / or variables derived therefrom as input variables, and calculates one or more surfaces of an ophthalmic lens or a pair of ophthalmic lenses from them. Here, the coefficients of the regression model represent at least a portion of the model parameters of the surface model.

[0105] As an addition to or alternative to the design of a regression model, a surface model, or a portion thereof, can also be designed as a classification model, or contain a classification model. For example, if, in the field of spectacle lens manufacturing, only a specific lens diameter is available for the blank, and if a diameter of the lens blank should be selected, this can be achieved using a classification model. Such a classification model can, for example, calculate the applicability probability of the available lens blank diameters for manufacturing ophthalmic lenses, thereby ultimately selecting the lens blank with the highest probability and thus the most suitable for manufacturing the ophthalmic lens.

[0106] The classification model can also be used similarly to calculate the optimal basic curve and / or optimal diameter of ophthalmic lenses (e.g., spectacle lenses) in the manufacture of ophthalmic lenses (e.g., spectacle lenses), i.e., to calculate the probability of the applicability of the available basic curve and select the basic curve with the highest probability to manufacture or calculate ophthalmic lenses (e.g., spectacle lenses).

[0107] In order to flexibly map different designs of modern ophthalmic lenses, it is advantageous for the surface model to have a sufficient number of model parameters, such as more than 10, 30, 50, 100, 500 or 1000, 10000, 100000 or even more model parameters.

[0108] If the surface model is designed, for example, as a regression model or contains a regression model, the definition of the surface model may include setting the model parameters of the surface model based on an ordering parameter set (e.g., an ordering parameter set for a base lens) such that any ophthalmic lens, one or more of its surfaces, can be computed from its ordering parameter set by means of the surface model, and is only slightly different from ophthalmic lenses that can be computed or have been computed from the same ordering parameter set by a predetermined criterion according to a predetermined method in accordance with the art.

[0109] The regression model used for or as a surface model can be a linear regression model, which usually makes the calculations required to define the surface model easier, since the model parameters can be determined from the system of linear equations.

[0110] However, nonlinear regression models can be readily used instead of linear regression models. Such models are more flexible and can map more complex relationships between ordered parameters and one or more surfaces of the ophthalmic lens. However, it is also more difficult to properly determine the model parameters, as this is often done using nonlinear optimization algorithms that do not necessarily converge to the global optimum of the model parameters. As nonlinear regression models, for example, neural networks, including deep neural networks, can be used, but other nonlinear regression models known in the field of machine learning can also be used. These regression models, such as neural networks, can be trained on a training dataset with corresponding target values ​​using the provided ordered parameters.

[0111] Surface models can also be combinations of linear and / or nonlinear regression models, classification models, and / or neural networks. By combining these models, reductions in surface model complexity and savings in computation time and / or resource consumption can be expected. Exemplary combinations are as follows:

[0112] –Example: Classification models precede regression models and / or neural networks:

[0113] By leveraging ordered data, a model with minimal complexity that still produces sufficiently good surfaces is selected from a set of regression models with varying degrees of complexity. The advantage of this approach is that it may improve computation time and / or require fewer resources.

[0114] – Example: Regression Model Before Classification Model Before Regression Model and / or Neural Network: Based on order data, the geometry of the lens is approximated using a low-complexity regression model. The following classification model determines the lens blank based on the order data and the approximate geometry. The following regression model determines the final lens based on the order data and the lens blank. The advantage of this approach is that it reduces the complexity of the regression model used to determine the lens.

[0115] Also advantageous is the ability to control or optimize the complexity of the surface model so that its ordered parameter set can be computed for ophthalmic lenses whose surfaces are not included in the training dataset. This can be done, for example, by regularization and / or by selecting ordered parameters and / or by computed a sufficient number of different types of variables (auxiliary variables) derived from the ordered parameters and / or by appropriately selecting the number of model parameters and / or the type of model.

[0116] For reasons of numerical stability, it is also meaningful to transform the ordering parameters and / or auxiliary variables derived from or dependent on them into the surface model such that they have a mean of 0 and, for example, a standard deviation of 1, through the distribution of the ordering parameters of the ophthalmic lens used when defining the model parameters.

[0117] Define the model parameters of the surface model and adjust its complexity.

[0118] Define or determine model parameters

[0119] First, at least one surface model parameterized by model parameters is provided or pre-defined, which, given the model parameter values, can be used to calculate at least one surface of at least one ophthalmic lens based at least on the pre-defined parameters and / or on variables that depend on the pre-defined parameters.

[0120] The initial parameterization and initial complexity of the surface model can be provided or defined here. Providing the initial parameterization of the surface model may include providing initial values ​​for the model parameters of the surface model. Providing the initial complexity of the surface model may include defining or prescribing an initial number of model parameters for the surface model. The final model parameters, and if necessary, the complexity, are determined or defined through appropriate optimization methods. Thus, the final model parameters form an optimal set of model parameters.

[0121] The model parameters of the surface model are preferably defined as the optimal set of model parameters that minimizes or maximizes a predetermined objective function of the model parameters.

[0122] The optimal set of model parameters can be found using common mathematical optimization algorithms (such as simple gradient descent, conjugate gradient descent, stochastic gradient descent, or similar algorithms).

[0123] If a neural network is used as a regression model, the backpropagation algorithm can be used to minimize the objective function. The backpropagation algorithm itself is only a gradient-based algorithm adapted to this type of model.

[0124] If the objective value provided for at least one characteristic of at least one ophthalmic lens for each set of ordered parameters is consistent with the value of the same characteristic of at least one lens that can be calculated or computed using the surface model given the model parameter values ​​of the surface model in the corresponding set of ordered parameters, then the objective function of the model parameters for each set of ordered parameters may contain at least one term having a minimum or maximum value.

[0125] The objective function can contain a single term, a sum of multiple terms, or a weighted sum of multiple terms. In principle, different objective functions can be used for different model parameters. For example, different objective functions can be used depending on whether (i) existing surfaces (e.g., surfaces calculated using conventional methods) already exist for the ordered parameter set and whether these surfaces will be used in the objective function, or (ii) whether it is necessary to first compute the surfaces corresponding to the ordered parameter set, or (iii) whether the objective function should not be defined using surfaces.

[0126] Furthermore, it is advantageous that the gradient of the objective function with respect to the parameters in the parameterization of the surface output by the surface model can be quickly calculated, for example, as an analysis function.

[0127] The parameterization of the surface model and, if necessary, the optimization of its complexity can be performed to minimize the deviation of the value of at least one property of the ophthalmic lens, wherein at least one surface of the ophthalmic lens is calculated from the ordered parameter set by means of the surface model, and the corresponding objective value of that property (if necessary, depending on the ordered parameters) is minimized.

[0128] The deviation between at least one value of at least one predetermined characteristic of a lens calculated or calculable from a specific set of ordered parameters based on a surface model and at least one target value of that characteristic in the same set of ordered parameters can be quantified in different ways. Therefore, as a measure of this deviation, the difference between at least one value of at least one predetermined characteristic of a lens calculated or calculable from a specific set of ordered parameters based on a surface model and at least one target value of that characteristic in the same set of ordered parameters, or a convex or concave function of that difference (e.g., square, numerical, or negative), can be used.

[0129] At least one of the objective functions of the model parameters may accordingly include a convex or concave function of the difference between at least one value of at least one predetermined characteristic of a lens calculated based on a surface model for a set of ordered parameters and at least one objective value of that characteristic in the same set of ordered parameters. Convex functions can be used, in particular, for minimizing the objective function. Concave functions can be used for maximizing the objective function.

[0130] Equally feasible is to describe or quantify the deviation between these values ​​using other functions of at least one value of at least one predetermined property of a lens calculated or computable from a specific set of ordered parameters based on a surface model, and at least one target value of that property from the same set of ordered parameters. For example, such a function could be the ratio of at least one value of at least one predetermined property of a lens calculated or computable from a specific set of ordered parameters based on a surface model to at least one target value of that property from the same set of ordered parameters. Other functions, such as logarithmic functions of the ratio, are also feasible.

[0131] Alternatively, it is feasible to use an objective function for at least one optical characteristic, which is used in the routine optimization or calculation of at least one ophthalmic lens. One or more terms of the objective function for the model parameters can be accordingly formed or understood as an objective function for optimizing or calculating at least one ophthalmic lens given a set of ordered parameters, wherein the objective function is evaluated for different sets of ordered parameters. The objective function can depend in a known manner on the actual value of at least one optical characteristic (evaluated for an ophthalmic lens for which at least one surface has been calculated or is calculable from a specific set of ordered parameters and / or variables derived therefrom according to a surface model) and the corresponding target value. It is also feasible to use different objective functions for different sets of ordered parameters. In this case, it is not necessary to define the surface model using calculated and / or manufactured surfaces. For example, such an objective function could be the sum or average of the squares of the refractive errors and astigmatism deviations of the individual target values ​​calculated directly from the set of ordered parameters (which in turn are summed or averaged over multiple sets of ordered parameters) at multiple viewpoints.

[0132] The objective function of the model parameters can contain multiple terms that quantify or describe the difference between the ophthalmic lens surface calculated using the surface model and the corresponding target value by means of different properties (e.g., optical and / or geometric properties, direct and / or indirect properties). Here, additional properties (e.g., additional optical and / or geometric properties, direct and / or indirect properties) can depend on the ordered parameters. Exemplary properties include the vector component or residual astigmatism at the location of use, the refractive error at the location of use, the deviation of the minimum or maximum lens thickness from the corresponding ordered value of the lens thickness, etc.

[0133] The objective function may also additionally include terms that quantify or describe the differences in binocular characteristics between two pairs of ophthalmic lenses (one pair calculated using a surface model and the other using a method according to the prior art).

[0134] Furthermore, the objective function may include at least one term that incorporates design differences between ophthalmic lenses with different ordering parameters. Therefore, this additional term no longer pertains only to a single ophthalmic lens, but rather to the differences between two or more adjacent ophthalmic lenses within an ordering range, and represents the advantageous characteristics of a product containing multiple ophthalmic lenses.

[0135] In this way, for example, the similarity (but not necessarily the sameness) of the perceived design of progressive lenses for different refractive errors can be expressed as an objective function, so that only the desired design needs to be specified for, for example, a single effect that is particularly common, and designs for other effect cases are thus generated without specific specification. The advantage of including such a term that incorporates the differences between two or more ophthalmic lenses is that it is generally difficult to specify a constant surface design within the ordering parameter range because it cannot be constant based on other more fundamental principles (such as Minkowitz's theorem).

[0136] The objective function can include a weighted or unweighted sum of terms set for each ordered parameter set across all ordered parameter sets in the training dataset. As an alternative to summation, the mean or median can be calculated. More complex functions, such as nonlinear functions, can also be used instead of summation.

[0137] As mentioned above, different optimization algorithms (such as simple gradient descent, conjugate gradient descent, stochastic gradient descent, or similar algorithms) can be used to determine the optimal set of model parameters. For example, the optimization of model parameter values ​​may include regularization of the objective function used in the optimization of model parameters.

[0138] If optimization methods that require the gradient of the objective function (such as backpropagation in a neural network as a surface model, or gradient descent) are used to optimize the surface model parameters, they can be computed analytically, numerically, or by means of a combination of analytical and numerical methods. In particular, in the backpropagation algorithm, the gradient of the objective function is propagated back through the network in the backpropagation step instead of the commonly used residual (which is the gradient of the commonly used squared objective function).

[0139] The above explanation pertains to the objective function used to determine model parameters. Of course, other objective functions can be established or predefined in the same manner, such as verification objective functions or objective functions used to test surface models (test objective functions).

[0140] The objective function can be normalized. For example, the sum of the characteristics of the ophthalmic lenses (pairs) can be divided by the number of ophthalmic lenses (pairs) (with respect to the number of lenses (pairs) in the training, validation, or testing datasets, depending on whether the objective function is used to determine model parameters, to validate the model, or to test it.

[0141] Adjusting the complexity of the surface model

[0142] As mentioned above, at least two surface models with different complexities can be provided first to determine the optimal complexity of the model. The complexity of the surface model can include one or more of the following variables:

[0143] – The type and / or number of ordering parameters used in the model;

[0144] – The type and / or quantity of variables derived from the order parameters;

[0145] – The number of model parameters;

[0146] – The type and / or strength of regularization used for the objective function to optimize model parameters.

[0147] Furthermore, adjusting or optimizing the complexity of the surface model may also include providing:

[0148] - A validation dataset containing multiple ordering parameter sets, each containing values ​​for at least a subset of parameters required to order at least one ophthalmic lens; and

[0149] – A target value for at least one characteristic of at least one ophthalmic lens for each ordered parameter set in the validation dataset.

[0150] In addition, obtaining a surface model for calculating at least one surface of at least one ophthalmic lens may include:

[0151] Given previously predetermined optimized values ​​for the model parameters of each surface model, calculate the values ​​of the verification objective function and / or the values ​​of variables derived from the verification objective function for surface models of varying complexities; and

[0152] Based on the calculated values ​​of the verification objective function and / or with the aid of the values ​​of variables derived from the verification objective function, a surface model for calculating at least one surface of at least one ophthalmic lens is selected or determined from surface models of different complexities parameterized with the optimized values ​​of the model parameters.

[0153] As stated above, the verification objective function depends on the provided target value. If the provided target value for at least one characteristic of at least one ophthalmic lens for each ordering parameter set is consistent with the value of the same characteristic of at least one lens that can be computed or calculated using the surface model given the optimized value of the model parameters of the surface model for the corresponding ordering parameter set, then the verification objective function contains at least one term with a minimum or maximum value for each ordering parameter set in the verification dataset.

[0154] The validation objective function can be set to be the same as or similar to the objective function of the model parameters. However, different objective functions can be used.

[0155] For example, if regularization is not used in the optimization of model parameters, the objective function used for model parameter optimization and the validation objective function may contain the same terms that depend on the individual objective values ​​(i.e., with respect to the training dataset or validation dataset, respectively). If regularization is applied, the terms used for optimizing the objective function of the model parameters that include the regularization parameter can be omitted from the computation of the validation objective function. This can also be achieved by setting the regularization parameter such that the corresponding terms do not contribute to the validation objective function (e.g., by setting the regularization parameter to 0). Of course, in all these cases, the corresponding objective values ​​must be replaced with objective values ​​based on the validation dataset, not the training dataset. However, additional properties of the ophthalmic lens can also be used in validation (compared to the optimization of model parameters), either additionally or solely. For example, in optimization, the square of the sag difference can be minimized (i.e., the corresponding property is the sag of a given evaluation point on the ophthalmic lens), and in validation, the sum of the squares of the ophthalmic lens effect differences and the corresponding objective value can be minimized. (Here, the property is the effect, such as as a power vector, spherical / cylindrical / axial, or one or more components of the effect).

[0156] Training based on calculated or known surfaces

[0157] If at least partially computed surfaces of the ophthalmic lens are provided (e.g., surfaces or lenses computed according to conventional optimization methods), the model parameters can be selected such that the surface output by the surface model is as consistent as possible with the computed surface (target surface). Possible criteria for this can be defined in the objective function of the model parameters. In the simplest case, the objective function contains a term that is the sum of convex functions (e.g., squares) of the elevation differences between the surface computed or computeable by the surface model with a given set of model parameters and the target surface. Here, this summation is performed point-by-point over all elevation pairs of the target surface and the surface computed or computeable by the surface model, and over the base lens or ordered parameter set. Here, the computed surfaces of the base lens, along with their corresponding ordered parameters and / or variables derived therefrom, can be considered as the training dataset.

[0158] Different weighted sums on the sagitta of the ophthalmic lens can also be used. Thus, for example, the weight of a location on the ophthalmic lens that can be assessed as particularly critical can be higher than that of other locations. For example, the weight in areas of the ophthalmic lens that are more frequently observed by it can be higher to ensure higher optical quality (e.g., for areas of tubular lenses that are ground inside the frame, or for progressive lenses, such as areas where residual astigmatism is below a certain threshold, e.g., 0.5 dpt).

[0159] As an alternative to the difference in sag, its ratio or the logarithm of its ratio can also be used.

[0160] Other terms can also be used in the objective function of the model parameters. For example, it is feasible for the diameter of the ophthalmic lens calculated by the surface model to differ from the target diameter. In this case, the objective function of the surface model's model parameters may also include a term penalized for deviations in diameter calculated by the surface model or implicitly derived from the calculation results (e.g., due to excessive curvature). (For example, if the calculated diameter is smaller than the target diameter, the objective function will increase significantly.)

[0161] If the calculated base lens surface and the surface calculated by the surface model are given with different parameterizations (e.g., specifying the sag under different point grids), it is advantageous to convert the calculated base lens surface to the parameterization output by the surface model, for example, by interpolation. However, the surface parameterization can also be adjusted in the opposite direction, or entirely different parameterizations can be chosen (e.g., by Zelnik polynomial representation).

[0162] The objective function of the model parameters may additionally or alternatively include other terms that quantify the difference between the ophthalmic lens surface calculated by the surface model and the base lens by means of optical and / or geometric properties. Here, optical or geometric properties may also depend on ordering parameters (e.g., the vector component or value of residual astigmatism at the location of use, the refractive error at the location of use, or the deviation of the minimum or maximum lens thickness from the corresponding ordering value of the lens thickness).

[0163] These terms typically consist of a sum or weighted sum of point-by-point differences in the optical variables of the lens and base lenses calculated using the surface model, which is then summed over all base lenses. The summation points can be predetermined via a grid of evaluation points for the ophthalmic lens or via a grid of viewing directions. Alternatively, other functions, such as nonlinear functions, can be used as an alternative to the (weighted) sum.

[0164] As mentioned above, the objective function may also additionally include terms that quantify the differences between the binocular characteristics of two pairs of ophthalmic lenses (one pair calculated using a surface model and the other pair calculated using conventional optimization methods).

[0165] Global optimization based on objective function

[0166] In the second example, the objective function of the model parameters used does not depend on the surface of the base lens. This could be, for example, in cases where the calculated surface is insufficient to determine the model parameters, or where a suitable surface for calculation does not yet exist for the ordered parameter set of the base lens.

[0167] In this objective function, the difference between predetermined properties of the surface calculated using a surface model and desired target values ​​of these properties, which may depend on the ordered parameters, can be calculated. Possible properties include the aforementioned optical properties, such as optical characteristics (e.g., refractive error distribution, vector components and / or values ​​and / or axes of astigmatism or residual astigmatism at the location of use, prisms, prism substrates, distribution of vector components of prisms or variables derived therefrom), geometric properties, binocular characteristics or visual perception characteristics of the future wearer of the ophthalmic lens calculated using the surface model.

[0168] The objective function of the model parameters may include terms representing the weighted deviation between the properties of the ophthalmic lens calculated or computable using the surface model and the desired curve. Weighting, for example, controls the achievement of the effects required in the standard (e.g., high weighting of the spectacle lens reference point). The objective function of the model parameters may also include terms that minimize the desired center thickness or thickness distribution at the edge. The objective function may also include terms representing desired mechanical properties, such as actual or simulated fracture strength.

[0169] The objective function can be one of the aforementioned objective functions. In particular, all the examples of model parameter objective functions in the previous chapter that do not depend on the surface of the base lens can be used by replacing the corresponding characteristics of the base lens with an appropriately chosen objective value that depends on the ordered parameters.

[0170] The objective function of the model parameters can also include terms that have already been used as the objective function when optimizing ophthalmic lenses using common optimization methods. Therefore, the objective function of the model parameters includes terms that sum or average the objective functions of the optimization methods using other ophthalmic lenses.

[0171] Therefore, the model parameters are defined by simultaneously optimizing multiple ophthalmic lenses obtainable from the ordered parameter set by optimizing an objective function that does not depend on the surface of the base lens. Here, instead of directly changing the parameterization (e.g., sag or spline coefficients) of the surface of each individual lens as is typically done, the model parameters of the control surface curves of the surface model are changed to minimize the sum of the individual objective functions used to define the model parameters for each ophthalmic lens, which are computeable or optimizable from the ordered parameter set.

[0172] Of course, new, yet-to-be-known objective functions representing the advantageous properties of ophthalmic lenses can also be used for individual ophthalmic lenses.

[0173] Furthermore, in addition to the terms having an objective function for a single ophthalmic lens, the objective function for the model parameters of the surface model can also include terms that incorporate design differences between ophthalmic lenses with different ordering parameters. The advantages of these terms have already been discussed above.

[0174] If the surface calculated by the surface model is a continuous or even continuously differentiable function of ordered parameters and / or variables derived from it, it can be expected that, with appropriate adjustment of the surface model complexity, there will be only minor differences between the surface calculated by the surface model and the surface calculated by optimizing the same objective function using conventional optimization methods.

[0175] The complexity of a surface model is defined by the calculated quality of the surface.

[0176] To appropriately tune the complexity of the surface model so that ophthalmic lenses can be correctly computed even from a set of ordered parameters not present in the training dataset, in addition to direct variations in the number of model parameters (or ordered parameters and / or variables derived from them) that can be appended to or replaced by the surface model, so-called regularization can be used. This involves adding additional terms, weighted by one or more different factors, to the objective function of the surface model's parameters. Typically, these terms are squared terms in the model parameters. However, other powers (e.g., quantities that can be used for the model parameters) or other functions of the model parameters can be used instead of the model itself (e.g., the difference in spline coefficients between adjacent splines representing the ophthalmic lens surface).

[0177] To verify the quality of a surface model after tuning its parameters, it is recommended that instead of training the model parameters on all available datasets (i.e., at least the dataset containing the ordered parameters, the variables derived from them if necessary, and the computed surfaces corresponding to them if necessary), a portion of the dataset be used for model validation or final testing. Validation of the tuned model complexity and final testing of the surface model can be accomplished using the same objective function for tuning the model parameters, but preferably without terms derived from regularization. Alternatively, it is feasible to use a different objective function than the one used to determine the model parameters to validate or test the surface model.

[0178] Thus, for example, it can be tested whether there are enough other sets of ordering parameters not present in the training dataset that allow the surface calculated by the surface model to deviate slightly from the target surface. This can typically be achieved by dividing the ordering dataset, which includes the base lens surface, into a training dataset and validation and / or test datasets. As mentioned above, the complexity of the surface model can be selected using the validation dataset.

[0179] Therefore, the method for defining a surface model may include the following steps:

[0180] Provides a validation dataset that includes a large number of order datasets;

[0181] To validate each set of ordered parameters in the dataset, provide at least one target value for at least one predetermined characteristic of the ophthalmic lens; and

[0182] Based on the validation dataset, the obtained surface model used to calculate at least one surface of at least one ophthalmic lens is validated.

[0183] Alternatively or additionally, methods for defining a surface model may include the following steps:

[0184] Provide a test dataset that includes a large number of order datasets;

[0185] For each set of ordered parameters in the test dataset, provide at least one target value for at least one predetermined characteristic of the ophthalmic lens; and

[0186] Based on the test dataset, the surface model obtained by the test is used to calculate at least one surface of at least one ophthalmic lens.

[0187] Different parts of the same dataset can be used for validation and testing. The purpose of validation is to determine the appropriate model architecture (also known as model complexity) or suitable values ​​for regularization parameters. The purpose of testing is to examine the trained and selected model to avoid overfitting.

[0188] The functionality evaluated in validation and testing can be the same, such as the validation function described above (also known as the test target function). As mentioned above, the validation target function typically does not include additional terms that include regularization parameters.

[0189] During testing, the validation objective function can be evaluated on the test dataset with fixed model parameters and compared to the value of the validation objective function evaluated on the validation dataset and / or the objective function of the model parameters (but without regularization). The test is successful if the value of the validation objective function evaluated on the validation dataset is similar in magnitude to the value evaluated on the test dataset. The actual magnitude of the difference between them depends on the amount of data in each validation or test dataset (especially the amount that would have a significant impact if an objective function based on data quantity standardization was not used).

[0190] The values ​​of validation and testing objective functions that are not standardized based on the amount of data (e.g., the sum of the squared differences of the sag of a lens calculated using conventional methods and the difference calculated using a surface model at evaluation points defined on the lens) are only comparable if the test and validation datasets match and contain the same amount of data. By dividing these functions by the amount of data, standardized objective functions are obtained, which are comparable even when the test and validation datasets contain different numbers of data points.

[0191] Using a standardized objective function is advantageous because the values ​​of the objective functions being compared (i.e., the values ​​of the validation objective function when evaluated using test and validation datasets) do not differ significantly from each other (e.g., the difference between two values ​​of the objective function should be less than a predetermined threshold). The value of this threshold depends heavily on the type of objective function used and should be a small fraction (e.g., 0.3 to 0.01 times) of the variation in the validation objective function when evaluated using different models or different values ​​of regularization parameters (e.g., maximum, minimum values). When using an unstandardized objective function, it can be standardized by pre-dividing it by the number of ophthalmic lenses (pairs) in the corresponding dataset.

[0192] Calculation of variables depending on ordering parameters

[0193] As mentioned above, variables that depend on the ordering parameters (auxiliary variables) can be used as input variables for the surface model, such as variables derived from the ordering parameters.

[0194] For example, if the surface model includes a regression model or the surface model consists of a regression model, it may be advantageous to include, in addition to or in lieu of the ordered parameters, one or more variables (auxiliary variables) calculated from the ordered parameters as input variables of the regression model from which the surface is calculated.

[0195] Examples of auxiliary variables are as follows:

[0196] – For progressive lenses, the desired distribution of residual astigmatism and / or refractive error depends on the eye's viewing direction and, preferably, the position of use;

[0197] – For progressive lenses, the desired distribution of residual astigmatism and / or refractive error standardized by addition, preferably as far as possible in the position of use, depends on the eye's viewing angle;

[0198] – The desired thickness distribution at one or more points (e.g. at the edge) of an ophthalmic lens, which may also depend, for example, on the material and / or layers or coatings of the ophthalmic lens, or the optical and / or mechanical properties of the material and / or layers or coatings;

[0199] - Optical and / or mechanical properties of ophthalmic lens materials (e.g., refractive index, elastic modulus, coefficient of thermal expansion);

[0200] – Optical and / or mechanical properties of ophthalmic lens coatings (e.g., thickness distribution, elastic modulus, coefficient of thermal expansion).

[0201] Here, it is preferable to select parameters that have a significant impact on the surface of the ophthalmic lens or are expected to have a significant impact on the surface.

[0202] Neural Networks as Surface Models

[0203] If the surface model contains or is composed of a neural network, then the input layer of the neural network is assigned ordered parameters and / or auxiliary variables calculated therefrom.

[0204] Here, the weights of a neural network (i.e., the strength of neuron connections) represent at least a portion of the model parameters.

[0205] The output layer can represent the entire computed surface of an ophthalmic lens or a portion of the computed surface (e.g., as the sag in a defined mesh or grid with the desired resolution and, if necessary, the resolution to be set).

[0206] In addition to input and output layers, neural networks can also contain one or more hidden layers.

[0207] The way a neural network is constructed, such as the number of layers, the number of neurons in different layers, and the type of interconnection between layers, is implicitly defined by model parameters (such as their number).

[0208] In particular, it is advantageous that the input layer is additionally or alternatively assigned one or more variables (auxiliary variables) calculated from the ordering parameters (see the exemplary auxiliary variables in the section “Calculation of Variables Derived from Ordering Parameters”, which can be used as input variables for the surface model).

[0209] It is also advantageous to design the neural network such that one or more of these auxiliary variables in the network are at least approximately represented or set during network training. Model parameters not used as neural network weights can also be included in the calculation of the auxiliary variables.

[0210] It is also advantageous to restrict the variables of the neural network such that the output layer represents only a relatively coarse grid of the ophthalmic lens surface (e.g., a grid with a sagittal height of only 10×10 or 20×20). To compute a manufacturing-ready representation of the ophthalmic lens surface from this, it is suggested to interpolate the sagittal height output by the neural network on a higher resolution grid (e.g., by means of linear or bicubic interpolation on, for example, a 100×100-point grid), and, if necessary, perform subsequent optimization using a few steps of an optimization method according to the prior art. Such subsequent optimization typically requires only a few iterations to converge, provided the neural network has been trained using the results of an optimization method with the same objective function.

[0211] The determined or defined surface model, with optimized model parameters and optional optimization complexity, can be appropriately stored and then provided for calculating the ophthalmic lens from the ordered parameter set. The surface model, or a portion thereof (e.g., model parameters), can be stored, for example, in a suitable memory, such as a database. Similarly, at least a portion of the ordered parameter set required to define the surface model and / or corresponding target values ​​can also be stored in the memory. As mentioned above, the target value can be, for example, a surface value of the ophthalmic lens (base lens) that has been at least partially calculated according to conventional methods, or a variable derived therefrom. The target value can also be a setpoint input to an objective function (e.g., an objective function according to the prior art) used to optimize the ophthalmic lens.

[0212] The surface model determined as described above can be further modified. Therefore, the method can include modifications to the surface model. Exemplary modifications include adding additional layers to the neural network or embedding the surface model into another function, such as interpolating or transforming the surface elevation (e.g., transforming the neural network into a support vector machine, decision tree, or any other regression model).

[0213] The surface model calculated according to the method and implementation variations of the above aspects of the present invention, and the method of using the surface model, preferably have at least one of the following characteristics or advantages:

[0214] – The evaluation of surface models with ordered parameter sets requires less computation compared to optimization methods based on existing techniques.

[0215] Typically, less than 90% (preferably less than 50%, 20%, 10%, 5%, 2%, or 1%) of the computational power or time allocated to calculating the surface is used for iterative changes to the optical lens surface. This is more advantageous than common iterative algorithms because the computational workload remains constant in each iteration, while the surface changes decrease with each iteration.

[0216] – The surface model does not necessarily need to provide an initial surface (starting surface) as input; this input is included in the calculation as an input variable and modified in the optimization method.

[0217] – No need to pre-calculate and store surface changes based on order parameters;

[0218] – It is feasible to perform hybrid calculations on the surface using subsequent corrections (e.g., subsequent optimization). Such hybrid calculations can ultimately achieve shorter optimization times due to a better initial surface.

[0219] – Surface model can be continuously improved.

[0220] By using a surface model defined according to the foregoing aspects and the method of implementing variations, the surface of an ophthalmic lens can be quickly and efficiently calculated, manufactured, and / or visualized for any ordering parameters of the customer.

[0221] Furthermore, the approach described above is also advantageous when developing a series of ophthalmic lenses (involving both individual ophthalmic lenses and pairs of ophthalmic lenses), because the surface model can be used invariably as long as the ordering parameters (e.g., refractive index) or related variables (e.g., basic curve system) that distinguish between the two different series exist and are changed in the training dataset.

[0222] Another application of the method described above is interpolation between different series of ophthalmic lenses (e.g., between different products, such as progressive lens series set for different purposes, or, for example, between progressive lenses and single-vision lenses). For this, the ordering dataset only needs to be expanded with variables corresponding to a series of ophthalmic lenses. For N series, it is recommended to use N tuples (s1, s2, ..., s...) of numbers between 0 and 1. N Here, a series of ophthalmic lenses i are composed of tuples (δ). 1,i ,δ 2,i ,…,δ N,i ) represents, where δ j,i This is the Kronecker-Delta notation. Then, by selecting a value s between 0 and 1... j (its sum s) j (1), which enables interpolation between different series of ophthalmic lenses. This tuple is then used with a general ordering dataset to compute at least one surface of the ophthalmic lens through a properly trained surface model.

[0223] Other aspects

[0224] A second aspect of the invention relates to a computer-implemented method and corresponding apparatus for determining at least one surface of one or more ophthalmic lenses from ordered parameters and / or variables derived therefrom using a predetermined surface model. In the context of this application, the term "determine" includes obtaining or calculating at least one surface of one or more ophthalmic lenses.

[0225] The method includes:

[0226] Provide a set of ordering parameters for at least one ophthalmic lens;

[0227] Provides a function for calculating at least one surface of at least one ophthalmic lens from a set of ordering parameters and / or from variables depending on the ordering parameters, wherein the function is a surface model or a function that approximately performs a mapping of the set of ordering parameters onto at least one surface of at least one ophthalmic lens, the mapping being performed using the surface model; and

[0228] Using the provided function, surface data of at least one surface of at least one ophthalmic lens are obtained (directly, non-iteratively) from the provided set of ordering parameters.

[0229] The surface model can be the surface model described above, i.e., the surface model determined or obtained according to the method described above. Surface data for at least one surface is preferably obtained directly (i.e., non-iteratively) or using a few iterative steps from the provided set of ordered parameters, for example, using fewer than 30, 25, 15, 10, 5, or 3 iterative steps. As mentioned above, this significantly reduces the computation time required to calculate surfaces or lenses for any set of ordered parameters. Furthermore, there is no need to pre-calculate and store surface variations based on the ordered parameters, which reduces storage space requirements. It is also feasible to continuously update and improve the surface model in a simple manner.

[0230] The surface model can be used directly to calculate at least one lens surface.

[0231] Alternatively, functions of the surface model can be used, such as functions that approximate computations using the surface model determined according to the invention. Such functions can be generated within a simplified category of the surface model, for example by combining neurons of a neural network with similar activation patterns, or within the category of another transformation of the surface model used.

[0232] Furthermore, the aforementioned preferred embodiments or advantages also apply in a similar manner to the method or the apparatus.

[0233] The method may also include determining other variables related to the fabrication of the surface (e.g., the existing diameter and type of the blank used to fabricate the lens), so that the surface calculated in this way no longer needs further optimization, or only requires correction with a relatively low computational cost.

[0234] Furthermore, a method for determining at least one surface of at least one ophthalmic lens may include performing correction of at least one surface calculated using a surface model, wherein the correction includes optimization of the surface calculated using the surface model and / or correction of overlap with overlapping surfaces and / or correction of manufacturing-related deviations of the ophthalmic lens surface or optical properties and / or extending the surface to the ophthalmic lens diameter required for manufacturing. An exemplary method for extending a surface is described in EP 2087396.

[0235] Furthermore, a method for determining at least one surface of at least one ophthalmic lens may include storing surface data of at least one surface calculated using a surface model and, if necessary, corrected and / or expanded. The surface data may optionally be stored together with at least a portion of an ordered set of parameters used to obtain the surface data. The surface data may, for example, be stored on a suitable data carrier or in a storage device. The storage device may also be a computer or a data cloud.

[0236] A method for determining at least one surface of at least one ophthalmic lens may also include transmitting surface data of at least one surface, calculated using a surface model and corrected and / or expanded where necessary, to an external unit, such as an ophthalmic lens manufacturer, manufacturing unit, manufacturing equipment, etc. Surface data may optionally be transmitted along with at least a portion of an ordered set of parameters used to obtain the surface data.

[0237] Furthermore, the method for determining at least one surface of at least one ophthalmic lens may include verifying whether at least one surface calculated using a surface model meets desired or required characteristics, and storing information about whether the desired characteristics are met or not, as well as at least a portion of the ordered parameter set for determining surface data and / or at least one surface calculated using a surface model and, where necessary, corrected and / or expanded, and / or the desired or required characteristic values ​​may be provided as characteristic target values ​​when determining the surface model according to the first aspect of the invention.

[0238] Furthermore, the method for determining at least one surface of at least one ophthalmic lens may include adjusting the model parameters of the surface model after obtaining and / or storing each surface or a predetermined number of surfaces calculated using a surface model and corrected as necessary.

[0239] Surface calibration and design sustainability verification using surface model calculations

[0240] If, for example, an ophthalmic lens calculated using a surface model does not meet at least one desired or required optical and / or geometric characteristic, at least one surface of the ophthalmic lens calculated using the surface model can be further corrected. For this purpose, it can be verified whether the ophthalmic lens calculated using the surface model meets the desired or required characteristics, for example, by exceeding or falling below an appropriately selected threshold.

[0241] For progressive lenses, one or more of the following characteristics can be tested:

[0242] - Residual astigmatism along the main line of sight (as far as possible in the usage location);

[0243] - Permissible deviations of optical effects (e.g., spherical and / or cylindrical and / or prism) at standard or reference points that satisfy optical effects;

[0244] – At least one vertical and / or horizontal prism that is desired or permitted at a prism reference point;

[0245] – The desired or permissible deviation of the vertical and / or horizontal prisms at at least one prism reference point between the left and right lenses;

[0246] – The maximum permissible gradient of residual astigmatism and / or refractive error (as far as possible in the usage location);

[0247] – Distribution of residual astigmatism and / or refractive error (as far as possible in the usage location);

[0248] - Expected width of a good field of view;

[0249] -Sufficient surface smoothness;

[0250] - Surface manufacturability (e.g., no undercut);

[0251] - No surface undercut to ensure manufacturability;

[0252] - Sufficient thickness to achieve fracture strength (e.g., quantified by static or dynamic load tests).

[0253] It can also be used to test other or additional characteristics.

[0254] However, it is advantageous to determine whether the surface calculated using the surface model needs correction before performing calculations using the surface model. This can be done, for example, by using the proportion of surfaces that do not meet the desired characteristics (e.g., if the proportion exceeds a defined threshold).

[0255] It is also advantageous to continuously examine whether each ophthalmic lens generated from the surface model meets the desired or required characteristics, so as to determine individually whether correction is needed for each lens. Preferably, this examination is used only when the computational power consumed on average on the ophthalmic lens to be calculated for the examination is less than the computational power saved for correction computation (e.g., subsequent optimization or subsequent computation).

[0256] Therefore, regardless of whether the required characteristics of the ophthalmic lens are verified, the ophthalmic lens calculated using the surface model can be corrected starting from these surfaces.

[0257] Correction can be performed, for example, using methods based on existing techniques. For instance, it is feasible to calculate the surface of the ophthalmic lens in subsequent optimization, which includes a few optimization steps of commonly used optimization methods for ophthalmic lenses. The surface output from the surface model can be used as the initial point for subsequent optimization (the so-called starting surface).

[0258] Alternatively, the surface of the ophthalmic lens can be generated in subsequent calculations by superimposing the surface calculated by the model with one or more superimposed surfaces. Superimposed surfaces can be, for example, simple spherical superimposed surfaces or more complex superimposed surfaces, as described in US 2018 / 0088353A1 or EP 1 240 541 B1.

[0259] Alternatively, a second surface model can be used for calculations. This second surface model can, for example, include a regression model.

[0260] It is also advantageous to further correct surfaces calculated using surface models and, where necessary, corrective measures. For example, if systematic deviations in the surface or optical properties of ophthalmic lenses are known to have occurred during manufacturing, they can also be corrected using common methods, such as those described in WO 2014 / 076155 A1.

[0261] Furthermore, after calibration, the surface of the ophthalmic lens can be re-inspected to ensure it meets the expected or required characteristics. If the ophthalmic lens does not meet the expected or required characteristics, lens manufacturing can be stopped for manual inspection of the order. This ensures that unsuitable lenses are prevented from being manufactured or even delivered. In particular, it allows for the identification of subsequent optimizations to address failures.

[0262] It is also advantageous to store information about whether the required characteristics are met or not, along with the ordering parameters, in a database, for later evaluation.

[0263] If an ophthalmic lens undergoes further optimization after calculation using a surface model, its surface, along with ordering parameters and, if necessary, other variables derived from it, can be stored as a new dataset in a database. This dataset can be used to improve the surface model by redefining or refining it in consideration of the newly added data. Therefore, the data base of the method according to the invention grows steadily. Alternatively, the surface model can be redefined using only a portion of the dataset stored in the database. Thus, the quality of the surface calculated using the surface model can be improved with each subsequently optimized lens.

[0264] If, for example, the set of ordered parameters of the ophthalmic lens to be calculated and / or the variables derived therefrom deviate from the set of ordered parameters required to define the surface model (the set of ordered parameters that best approximates the set of ordered parameters of the lens to be calculated), the surface correction calculated using the surface model can be omitted. The deviation can be measured by an appropriately defined distance measure, which can be chosen to account for surface sensitivity to the ordered parameters. For example, the deviation can be described or quantified by the sagittal difference or the square of the difference in desired characteristics between two ophthalmic lenses with different ordered parameters.

[0265] Continuous improvement of surface models

[0266] The model parameters of the surface model can be continuously or periodically examined and / or modified. If the ophthalmic lens requires further optimization or re-optimization, the necessary data for the ophthalmic lens surface is generated and can be used for model parameter tuning along with the corresponding ordered parameters. Optimization algorithms that use only partial data (e.g., stochastic gradient descent or limited-memory BFGS) can preferably be used for tuning. However, optimization algorithms that require the complete dataset can also be used.

[0267] For example, after each or a predetermined number of new calculations or subsequent optimizations of ophthalmic lenses, the model parameters of the surface model can be verified and / or adjusted. In the simplest case, this number can be constant.

[0268] Another possibility is that adjustments are only made when a fixed proportion (e.g., 10%) of the data already used to determine the model parameters is re-optimized or subsequently optimized. It is also advantageous to adjust the model parameters of the surface model when computation time is available (e.g., when fewer ophthalmic lenses must be computed).

[0269] If the model parameters of the surface model are tuned using only the new dataset from subsequent optimizations, it is also feasible to choose the learning rate (i.e., the intensity of tuning the model parameters in the tuning step) in proportion to the proportion of the new dataset to the total dataset used for training. In this way, the learning rate decreases with each tuning and ensures the convergence of the model parameters.

[0270] Hybrid computation and optimal selection of surface model complexity

[0271] According to one example, a hybrid method for determining at least one surface of one or more ophthalmic lenses may be provided, comprising determining at least one surface from ordered parameters and / or variables derived therefrom using a predefined surface model, and performing subsequent corrections or calculations on the at least one surface determined by the surface model. The correction may be one of the corrections described above.

[0272] Advantageously, the complexity of the surface model is set such that the average computational workload of calculating the surface of the ophthalmic lens using the surface model is minimized along with the computational workload used for subsequent calculations or corrections.

[0273] Suppose Z(F_m(a_m)) is the quality of surface F_m(a_m) calculated using a surface model, measured by an objective function Z, where a_m is the computational effort of the surface model. Suppose Z(F_n(a_n; F_m(a_m))) is correspondingly the quality of surface F_n(a_n; F_m(a_m)) calculated based on surface F_m(a_m) through subsequent calculations with a computational effort a_n. To minimize the computational effort, the complexity of the surface model can be chosen such that the improvement in the objective function obtained by each further computational effort a_m using the surface model is equal to or greater than the initial improvement in the objective function obtained by subsequent calculations based on the surface calculated using the surface model when the computational effort a_n = 0 disappears. Therefore, the evaluation of the surface model must have a minimum computational effort a_m, for which:

[0274] dZ(F_m(a_m)) / da_m(a_m)>=dZ(F_n(a_n; F_m(a_m=0))) / da_n

[0275] In this regard, it should be noted that the derivatives on both sides have negative signs because the objective function decreases as the computational workload increases.

[0276] The range of ordering parameters using the surface model can be limited to frequently ordered parameters to maintain a low overall model complexity and minimize the average computational effort for all ordered ophthalmic lenses. For example, it may be meaningful if some sets of ordering parameters are rare, while others are very frequent. For instance, the surface model could be used only for lenses with standard individual parameters and standard designs within the main ordering range (e.g., spherical power between -4dpt and +4dpt; cylindrical power less than 2dpt; additional power between 1.5dpt and 2.5dpt). For the remaining range of ordering parameters, methods according to existing techniques can be used.

[0277] For example, the complexity of the surface model can be limited to only processing the ordering parameters that have the greatest impact on the surface of the ophthalmic lens. The influence of other ordering parameters on the surface can then be corrected using subsequent calculations or optimizations. In one possible scenario when calculating spectacle lenses, the ordering parameters mapped in the surface model or used to define the surface model are reduced to the prescription values ​​and centering parameters of the ophthalmic lens, including tilt, eyeglass holder angle, and corneal vertex distance. Here, the calculation of the ophthalmic lens surface is more efficient than the optimization based on a standard starting surface as previously practiced.

[0278] In extreme cases, in order to use the surface model for calculations, only the refractive index can be used. In the most extreme case, only the spherical mirror equivalent can be used, and additional degrees can also be used if necessary.

[0279] Also useful is defining the range of surface models used for calculation based on whether they conform to or not conform to the characteristics required by the ophthalmic lens. For this purpose, information about conforming to or not conforming to these characteristics can be stored based on the order parameters. The range of surface models used can be determined using common classification algorithms, such as logistic regression or support vector machines.

[0280] The range of ordering parameters for calculating surfaces using surface models can be continuously expanded: for example, if a surface calculated using methods based on existing techniques is ultimately sufficient for use outside the range of ordering parameters calculated using surface models, the model parameters of the surface model can be retrained. Then, the expanded range can be recalculated as described above.

[0281] In the most general case, depending on the ordering parameters, multiple surface models with different complexities and / or implementation methods can be used.

[0282] Particularly for individualized or personalized ophthalmic lenses, a subset of the ordering parameters may exhibit standard values ​​particularly frequently within the distribution of ordering parameters. For partially individualized ophthalmic lenses, certain ordering parameters are set to standard values ​​and cannot be changed at the time of ordering. It is recommended that, for cases where a subset of ordering parameters has standard values, a surface model with reduced complexity be used. This allows for simpler and faster calculations because deviations from the standard values ​​of a subset of ordering parameters do not need to be mapped by the surface model. The remaining orders can be calculated using a surface model with higher complexity or similarly, according to existing methods.

[0283] Experiments can be used to determine the distribution of which surface model to use within which range of ordering parameters. The goal of the optimal distribution is to calculate ophthalmic lenses quickly and efficiently.

[0284] According to a third aspect of the invention, a computer program product is provided that, when loaded into the memory of a computer and run on the computer, causes the computer to perform the method according to any one of the preceding aspects. The computer may also be a computer system.

[0285] The method according to any one of the foregoing aspects can be performed by means of a suitably designed device.

[0286] A fourth aspect of the invention relates to an apparatus for defining a surface model for calculating at least one surface of at least one ophthalmic lens (e.g., a contact lens or spectacle lens) from at least a set of ordered parameters and / or variables dependent on the ordered parameters. The apparatus includes a computing device designed to perform the method according to a first aspect of the invention.

[0287] Devices for defining surface models particularly include:

[0288] A device for providing a training dataset comprising a large set of ordering parameters, each set of ordering parameters containing values ​​of at least a subset of parameters required to order at least one ophthalmic lens;

[0289] A means for providing at least one target value for at least one predetermined characteristic of at least one ophthalmic lens for each ordered parameter set in the training dataset;

[0290] A means for providing at least one surface model parameterized by model parameters, which allows at least one surface of at least one ophthalmic lens to be calculated, given the values ​​of the model parameters, from at least an ordered parameter set and / or from variables dependent on the ordered parameter set; and

[0291] A computing device designed to obtain or obtain a surface model for calculating at least one surface of at least one ophthalmic lens, wherein obtaining or obtaining the surface model includes:

[0292] By using the provided target values, the optimized values ​​of the model parameters for at least one surface model are determined.

[0293] Determining optimized values ​​for model parameters used for at least one surface model includes, for example:

[0294] The aim of optimizing the values ​​of model parameters for at least one surface model is to minimize or maximize an objective function for the model parameters of at least one surface model that depends at least on the model parameters and on the provided objective values. If the provided objective value for at least one characteristic of at least one ophthalmic lens for each set of ordered parameters is consistent with the value of the same characteristic of at least one lens calculated or computable using the surface model given the values ​​of the model parameters of the surface model in the corresponding set of ordered parameters, then the objective function for the model parameters of each set of ordered parameters contains at least one term with a minimum or maximum value.

[0295] A fifth aspect of the invention relates to an apparatus for determining at least one surface of one or more ophthalmic lenses from ordered parameters and / or variables dependent on the ordered parameters using a predetermined surface model. The apparatus is designed to perform a method according to one of the foregoing aspects for determining at least one surface of at least one ophthalmic lens. The apparatus for determining at least one surface of an ophthalmic lens particularly comprises:

[0296] A device for providing an ordering parameter set for at least one ophthalmic lens;

[0297] A means for providing a surface model for calculating at least one surface of at least one ophthalmic lens from a set of ordered parameters and / or from variables depending on the ordered parameters; and

[0298] A computing device designed to obtain surface data of at least one surface of at least one ophthalmic lens from a provided set of ordered parameters by means of a surface model.

[0299] The surface model can be a surface model determined or obtained according to one of the aforementioned methods.

[0300] Furthermore, the aforementioned preferred embodiments or advantages of the aforementioned apparatus also apply in a similar manner.

[0301] A sixth aspect of the invention relates to a dataset of surface data comprising at least one surface of at least one ophthalmic lens, wherein the at least one surface is determined according to a method for determining at least one surface of at least one ophthalmic lens according to one of the preceding aspects. The dataset may be permanently or non-permanently stored, or has been stored, on a suitable data carrier or storage device, such as a database, computer, or data cloud.

[0302] The method and corresponding apparatus described above for determining at least one surface of one or more ophthalmic lenses using a surface model can be used in the manufacture of ophthalmic lenses to define the surface to be manufactured when designing the ophthalmic lens, or to verify the manufacturability of the ophthalmic lens by means of the geometric properties of the surface. In other words, the method for determining at least one surface of one or more ophthalmic lenses can be part of the manufacturing or production method of ophthalmic lenses.

[0303] It is also feasible to use a method of determining at least one surface of one or more ophthalmic lenses by means of a surface model in consultations (e.g., with an optometrist), for example, to explain to future wearers of such lenses the optical and geometric characteristics of individualized or personalized ophthalmic lenses (e.g., the location of the clear vision zone and the thickness of progressive lenses). Thus, other aspects of the invention relate to a method and corresponding apparatus for manufacturing ophthalmic lenses.

[0304] Methods for manufacturing ophthalmic lenses particularly include:

[0305] At least one surface of at least one ophthalmic lens is determined according to one of the methods described above;

[0306] Manufacturing an ophthalmic lens having at least one surface.

[0307] Devices for manufacturing ophthalmic lenses particularly include:

[0308] A means for determining at least one surface of at least one ophthalmic lens, according to any of the foregoing aspects;

[0309] Manufacturing apparatus for manufacturing ophthalmic lenses having at least one surface.

[0310] The aforementioned preferred embodiments or advantages of the method and apparatus also apply in a similar manner.

[0311] The aforementioned apparatus for providing, determining, defining, or calculating data (e.g., variables derived from ordered parameters, model parameters, target values, surface data, weights, etc.) and / or for evaluating functions (e.g., objective functions) can be implemented using appropriately configured or programmed data processing apparatus (particularly dedicated hardware modules, computers, or computer systems, such as computers or data clouds) with corresponding computing units, electronic interfaces, memory, and data transmission units. Furthermore, these apparatuses may also include at least one preferably interactive graphical user interface (GUI) that allows a user to view and / or input and / or modify data.

[0312] Furthermore, the aforementioned apparatus may also have a suitable interface for transmitting, inputting, or retrieving data (e.g., order parameter sets, model parameters, target values, surface data, etc.). The apparatus may also include at least one storage unit, for example in the form of a database, which stores the data used, such as order parameter sets, target values, surface data, weights, etc.

[0313] The manufacturing apparatus may include, for example, at least one CNC-controlled machine for directly machining the blank according to determined optimization specifications. Alternatively, the ophthalmic lens may be manufactured by means of a casting process. The finished ophthalmic lens preferably has a simple spherical or rotationally symmetric aspherical surface and a surface obtained by a surface model according to one aspect of the method of the invention. The simple spherical or rotationally symmetric aspherical surface is preferably the front surface (i.e., the object-side surface) of the ophthalmic lens. Of course, the surface calculated by the surface model can be set as the front surface of the ophthalmic lens. The arrangement of the two surfaces of the ophthalmic lens and / or their relative to each other can also be determined by means of a surface model.

[0314] Furthermore, the present invention provides the use of an ophthalmic lens manufactured according to the method of the present invention in a predetermined average or ideal use position of a spectacle lens in front of a particular wearer's eye to correct the wearer's visual defects. Attached Figure Description

[0315] Preferred embodiments of the invention will be described exemplarily below with reference to the accompanying drawings. Individual elements of these embodiments are not limited to specific embodiments. Rather, elements of the embodiments can be arbitrarily combined with each other to create new embodiments. Wherein:

[0316] Figure 1 An exemplary method for calculating ophthalmic lenses using a surface model is shown;

[0317] Figure 2 An exemplary method for calculating ophthalmic lenses using a parametric surface model is shown;

[0318] Figure 3 Another exemplary method for calculating ophthalmic lenses with corrections using a surface model is shown;

[0319] Figure 4 Another exemplary method for calculating ophthalmic lenses with optional corrections using a surface model is shown;

[0320] Figure 5 An exemplary method for defining a surface model using a calculated ophthalmic lens is shown;

[0321] Figure 6 An exemplary method for defining a surface model without having already calculated ophthalmic lenses is shown;

[0322] Figure 7 An exemplary partition of the dataset is shown, which includes a large number of ordered parameter datasets in the training dataset, a validation dataset, and a test dataset;

[0323] Figure 8A The correlation between the center thickness of the spectacle lens calculated using a first exemplary surface model and the center thickness of the test spectacle lens is shown.

[0324] Figure 8B The frequency histogram of the center thickness residual is shown;

[0325] Figure 8C The correlation between the rear surface curvature of the first principal meridian plane of the spectacle lens calculated using the first surface model and the rear surface curvature of the first principal meridian plane of the test spectacle lens is shown.

[0326] Figure 8D The frequency histogram of the residuals of the surface curvature behind the first principal meridion is shown.

[0327] Figure 8E The correlation between the rear surface curvature of the second principal meridian plane of the spectacle lens calculated using the first surface model and the rear surface curvature of the second principal meridian plane of the test spectacle lens is shown.

[0328] Figure 8F The frequency histogram of the residuals of the surface curvature behind the second principal meridion is shown.

[0329] Figure 8G The correlation between the vertex power of the spectacle lens in the first principal meridian plane calculated using the first surface model and the vertex power of the test spectacle lens in the first principal meridian plane is shown.

[0330] Figure 8H A frequency histogram showing the deviation between the vertex power calculated according to the first surface model in the first principal meridian and the vertex power in the first principal meridian of the test lens;

[0331] Figure 8I The correlation between the vertex power of the spectacle lens in the second principal meridian plane calculated using the first surface model and the vertex power of the test spectacle lens in the second principal meridian plane is shown.

[0332] Figure 8J A frequency histogram showing the deviation between the vertex power calculated based on the first surface model in the second principal meridian and the vertex power in the second principal meridian of the test lens;

[0333] Figure 9A The correlation between the center thickness of the spectacle lens calculated using a second exemplary surface model and the center thickness of the test spectacle lens is shown.

[0334] Figure 9B The frequency histogram of the residual at the center thickness is shown;

[0335] Figure 9C The correlation between the rear surface curvature of the first principal meridian plane of the spectacle lens calculated using the second surface model and the rear surface curvature of the first principal meridian plane of the test spectacle lens is shown.

[0336] Figure 9D The frequency histogram of the residuals of the surface curvature behind the first principal meridion is shown.

[0337] Figure 9E The correlation between the rear surface curvature of the second principal meridian plane of the spectacle lens calculated using the second surface model and the rear surface curvature of the second principal meridian plane of the test spectacle lens is shown.

[0338] Figure 9F The frequency histogram of the residuals of the surface curvature behind the second principal meridion is shown.

[0339] Figure 9G The correlation between the vertex power of the spectacle lens in the first principal meridian plane calculated using the second surface model and the vertex power of the test spectacle lens in the first principal meridian plane is shown.

[0340] Figure 9H A frequency histogram showing the deviation between the vertex power calculated according to the second surface model in the first principal meridian and the vertex power in the first principal meridian of the test lens is shown.

[0341] Figure 9I The correlation between the vertex power of the spectacle lens in the second principal meridian plane calculated using the second surface model and the vertex power of the test spectacle lens in the second principal meridian plane is shown.

[0342] Figure 9JThe frequency histogram shows the deviation between the vertex power calculated according to the second surface model in the second principal meridian and the vertex power in the second principal meridian of the test lens.

[0343] Figure 10 The diagram shows the correspondence between the minimum edge thickness and the center thickness of the spectacle lens calculated using the second surface model. Detailed Implementation

[0344] Used to calculate about the order parameter set d i L-shaped ophthalmic lenses i The conventional method typically includes the following steps:

[0345] Provide order data d i (Ordering parameter set);

[0346] Calculate or optimize at least one surface of an ophthalmic lens; and

[0347] Get order data d i Ophthalmic lenses L to be manufactured i The surface.

[0348] Optimization is typically performed iteratively by minimizing or maximizing an objective function, where at least one setpoint for a lens property (e.g., optical property) is input. The objective function is usually evaluated against a parameterization of the surface to be computed. Surface parameters are modified until predetermined criteria are met.

[0349] Figure 1 An exemplary method is shown for calculating one or a pair of ophthalmic lenses based on ordered data using surface models and direct non-iterative calculations or calculations with a few iterative steps. The method includes the following steps:

[0350] S1-1: Provides a set of ordering parameters including ophthalmic lenses. k Order data;

[0351] S1-2: Calculate / optimize at least one surface of the lens using a surface model;

[0352] S1-3: Obtain information about the order parameter set d k Ophthalmic lenses L to be manufactured K The surface.

[0353] The calculation of at least one surface of a lens using a surface model can be performed directly and non-iteratively, or according to an iterative method with a few iterative steps. This significantly reduces the time required to calculate the surface.

[0354] The surface model can be a model defined according to one of the above aspects and embodiments. For example, the surface model can be defined parametrically, wherein model parameters (parameters represented by the parameters of the surface model) together with at least a portion of the ordered parameters and / or variables derived therefrom are used for calculations of one or more surfaces of an ophthalmic lens. The surface model can be a linear or nonlinear regression model. A nonlinear regression model can be, for example, a neural network. In this regard, reference can be made to the above-described preferred embodiments or advantages of different surface models.

[0355] Figure 2 An exemplary method is shown for calculating one or a pair of ophthalmic lenses based on order data using a parametric surface model and direct calculation. The method includes the following steps:

[0356] S2-1: Provide an order parameter set including one or more ophthalmic lenses. k Order data;

[0357] S2-2: Provides parameters for the surface model;

[0358] S2-3: Calculate / optimize ophthalmic lenses using surface models (directly, non-iteratively, or according to iterative methods with a few iterative steps);

[0359] S2-4: Obtain information about the order parameter set d k Ophthalmic lenses L to be manufactured K The surface.

[0360] A surface model can be defined using an existing set of ordered parameters with corresponding target values. For this purpose, initial complexity and initial parameterization can be determined or defined. The model parameters can then be determined using optimization methods, where the model parameters are iteratively changed. The goal of the optimization methods is to make the surface and / or its properties output by surface models with different sets of ordered parameters correspond as closely as possible to the target values ​​of the same set of ordered parameters.

[0361] As described above, parameterization optimization can be performed by minimizing or maximizing the objective function of the model parameters, and surface model complexity optimization can be performed if necessary. Preferably, the objective function is evaluated on all ordered parameter sets in the training dataset. The objective function includes at least one term that depends on the deviation of the value of at least one predetermined characteristic of the ophthalmic lens calculated from the surface model from at least one target value of the characteristic of the same ordered parameter set, and this deviation is determined for each ordered parameter set in the training dataset.

[0362] In one example, the objective function for the model parameters can include the following items:

[0363] f i =f(Z) i Z soll)=∑ j g z (j)(z i (j)-z i (j) Soll ) 2 +…,

[0364] in:

[0365] Z i (j) represents the j-th value of at least one property Z of the lens calculated based on the surface model for the i-th order parameter set;

[0366] Z i (j) Soll This represents the j-th value of at least one characteristic Z in the i-th order parameter set; and

[0367] g z (j) represents the j-th value of at least one characteristic Z.

[0368] The j-th value of at least one property Z of the lens can be obtained using the current parameterization of the surface model or the current model parameters. For example, the j-th value of at least one property Z of the lens can be the value of that property at the j-th evaluation point of the lens.

[0369] function f i =f(Z) i Z Soll It may also include other items depending on other or more characteristics of the ophthalmic lens.

[0370] function f i For example, it could be an objective function used to optimize ophthalmic lenses according to conventional methods, and evaluated for the current parameterization or current parameters used in the surface model.

[0371] One or more target values ​​Z i (j) Soll It can be equal to 0. Thus, for example, astigmatism at one or more evaluation points of the lens can have a target value of 0dpt.

[0372] Then, the above function f i And / or its derivative with respect to the surface can be evaluated with respect to all ordered parameter sets in the training dataset, where the evaluation is based on the parameterization of the surface model. For example, it can be based on a function f obtained for all ordered parameter sets. i And / or its derivative with respect to the surface to form and evaluate the weighted or unweighted sum f.

[0373]

[0374] Where N represents the number of ordered parameter sets (e.g., the number of ordered parameter sets in the training set); and

[0375] g i It represents the i-th item in the i-th order parameter set, which is equal to 1 in the unweighted sum.

[0376] If the evaluation of the objective function f indicates that the predetermined criteria have not yet been met, the model parameters are changed and the objective function f is re-evaluated. This process is repeated iteratively until the predetermined criteria are met.

[0377] A surface model with the model parameters thus obtained can be appropriately stored and used to calculate new ophthalmic lenses as described above.

[0378] Figure 3 Another exemplary method is shown to calculate one or a pair of ophthalmic lenses based on order data using surface modeling and direct calculation. This method is similar to... Figure 1 The method shown also includes surface correction calculated using a surface model. Surface correction can be one of the corrections described above. The method includes the following steps:

[0379] S3-1: Provide an ordering parameter set including one or more ophthalmic lenses. k Order data;

[0380] S3-2: Calculate / optimize ophthalmic lenses using surface models (directly, non-iteratively);

[0381] S3-3: Surface correction calculated using the surface model (subsequent calculations / subsequent optimizations);

[0382] S3-4: Obtain information about the order parameter set d k Ophthalmic lenses L to be manufactured k The surface.

[0383] The correction of one or more surfaces calculated using a surface model can be one of the corrections mentioned above. Based on the optimal starting surface obtained from subsequent calculations or optimizations, this correction typically requires one or only a few iterations. This can significantly reduce the overall computation time.

[0384] Figure 4 Another exemplary method is shown for calculating one or a pair of ophthalmic lenses with optional corrections based on ordered data using surface modeling and direct calculation. The method includes the following steps:

[0385] S4-1: Provides a large set of ordering parameters including one or more ophthalmic lenses. k Order data;

[0386] S4-2: Calculate / optimize ophthalmic lenses using surface models (directly, preferably non-iteratively, or with a few iterative steps);

[0387] S4-3: Check if correction is needed;

[0388] S4-4: If correction is required, perform surface correction calculated using the surface model (with one or only a few iterations of subsequent calculation / optimization);

[0389] S4-5: Obtain information about the order parameter set d k Ophthalmic lenses L to be manufactured k The surface.

[0390] Figure 5 An exemplary method for defining a surface model using a pre-calculated ophthalmic lens is shown. The method includes the following steps:

[0391] S5-1: Provides a large set of ordering parameters {d i} and a large number of ophthalmic lenses L i A large number of calculated surface ordering datasets {d i ,L i The dataset is then divided into a training dataset, (potentially a validation dataset), and a test dataset. The provided ophthalmic lens L... i It is a lens calculated for the order parameter set in the order dataset based on known computational or optimization methods. The provided lens can be respectively calculated using the objective function f. i Optimized lens;

[0392] S5-2: Provides the initial complexity and parameterization of the surface model;

[0393] S5-3: Parametric (iterative) optimization and, if necessary, iterative optimization of the surface model complexity, with the aim of making the surface model reproduce the training dataset as well as possible (and, if necessary, the validation dataset). Optimization is performed using the objective function G of the model parameters. Here, information about the ordering data d is used. i Surface model calculation of ophthalmic lens BL i Or its surface. Using the objective function G, the surface or lens calculated from the surface model is compared with the provided lens L. i The surface is compared to the provided lens. The model is compared to the provided lens. In the optimization of model parameters, for example, the objective function G(BL) is compared. i ,L i Minimize the sum of i on i;

[0394] S5-4: Test the optimization parameters of the surface model by reproducing the test dataset, and, if necessary, test the optimization complexity of the surface model; and

[0395] S5-5: Obtain the optimization parameters of the surface model and, if necessary, the optimization complexity of the surface model, in order to provide a basis for directly calculating ophthalmic lenses from the order data.

[0396] The above method can also be performed using the measured surface and / or surface distance of a pre-manufactured lens instead of the calculated surface.

[0397] Figure 6 An exemplary method for defining a surface model when there is no pre-calculated ophthalmic lens is shown. The method includes the following steps:

[0398] S6-1: Provides a large dataset of hypothetical ophthalmic lens ordering data. i The dataset was then divided into a training dataset, a (possibly validation dataset), and a test dataset.

[0399] S6-2: Provides the initial complexity and parameterization of the surface model;

[0400] S6-3: Perform parameterization optimization of the surface model and, if necessary, complexity optimization, with the aim of calculating the lens L from the surface model. i The objective function f used to optimize a single lens i Minimize the sum across the training dataset (and possibly the validation dataset). Objective function f i It can be an objective function known from existing technology;

[0401] S6-4: Using existing techniques to optimize the objective function f for a single lens i The optimization parameters of the surface model are tested on the test dataset, and the optimization complexity of the surface model is tested as needed; and

[0402] S6-5: Obtain the optimization parameters of the surface model and, if necessary, the optimization complexity of the surface model, in order to provide a basis for directly calculating ophthalmic lenses from the order data.

[0403] In the example above, each order parameter set d k This may include one or more ordering parameters required for ordering a single ophthalmic lens or a pair of ophthalmic lenses. Examples of ordering parameters can be found in general standards for eyeglass lenses (see, for example, EU Regulation 93 / 42 / EEC on medical devices). Further examples of ordering parameters and variables derived therefrom, as well as other details, can be found in the descriptions above in the relevant sections. All features, implementation variations, and / or advantages described herein are adapted to the examples above.

[0404] The calculation of ophthalmic lenses (spectacles lenses) will be explained in more detail below with the help of two more examples.

[0405] Example of using regression models for lens calculation

[0406] The first example involves lens calculations using a regression model. In this example, the posterior surface curvature and central thickness of the single-vision lens are calculated directly from the ordered values ​​of the spherical and cylindrical lenses for refraction, using a surface model designed as a regression model. The parameters and complexity of the regression model are determined based on already calculated data from ophthalmic lenses. In this example, the lens diameter is predetermined to be 65 mm.

[0407] Traditionally, complex iterative algorithms are used to calculate the center thickness. In this example, the traditional iterative algorithm is replaced by a regression model that is evaluated without iteration.

[0408] The initial point of calculation is a dataset of 825 lenses, calculated according to existing methods, with spherical and cylindrical lenses varying in steps of 0.25 dpt. For example... Figure 7 As shown, the dataset is divided into a training dataset with 425 lenses, a validation dataset with 192 lenses, and a test dataset with 208 lenses. This division is based on a certain pattern (see...). Figure 7 Instead of being random as usual, the data forms an equidistant grid in spherical and cylindrical lenses. However, the initial dataset can be randomly divided into training, validation, and test datasets.

[0409] First, the front surface curvature KVFL is calculated using a table, where the basic curves are tabulated based on spherical and cylindrical lenses. Of course, in more complex surface models, the front surface curvature can also be calculated using a classification model consisting of spherical and cylindrical lenses, and, if necessary, the material's refractive index, along with information about the lens blanks available for manufacture. However, this is intentionally omitted in this example for clarity.

[0410] First, determine the curvatures K1 and K2 of the principal meridional plane with the maximum or minimum curvature (in the case of using the cylinder convention):

[0411] K1 = spherical lens + cylindrical lens, and K2 = spherical lens

[0412] The regression model is then determined, constructed in this example using spline functions. Cubic spline curves in K1, K2, or KVFL are used, along with their linear interaction terms. The nodes of the spline curves are equidistantly distributed within the ranges of K1, K2, and KVFL, forming a grid with equal spacing across the parameters K1, K2, and KVFL. The spline curve coefficients represent the model parameters.

[0413] As a measure of how well the model describes the existing data, the sum of squares of the residuals (i.e., the difference between the variable to be calculated and the corresponding value in the dataset) was used. Therefore, in separate adjustments, the squared deviation of the center thickness (mm) and the two curvatures (dpt) of the back surface were minimized respectively.

[0414] To adapt to the training dataset, the model complexity was varied by changing the number of spline nodes. Ultimately, the model with the minimum sum of squared errors calculated based on the validation dataset was selected. The models used for center thickness can be summarized as follows (see Table 1):

[0415] Table 1:

[0416]

[0417]

[0418] The curvature of the back surface can be handled similarly. Finally, splines with 3 nodes (within the same range) in K1, K2 and KVFL were selected, so that each curvature of the back surface was adjusted using a model with 15 parameters (total 1 (constant) + 2 (K1) + 2 (K2) + 2 (KVFL) + 2^3 (mixture term) = 15 parameters).

[0419] In this example, the curvature of the rear surface is expressed in diopters based on a refractive index of 1.525.

[0420] The single-vision lens calculated here is entirely described by the material's refractive index (1.668 in this case), diameter (65 mm in this case), center thickness, and the curvature of the front and rear surfaces (the latter being due to its spherical front surface and complex spherical rear surface). In this case, there is also no tilt of the rear surface relative to the front surface, because in this example, the prism is predetermined to be 0 dpt, and centering is performed according to the eye axis point requirements.

[0421] The model parameters included in Table 2 were determined by minimizing the deviation between the actual center thickness and the center thickness (model parameters, in mm) calculated using splines from the training dataset. The spline base functions are numbered below with multiple indices, where 0 indicates that the spline function is equal to a constant 1 in the ordering parameter or derived variable, and higher indices correspond in ascending order to the cubic spline base functions, which have positions from near the bottom edge to the top edge within the value range of the corresponding ordering parameter or variable derived from it:

[0422] Table 2:

[0423]

[0424]

[0425] Similarly, the following model parameters (in dpt) are derived from the adjustment of the first principal meridional plane of the rear surface curvature (see Table 3):

[0426] Table 3:

[0427]

[0428]

[0429] Similarly, the following model parameters (in dpt) are derived from the adjustment of the second principal meridional plane of the rear surface curvature (see Table 4):

[0430] Table 4:

[0431] Spline (K1) number 0 1 2 0 0 0 0 Spline (K2) number 0 0 0 1 2 0 0 Number of splines (KVFL) 0 0 0 0 0 1 2 Parameter value -5.48 -0.01 -0.18 2.14 3.90 -2.35 -4.41 Spline (K1) number 1 2 1 2 1 2 1 2 Spline (K2) number 1 1 2 2 1 1 2 2 Number of splines (KVFL) 1 1 1 1 2 2 2 2 Parameter value 0.00 -0.06 0.00 0.03 0.02 -0.15 0.03 -0.15

[0432] In the following text, based on spectacle lenses (test spectacle lenses) from a test dataset, it is shown that the method according to the present invention will produce spectacle lenses with nearly identical characteristics compared to methods according to the prior art. For this purpose, histograms of deviations between the center thickness, posterior surface curvature, and apical diopter of the spectacle lenses were plotted relative to each other, or rather, histograms of deviations of these variables were calculated. Figures 8A to 8J The corresponding results are shown.

[0433] Figure 8A The correlation between the center thickness of the spectacle lens calculated using a surface model and the measured center thickness of the test spectacle lens is shown. Figure 8A The x-axis plots the center thickness (mm) based on test data or measured with the aid of test lenses, and the y-axis plots the center thickness (mm) calculated from the model. Figure 8B The frequency histogram (mm) of the center thickness residual is shown, which is the frequency histogram (mm) of the deviation calculated from the measured center thickness of the test lens.

[0434] Figure 8C The correlation between the back surface curvature of the first principal meridian plane of the spectacle lens calculated using a surface model (the curvature of the first principal meridian plane of the back surface or back surface curvature 1) and the measured back surface curvature of the first principal meridian plane of the test spectacle lens is shown. Figure 8C The x-axis plots the back surface curvature 1 (dpt) based on test data or measured with the aid of test spectacle lenses. The y-axis plots the back surface curvature 1 (dpt) calculated from the surface model. Figure 8D The frequency histogram (mm) of the residual of the back surface curvature 1 (dpt) is shown, which is the frequency histogram (mm) of the deviation calculated from the measured back surface curvature 1.

[0435] Figure 8EThe correlation between the back surface curvature of the second principal meridian plane of the spectacle lens calculated using a surface model (the curvature of the second principal meridian plane of the back surface, or back surface curvature 2) and the measured back surface curvature of the first principal meridian plane of the test spectacle lens is shown. Figure 8E The x-axis plots the back surface curvature 2 (dpt) based on test data or measured with the aid of test spectacle lenses. The y-axis plots the back surface curvature 2 (dpt) calculated from the surface model. Figure 8F The frequency histogram (mm) of the residual of the back surface curvature 2 (dpt) is shown, which is the frequency histogram (mm) of the deviation calculated from the measured back surface curvature 2.

[0436] Figure 8G The correlation between the vertex power of the spectacle lens calculated using a surface model in the first principal meridian (vertex power in principal meridian 1) and the vertex power measured in the first principal meridian of the test spectacle lens is shown. Figure 8G The x-axis plots the vertex power (dpt) in the principal meridian 1 measured using test data or test lenses, and the y-axis plots the vertex power (dpt) in the principal meridian 1 calculated based on the model. Figure 8H The frequency histogram shows the deviation (dpt) between the refractive power (dpt) of the principal meridian 1 calculated according to the model and the measured refractive power (dpt) of the principal meridian 1.

[0437] Figure 8I The correlation between the vertex power of the spectacle lens calculated using a surface model in the second principal meridian (vertex power in principal meridian 2) and the vertex power measured in the second principal meridian of the test spectacle lens is shown. Figure 8I The horizontal axis plots the vertex power (dpt) in the principal meridian 1 measured using test data or test lenses, and the vertical axis plots the vertex power (dpt) in the principal meridian 2 calculated based on the model. Figure 8J The frequency histogram shows the deviation (dpt) between the refractive power (dpt) in the principal meridian 2 calculated according to the model and the measured refractive power (dpt) in the principal meridian 2.

[0438] To calculate the center thickness and two back surface curvatures at arbitrary values ​​of spherical lens sph and cylindrical lens cyl, spline fundamental functions at corresponding points in KVFL(sph, cyl), K1(sph, cyl), and K2(sph, cyl) were evaluated, multiplied by parameters generated by adjustment (see table), and summed from them without iterative calculation.

[0439] Of course, the surface model described herein can also be extended by ordering parameters of the prism and prism substrate, for example by extending the surface model by the prism itself, and by extending the surface model by using the angle between the prism substrate and the astigmatic axis as a derived parameter.

[0440] An example of determining a regression model without using pre-calculated data.

[0441] Unlike the previous example, when determining the surface model designed as a regression model below, it is not necessary to call upon already calculated data of the ophthalmic lens. Instead, the parameters of the surface model are directly formed by minimizing the sum of objective functions, which are used for (iterative) calculations of multiple lenses according to known methods in the prior art. Therefore, the surface model thus determined can perform calculations of a monocular lens with any effect, specified only by one or more objective functions and the desired effect and diameter.

[0442] The refractive power of a single lens i is determined by the curvature of the spherical front surface, KVFL. i and diameter D i The two main meridians K1 i and K2 i The exemplary objective function of the lens according to the prior art is as follows:

[0443]

[0444] The center thickness is determined by d M,i The order value for the two main meridians is given by... and The minimum allowable center thickness and edge thickness are given. and express. and The square deviation of the principal meridian plane, representing the refractive power of the lens apex. and This represents the squared deviation of the lens diameter, and and This represents the squared deviation of the thickness at the midpoint and edge in the two principal meridional planes of the rear surface. Here, the weights of the different terms are chosen as follows: g S =(0.005dpt) -2 g D = (0.5mm) -2 And g d = (0.1mm) -2 The squared deviation is calculated as follows. It should be noted that the diameter deviation is calculated from the curvature of the front or rear surface in its two principal meridional planes:

[0445]

[0446]

[0447]

[0448]

[0449]

[0450]

[0451]

[0452]

[0453] Here, r VFL，i r RFL1，i and r RFL2，i denoted as the radius of curvature of the front or rear surface in its two principal meridional planes, and p is a factor for penalizing insufficient lens thickness (used here for p = 100).

[0454] In this example, the minimum permissible center thickness and edge thickness are constant for all lenses. and However, these values ​​can also be easily expressed as a function of the lens material, diameter, target effect, or even the lens coating. These minimum permissible center and edge thickness values ​​represent the target values.

[0455] Of course, other objective functions can also be used alone or as an addendum, as long as they reflect the ideal characteristics of the lens, such as the desired distribution of refractive error and unwanted astigmatism in the position of use.

[0456] The objective function used to optimize the surface model parameters consists of the sum of the objective functions of individual lenses, where the summation is performed over all lenses i from each dataset (i.e., the training dataset, validation dataset, or test dataset), and the center thickness and curvature of the back surface are now parameterized to depend on the surface model parameters:

[0457]

[0458] Here, θ = (θ dM θ K1 θ K2 The parameters of the surface model are represented by ( ), which can be divided into three independent sets of spline coefficients for the center thickness and the two principal curvatures of the back surface. The predetermined front surface curvature value, lens diameter, principal curvature settings for the apex diopter, and minimum center and edge thicknesses for each lens are collectively determined by ( ). express.

[0459] The values ​​calculated using the surface model are now used for the center thickness and the curvature of the two back surfaces, which in turn depend on the current parameters of the surface model:

[0460]

[0461]

[0462]

[0463] The dataset used for training, validating, and testing the trained regression model consists of the same spherical and cylindrical values ​​as in the previous example (see...). Figure 7 The same spline-based regression model is also used, however, it initially has the parameter set corresponding to a lens with a center thickness of 2 mm and a rear surface curvature of -5 dpt (independent of its front surface curvature) as the starting point for optimization (that is, only those parameters that are constant, i.e. those parameters with multiple refractive indices (spline (K1), spline (K2), spline (KVFL)) = (0, 0, 0) have 2 mm or -5 dpt under the corresponding different adjustments of KVFL, K1, and K2, and all other parameters are 0).

[0464] To determine the optimal parameters of the surface model, the Nelder-Mead algorithm (with 20,000 function evaluations) is first used because it is relatively robust and does not require differentiation of the parameters. Then, the BFGS algorithm (Broyden-Fletcher-Goldfarb-Shanno algorithm) is used for 200 iterations because it converges to a local optimum more quickly. The gradient of the latter algorithm is calculated numerically, but it can also be given analytically, which would further accelerate the optimization. The number of iterations can be increased by choosing a more appropriate starting point for optimization. For example, it may be helpful if a new surface model is to be determined, and the objective function of its individual lenses differs slightly from that of the first surface model (e.g., in minimum thickness, mutual weighting of terms, or additional terms), then the parameters of the already determined surface model are used.

[0465] For the center thickness (unit: mm), the following model parameters θ are obtained. dM (See Table 5):

[0466] Table 5:

[0467]

[0468]

[0469]

[0470] For a single name, refer to the example above:

[0471] For the first principal meridional plane of the back surface curvature, the following model parameters θ are obtained. K1 (Unit: dpt):

[0472] Table 6:

[0473] Spline (K1) number 0 1 2 0 0 0 0 Spline (K2) number 0 0 0 1 2 0 0 Number of splines (KVFL) 0 0 0 0 0 1 2 Parameter value -3.12 4.72 6.00 0.00 0.00 -2.35 -4.41 Spline (K1) number 1 2 1 2 1 2 1 2 Spline (K2) number 1 1 2 2 1 1 2 2 Number of splines (KVFL) 1 1 1 1 2 2 2 2 Parameter value -0.01 -0.01 -0.02 0.00 0.03 -0.20 0.05 -0.16

[0474] For the second principal meridional plane of the back surface curvature, the following model parameters θ are obtained. K2 (Unit: dpt):

[0475] Table 7:

[0476]

[0477]

[0478] In the following text, based on ophthalmic lenses in a test dataset, it is shown that the method according to the invention results in ophthalmic lenses with nearly identical properties compared to methods according to the prior art. For this purpose, histograms of the lens's center thickness, posterior surface curvature, and apical diopter are plotted relative to each other, or histograms of deviations of these variables are calculated. Minimum center thickness and minimum edge thickness are also followed. Figures 9A to 9J The corresponding results are shown.

[0479] Figure 9A In particular, the correlation between the center thickness calculated based on the surface model and the center thickness of a spectacle lens (test spectacle lens) according to the prior art is shown. Figure 9A The horizontal axis plots the center thickness (in mm) of the spectacle lens according to existing technology, and the vertical axis plots the center thickness (in mm) calculated based on the model. Figure 9B The frequency histogram of the residuals of the center thickness (in mm) is shown, which is the frequency histogram of the deviation between the center thickness calculated from the surface model and the center thickness of the spectacle lens according to the prior art.

[0480] Figure 9C The correlation between the back surface curvature (back surface curvature 1) of the first principal meridian calculated based on the surface model and the back surface curvature 1 of a spectacle lens (test spectacle lens) according to the prior art is shown. Figure 9C The horizontal axis plots the posterior surface curvature 1 (in dpt) of the spectacle lens according to the prior art, and the vertical axis plots the posterior surface curvature 1 (in dpt) calculated according to the model. Figure 9D The frequency histogram of the residuals of the back surface curvature 1 (unit: dpt) is shown, that is, the frequency histogram of the deviation between the back surface curvature 1 calculated according to the model and the back surface curvature 1 of the spectacle lens according to the prior art.

[0481] Figure 9E The correlation between the back surface curvature (back surface curvature 2) of the second principal meridian calculated based on the surface model and the back surface curvature 2 of a spectacle lens (test spectacle lens) according to the prior art is shown. Figure 9E The horizontal axis plots the posterior surface curvature 2 (in dpt) of the spectacle lens according to the prior art, and the vertical axis plots the posterior surface curvature 2 (in dpt) calculated based on the surface model. Figure 9F The frequency histogram of the residuals of the back surface curvature 2 (unit: dpt) is shown, that is, the frequency histogram of the deviation between the back surface curvature 2 calculated according to the model and the back surface curvature 2 of the spectacle lens according to the prior art.

[0482] Figure 9G The correlation between the vertex power in the first principal meridian plane calculated based on the surface model (vertex power in principal meridian plane 1) and the vertex power in the first principal meridian plane of a spectacle lens (test spectacle lens) according to the prior art is shown. Figure 9G The x-axis plots the apex diopter (in dpt) in the principal meridian plane 1 of the spectacle lens according to the prior art, and the y-axis plots the apex diopter (in dpt) in the principal meridian plane 1 calculated based on the surface model. Figure 9H The frequency histogram (in dpt) shows the deviation (difference) between the refractive power of the lens in the principal meridian 1 calculated according to the model and the refractive power of the lens in the principal meridian 1 according to the prior art.

[0483] Figure 9I The correlation between the vertex power in the second principal meridian (vertex power in principal meridian 2) calculated based on the surface model and the vertex power in the second principal meridian of the spectacle lens (test spectacle lens) is shown. Figure 9I The x-axis plots the apex diopter (in dpt) in the principal meridian plane 2 of the spectacle lens according to the prior art, and the y-axis plots the apex diopter (in dpt) in the principal meridian plane 2 calculated based on the surface model. Figure 9J The frequency histogram (in dpt) shows the deviation (difference) between the apex diopter in principal meridian 2 calculated according to the model and the apex diopter in principal meridian 2 of a spectacle lens according to the prior art.

[0484] Figure 10 The correspondence between minimum edge thickness and center thickness is shown. Figure 10 The horizontal axis plots the middle thickness (unit: mm), and the vertical axis plots the edge thickness (unit: mm).

[0485] The calculation of the center thickness and the curvature of the two back surfaces using a surface model is performed in the same way as in the first example, with arbitrary values ​​of sph for the spherical lens and cyl for the cylindrical lens.

[0486] Preferred embodiments of the invention have been illustrated above with the aid of examples. Individual elements of these embodiments are not limited to any particular embodiment. Rather, elements can be arbitrarily combined to create new embodiments. Furthermore, individual features can be modified. Therefore, other suitable functions (e.g., polynomial functions) can be used to define the surface model as an alternative to spline functions. Similarly, the number of model coefficients or model parameters (e.g., spline curve coefficients) can be changed. Additionally, other representations of the surface to be computed, other sets of ordered parameters, objective values, objective functions, and / or optimization methods can be used.

Claims

1. A computer-implemented method for determining a surface model, the surface model being used to calculate at least one surface of the at least one ophthalmic lens from at least one set of ordered parameters and / or from variables dependent on the ordered parameters, wherein the surface model is based on a machine learning model, wherein the method comprises: Provide a training dataset comprising a large set of ordering parameters, each set containing values ​​for at least a subset of the parameters required to order at least one ophthalmic lens; For each set of ordering parameters in the training dataset, at least one target value for at least one characteristic of the at least one ophthalmic lens is provided, wherein the target value for at least one characteristic of the at least one ophthalmic lens is set as: a measured value of at least one characteristic of a manufactured ophthalmic lens, the ordering parameters of which are known; or a value determined or determinable from one or more measured values ​​of a manufactured ophthalmic lens; or a set value of an ophthalmic lens to be manufactured, the ordering parameters of which are at least partially known. Provide at least one surface model parameterized by model parameters, using said surface model, given the values ​​of said model parameters, it is possible to calculate at least one surface of at least one ophthalmic lens from at least an ordered parameter set and / or from variables depending on the ordered parameter set; Obtaining a surface model for calculating at least one surface of at least one ophthalmic lens includes: determining optimized values ​​for model parameters of the at least one surface model by using provided target values; Determining the optimized values ​​of the model parameters for the at least one surface model includes: The objective of optimizing the model parameters of the at least one surface model is to minimize or maximize the objective function of the model parameters of the at least one surface model, which depends at least on the model parameters and on the provided target values, wherein if the provided target value for at least one characteristic of the at least one ophthalmic lens for each ordering parameter set is consistent with the value of the same characteristic of at least one lens calculated or computable using the surface model given the values ​​of the model parameters of the surface model in the corresponding ordering parameter set, the objective function of the model parameters of each ordering parameter set contains at least one term having a minimum or maximum value; The calculation of the at least one surface includes: Calculate at least one parameter of the parametric function describing the at least one surface, based on the ordering parameters or a variable dependent on the ordering parameters; or The sagitta of the at least one surface in a large number of grid points is calculated based on the ordering parameters or variables that depend on the ordering parameters.

2. The method according to claim 1, wherein Providing at least one surface model parameterized by model parameters includes: Provide at least two surface models with different complexities, where the complexity of the surface models includes one or more of the following variables: – The type and / or quantity of ordering parameters used in the model; –Depending on the type and / or number of variables ordered as parameters; – The number of model parameters; – The type and / or strength of regularization used to optimize the objective function of the model parameters; and The method further includes: A validation dataset is provided, comprising a large set of ordering parameters, each containing values ​​for at least a subset of parameters required for ordering at least one ophthalmic lens; For each set of ordering parameters in the validation dataset, provide at least one target value for at least one characteristic of the at least one ophthalmic lens; and Obtaining a surface model for calculating at least one surface of at least one ophthalmic lens further includes: Given previously determined optimized values ​​of the model parameters for each surface model, calculate the values ​​of a verification objective function and / or the values ​​of variables derived from the verification objective function for the provided surface models of varying complexities, wherein the verification objective function depends on the provided target values, and if the provided target value for at least one characteristic of at least one ophthalmic lens for each ordering parameter set is consistent with the value of the same characteristic of at least one lens calculated or computable using the surface model given the optimized values ​​of the model parameters of the surface model for the corresponding ordering parameter set, then the verification objective function contains at least one term with a minimum or maximum value for each ordering parameter set in the verification dataset; and Based on the calculated value of the verification objective function and / or by means of the value of the variable derived from the verification objective function, a surface model for calculating at least one surface of at least one ophthalmic lens is selected or determined from surface models of different complexities parameterized using the optimized values ​​of the model parameters.

3. The method according to claim 1 or 2, wherein At least one term of the objective function of the model parameters and / or at least one term of the verification objective function include: The difference between at least one value of at least one predetermined characteristic of the lens and at least one target value of that characteristic in the same set of ordered parameters, or a convex or concave function of the difference, wherein at least one surface of the lens is calculated or computable based on a surface model for the set of ordered parameters.

4. The method according to claim 1 or 2, wherein one or more terms of the objective function of the model parameters and / or the verification objective function form an objective function for optimizing or computing at least one ophthalmic lens given a set of ordered parameters.

5. The method according to claim 1 or 2, wherein The objective function of the model parameters and / or the verification objective function include: The weighted or unweighted sum of all ordered parameter sets in the training and / or validation datasets for each ordered parameter set being evaluated.

6. The method according to claim 1 or 2, wherein the ordering parameter set includes one or more of the following parameters: At least one diopter; At least one geometric or material parameter of the ophthalmic lens; At least one geometric parameter of the eyeglass frame; At least one use of the ophthalmic lens; At least one parameter for individualization and / or personalization of ophthalmic lenses; At least one physiological characteristic of the future wearer of the ophthalmic lens; At least one biological characteristic of the eye of the future wearer of the ophthalmic lens.

7. The method according to claim 1 or 2, wherein the at least one predetermined characteristic is one of the following characteristics: The sag and / or derivative of at least one surface; The surface parameters or combinations of surface parameters of at least one surface; The optical properties and / or gradients and / or distribution of the ophthalmic lens; The width of at least one good visual area of ​​the ophthalmic lens; The geometric characteristics of the ophthalmic lens; The discomfort experienced by the wearer of the ophthalmic lens, calculated using the surface model, related to visual quality and / or body posture; Visual perception characteristics of the wearer of the ophthalmic lens calculated using the surface model; Geometric or material parameters of the ophthalmic lens that are not included in the ordering parameters; Geometric parameters of the eyeglass frame that are not included in the order parameters.

8. The method according to claim 1 or 2, wherein the at least one ophthalmic lens is one of a pair of lenses. The large set of ordering parameters each contains values ​​of at least a portion of the parameters required to order the pair of lenses; and The at least one characteristic includes the binocular characteristics of the pair of lenses.

9. The method according to claim 1 or 2, wherein the surface generated by the surface model is a continuous function and / or a continuously differentiable function of the ordering parameters in the ordering parameter set.

10. The method according to claim 1 or 2, wherein The surface model is a linear or nonlinear regression model, or includes a linear or nonlinear regression model, wherein the coefficients of the regression model represent at least a portion of the model parameters of the surface model; and / or The surface model is a classification model or includes a classification model; and / or The surface model is a neural network or includes a neural network.

11. The method according to claim 1 or 2, wherein optimizing the values ​​of the model parameters comprises: Regularization of the objective function used in the optimization of the model parameters.

12. The method according to claim 1 or 2, further comprising: Provide a test dataset that includes a large number of order datasets; For each set of ordered parameters in the test dataset, provide at least one target value for at least one predetermined characteristic of the ophthalmic lens; and Based on the test dataset, a surface model obtained from the test is used to calculate at least one surface of at least one ophthalmic lens.

13. A computer-implemented method for determining at least one surface of at least one ophthalmic lens, comprising: Provide a set of ordering parameters for the at least one ophthalmic lens; Provides a function for calculating at least one surface of at least one ophthalmic lens from a set of ordered parameters and / or from variables dependent on said ordered parameters, wherein said function is a surface model obtained by the method according to any one of claims 1 to 12; and Using the provided function, surface data of at least one surface of the at least one ophthalmic lens is obtained from the provided set of ordering parameters, wherein obtaining the surface data includes: calculating at least one parameter of a parametric function describing the at least one surface based on the ordering parameters or a variable depending on the ordering parameters; Alternatively, the sagitta of the at least one surface in a large number of grid points can be calculated based on the ordering parameters or variables dependent on the ordering parameters.

14. The method of claim 13, further comprising: Perform corrections on at least one surface calculated using the surface model, wherein the corrections include optimizing the surface calculated using the surface model and / or correcting for overlap with overlapping surfaces and / or for manufacturing-related deviations in the surface or optical properties of the ophthalmic lens and / or extending the surface to the ophthalmic lens diameter required for manufacturing.

15. The method according to claim 13 or 14, further comprising: Verify whether at least one surface calculated using the surface model meets the expected or required characteristics; and The system stores information about whether the surface meets or does not meet the required characteristics, as well as at least a portion of the ordered parameter set used to obtain the surface data and / or the at least one surface calculated using the surface model and corrected where necessary, and / or the desired or required characteristic values ​​that can be provided as characteristic target values ​​when determining the surface model according to any one of claims 1 to 14.

16. The method according to claim 13 or 14, further comprising: After obtaining and / or storing each surface or a predetermined number of surfaces calculated using the surface model and corrected as necessary, the model parameters of the surface model are adjusted.

17. A computer-readable storage medium comprising a computer program that, when loaded into a computer's memory and executed on the computer, causes the computer to perform the method according to any one of claims 1 to 16.

18. An apparatus for defining a surface model for calculating at least one surface of at least one ophthalmic lens from a set of ordered parameters and / or from variables depending on the ordered parameters, wherein the apparatus includes a computing device designed to perform the method according to any one of claims 1 to 12.

19. An apparatus for determining at least one surface of at least one ophthalmic lens, wherein the apparatus includes a computing device configured to perform the method according to any one of claims 13 to 16.

20. A method for manufacturing an ophthalmic lens, comprising: The method according to any one of claims 13 to 16 determines at least one surface of the at least one ophthalmic lens; Manufacturing an ophthalmic lens having at least one of the aforementioned surfaces.

21. An apparatus for manufacturing ophthalmic lenses, comprising: The apparatus for determining at least one surface of at least one ophthalmic lens according to claim 19; Manufacturing apparatus for manufacturing ophthalmic lenses having at least one of the said surfaces.

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