Method and device for optimizing spectacle lenses, in particular for wearers of implanted intraocular lenses

Abstract

The present invention relates to a computer-implemented method for identifying relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing an ophthalmic lens for said at least one eye of said spectacle wearer, said method comprising the following steps: - providing individual data of characteristics of said at least one eye of said spectacle wearer; - constructing an individual eye model by defining a set of parameters of said individual eye model; - based on said individual data, determining a probability distribution of values ​​of parameters of said individual eye model.

Description

Technical Field

[0001] The present invention relates to a method, a device and a corresponding computer program product for determining relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of a spectacle lens for at least one eye of the spectacle wearer, as well as to a corresponding method, a device and a computer program product for calculating (optimizing) and manufacturing a spectacle lens with the help of a partial individual eye model. In particular, at least one eye of the spectacle wearer has an implanted intraocular lens (IOL). For example, instead of a natural eye lens or in addition to a natural lens, an intraocular lens can be implanted in at least one eye during surgery. In other words, the spectacle wearer can be a wearer of an implanted intraocular lens. Furthermore, the present invention relates to a method, a device and a corresponding computer program product for calculating (optimizing) and manufacturing a spectacle lens with the help of a partial individual eye model, in particular a spectacle lens for a wearer of an implanted intraocular lens. Background Art

[0002] In order to manufacture or optimize spectacle lenses, in particular individual spectacle lenses, each spectacle lens is manufactured in such a way that for each desired viewing direction or each desired object point, the best possible correction of the refractive error of the respective eye of the spectacle wearer is achieved. In general, a spectacle lens is considered to be fully corrected for a given viewing direction if the values ​​of the sphere, cylinder and axis of the wavefront when passing through the vertex sphere coincide with the values ​​of the sphere, cylinder and axis of the prescription for the eye with impaired vision. When determining the refractive power of the eye of the spectacle wearer, the refractive values ​​for the far (usually infinite) distance (in particular the sphere, cylinder, cylinder axis - ie in particular the sphero-cylindrical deviation) and (for multifocal lenses or progressive lenses) the optional additional or complete near refraction for the near distance (e.g. according to DIN 58208) are determined. In the case of modern spectacle lenses, it is also possible to specify an object distance that deviates from the standard, which is used to determine the refractive power. In this way, the prescription (in particular the sphere, cylinder, cylinder axis and the optional additional or near refraction) to be communicated to the lens manufacturer is specified. In this case, no knowledge is required of the special or individual anatomy of the respective eye or of the diopter value of the eye with impaired vision, which knowledge is actually present in the individual case.

[0003] However, it is usually not possible to have a perfect correction for all viewing directions at the same time. Therefore, spectacle lenses are manufactured so that they can correct the visual impairment of the eye very well and only produce small aberrations in the main areas of use, especially in the central visual area, while allowing larger aberrations in the peripheral areas.

[0004] In order to be able to manufacture a spectacle lens in this way, the spectacle lens surface or at least one spectacle lens surface is first calculated so that the desired distribution of the unavoidable aberrations is achieved. This calculation and optimization is usually performed by means of an iterative variation method by minimizing an objective function. As objective function, in particular, a function F is considered which has the following functional relationship with the size of the spherical power S, the cylindrical power Z and the cylinder axis Δ (also referred to as "SZA" combination), and said function F is minimized:

[0005]

[0006] In the objective function F, at the evaluation point i of the spectacle lens, at least the spherical diopter S Δ,i and cylindrical diopter Z Δ,i The actual diopter difference and spherical diopter S Δ,i,target and cylindrical focal power Z Δ,i,target The target specification of the diopter difference is taken into account.

[0007] DE 10313275 found that it is advantageous to express the target specifications not as absolute values ​​of the properties to be optimized, but as their deviation from the recipe, i.e. as the desired local misadjustment. The advantage is that the target specifications are related to the recipe (Sph V ,Zyl V ,Axis V ,Pr V ,B V ) and the target specifications do not have to be changed for each individual prescription. Therefore, as the "actual" value of the property to be optimized, the absolute values ​​of these optical properties are not considered in the objective function, but the deviation from the prescription. This has the advantage that the target values ​​can be specified independently of the prescription and do not have to be changed for each individual prescription.

[0008] The respective refractive power defect at the respective evaluation point is preferably related to the weighting factor g i.SΔ and g i.ZΔ Here, the spherical diopter S Δ,i,target and / or cylinder Z Δ,i,target The target specification of the refractive defect, in particular with the weighting factor g i.SΔ and g i.ZΔ Together they form the so-called spectacle lens design. Furthermore, in particular further residuals, in particular further parameters to be optimized such as coma and / or spherical aberration and / or prism and / or magnification and / or anamorphic distortions etc. can be taken into account, which is in particular implied by the expression "+...." in the formula of the above-mentioned objective function F.

[0009] Taking into account not only second-order aberrations (sphere, astigmatism amplitude and cylindrical axis) but also higher-order aberrations (e.g. coma, trefoil, spherical aberration) can in some cases contribute to a significant improvement, especially with the individual adjustment of spectacle lenses.

[0010] It is known from the prior art to determine the wavefront shape of an optical element, in particular a spectacle lens, which is bounded by at least two refractive boundary surfaces. This can be done, for example, by means of a numerical calculation of a sufficient number of adjacent rays and subsequent fitting of the wavefront data by means of Zernike polynomials. Another method is based on local wavefront tracing in refraction (see WO 2008 / 089999 A1). Here, only one single ray (the principal ray) is calculated per viewpoint, along with a derivative of the depth of the wavefront vertex according to the transverse coordinate (perpendicular to the principal ray). These derivatives can be formed to a certain order, where second-order derivatives describe local curvature properties of the wavefront (such as diopter, astigmatism), higher derivatives are associated with higher-order aberrations.

[0011] When tracing rays through a spectacle lens, local derivatives of the wavefront are calculated at suitable locations in the beam path in order to compare them with expected values ​​obtained from the diopter of the spectacle lens wearer. The vertex sphere or, for example, the principal plane of the eye for the corresponding sight direction is usually considered as the location for evaluating the wavefront. In this respect, a spherical wavefront is assumed to originate from the object point and propagate to a first spectacle lens surface. There, the wavefront is refracted and subsequently propagates to a second spectacle lens surface, where it is refracted again. The last propagation occurs from the second boundary surface to the vertex sphere (or principal plane of the eye), where the wavefront is compared with a predetermined value for correcting the diopter of the eye of the spectacle wearer.

[0012] In order to make such a comparison based on the determined refractive data of the respective eye, an established model of an eye with a visual impairment is assumed for the evaluation of the vertex spherical wavefront, in which a baseline eye with normal vision is superimposed with the visual impairment (refractive error). This has proven to be particularly successful, since no further knowledge of the anatomy or optics of the respective eye (e.g. distribution of refractive power, eye length, refractive power and / or refractive power) is required. For example, in Optische Dr. Roland Enders, “DieOptik des Auges und der Sehhilfen”, Optische A detailed description of this model of spectacle lenses and refractive errors can be found in "Optik und Technik der Brille" by Diepes, Blendowske GmbH, Heidelberg, 2002, page 47 et seq. As a tried and tested model, in particular the correction model according to REINER is used.

[0013] Here, the refractive error is considered to be the lack or excess of the refractive power of the optical system of the eye with impaired vision compared to an eye of equivalent length with normal vision (residual eye). The refractive power of the refractive defect is in particular approximately equal to the distance point diopter with a minus sign. In order to fully correct the visual impairment, the spectacle lens together with the refractive error is separated from the telescopic system (afocal system). The residual eye (eye with impaired vision but without additional refractive defect) is considered to have normal vision. Therefore, a spectacle lens is said to be fully distance corrected if its image-side focal point coincides with the distance point of the eye with impaired vision and therefore also with the object-side focal point of the refractive defect.

[0014] The documents DE 10 2017 007 975 A1 or WO 2018 / 138140 A2, to which reference is explicitly made herein or whose content is fully incorporated into the present description, describe methods and devices which allow an improved calculation or optimization of spectacle lenses which can be very effectively adapted to the individual needs of the spectacle wearer by simple measurement of personal, optical and ocular anatomical data.

[0015] Currently, commercially available spectacle lenses are only available for patients with an implanted intraocular lens (IOL), i.e. patients who have undergone cataract surgery (e.g. due to cataracts), and these spectacle lenses are also used for patients with a natural eye lens. Therefore, there are currently no spectacle lenses that are specifically suitable for patients with intraocular lenses. This means that the properties of an implanted intraocular lens cannot be taken into account, which properties of an implanted lens, however, differ greatly from those of a natural lens. For example, an IOL has a different spherical power for at least partially compensating for corneal or length ametropia, and / or has a different cylindrical power for at least partially compensating for corneal astigmatism or at least partially counteracting crystalline astigmatism. In the case of conventionally optimized spectacle lenses, it is assumed that the spectacle lens has model-based properties, so that the eye model used for optimization in these cases may no longer correspond to the actual structure of the eye with the IOL, for example if the IOL at least partially compensates for the length ametropia due to the power of the IOL (mean sphere). Summary of the invention

[0016] The object of the invention is to improve the calculation or optimization of spectacle lenses, preferably progressive spectacle lenses. In particular, it is possible to provide patients with specially designed spectacle lenses after cataract surgery. In particular, the object may be to improve the calculation or optimization of spectacle lenses, preferably progressive spectacle lenses, for patients with implanted intraocular lenses. This object is achieved in particular by a computer-implemented method, a device, a computer program product, a storage medium and a corresponding spectacle lens having the features defined in the independent claims. Preferred embodiments are subject matter of the dependent claims.

[0017] A first aspect for solving the object relates to a computer-implemented method for identifying relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing an ophthalmic lens, in particular a spectacle lens, for the at least one eye of the spectacle wearer, the method comprising the following steps:

[0018] - providing individual data of the characteristics of the at least one eye of the spectacles wearer;

[0019] - constructing an individual eye model by defining (and / or specifying) a set of parameters of the individual eye model;

[0020] - Based on the individual data, determine a probability distribution (or probability density) of the values ​​of the parameters of the individual eye model.

[0021] The individual data about the properties of the at least one eye of the spectacles wearer in particular comprise measured data about the properties of the at least one eye of the spectacles wearer. These known individual data may for example comprise: refractive data (in particular the current subjective and / or objective refraction and / or an earlier subjective and / or objective refraction, for example the term earlier refers to a preoperative time point), the refractive power and / or shape and / or position (in particular the axial position) of a specific refractive surface of the eye, the size and / or shape and / or position of the entrance pupil, the refractive index of the refractive medium, the refractive index distribution in the refractive medium, the opacity, etc.

[0022] A set of parameters defining an individual eye model is in particular to be understood as meaning that the eye model is established or defined via or by a set of specific parameters. In other words, which parameters are included in setting up the eye model and / or by which parameters the individual eye model is defined or characterized. The parameters defined for the eye model may initially be variables (i.e. parameters without specific values). With the aid of the method described in the context of the present invention, the parameters or the values ​​of the parameters may then be determined or defined (e.g. as the most probable parameters for the individual eye model).

[0023] In a preferred embodiment, constructing the individual eye model comprises providing an initial probability distribution of the eye model parameters. Furthermore, a probability distribution (or probability density) of the parameter values ​​of the individual eye model is determined based on the initial probability distribution of the parameters of the eye model. The initial probability distribution is preferably based on a population analysis. In particular, the initial probability distribution is based on (or corresponds to) information about the probability distribution of the parameters of the individual eye model in the general public or in a specific group.

[0024] Therefore, the method according to the invention is based on probability calculations, wherein in particular Bayesian statistics can be used. Accordingly, in a further preferred embodiment, an individual eye model is constructed and / or a probability distribution of values ​​of parameters of the eye model is determined using Bayesian statistics.

[0025] In a further preferred embodiment, determining the probability distribution of the values ​​of the parameters of the individual eye model comprises: calculating a consistency measure, wherein in particular the product of the probability or probability density of the individual data for a given parameter of the individual eye model and the probability or probability density of the parameters of the individual eye model is used as a consistency measure, in particular, given background knowledge. The background knowledge (i.e. the current state of knowledge when evaluating the data) in particular comprises available background information, for example about the measurement process of the diopter, the parameter distribution of the individual eye model or other relevant variables in the public. The probability or probability density of the parameters of the individual eye model with the given background knowledge (hereinafter also referred to as prob(θ)) is i |I)) can specifically correspond to a "prior" of Bayesian statistics. The probability or probability density of the individual data for given parameters of the individual eye model (hereinafter also referred to as prob(di|θ) i , I)) can specifically correspond to the "likelihood" of Bayesian statistics. In addition, with prob(θ i |I)prob(d i |θ i , I) is proportional to the consistency measure prob(θ i |d i , I) can specifically correspond to the "posterior" of Bayesian statistics.

[0026] In a further preferred embodiment, the method further comprises the following steps:

[0027] - using at least one parameter of the individual eye model, calculating a probability distribution (or probability density) of a parameter of the ophthalmic lens to be calculated or to be optimized; preferably,

[0028] - Determining the most probable values ​​of the parameters of the ophthalmic lens to be calculated or to be optimized, in particular by maximizing the probabilities of the respective parameters of the ophthalmic lens to be calculated or to be optimized.

[0029] As explained in more detail below, the parameter L of the ophthalmic lens to be calculated or optimized i The probability distribution (or probability density) of can be specified as follows:

[0030] prob(L i |d i , I) = ∫dθ i prob(θ i , L i |d i , I) = ∫dθ i prob(L i |θ i ,I)prob(θ i |d i , I)

[0031] =∫dθ i δ(L i -L(θ i ))prob(θ i |d i , I)

[0032] In a further preferred embodiment, providing individual data comprises providing individual refractive data about at least one eye of the eyeglass wearer. Furthermore, constructing the individual eye model comprises defining an individual eye model, wherein at least

[0033] - the shape and / or the refractive power of the cornea of ​​the model eye (12), in particular the shape and / or the refractive power of the anterior corneal surface (18); and / or

[0034] -- cornea to lens distance; and / or

[0035] -- parameters of the lens of the model eye; and / or

[0036] - lens to retina distance; and / or

[0037] -- the size of the entrance pupil; and / or

[0038] The size and / or position of the physical aperture stop (or iris opening) can be determined based on individual measurements and / or standard values ​​of the eye of the spectacle wearer and / or based on the provided individual refractive data. The method further comprises the following steps:

[0039] - a consistency check of the defined eye model using the provided individual refractive data,

[0040] - Resolving any inconsistencies, in particular with the aid of analytical and / or numerical and / or probabilistic methods.

[0041] Since the entrance pupil represents the aperture stop for corneal imaging, the position and size of the aperture stop of the eye can be converted into the position and size of the entrance pupil if the eye model contains the parameters of the cornea, and vice versa. In particular, it may be sufficient if the position or size of the aperture stop or the entrance pupil is used as a (possibly additional) parameter of the eye model in this case.

[0042] A computer-implemented method for determining relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing a spectacle lens for the at least one eye of the spectacle wearer, the at least one eye of the spectacle wearer having an implanted intraocular lens, the method may in particular comprise the following steps:

[0043] -Provide intraocular lens data about an intraocular lens implanted in the eye of a spectacle wearer;

[0044] - providing individual refractive data of the at least one eye of the spectacle wearer;

[0045] - defining an individual eye model, wherein in particular at least the following items are defined based on the provided intraocular lens data and also based on individual measurements and / or standard values ​​of the eye of the spectacle wearer and / or based on the provided individual refractive data, so that the model eye has the provided individual refractive data:

[0046] - the shape and / or refractive power of the cornea of ​​the model eye, in particular the shape and / or refractive power of the anterior surface of the cornea;

[0047] --The distance from cornea to lens;

[0048] --Parameters of the lens of the model eye;

[0049] --The distance from the lens to the retina,

[0050] The parameters of the lens of the model eye are defined based on the provided intraocular lens data. Preferably, the lens-to-retina distance is defined at least by calculation.

[0051] The intraocular lens may in particular be an aphakic intraocular lens or a phakic intraocular lens. An aphakic intraocular lens replaces the natural lens, i.e. the at least one eye of the spectacle wearer has only an intraocular lens (and no longer a natural lens) after surgery. In contrast, a phakic intraocular lens is inserted or implanted into the at least one eye of the spectacle wearer in addition to the natural eye lens, i.e. the at least one eye of the spectacle wearer has both an intraocular lens and a natural eye lens after surgery.

[0052] In the context of the present invention, the term "lens of a model eye" may refer not only to a single real lens (e.g. a natural human eye lens or an artificial lens), but also to a lens system. A lens system may comprise one or more lenses, in particular two lenses (i.e. a natural lens of the eye as well as an artificial lens). In other words, in the context of the present invention, a "lens of a model eye" may be a lens, in particular a model-based lens or a virtual lens, which describes a natural eye lens or an (aphakic) artificial lens. Alternatively, in the context of the present invention, a "lens of a model eye" may also be a lens system or a virtual lens system, in particular based on a model, which describes a natural eye lens and an additional (phakic) artificial lens. For example, a "lens of a model eye" may be understood as a thick lens of a model eye (or a "lens of a model eye" may be a thick lens of a model eye), which combines and / or describes both the properties of a natural eye lens and the properties of an additional artificial lens. In particular, in the context of the present invention, the term "lens of the model eye" is understood to mean the "lens system of the model eye". Correspondingly, in the context of the present invention, the term "lens-to-retina distance" is understood to mean in particular the "distance from the lens system to the retina". However, for the sake of simplicity, only the terms "lens of the model eye" and "lens-to-retina distance" will be used below.

[0053] The phakic intraocular lens can, for example, be considered as an own / independent or additional element in the eye model. As an alternative, the refractive power of the phakic intraocular lens can influence the refractive power of the cornea (or one surface or both surfaces). In this case, the intraocular lens can be, for example, an anterior chamber lens. As a further alternative, the refractive power of the phakic intraocular lens can influence the refractive power of the natural eye lens (or the refractive power in one surface or both surfaces). In this case, the intraocular lens can be, for example, a posterior chamber lens. If an intraocular lens is introduced as an additional element, its properties (in particular the refractive power, surface and / or thickness) can be taken into account in the eye model as additional parameters of the eye model. For example, the position of the additional lens can be defined as a known position or taken into account as an additional parameter in the eye model (e.g. a measured parameter or a model-based parameter). The defined position may be, for example, directly behind or at a certain distance behind the cornea (in the case of an anterior chamber lens), or directly in front of or at a certain distance in front of the eye lens (in the case of a posterior chamber lens).

[0054] An ophthalmic lens or spectacle lens can be optimized by tracking into the eye according to one of the methods described in WO2013 / 104548A1 or DE102017007974A1. As described in DE102017007975A1 or WO2018 / 138140A2, the eye model required for this is assigned individual values, with known properties of the IOL, such as information from the manufacturer contained in the lens of the eye model. The intraocular lens data includes data on the properties of the implanted intraocular lens. These can be specified directly when ordering or obtained from a database by specifying the type or a single serial number. This is helpful or advantageous because the model-based values ​​used in DE102017007975A1 or WO2018 / 138140A2 do not necessarily correspond to the properties of the actual implanted lens. For example, this can be the case when the length myopia is at least partially compensated by an intraocular lens with less diopter. In this case, the methods described in DE 10 2017 007 975 A1 or WO 2018 / 138140 A2 would result in an eye length that is too short.

[0055] The eye model preferably comprises various components and parameters or a set of parameters of these components such as cornea, lens, retina etc. The parameters of the eye model are e.g. the shape of the front surface of the cornea of ​​the model eye, the cornea-lens distance, parameters of the lens of the model eye, lens-to-retina distance etc.

[0056] In a preferred embodiment, the distance: lens-retina (hereinafter referred to as DLR or d LR ) is a function of the defocus term of the entire eye, the defocus term of the corneal surface, and the cornea-lens distance (hereinafter referred to as DCL or d CL ) and for an IOL having one of the forms described in DE102017007975A1 or WO2018 / 138140A2. The term defocus term will be used below for the symmetrical second term (c 2,0 ) value.

[0057] In particular, one or more of the following data may be used:

[0058] - IOL data: This can be the defocus of the refractive surfaces (front and back surfaces) and the propagation length (thickness of the lens, DLL in the following) or the defocus of the diopter of the IOL. While surface- and distance-based models can provide more accurate results during optimization, the optimization requires more calculation steps (refraction-propagation-refraction, not just refraction) and corresponding detailed information about the IOL that may not be available.

[0059] - Defocus term for the entire eye: Results of aberration measurements or auto-optometry, subjective optometry or other determinations (e.g. retinoscopy) can be used here. As an alternative, a so-called "optimized refraction" can be used, i.e. a calculation result from several components (e.g. subjective refraction and aberration measurements). Examples of such optimizations are disclosed in DE102017007975A1 or WO2018 / 138140A2. In particular, the individual refractive data of at least one eye of the spectacle wearer include the defocus or defocus term of the (overall) eye.

[0060] - Corneal defocus term: can be taken, for example, from topography or topographic measurements, or can be based on model assumptions.

[0061] - Cornea to lens distance: can be determined by measurement (eg, Scheimpflug imaging or OCT) or based on model assumptions.

[0062] Instead of or in addition to defocus, another variable may be used, preferably a second order term, such as the diopter in the main part with the highest or lowest diopter or in a meridian with a defined position (eg horizontal or vertical).

[0063] On request, the eye model can be supplemented with astigmatism (magnitude and axis, or other second-order variables according to the previous paragraph) as well as higher-order components of the entire eye and components (see DE102017007975A1 or WO2018 / 138140A2). These can be taken from, for example, IOL data, measured values ​​(e.g., topography / morphology or aberrations / autorefraction), model assumptions and / or calculated values ​​(e.g., optimized refraction).

[0064] Typically, an IOL is provided with information about asphericity or higher-order aberrations. These can be used when assigning higher-order aberrations to an eye model.

[0065] First, individual refractive data of at least one eye of a spectacle wearer are provided. The individual refractive data are determined based on the individual refraction. The refractive data include at least the spherical and astigmatic visual impairments of the eye. In a preferred embodiment, the refractive data obtained also describe higher-order aberrations (HOA). Preferably, the refractive data (also called aberration data, in particular if they include higher-order aberrations) are measured by an optician, for example, using an automatic refractometer or an aberrometer (objective refractive data). As an alternative or in addition, subjectively determined refractions may also be used. Subsequently, the refractive data will preferably be communicated to the lens manufacturer and / or provided to a calculation or optimization program. Thus, for the method according to the invention, the data may be accessible, in particular read out and / or received in digital form.

[0066] Preferably, providing individual refractive data comprises providing or identifying a vergence matrix S of a visual impairment of at least one eye.M . Here, the vergence matrix describes the wavefront in front of the eye of light emanating from or converging at a point on the retina. In terms of measurement technology, such refraction data can be determined, for example, by illuminating a point on the retina of a spectacle wearer with the aid of a laser, from which the light propagates. Although the light from the illumination point initially diverges essentially spherically in the vitreous body of the eye, the wavefront changes while passing through the eye, in particular at the optical boundary surfaces of the eye (e.g. the eye lens and / or the cornea). The refraction data of the eye can therefore be measured by measuring the wavefront in front of the eye.

[0067] Furthermore, the method may comprise defining an individual eye model which individually defines at least certain specifications regarding the geometrical and optical properties of the model eye. Thus, in the individual eye model according to the invention, at least the shape (topography) and / or the diopter of the cornea, in particular the front surface of the cornea of ​​the model eye, the cornea-lens distance d CL (this distance between the cornea and the anterior surface of the lens of the model eye is also called the anterior chamber depth), parameters of the lens of the model eye, in particular at least partially defining the optical power of the lens of the model eye, and the lens-to-retina distance d LR (the distance between the lens, in particular the rear surface of the lens, and the retina of the model eye is also referred to as the vitreous length), i.e. in such a way that the model eye has the individual refractive data provided, i.e. the wavefront emanating in the model eye from a point on the retina of the model eye matches (up to the required accuracy) the wavefront identified (e.g. measured or otherwise identified) for the real eye of the spectacle wearer. As parameters of the lens of the model eye (lens parameters), for example geometrical parameters (the shape of the lens surfaces and their distances) and preferably material parameters (e.g. the refractive indices of the individual components of the model eye) can be defined, so that completely they at least partially define the optical power of the lens. Alternatively or additionally, parameters directly describing the optical power of the lens of the model eye can also be defined as lens parameters. For the cornea, the shape of the anterior corneal surface is usually measured, but as an alternative or additionally, the optical power of the cornea as a whole can be specified (without distinction between anterior and posterior surfaces). It is also possible to specify the posterior corneal surface and / or the corneal thickness.

[0068] The parameters of the lens of the model eye can be defined (uniquely) based on the provided intraocular lens data. In particular, the parameters of the lens of the model eye correspond to the provided individual intraocular lens data. In other words, the provided intraocular lens data are defined as the parameters of the lens of the model eye.

[0069] In the simplest case of an eye model, the refraction of the eye is determined by an optical system including the front surface of the cornea, the eye lens and the retina. In this simple model, the refraction of light at the front surface of the cornea and the refractive power of the eye lens (preferably including spherical aberration and astigmatism and higher-order aberrations) and their position relative to the retina define the refraction of the model eye.

[0070] Here, the individual variables (parameters) of the model eye are defined accordingly based on the provided intraocular lens data and further based on the individual measurements of the eye of the eyeglass wearer and / or based on standard values ​​and / or / or based on the provided individual refractive data. In particular, some parameters (e.g., the topography of the anterior surface of the cornea and / or the depth of the anterior chamber and / or the curvature of at least the lens surface, etc.) can be provided directly as individual measurements. Other values ​​can also be obtained from the values ​​of the standard model of the human eye, especially when the parameters involved are very complex and cannot be measured individually. However, in general, not all (geometric) parameters of the model eye must be specified from individual measurements or standard models. In contrast, in the context of the present invention, individual adaptation is performed for one or more (free) parameters by performing calculations taking into account predefined parameters, so that the model eye subsequently generated has the provided individual refractive data. According to the number of parameters contained in the provided individual refractive data, the corresponding number of (free) parameters of the eye model can be individually adjusted (fitted). Deviating from the models proposed, for example, in WO 2013 / 104548 A1, at least the lens-to-retina distance can be defined by calculation in the context of the present invention.

[0071] For calculating or optimizing the spectacle lens, the first surface and the second surface of the spectacle lens are in particular designated as starting surfaces with a predetermined (individual) position relative to the model eye. In a preferred embodiment, only one of the two surfaces is optimized. This is preferably the back surface of the spectacle lens. Preferably, a corresponding starting surface is designated for both the front surface and the back surface of the spectacle lens. However, in a preferred embodiment, only one surface is iteratively changed or optimized during the optimization process. For example, the other surface of the spectacle lens can be a simple spherical surface or a rotationally symmetric aspherical surface. However, it is also possible to optimize both surfaces.

[0072] Starting from two predetermined surfaces, the method for calculating or optimizing comprises determining the path of a chief ray through at least one viewpoint (i) of at least one surface of a spectacle lens to be calculated or optimized into a model eye. The chief ray describes a geometrical beam path emanating from an object point, passing through the two spectacle lens surfaces, the anterior corneal surface and the lens of the model eye, preferably reaching the retina of the model eye.

[0073] Furthermore, the method for calculation or optimization may comprise evaluating the aberrations of the wavefront caused by a spherical wavefront incident on a first surface of a spectacle lens along a principal ray on an evaluation surface, in particular in front of or within a model eye, in particular compared to a wavefront converging at a point on the retina of the eye model (reference light).

[0074] In particular, a spherical wavefront (w0) incident on a first surface (front surface) of the spectacle lens along a principal ray is specified for this purpose. The spherical wavefront describes the light emanating from an object point (object light). The curvature of the spherical wavefront corresponds to the inverse of the object distance when incident on the first surface of the ophthalmic lens. Therefore, the method preferably comprises specifying an object distance model which assigns an object distance to each viewing direction or each viewpoint of at least one surface of the spectacle lens to be optimized. This preferably describes the individual wearing situation in which the spectacle lens to be manufactured will be used.

[0075] The wavefront incident on the spectacle lens is now preferably refracted for the first time on the front surface of the spectacle lens. The wavefront then propagates along the principal rays within the spectacle lens from the front surface to the back surface, where it is refracted a second time. Preferably, the wavefront transmitted through the spectacle lens now propagates along the principal rays to the corneal front surface of the eye, where it is preferably refracted again. Preferably, after further propagation within the eye to the eye lens, the wavefront is also refracted again there, in order to finally preferably propagate to the retina of the eye. Depending on the optical properties of the individual optical elements (spectacle lens surface, corneal front surface, eye lens), each refraction process also results in a deformation of the wavefront.

[0076] In order to achieve an accurate mapping of the object point to the image point on the retina, the wavefront preferably has to leave the eye lens as a converging spherical wavefront, the curvature of which corresponds exactly to the inverse value of the distance to the retina. The wavefront emitted from the object point is compared (in the ideal case of a perfect image) with the wavefront converging at a point on the retina (reference light), so that the mismatch can be evaluated. This comparison and thus the evaluation of the wavefront of the object light in the individual eye model can be performed at different points along the path of the chief ray, in particular between the second surface of the optimized spectacle lens and the retina. In particular, the evaluation surface can therefore be located at different positions, in particular between the second surface of the spectacle lens and the retina. The refraction and propagation of the light emitted from the object point is calculated accordingly in the individual eye model, preferably for each viewpoint. The evaluation surface can be related to the actual beam path or to a virtual beam path, such as for example for constructing the exit pupil AP. In the case of a virtual beam path, the light must propagate back through the rear surface of the eye lens after refraction to the required level (preferably to the AP level), wherein the refractive index used must correspond to the medium of the vitreous body, not to the eye lens. If the evaluation surface is arranged behind the lens or after refraction by the rear surface of the lens of the model eye, or if the evaluation surface is by back propagation along the virtual beam path (as in the case of AP), the final wavefront of the object light can preferably be simply compared with the spherical wavefront of the reference light. To this end, the method therefore preferably comprises specifying a spherical wavefront incident on a first surface of the spectacle lens, identifying the wavefront due to at least the first and second surfaces of the spectacle lens, the anterior corneal surface and the diopter of the lens of the model eye in at least one eye, and evaluating the aberration of the resulting wavefront with the spherical wavefront converging on the retina.

[0077] However, if an evaluation surface is to be provided within the lens or between the lens of the model eye and the spectacle lens to be calculated or to be optimized, backpropagation of the evaluation surface from a point on the retina through the individual components of the model eye upwards is simulated as reference light in order to compare the object light there with the reference light.

[0078] However, as already mentioned at the beginning, a complete correction of the refraction of the eye is generally not possible for all viewing directions of the eye, i.e. for all viewpoints of the at least one spectacle lens surface to be optimized. Depending on the viewing direction, it is therefore preferred to provide for a deliberate misalignment of the spectacle lens, which, depending on the application, is in particular smaller in the main use area of ​​the spectacle lens (e.g. central viewpoint) and slightly higher in less used areas (e.g. peripheral viewpoints). In principle, this procedure is known from conventional optimization methods.

[0079] For optimizing a spectacle lens, at least one surface of the spectacle lens to be calculated or to be optimized is iteratively changed until the aberration of the resulting wavefront corresponds to a specified target aberration, i.e. in particular deviates from a wavefront of reference light (e.g. a spherical wavefront with the center of curvature on the retina) by a specified value. The wavefront of the reference light is also referred to here as reference wavefront. Preferably, the method comprises minimizing an objective function F, in particular an objective function similar to that described at the beginning. Further preferred objective functions, in particular when taking higher-order aberrations into account, will be described further below. If the propagation of the object light to the retina is calculated, an evaluation can be performed there instead of comparing the wavefront parameters, for example with the aid of a so-called "point spread function".

[0080] In the context of the present invention, it is therefore proposed, in particular for the calculation or optimization of spectacle lenses, to define an individual eye model defined by at least the vitreous length of the model eye being calculated individually as a function of other individual identifications, in particular measured data of the eye. This parameter does not have to be defined in advance nor does it have to be measured directly. In the context of the present invention, it was found that, since the wavefront tracking results depend very sensitively on this length parameter, this leads to a significant improvement of the individual adaptation with relatively little effort.

[0081] Individual calculations of the eye model, in particular the lens-to-retina distance (vitreous length), can already be performed, for example, in an aberrometer or topograph with corresponding extended functionality. Preferably, the length of the eye is individually identified. Particularly preferably, the measured and / or calculated vitreous length and / or the identified (measured and / or calculated) eye length are displayed to the user. For this purpose, the corresponding device, in particular the aberrometer or topograph, has a corresponding display device.

[0082] In the context of the present invention, it is particularly proposed to use the known properties of the implanted IOL when calculating the spectacle lens. This advantageously results in a spectacle lens that is better suited to the patient with the implanted IOL and optimizes imaging on the retina and design retention.

[0083] In a preferred embodiment, the individual intraocular lens data comprises at least the defocus of the front surface of the intraocular lens, the defocus of the back surface of the intraocular lens and the thickness of the intraocular lens. Alternatively or additionally, the individual intraocular lens data comprises at least the defocus of the diopter of the intraocular lens or the optical power of the intraocular lens. Therefore, the intraocular lens data can be the defocus of the refractive surface (front surface and back surface) and the propagation length (thickness of the lens, hereinafter referred to as DLL) or the defocus of the IOL diopter. Although the surface and distance-based model can provide more accurate results in the optimization process, the optimization requires more calculation steps (refraction-propagation-refraction, not just refraction) and corresponding detailed information about the IOL that may not be available. Alternatively or additionally, the individual intraocular lens data can include information related to the so-called A constant, in particular the value. The A constant is an individual lens constant, in particular a correction factor that can appear in IOL calculation formulas of different names. It is also called the IOL constant or "surgeon factor". Each IOL of each manufacturer has a different A constant specified for each calculation formula. This constant represents the intraocular lens in various calculation formulas. Since all IOL constants are interconvertible, there is in principle only one constant (number) that can be used to characterize a given intraocular lens over the entire available power range, regardless of form factor, optical material, IOL diameter, etc. By using the A or IOL constant, the effects of individual surgical technique, the measurement and surgical equipment used, and individual physiological differences in the cohort of patients undergoing surgery on the IOL calculation are minimized. The A constant specifically reflects any accommodation in power and can be part of either the lens prescription or the IOL prescription.

[0084] In a further preferred embodiment, individual intraocular lens data are provided based on type or serial number information, in particular by the manufacturer of the IOL. This information can be indicated, for example directly at the time of ordering, or retrieved from a database.

[0085] In a further preferred embodiment, the method further comprises the following steps:

[0086] - consistency check on the defined eye model,

[0087] - Resolving any inconsistencies, in particular with the aid of analytical and / or numerical and / or probabilistic methods.

[0088] In any case, the process according to the invention provides a consistent model with respect to defocus (or other variables used to calculate the length of the eye). However, the consistency of the model is no longer guaranteed by other second-order variables (e.g., the magnitude and direction of the astigmatism). In other words, the eye model may be overdetermined and therefore no longer consistent. On the one hand, this may be due to manufacturing inaccuracies and measurement inaccuracies of the IOL, which may occur, for example, in the measurement of topography or morphology, aberrations or autorefraction and / or anterior chamber depth. On the other hand, when subjective refraction is used, inconsistencies may occur in principle if the subjective refraction or optimized refraction does not correspond to the objective optical power of the entire eye. In the context of this specification, a consistent eye model is understood to mean an eye model in which the incident wavefront corresponding to the aberration of the entire eye converges at a point on the retina. This is synonymous with the fact that the wavefront emitted from the light point on the retina corresponds to the aberration of the entire eye after passing through the entire eye.

[0089] In particular, probabilistic methods can be used for consistency checking. In this case, the consistency measure can be given as a probability. Any inconsistency can be resolved, for example by determining the maximum value of the probability.

[0090] Performing a consistency check and resolving any inconsistencies particularly improves the calculation or optimization of a spectacle lens for a patient with an IOL. However, performing a consistency check and resolving any inconsistencies is also advantageous in cases where the spectacle lens is not specifically for a patient with an IOL. Thus, the present invention generally provides a computer-implemented method for identifying relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing a spectacle lens for at least one eye of the spectacle wearer, comprising the following steps:

[0091] - providing individual refractive data of at least one eye of the spectacle wearer;

[0092] - defining an individual eye model, wherein in particular one or more of the following information or parameters, namely

[0093] - the shape and / or the refractive power of the cornea of ​​the model eye (12), in particular the shape and / or the refractive power of the anterior corneal surface (18); and / or

[0094] -- cornea to lens distance; and / or

[0095] -- parameters of the lens of the model eye; and / or

[0096] - lens to retina distance; and / or

[0097] -- the size of the entrance pupil; and / or

[0098] --The size and / or position of the physical aperture stop

[0099] is defined based on individual measurements of the eye of the spectacle wearer and / or standard values ​​and / or based on provided individual refractive data,

[0100] - consistency check of the defined eye model, in particular the individual refractive data provided, and optionally

[0101] - Resolving any inconsistencies, in particular with the aid of analytical and / or numerical methods and / or probabilistic procedures or methods.

[0102] "Defining an individual eye model" may mean defining a model parameter to a specific value. However, as an alternative or in lieu thereof, "defining an individual eye model" may also comprise defining at least one consistency measure (or at least one probability). In particular, there may be a plurality of model parameter values. A consistency measure or probability may be defined for each combination of these values. For example, a Bayesian approach may be used to define such a consistency measure or probability.

[0103] Preferably, the definition of the lens-retina distance is performed at least by calculation. In the context of the present invention, the term "calculation" may include not only calculations using equations, but also steps performed in a statistical manner, such as the selection of values ​​based on statistical considerations or probabilities. For example, using a Bayesian approach, it is possible to select or define only possible or most likely lens-to-retina distances (which then still have to be solved). Therefore, in the context of the present invention, in particular, the term "calculation" may also include the selection of possible or most likely values ​​of one or more parameters and / or the definition of an optimization problem. In particular, the term "calculation" also includes selection, determination and / or definition in the context of statistical procedures, for example in the context of or using a Bayesian approach. The term "calculation" may also include optimization in particular.

[0104] In addition or as an alternative to performing a consistency check on the defined eye model and resolving any inconsistencies, the computer-implemented method may further comprise defining or constructing a consistent eye model, in particular using a Bayesian approach and / or a maximum likelihood approach. In other words, the individual eye model used or to be defined is a consistent eye model, wherein consistency is made possible or established by statistical or probabilistic methods, in particular using a Bayesian approach and / or a maximum likelihood approach.

[0105] In particular, in this regard, a computer-implemented method and a corresponding device are provided for performing such a method to identify relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing a spectacle lens for at least one eye of the spectacle wearer, comprising one or more of the following steps or functions:

[0106] - providing individual refractive data for at least one eye of the spectacles wearer; and / or

[0107] - defining an individual eye model, wherein in particular one or more of the following information or parameters, namely

[0108] - the shape and / or optical power of the cornea of ​​the model eye, in particular the shape and / or optical power of the anterior surface of the cornea; and / or

[0109] -- cornea to lens distance; and / or

[0110] -- parameters of the lens of the model eye; and / or

[0111] - lens to retina distance; and / or

[0112] -- the size of the entrance pupil; and / or

[0113] --The size and / or position of the physical aperture stop

[0114] is defined in particular based on individual measured values ​​and / or standard values ​​of the eye of the spectacle wearer and / or based on provided individual refractive data,

[0115] Wherein one or more of the information or parameters and / or the at least partially provided individual refractive data are initially defined in the form of a probability distribution, and wherein defining the individual eye model comprises identifying the model eye by identifying values ​​of the information or parameters within the probability distribution defined by a probabilistic method.

[0116] While in some aspects the model eye is first created by defining parameter values ​​in order to then possibly modify the model eye based on a consistency check using a probabilistic method so that the eye model is consistent, in the present case, instead of possibly for inconsistent parameter values, a probability distribution is started for at least one parameter in order to consistently identify the most likely parameter value and thus the most likely model eye using a probabilistic method. The parameters of the probability distribution, such as the mean and / or the standard deviation, may in particular be based on individual measurements and / or standard values ​​of the eye of the eyeglass wearer and / or on the individual refractive data provided. Further details and specific exemplary embodiments of such a method will be described below.

[0117] In the following, several examples will be used to describe how to adjust the parameters with the help of analytical calculations to eliminate any inconsistencies in the eye model.

[0118] The simplest possibility is to transfer the deviations to elements or components of the eye model (e.g. cornea, anterior surface of the IOL, posterior surface of the IOL, diopter of the IOL). For example, the posterior surface of the IOL can be selected (contrary to the manufacturer's instructions) so that the model is consistent. To this end (when using a defocus term), after calculating the DLR, first the astigmatism, in particular according to the amplitude and direction (e.g. according to DE102017007975A1 or WO2018 / 138140A2) can be defined so that the eye model becomes consistent in terms of astigmatism. In addition, the higher-order components of this surface can be defined in a subsequent step (e.g. with the aid of the methods described in DE102017007975A1 or WO2018 / 138140A2), for example, so that the eye model is also consistent in these components. As an alternative or in addition, the corneal surface can be adjusted accordingly. This will be particularly useful if, due to topography measurements, only model-based corneal information or no information on astigmatism or higher-order components is available.

[0119] In a further preferred embodiment, any inconsistency is resolved by adjusting or refining one or more parameters of the eye model. Preferably, several parameters of the eye model are adapted and the adaptation is distributed among a plurality of parameters of the eye model. For example, the known deviations may be divided between several elements or components and / or several parameters of the eye model, such as the cornea, the anterior surface of the IOL, the posterior surface of the IOL and / or the diopter of the IOL. In the simplest case, fixed or predetermined factors or proportions may be assumed, such as 33% on the cornea and 67% on the lens. Alternatively or additionally, a physiologically based distribution may also be used.

[0120] Alternatively or additionally, further or new parameters may be added to the eye model and defined so that the eye model becomes consistent. For example, the shape of the posterior corneal surface of the model eye may be such an additional parameter. For example, in the case of a toric lens with fixed astigmatism, the cylinder axis and / or the lateral offset or tilt may be selected so that the resulting astigmatism of the model eye meets the specifications (as best as possible).

[0121] As an alternative or in addition, the lengths DCL, DLL and / or DLR can be adjusted. If necessary, the power of the entire eye can also be adjusted. Here, the target diopter of the spectacle lens can be changed accordingly to make the eye model consistent.

[0122] In a further preferred embodiment, the parameters of the eye model are determined with the help of probabilistic methods, ie using probability calculations. For this purpose, in particular, Bayesian statistics and / or maximum likelihood algorithms can be used.

[0123] As an alternative or in addition to the analytical calculation of the eye length based on a set of parameters, in particular all known parameters (hereinafter referred to as input parameters) can be combined and the parameters of the eye model (hereinafter referred to as output parameters) can be determined with the aid of statistical methods such as maximum likelihood and Bayesian. Here, one or more of the following information about at least the individual input parameters can be used:

[0124] -Confidence in correctness;

[0125] - Measurement and manufacturing accuracy;

[0126] - the range of fluctuations in a collective or ensemble;

[0127] -Impact on the optimization of eyeglass lenses.

[0128] Descriptions of two such methods and specific examples are given below in the detailed description.

[0129] In a further preferred embodiment, an initial distribution of parameters of the eye model and individual data about the characteristics of at least one eye are provided, and the parameters of the individual eye model are determined based on the initial distribution of parameters of the eye model and the individual data using the probability calculation. In other words, an initial eye model and individual data about the characteristics of at least one eye are provided, and the parameters of the individual eye model are determined based on the initial eye model and the individual data using the probability calculation.

[0130] In a further preferred embodiment, the eye length of the model eye is determined taking into account the measured and / or calculated lens-to-retina distance.Preferably, the identified eye length is displayed on a display device or monitor.

[0131] The above method relates in particular to the characteristics or data of an implanted intraocular lens, i.e., the intraocular lens data are known. However, if this data is unknown, then in the context of the present invention, an alternative method is proposed, which will be described below. According to this alternative method of the present invention, i.e., if the characteristics of the implanted lens are not directly known, conclusions about the characteristics of the implanted IOL are drawn by measurements on the patient.

[0132] An alternative method for solving this object (i.e. in case the characteristics or data of the implanted intraocular lens are unknown) involves a method for identifying relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing a spectacle lens for at least one eye of the spectacle wearer, wherein the intraocular lens has been implanted in at least one eye of the spectacle wearer as part of an operation, the method comprising the following steps:

[0133] - providing individual post-operative refractive data for at least one eye of the spectacle wearer;

[0134] - Identify the lens-retina distance (or eye length) of the eyeglass wearer's eye;

[0135] - defining an individual postoperative eye model, wherein in particular at least

[0136] - the shape and / or refractive power of the cornea of ​​the model eye of the postoperative eye model, in particular the shape and / or refractive power of the anterior corneal surface;

[0137] --The cornea-to-lens distance of the model eye of the postoperative eye model;

[0138] --Parameters of the lens of the model eye of the postoperative eye model;

[0139] --The lens-to-retina distance of the model eye of the postoperative eye model;

[0140] is defined based on a determined lens-to-retina distance (or eye length) and further based on individual measurements of the eye of the spectacle wearer (determined before or after surgery) and / or standard values ​​and / or based on provided individual post-operative refractive data, so that the model eye of the post-operative eye model has the provided individual post-operative refractive data, wherein the lens-to-retina distance of the model eye of the post-operative eye model is defined by the lens-to-retina distance of the eye of the identified spectacle wearer.

[0141] In particular, in another aspect, a computer-implemented method for identifying relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing a spectacle lens for at least one eye of the spectacle wearer may be provided, in case an intraocular lens is implanted in at least one eye of the spectacle wearer as part of surgery, the method specifically comprising the following steps:

[0142] - providing individual refractive data of at least one eye of the spectacle wearer;

[0143] - define individual eye models, where at least

[0144] - the shape and / or refractive power of the cornea of ​​the model eye, in particular the shape and / or refractive power of the anterior surface of the cornea;

[0145] --The distance from cornea to lens;

[0146] --Parameters of the lens of the model eye;

[0147] -- Distance from lens to retina;

[0148] defined by parameters of an individual eye model, wherein the step of defining the parameters of the individual eye model is performed based on data of vision correction of at least one eye with an artificial lens and further based on individual measurements and / or standard values ​​of an eye of a spectacle wearer and / or based on provided individual refractive data, so that the model eye has the provided individual refractive data.

[0149] Therefore, in another aspect, a device for determining relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing a spectacle lens for at least one eye of the spectacle wearer, the at least one eye of the spectacle wearer having an implanted intraocular lens, can be provided, the device comprising in particular:

[0150] - at least one data interface for providing individual refractive data of at least one eye of a wearer of the spectacles;

[0151] - a modeling module for defining an individual eye model, which defines at least

[0152] - the shape and / or the refractive power of the cornea of ​​the model eye, in particular the shape and / or the refractive power of the anterior corneal surface (18);

[0153] --The distance from cornea to lens;

[0154] --Parameters of the lens of the model eye;

[0155] -- Distance from lens to retina

[0156] As parameters of an individual eye model, wherein the parameter vision of the individual eye model is defined based on vision correction data of at least one eye with an artificial lens and further based on individual measured values ​​and / or standard values ​​of the eye of the glasses wearer and / or based on provided individual refractive data, so that the model eye has the provided individual refractive data.

[0157] In a preferred embodiment, the data for vision correction of at least one eye with an artificial lens comprise (in particular individual) artificial lens data. Thus, in this embodiment, the parameters of the individual eye model are based on the artificial lens data and further on individual measurements and / or standard values ​​of the eye of the spectacle wearer and / or on the provided individual refractive data, so that the model eye has the provided individual refractive data and the parameters of the lens of the model eye are defined based on the artificial lens data.

[0158] In a further preferred embodiment, the lens-to-retina distance of the eye of the spectacle wearer is identified, and the parameters of the individual eye model are defined based on the identified lens-to-retina distance and further based on individual measurements and / or standard values ​​of the eye of the spectacle wearer and / or based on the provided individual refractive data, so that the model eye has the provided individual refractive data and the lens-to-retina distance of the model eye is defined by the identified lens-to-retina distance of the eye of the spectacle wearer. In other words, in this embodiment, the data for vision correction of at least one eye with an artificial lens include the identified lens-to-retina distance. In particular, the data for vision correction of at least one eye with an artificial lens may include the identified lens-to-retina distance and / or artificial lens data.

[0159] In particular, in another aspect, a computer-implemented method (and corresponding manufacture) for identifying relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing a spectacle lens for at least one eye of the spectacle wearer is provided, wherein an artificial lens has been implanted in at least one eye of the spectacle wearer as part of surgery or at least one eye of the spectacle wearer has an implanted artificial lens (particularly instead of or in addition to a natural lens). The method may specifically include the following steps:

[0160] - providing individual refractive data of at least one eye of the spectacle wearer;

[0161] - define individual eye models, where at least

[0162] - the shape and / or refractive power of the cornea of ​​the model eye, in particular the shape and / or refractive power of the anterior surface of the cornea;

[0163] --The distance from cornea to lens;

[0164] --Parameters of the lens of the model eye;

[0165] -- Distance from lens to retina;

[0166] are defined as the parameters of the individual eye model, where:

[0167] a) defining parameters of an individual eye model based on the intraocular lens data and further based on individual measurements and / or standard values ​​of the eye of the spectacle wearer and / or based on the provided individual refractive data, such that the model eye has the provided individual refractive data, wherein the parameters of the lens of the model eye are defined based on the intraocular lens data; and / or

[0168] b) identifying a lens-to-retina distance of the eye of the spectacle wearer and performing, based on the identified lens-to-retina distance and further based on individual measurements and / or standard values ​​of the eye of the spectacle wearer and / or based on the provided individual refractive data, defining parameters of an individual eye model so that the model eye has the provided individual refractive data, wherein the lens-to-retina distance of the model eye is defined by the identified lens-to-retina distance of the eye of the spectacle wearer.

[0169] The term surgery (German: Operation) is often abbreviated to OP. The term "postoperative" (German: Nach-OP) refers to the situation after the surgery, while the term "preoperative" (German: Vor-OP) refers to the situation before the surgery. The surgery is, for example, cataract surgery, in which the natural eye lens is replaced by an artificial lens. However, it can also be a surgery on an aphakic eye (eye without a lens), in which an artificial lens is inserted or implanted into the patient's eye. Thus, an artificial lens can particularly denote a substitute for the natural eye lens. In particular, the natural lens of the wearer's eye has been replaced by the artificial lens during the surgery.

[0170] The spectacle lens is preferably optimized by tracking into the eye according to one of the methods described in WO 2013 / 104548 A1 or DE 10 2017 007 974 A1. By analogy with the description in DE 10 2017 007 975 A1 or WO 2018 / 138140 A2, the eye model required for this is assigned individual values. However, in this case, no information about the IOL is available and the model-based values ​​do not necessarily coincide with the actually implanted lens. This may be the case, for example, if the length myopia is at least partially compensated by an intraocular lens with less diopter. In this case, according to the procedure described in DE 10 2017 007 975 A1 or WO 2018 / 138140 A2, it will be assumed that the eye length is too short. Therefore, based on the data corresponding to the situation in which the original lens is located in the eye, the eye length or lens-retina distance as described in DE102017007975A1 or WO2018 / 138140A2 will be calculated.

[0171] Subsequently, further parameters (i.e. parameters of the eye lens, in this case the implanted intraocular lens) are determined based on the eye length thus calculated (or the calculated lens-to-retina distance) and the aberrations of the entire eye, the surface of the cornea and the postoperative values ​​of the cornea-to-lens distance, so that the refractive power of the eye model corresponds to the aberrations of the entire eye. This differs from the essential procedure in DE102017007975A1 or WO2018 / 138140A2 in that all values ​​of the lens (in this case the implanted IOL) are determined, whereas different second-order terms (e.g. defocus) are known in DE102017007975A1 or WO2018 / 138140A2. However, after determining this term, further terms can be determined as described in DE102017007975A1 or WO2018 / 138140A2. These can be further second-order terms but also higher-order terms (e.g. in a further step).

[0172] For the calculation of the eye length or lens-to-retina distance, the following data are preferably used in particular:

[0173] – Defocus of the entire eye before changing the lenses: This may be the result of aberration measurement or auto-optometry, subjective optometry or other determinations before surgery (e.g. retinoscopy). As an alternative, a so-called “optimized refraction” may be used, i.e. a calculation result from several components (e.g. subjective refraction and aberration measurement). Examples of such optimizations are compiled in DE102017007975A1 or WO2018 / 138140A2. Furthermore, the refractive defocus of the old glasses worn before surgery may be used;

[0174] - model-based values ​​of the diopter or structure of the eye lens;

[0175] - measured or model-based values ​​of the cornea-to-lens distance;

[0176] - A measured or model-based value of the corneal defocus.

[0177] The data for the last two points can come from measurements taken before or after surgery. The use of data determined after surgery is particularly useful if no corresponding measurements were taken before surgery.

[0178] By analogy, the following data are preferably used to calculate the characteristics of the lens:

[0179] – Aberrations of the entire eye after lens exchange: These may be the result of aberration measurements or auto-optometry, subjective optometry or other determinations after surgery (e.g. retinoscopy). As an alternative, a so-called "optimized refraction" may be used, i.e. a calculation result from several components (e.g. subjective refraction and aberration measurements). Examples of such optimizations are compiled in DE102017007975A1 or WO2018 / 138140A2.

[0180] - previously determined lens-to-retina distance;

[0181] - measured or model-based values ​​of the cornea-to-lens distance;

[0182] -Measured or model-based values ​​of corneal aberrations.

[0183] The data for the last two points can come from measurements taken before or after surgery. The use of data determined before surgery is particularly useful if no corresponding measurements were taken after surgery.

[0184] Providing individual intraocular lens data may in particular comprise the following steps:

[0185] – determination of the eye length based on data corresponding to the situation when the original natural lens was still in the eye of the spectacle wearer (the situation before implantation of the intraocular lens);

[0186] - Calculation of individual intraocular lens data based on the identified eye length, the provided individual refractive data, measured values ​​or model-based values ​​of the cornea-lens distance and measured values ​​or model-based values ​​of the corneal aberrations.

[0187] The following table exemplarily includes three scenarios. However, it should be understood that other combinations are also part of the present invention.

[0188]

[0189]

[0190] For example, the lens-retina distance or the ocular length of the eye of a spectacle wearer can be determined by direct measurement.

[0191] In a preferred embodiment, the method further comprises providing individual pre-operative refractive data regarding at least one eye of the spectacle wearer, wherein the determination of the lens-retina distance or the eye length of the eye of the spectacle wearer is based on correcting the individual pre-operative eye model using the provided individual pre-operative refractive data.

[0192] In a preferred embodiment, in the preoperative eye model, in particular at least

[0193] - the cornea of ​​the model eye of the preoperative eye model, in particular the shape and / or the refractive power of the anterior corneal surface;

[0194] --The cornea-lens distance of the model eye of the preoperative eye model;

[0195] -- model eye lens parameters of the preoperative eye model; and

[0196] -- Lens-retina distance of the model eye before surgery

[0197] The model eye is defined based on individual measurements of the eye of the spectacle wearer (determined before or after surgery) and / or standard values ​​and / or based on provided individual pre-operative refractive data, so that the model eye has provided individual pre-operative refractive data, wherein at least the lens-retina distance is preferably defined by measurement and / or calculation correction.

[0198] The anterior corneal surface is preferably measured separately and the eye lens of the individual preoperative eye model is calculated accordingly in order to meet the individually determined preoperative refractive data. Here, in a preferred embodiment, the anterior corneal surface (or its curvature) is measured separately along a major part (topography). In another preferred embodiment, the topography of the anterior corneal surface (i.e. the complete description of the surface) is measured separately. In another preferred embodiment, the cornea-lens distance is defined based on the individual measured values ​​of the cornea-lens distance.

[0199] Particularly preferably, defining the lens parameters of the preoperative model eye comprises defining the following parameters:

[0200] --The shape of the front surface of the lens;

[0201] -- lens thickness; and

[0202] --The shape of the posterior surface of the lens.

[0203] Even though not necessary for use of the present invention, such more accurate lens models may be used to further refine individual accommodation.

[0204] In this case, in a particularly preferred embodiment, the lens thickness and the shape of the back surface of the lens are defined based on a correction of predetermined values ​​(standard values, for example from technical literature), wherein the shape surface defining the front side of the lens further preferably comprises:

[0205] - provide a standard value for the mean curvature of the anterior lens surface; and

[0206] - Calculates the shape of the front surface of the lens taking into account the individual refractive data provided.

[0207] In a further preferred embodiment of the more detailed lens model, defining the shape of the front surface of the lens comprises:

[0208] - Provides a single measure of the curvature in normal sections of the anterior lens surface.

[0209] In this case, it is particularly preferred that the lens thickness and the shape of the rear lens surface are defined based on standard values, and even more preferably, that the shape of the front lens surface is defined including:

[0210] - Calculation of the shape of the front lens surface taking into account the provided individual refractive data and the provided individual measurements of the curvature in a normal section of the front lens surface.

[0211] As an alternative or in addition to the shape of the lens or lens surface, defining the lens parameters may include defining the optical power of the lens. In particular, at least one position of at least one principal plane of the lens of the model eye and the spherical power (or at least one focal length) are defined. The cylindrical power (size and axial position) of the lens of the model eye is also particularly preferred. In another preferred embodiment, the optical higher-order aberrations of the lens of the model eye can also be identified.

[0212] Another independent aspect for solving the object relates to a computer-implemented method for calculating or optimizing an ophthalmic lens, in particular a spectacle lens, for at least one eye of a spectacle wearer, comprising:

[0213] - a method according to the invention for identifying relevant individual parameters of at least one eye of a spectacle wearer;

[0214] - specifying a first surface and a second surface for the ophthalmic lens to be calculated or optimized;

[0215] - identifying the main ray entering the model eye through the route of at least one viewpoint of at least one surface of the spectacle lens for calculation or optimization;

[0216] - evaluating the aberration of the wavefront caused by a spherical wavefront incident on a first surface of a spectacle lens along a chief ray on the evaluation surface, compared to a wavefront converging at a point on the retina of the eye model;

[0217] - Iteratively changing at least one surface of the spectacle lens to be calculated or optimized until the evaluated aberration corresponds to a predetermined target aberration.

[0218] Another independent aspect for solving the object relates to a computer-implemented method for calculating or optimizing an ophthalmic lens, in particular a spectacle lens, for at least one eye of a spectacle wearer, comprising:

[0219] - a method according to the invention for identifying relevant individual parameters of at least one eye of a spectacle wearer;

[0220] - specifying a first surface and a second surface for a spectacle lens to be calculated or optimized;

[0221] - identifying the main ray entering the model eye through the route of at least one viewpoint of at least one surface of the spectacle lens for calculation or optimization;

[0222] - evaluating the aberration of the wavefront caused by a spherical wavefront incident on a first surface of a spectacle lens along a chief ray on the evaluation surface, compared to a wavefront converging at a point on the retina of the eye model;

[0223] - Iteratively changing at least one surface of the spectacle lens to be calculated or optimized until the evaluated aberration corresponds to a predetermined target aberration.

[0224] Preferably, the evaluation surface is located between the front surface of the cornea and the retina. In a particularly preferred embodiment, the evaluation surface is located between the lens of the model eye and the retina. In another particularly preferred embodiment, the evaluation surface is located on the exit pupil (AP) of the model eye. Here, the exit pupil can be located in front of the rear surface of the lens of the model eye. By means of this positioning, a particularly precise individual adaptation of the spectacle lens can be achieved.

[0225] Another independent aspect of solving this object relates to a method for manufacturing an ophthalmic lens, in particular a spectacle lens, comprising:

[0226] - calculating or optimizing a spectacle lens according to the spectacle lens calculation or optimization method according to the present invention; and

[0227] - manufacturing the thus calculated or optimized spectacle lenses.

[0228] Another independent aspect for solving this object relates to a device for identifying relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing an ophthalmic lens for at least one eye of the spectacle wearer, comprising:

[0229] - at least one data interface for providing individual data of characteristics of at least one eye of the spectacles wearer; and

[0230] - a modeling module for modeling and / or constructing an individual eye model by defining (and / or specifying) a set of parameters of the individual eye model; wherein

[0231] The modeling module is configured to determine a probability distribution of parameter values ​​of the individual eye model based on the individual data, in particular using a probability calculation.

[0232] In a preferred embodiment, providing individual data comprises providing individual refractive data about at least one eye of the eyeglass wearer. Furthermore, constructing the individual eye model comprises defining an individual eye model, wherein at least

[0233] - the shape and / or refractive power of the cornea of ​​the model eye (12), in particular the anterior corneal surface (18); and / or

[0234] --cornea-lens distance; and / or

[0235] -- parameters of the lens of the model eye; and / or

[0236] -- lens-retina distance; and / or

[0237] -- entrance pupil size; and / or

[0238] --Size and / or position of the physical aperture stop

[0239] In particular, it is defined based on individual measurements and / or standard values ​​of the eye of the eyeglass wearer and / or based on the provided individual refractive data. The modeling module is also configured to perform a consistency check of the defined eye model using the provided individual refractive data and to resolve any inconsistencies, in particular with the help of analytical and / or probabilistic methods.

[0240] In particular, the present invention therefore provides a device for identifying relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of an ophthalmic lens, in particular a spectacle lens, for at least one eye of the spectacle wearer, comprising:

[0241] - at least one data interface for providing individual data of characteristics of at least one eye of the spectacles wearer; and

[0242] - a modeling module for defining an individual eye model, in particular defining at least

[0243] - the shape and / or optical power of the cornea of ​​the model eye (12), in particular the anterior corneal surface (18); and / or

[0244] --cornea-lens distance; and / or

[0245] -- parameters of the lens of the model eye; and / or

[0246] -- lens-retina distance; and / or

[0247] -- entrance pupil size; and / or

[0248] --Size and / or position of the physical aperture stop

[0249] Based on individual measured values ​​and / or standard values ​​for the eye of the spectacle wearer and / or on provided individual refractive data, wherein at least the lens-retina distance is preferably determined by measurement and / or calculation; wherein

[0250] The modeling module is configured to perform a consistency check of the defined eye model using the provided individual refractive data and to resolve any inconsistencies, in particular with the help of analytical and / or probabilistic methods.

[0251] In particular, the present invention provides a device for identifying relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing a spectacle lens for at least one eye of the spectacle wearer, wherein at least one eye of the spectacle wearer has an implanted intraocular lens, in particular instead of or in addition to a natural lens, comprising:

[0252] - at least one data interface for providing individual intraocular lens data about an intraocular lens implanted in an eye of the spectacle wearer and for providing individual refractive data about at least one eye of the spectacle wearer; and

[0253] A modeling module for defining an individual eye model, in particular defining at least

[0254] - the cornea of ​​the model eye, in particular the shape and / or optical power of the anterior corneal surface;

[0255] --cornea-lens distance;

[0256] -- parameters of the lens of the model eye; and

[0257] --Lens-retina distance

[0258] The model eye is provided with individual refractive data based on the individual provided intraocular lens data and further based on individual measured values ​​and / or standard values ​​of the eye of the spectacle wearer and / or based on the provided individual refractive data, wherein the parameters of the lens of the model eye are defined based on the provided intraocular lens data. Preferably, the lens-retina distance is defined by measurement and / or calculation.

[0259] Preferably, the modeling module is configured to identify the eye length of the model eye taking into account the measured and / or calculated lens-retina distance. The device preferably also includes a display device for displaying the measured and / or calculated lens-retina distance and / or the determined eye length. The device is particularly preferably designed as an aberrometer and / or a topograph.

[0260] Preferably, the modeling module is configured to perform a consistency check on the identified eye model, in particular the identified preoperative eye model and / or the identified postoperative eye model. Furthermore, the modeling module is preferably configured to resolve any inconsistencies, in particular with the help of analytical and / or probabilistic methods (probability calculations, for example using Bayesian statistics and / or maximum likelihood methods).

[0261] In particular, the present invention provides a device for identifying relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing a spectacle lens for at least one eye of the spectacle wearer, wherein an intraocular lens is implanted in at least one eye of the spectacle wearer during surgery, comprising:

[0262] - at least one data interface for providing individual post-operative refractive data of at least one eye of a spectacle wearer; and

[0263] - a modeling module for identifying the lens-retina distance of the eye of the spectacle wearer and for defining an individual post-operative eye model, in particular defining at least

[0264] - the cornea of ​​the model eye of the postoperative eye model, in particular the shape and / or the refractive power of the anterior corneal surface;

[0265] --The cornea-lens distance of the model eye of the postoperative eye model;

[0266] -- lens parameters of the model eye of the post-operative eye model; and

[0267] --Lens-retina distance of the model eye after surgery

[0268] Based on the determined lens-retina distance and further based on individual measurements of the eye of the spectacle wearer (determined before or after surgery) and / or standard values ​​and / or based on provided individual postoperative refractive data, a model eye of the postoperative eye model has the provided individual postoperative refractive data, wherein the lens-retina distance of the model eye of the postoperative eye model is defined by the lens-retina distance of the identified eye of the spectacle wearer.

[0269] Another independent aspect for solving this object relates to a device for calculating or optimizing a spectacle lens for at least one eye of a spectacle wearer, comprising:

[0270] - a device according to the invention for identifying relevant individual parameters of at least one eye of a spectacle wearer;

[0271] - a surface model database for specifying a first surface and a second surface of the ophthalmic lens to be calculated or optimized;

[0272] - a chief ray identification module for identifying the path of a chief ray entering the model eye through at least one viewpoint of at least one surface of the spectacle lens for calculation or optimization;

[0273] - an evaluation module for evaluating the aberration of the wavefront resulting from a spherical wavefront incident on a first surface of a spectacle lens along a principal ray on the evaluation surface compared to a wavefront converging at a point on the retina of an eye model; and

[0274] - An optimization module for iteratively varying at least one surface of the spectacle lens to be calculated or optimized until the evaluated aberration corresponds to a predetermined target aberration.

[0275] Another independent aspect of solving this object relates to an apparatus for producing spectacle lenses, comprising:

[0276] - a calculation or optimization device configured to calculate or optimize a spectacle lens according to the inventive method for calculating or optimizing a spectacle lens; and

[0277] - The processing device is configured to process the spectacle lens according to the calculated or optimized result.

[0278] The device for producing eyeglass lenses can be designed as one piece or as an independent machine, i.e. all components of the device (in particular the computing or optimization device and the processing device) can be part of one and the same system, or one and the same machine. However, in a preferred embodiment, the device for manufacturing eyeglass lenses is not designed as one piece, but is implemented by different (in particular independent) systems or machines. For example, the computing or optimization device can be implemented as a first system (in particular comprising a computer) and the processing device can be implemented as a second system (in particular a machine comprising a machining device). Here, the different systems can be located in different places, i.e. they can be separated from each other locally. For example, one or more systems can be located at the front end, while one or more other systems can be located at the back end. The individual systems can, for example, be located at different company locations or operated by different companies. The individual systems have, in particular, communication devices in order to exchange data with each other (for example via data products). Preferably, the various systems of the device can communicate directly with each other, in particular via a network (for example, via a local network and / or via the Internet). The above statements about the device for manufacturing eyeglass lenses apply not only to this device, but also generally to all devices described in the context of the present invention. In particular, the device described here can be designed as a system. The system may in particular comprise a plurality of devices (possibly locally separated) which are configured to carry out the individual method steps of the respective method.

[0279] Furthermore, the present invention provides a computer program product or computer program product, in particular in the form of a storage medium or a data stream containing a program code, which program code is designed to perform the method according to the invention for identifying relevant individual parameters of at least one eye of a spectacle wearer and / or for calculating or optimizing an ophthalmic lens according to the invention when loaded and executed on a computer. In particular, a computer program product is to be understood as a program stored on a data product. In particular, the program code is stored on a data product. In other words, the computer program product comprises computer-readable instructions which, when loaded into the memory of a computer and executed by the computer, cause the computer to perform the method according to the invention.

[0280] Furthermore, the present invention provides a spectacle lens produced by a method according to the invention and / or using an apparatus according to the invention.

[0281] Furthermore, the present invention provides for the use of a spectacle lens produced by the production method according to the invention, in particular in a preferred embodiment, in a predetermined average or individual wearing position of the spectacle lens in front of a specific eye of the spectacle wearer for correcting a visual impairment of the spectacle wearer.

[0282] The present invention may particularly include one or more of the following aspects:

[0283] - Eyeglass lenses as products;

[0284] - Calculation and manufacture of eyeglass lenses;

[0285] - Calculate the characteristics of eyeglass lenses (especially design and surface);

[0286] - Calculation of eye length and assignment of eye model

[0287] (Also used for purposes other than lens calculations);

[0288] - methods, devices and / or systems for acquiring relevant data, for example in the form of or as part of a subscription and / or industry software, in particular for manual input and / or import from measuring devices and / or databases;

[0289] - methods, devices and / or systems, in particular protocols, for transmitting relevant data;

[0290] - a method, device and / or system for storing relevant data, which may be different from the method, device and / or system for calculating ophthalmic lenses;

[0291] - Methods, devices and / or systems for providing and retrieving IOL data, in particular type or serial number information based on the IOL manufacturer, eyeglass lens calculator or third party;

[0292] - Devices and computer program products for implementing the above points.

[0293] In particular, the computer-implemented method according to the present invention can be provided in the form of subscription and / or industrial software. In particular, the data required for calculating and / or optimizing and / or manufacturing eyeglass lenses, in particular intraocular lens data and / or prescription data and / or individual refractive data (preoperative and / or postoperative) can obtain and / or transmit surgical refractive data of at least one eye of the eyeglass wearer. The intraocular lens data can be transmitted, for example, from the manufacturer of the intraocular lens data to the calculator and / or the manufacturer of the eyeglass lenses. Prescription data and / or individual refractive data can be transmitted, for example, from an optician and / or an ophthalmologist or a surgeon to the calculator and / or the manufacturer of the eyeglass lenses. As an alternative or in addition, the data can be retrieved from a database, in particular by means of the type and / or serial number of the implanted intraocular lens or by means of a patient code (e.g., customer or patient number, name, etc.). For example, measurement or refractive data can also be called directly from a measuring device. Data can be transmitted using a public transmission protocol or a transmission protocol developed specifically for the method according to the present invention. As an alternative or in addition, the data to be transmitted can also be manually input at least partially through an input unit. In this way, the ophthalmologist or surgeon can, for example, transmit the so-called A constant or IOL constant of the artificial lens used. In particular, a lens or IOL prescription can also be created semi-automatically or fully automatically based on the transmitted data.

[0294] The device according to the invention and / or the system according to the invention, for example, for ordering ophthalmic lenses, may in particular comprise a computer and / or a data server configured to communicate via a network, such as the Internet. The computer is in particular configured to execute a computer-implemented method, such as ordering software for ordering at least one ophthalmic lens, and / or transmission software for transmitting relevant data, in particular intraocular lens data and / or prescription data and / or refraction data, and / or identification software for identifying relevant individual parameters of at least one ophthalmic lens for one eye of a spectacles wearer according to the invention, and / or calculation or optimization software for calculating and / or optimizing the ophthalmic lens to be produced.

[0295] The above or below statements made about the embodiment of the first aspect also apply to the above-mentioned other independent aspects or methods, in particular the preferred embodiments in this regard. In particular, the above and below statements about the embodiment of each other independent aspect also apply to the independent aspect of the present invention and the preferred embodiments of this aspect. BRIEF DESCRIPTION OF THE DRAWINGS

[0296] Preferred embodiments and examples of the present invention will be explained below, at least in part, by way of example, with reference to the accompanying drawings, which show:

[0297] Figure 1 is a schematic diagram of the physiological and physical model of the spectacle lens and eye and the beam path in the intended wearing position;

[0298] Figure 2 is a method for identifying parameters under constraint conditions according to a preferred embodiment of the present invention. mess For S IOL and L 2,IOL An exemplary dependency graph of

[0299] Figure 3a-3f is the marginal prior probability density for a first example of a method according to Bayes A as a contour representation of a sample from a prior distribution with equidistant lines from the same probability density;

[0300] Figure 4a-4f is the marginal posterior probability density as a contour representation of samples of the posterior distribution for a first example of the method according to Bayes A, with equidistant lines from the same probability density;

[0301] Figure 5a-5c are M, J0 and J for the first example according to the method of Bayes A or Bayes B 45 a marginal probability density histogram representing a sample from the posterior distribution of the diopters of ophthalmic lenses;

[0302] Figure 6a-6e is a scatter plot of marginal prior probability densities for samples from a prior distribution according to a second example of the method of Bayes A;

[0303] Figure 7a-7e is a scatter plot of marginal posterior probability density of samples as posterior distribution for a second example according to the method of Bayes A;

[0304] Figure 8a-8c are M, J0 and J for the second example according to the method of Bayes A or Bayes B 45 a marginal probability density histogram representing a sample from the posterior distribution of the diopters of ophthalmic lenses;

[0305] Figure 9a-9c are M, J0 and J for the second example according to the method of Bayes A or Bayes B 45 Histogram of the marginal probability densities of , which are derived from the prior distribution. DETAILED DESCRIPTION

[0306] Figure 1 Schematic diagram showing a physiological and physical model of a spectacle lens and an eye in a predetermined wearing position and exemplary beam paths, on which a single spectacle lens calculation or optimization according to a preferred embodiment of the present invention is based.

[0307] Here, preferably only a single ray is calculated for each viewpoint of the spectacle lens (the principal ray 10, which preferably passes through the eye rotation center Z'), but also the derivative transverse coordinate (perpendicular to the principal ray) of the vertex depth of the wavefront is calculated according to the following equation. These derivatives are taken into account in the required order, the second-order derivative describing the local curvature properties of the wavefront, higher derivatives are related to higher-order aberrations.

[0308] When the light rays are traced through the spectacle lens to the eye 12 according to a separately provided eye model, local derivatives of the wavefront are ultimately identified at suitable locations in the beam path in order to compare them there with a reference wavefront converging at a point on the retina of the eye 12. In particular, the two wavefronts, i.e. the wavefront from the spectacle lens and the reference wavefront, are compared with each other in an evaluation surface.

[0309] "Position" does not simply mean a specific value of the z-coordinate (in the direction of the light), but rather such coordinate value combined with the specification of all surfaces through which refraction occurs before reaching the evaluation surface. In a preferred embodiment, refraction occurs through all refractive surfaces including the posterior surface of the lens. In this case, the reference wavefront is preferably a spherical wavefront with its center of curvature located on the retina of the eye 12.

[0310] Particularly preferably, after the last refraction no further propagation occurs, so that the radius of curvature of the reference wavefront corresponds to the distance between the rear surface of the lens and the retina. In a further preferred embodiment, propagation still occurs after the last refraction, preferably up to the exit pupil AP of the eye 12. This is, for example, at a distance in front of the retina and therefore even in front of the posterior surface of the lens, so that the propagation in this case is reverse propagation (name This is described in the table below for steps 1-6.) In this case, the reference wavefront is also spherical with the center of curvature on the retina, but with a radius of curvature 1 / d AR .

[0311] For this purpose, it is assumed that a spherical wavefront w0 originates from the object point and propagates to the first spectacle lens surface 14. There it is refracted and then it propagates to the second lens surface 16 where it is refracted again. The wavefront w0 leaving the spectacle lens g1 Then it propagates along the principal ray in the direction of the eye 12 (the propagated wavefront w g2 ) until it hits the cornea 18 where it is refracted again (wavefront w c After further propagation to the eye lens 20 in the anterior chamber of the eye, the wavefront is also refracted again by the eye lens 20, whereby, for example, the wavefront w e . Compare it with the spherical reference wavefront w sThe comparison is performed and the deviation of all viewpoints in the objective function is evaluated (preferably using corresponding weights for each viewpoint).

[0312] Therefore, visual impairment is no longer described only by a thin sphero-cylindrical lens as is customary in many conventional approaches, but directly in the eye the corneal topography, the eye lens, distances in the eye and the deformation of the wavefront (including low-order aberrations, i.e. sphere, cylinder and cylinder axis, and preferably also higher-order aberrations) are taken into account. Here, the vitreous length d LR It is calculated separately in the eye model according to the invention.

[0313] Aberrometry preferably provides individual wavefront deformations of real eyes with distance and near vision defects (deviations, no absolute refractive index) and individual intermediate and photopic pupil diameters. From measurements of corneal topography (surface measurements of the anterior corneal surface), the individual real anterior corneal surface is preferably obtained, which typically constitutes almost 75% of the total refractive power of the eye. In a preferred embodiment, measurement of the posterior corneal surface is not required. Since the refractive index difference is small compared to the aqueous humor, and since the corneal thickness is small, it is preferably described by the adaptation of the refractive index of the cornea rather than by a separate refractive surface.

[0314] Generally speaking, in this specification, bold lowercase letters are used to represent vectors, while bold uppercase letters are used to represent matrices, such as a (2×2) convergence matrix or a refractive index matrix.

[0315]

[0316] Also, italics such as d are used to denote scalar quantities.

[0317] Furthermore, bold, italicized capital letters are used to refer to a wavefront or surface as a whole. For example, S is the vergence matrix of the eponymous wavefront S, including, in addition to S the second-order aberrations summarized in S, the whole of all higher-order aberrations (HOA) of the wavefront. From a mathematical point of view, S represents the set of all parameters required to describe the wavefront (with sufficient accuracy) relative to a given coordinate system. Preferably, S represents a set of Zernike coefficients with a pupil radius or a set of coefficients of a Taylor series. Particularly preferably, S represents a set of vergence matrices S for describing the characteristics of a second-order wavefront and a set of Zernike coefficients (with a pupil radius) for describing the characteristics of all remaining wavefronts except the second order, or a set of coefficients according to a Taylor decomposition. Instead of wavefronts, similar statements apply to surfaces.

[0318] Among others, the following data can in principle be measured directly:

[0319] -Wavefront S M , which is produced by a laser spot on the retina and passage through the eye (from aberration measurements)

[0320] - The shape of the anterior corneal surface C (by corneal topography)

[0321] - The distance d between the cornea and the anterior surface of the lens CL (By thickness measurement). This variable can also be determined indirectly by measuring the distance between the cornea and the iris; if necessary, a correction value can be applied here. Such a correction can be the distance between the front surface of the lens and the iris from a known eye model (e.g. literature value).

[0322] – The front surface of the lens is at L 1xx The curvature in the direction (measured by thickness). In this case, without limiting the generality, the x-plane can be defined exemplarily so that the part lies in the x-plane. If the coordinate system is defined such that this plane is inclined, the derivative must be supplemented by a function of the corresponding angle. It is not required that this is the main part. For example, it can be a section in a horizontal plane.

[0323] In addition, depending on the embodiment, the following data may be measured or taken from the literature:

[0324] The thickness of the lens d L

[0325] The curvature of the back surface of the lens is proportional to the curvature of the front surface of the lens. 2,xx In the same direction (by thickness measurement)

[0326] Therefore, the posterior lens surface has the following options:

[0327] L 2,xx (L 2,M ) and the rotational symmetry L 2,xx =L 2,yy =L2=L 2,M and L 2,xy =L 2,yx =0 assumption

[0328] From the literature (L 2,Lit ) 2,xx And rotationally symmetric L 2,xx =L 2,yy =L2=L 2,M and L 2,xy =L 2,yx =0 assumption

[0329] From the literature (L 2,Lit ) takes the complete (asymmetric) form L2

[0330] L 2,xx (L 2,M ) and the assumption of a cylinder or from the literature L 2,xx =L 2,M and L2,xy =L 2,yx =f(L 2,xx ,a Ltt ) and L 2,yy =g(L 2,xx ,a Lit ) other specified asymmetry a Lit

[0331] The following data can be found in the literature:

[0332] The refractive index of the cornea and anterior chamber of the eye is n CL and aqueous humor LR and the refractive index n of the lens L

[0333] This specifically places the distance d between the posterior surface of the lens and the retina LR and the component L of the anterior surface of the lens 1,yy and L 1,xy =L 1,yx As an unknown parameter. To simplify the form, the distance d LR It can also be written as the gathering and scattering matrix D LR =D LR 1, where D LR =n LR / d LR Furthermore, the variable τ is often used, which is defined as τ=d / n (wherein for the refractive index, the corresponding refractive index must always be used as n, and for d and τ, for example τ LR =d LR / n LR , τ CL =d CL / n CL ).

[0334] The modeling of the passage of the wavefront through the eye model used according to the invention, i.e. after passing through the surfaces of a spectacle lens, can be described as follows in a preferred embodiment, where the lens is described via the front and back surfaces, by means of the transformation, explicitly specifying the vergence matrix:

[0335] 1. The wavefront S with the vergence matrix S is refracted on the cornea C with the surface refractive matrix C to the wavefront S with the vergence matrix S′ C =S+C's wavefront S' C

[0336] 2. Depth of the anterior chamber d CL (the distance between the cornea and the anterior surface of the lens) to the vergence matrix S L1 =S′ C / (1-τ CL ·S′) of the wavefront S L1 Spread of

[0337]

[0338] 3. Refracted on the front surface L1 of the lens with surface refractive matrix L1 to the lens with vergence matrix S′ L1 =S L1 +L1 wavefront S′ L1

[0339] 4. Thickness around the lens d L To have a gathering and scattering matrix S L2 =S′ L1 / (1-τ L ·S′ L1 ) of the wavefront S L2 Spread of

[0340] 5. Refracting on the back surface L2 of the lens with the surface refractive power matrix L2 to the lens with the convergence matrix S′ L2 =S L2 +L2 wavefront S′ L2

[0341] 6. The distance between the lens and the retina d LR To have a gathering and scattering matrix S R =S′ L2 / (1-τ LR ·S′ L2 ) of the wavefront S R Spread of

[0342] Propagation distance τ CL , τ CL and τ CL Each of step 2, step 4, step 6 can be divided into two parts according to the following scheme to spread 2a, b), 4a, b) or 6a, b), where step 6a, b) is explicitly read:

[0343] 6a. Distance between the lens and the middle plane Propagate to the matrix with convergence and divergence The wavefront S LR

[0344] 6b. Distance between the median plane and the retina Propagate to the matrix with convergence and divergence The wavefront S R

[0345] here, and can be positive or negative, so it should always be kept and In any case, steps 6a and 6b can be completed by However, the division in steps 6a and 6b provides advantages, and the intermediate plane can be preferably placed in the plane of the exit pupil AP, which is preferably located in front of the posterior surface of the lens. In this case, and

[0346] The division of steps 2 and 4 can be similar to the division of step 6 in 6a and b).

[0347] The decisive factor for choosing the evaluation surface of the wavefront is not only the absolute position relative to the z coordinate (in the direction of the light), but also the number of surfaces through which refraction occurs up to the evaluation surface. Thus, the same level can be passed several times. For example, the plane of the AP (usually located between the anterior and posterior surfaces of the lens) is the first formal pass of the light after the imaginary step 4a, where the propagation length from the anterior surface of the lens is 1.2 m. The same plane is reached a second time after step 6a, this time after being refracted by the posterior surface of the lens, propagating back to the AP plane, i.e., Its Synonymous. In the text, the wavefront S of AP is mentioned AP In the case of AP =S LR (unless explicitly stated otherwise).

[0348] Reference will be made to these steps 1 to 6 in the further course of the description. They describe the preferred relationship between the vergence matrix S of the wavefront S on the cornea and the vergence matrices of all intermediate wavefronts generated thereby at the refractive intermediate surface of the eye, in particular the wavefront S′ L2 The gathering and scattering matrix S′ L2 (Even the wavefront S on the retina R ). These relations can be used to calculate a priori unknown parameters (e.g., d LR or L1), thereby assigning values ​​to the model individually or in general, can also be used to simulate the propagation of the wavefront in the eye for the purpose of optimizing eyeglass lenses using the model for the accepted task.

[0349] In a preferred embodiment, the surface and the wavefront are processed to the second order, for which a representation by means of a vergence matrix is ​​sufficient. Another preferred embodiment described later takes into account and also uses higher order aberrations.

[0350] In the second order description, in a preferred embodiment, the eye model has twelve parameters as degrees of freedom of the model that must be assigned values. These preferably include three degrees of freedom of the surface refractive matrix C of the cornea C, three degrees of freedom of the surface refractive matrices L1 and L2 of the front and back surfaces of the lens, and a length parameter anterior chamber depth d corresponding to each degree of freedom.CL , lens thickness d L and vitreous length d LR .

[0351] In principle, these parameters can be assigned values ​​in several ways:

[0352] i. Direct, i.e. individual measurement of parameters

[0353] ii. a parameter value given a priori, e.g. as a value from the literature or from an estimate, e.g. due to the existence of measurements of another variable that is related in a known way to the parameter determined based on a previous population analysis

[0354] iii. Calculation from consistency conditions, such as compatibility with known refraction

[0355] The total number of second-order degrees of freedom of the eye model df2 (df stands for 'degrees of freedom' and the index '2' stands for second order) is thus composed

[0356] df2=df2(i)+df2(ii)+df2(iii)

[0357] For example, if all twelve model parameters have direct measured values, then df2(i)=12, df2(ii)=0, and df2(iii)=0, which for simplicity will be indicated below as df2=12+0+0. In this case, the objective refraction of the relevant eye is also defined, so that there is no need to perform an additional objective refraction determination.

[0358] The central aspect of the invention relates precisely to the purpose of not having to measure all parameters directly. In particular, it is much easier to measure the refraction of the eye in question or to determine it objectively and / or subjectively than to measure all parameters of the model eye individually. Preferably, there is therefore at least one refraction, i.e. the wavefront S of the eye M The measurement data is up to the second order, which corresponds to the gathering and scattering matrix S M If the eye model is assigned values ​​based on purely objective measured data, these values ​​can be obtained from aberrometry or autorefractive measurements, or assigned according to (ii) together with other given data. Consideration of subjective methods (i.e., subjective refraction) will be described later, which can be an alternative to objective measurements of refraction, or by combining the two results. With the vergence matrix S M The three conditions of agreement of the three independent parameters of therefore make it possible to derive three parameters of the eye model, which corresponds to df2(iii)=3 in the above notation.

[0359] Therefore, in cases where not all model parameters can be measured directly or where these measurements are very complex, the present invention exploits the possibility of allocating missing parameters in a useful way. For example, if direct measurements (df2(i)≤9) are available for up to nine model parameters, the refraction condition can be used to calculate three model parameters (df2(iii)=3). If exactly df2(i)=9, all twelve model parameters are uniquely determined by measurement and calculation and hold (df2(ii)=0). On the other hand, if df2(i)<9, then df2(ii)=9-df2(i)>0, i.e., the model is underdetermined in the sense that the df2(ii) parameter must be defined a priori.

[0360] By providing a single refraction, the wavefront S of the eye M On the measured data, especially up to second order, the convergence matrix S M The necessary data on are available accordingly. According to the conventional method described in WO 2013 / 104548 A1, in particular, the measurement parameters {C, d CL ,S M}. In contrast, the two length parameters d L and d LR (or D LR ) is usually defined a priori (e.g., by literature values ​​or estimates). In WO2013 / 104548A1, in particular, two cases are distinguished, in which L2 is defined a priori and L1 is calculated therefrom, and vice versa. The above publication discloses equations (4) and (5) as calculation rules. For both cases, df2=4+5+3 holds.

[0361] In the terms used in the above steps 1 to 6, L1 is suitable for measuring, in particular, by means of steps 1 and 2, the measured vergence matrix S is calculated by means of the also measured matrix C M and propagates it to the object side of the front surface of the lens. On the other hand, by means of steps 6, 5, and 4 performed in reverse, by applying the surface refractive matrix L2 on the back surface of the lens previously defined and propagating the wavefront obtained at that time from the back surface of the lens to the image side of the front surface of the lens, the spherical wave is calculated from the front to the back of an imaginary point-shaped light source on the retina. Because in aberration measurement, the measured wavefront comes from the wavefront emitted from the pm point of the retina, and therefore due to the reversibility of the beam path, the measured wavefront is different from the incident wavefront (S=S) converging on this point of the retina. M ) is the same, so the vergence matrix S on the object side or image side of the anterior surface of the lens determined in this way is L1 and S′ L1 The difference must be obtained through the matrix L1. This leads to equation (4) in the mentioned publication:

[0362]

[0363] Another case in the cited publication involves adjusting the matrix L2 to the measured values ​​after the matrix L1 has been defined. The only difference is that the measured wavefront S M Going through steps 1, 2, 3, 4 and assuming the wavefront is from a point source only to step 6, the step to be performed to accommodate the lack of the posterior surface L2 of the lens is now step 5, according to equation (5) of the above publication:

[0364]

[0365] The central idea of ​​the invention is to calculate at least the length parameter d from other measured data and a priori assumptions about the other degrees of freedom. LR (or D LR ), rather than assuming the prior itself as is conventionally done. In the context of the present invention, it turns out that this leads to a significant improvement in individual adaptation with relatively little effort, since wavefront tracking turns out to be very sensitive to this length parameter. This means that if at least the length parameter d LR df2(iii)=3 parameters are calculated, which is advantageous according to the invention. In particular, these parameters are difficult to measure directly, vary greatly between different test subjects, and these variations have a great influence on the imaging of the eye.

[0366] Gathering matrix S M The data on A and particularly preferably on C are preferably obtainable from separate measurements. In a further preferred aspect, which is also preferably taken into account in the following embodiments, in the assumptions about the data on the rear surface of the lens, a spherical rear surface, i.e. a rear surface without an astigmatic component, is taken as the basis.

[0367] In a preferred embodiment of the invention, second-order measurement data of the cornea C are available, which correspond to data on the surface diopter matrix C. Although these values ​​can be obtained from topographic measurements, the latter are not essential. In contrast, topographic measurements are sufficient. This case corresponds to the case df2=3+6+3, in particular the anterior chamber depth d CL is one of six parameters to be defined a priori.

[0368] If no more individual measurements are made, then the situation is df2 = 3 + 6 + 3. In order to be able to uniquely determine d LR , from {L1,L2,d L ,d CL The six parameters of} must be assigned values ​​by assumption or literature. LRIn a preferred embodiment, the parameters of the posterior surface of the lens, the average curvature of the anterior surface of the lens, and the two length parameters d L and d CL Experience a priori assignment (as a predetermined standard value).

[0369] In a case of particular importance to the present invention, the anterior chamber depth d CL , the distance between the cornea and the anterior surface of the lens, is also known, for example from a pachymeter or OCT measurement. Thus, the measured parameters include {C,d CL ,S M}. This case corresponds to the case df2 = 4 + 5 + 3. Therefore, the problem remains mathematically undetermined and the equations {L1, L2, df2 = 4 + 5 + 3} must be eliminated a priori by assumption or literature values. L In a preferred embodiment, these are the parameters of the posterior lens surface, the average curvature of the anterior lens surface and the lens thickness.

[0370] Only in terms of accuracy of individual adaptation, it is advantageous to be able to assign individual measurements to as many parameters as possible. In a preferred embodiment, the lens curvature is additionally provided in the normal section based on the individual measurements. This will lead to the situation according to df2=5+4+3, and from {L 1yy ,α L1 ,L2,d L It is sufficient to define four parameters a priori. Here, in a preferred embodiment, parameters of the rear surface of the lens and the lens thickness are also involved. The specific calculation will be described below.

[0371] In particular, as an alternative to the normal section of the anterior lens surface and particularly preferably in addition to the anterior chamber depth, the lens thickness can also be obtained from the individual measurement. This eliminates the need to assign model data or estimated parameters to this parameter (df2=5+4+3). Otherwise, what has already been said above applies. This embodiment is particularly advantageous if a pachymeter is used, the measurement depth of which allows the posterior lens surface to be identified, but not the lens curvature to be determined sufficiently reliably.

[0372] In addition to the anterior chamber depth and the normal section of the anterior lens surface, one (e.g. measurements in two normal sections) or two further parameters of the anterior lens surface (measurements of the main part and the axial position) can be obtained by individual measurements. In particular, this additional information can be exploited in two ways:

[0373] Abandoning the a priori assumptions: One or two of the assumptions that were otherwise a priori can be abandoned and determined by calculation. In this case, the cases df2=6+3+3 and df2=7+2+3 occur. In the first case, the mean curvature of the back surface can be determined (assuming a back surface without astigmatism), while in the second case the astigmatism of the surface with a given mean curvature (including the cylinder axis) can be determined. As an alternative, the lens thickness can also be determined from the measured values ​​in both cases.

[0374] However, such a procedure generally requires a degree of caution, since noisy measured data can easily cause the published parameters to "run away". As a result, the model may become worse instead of better overall. One possibility to prevent this is to specify anatomically plausible limits for these parameters and restrict the variation of the parameters to within that range. Of course, these limits can also be specified as a function of the measured values.

[0375] Reducing measurement uncertainty: On the other hand, if the same a priori assumptions are made (preferably, {L2,d L}), then the cases df2=6+4+3 and df2=7+4+3 exist, so the system is mathematically overdetermined.

[0376] Instead of using the following explanation for D LR Instead of simply determining (“fitting”) D LR (and possibly the missing parameters from L1) so that the distance between L1 obtained by the equation and the measured L1 (or L1 supplemented by the missing parameters) becomes minimum. Obviously, a reduction in measurement uncertainty can be achieved by this procedure.

[0377] In a further preferred embodiment, the anterior chamber depth, two or three parameters of the anterior lens surface and the lens thickness are measured respectively. The other variables are calculated in the same way, whereby the a priori assumptions about the lens thickness can be replaced by the corresponding measured values.

[0378] In a further preferred embodiment, separate measurements of the anterior chamber depth, at least one parameter of the anterior lens surface, the lens thickness and at least one parameter of the posterior lens surface are provided. This is in addition to the above. The corresponding additional measurement parameters can be performed similarly to the step-by-step expansion of the above sections. These are particularly advantageous if the above thickness measurement unit measuring in one plane, two planes or the entire surface is correspondingly expanded in the measurement depth and is accurate enough to identify the curvature data accurately enough.

[0379] If the formula (1b) mentioned above is for D LR Solve to calculate the posterior surface of the lens for a given eye length (where D LR =n LR / d LR is the inverse vitreous length d LR Multiply by the refractive index n LR ),Right now

[0380]

[0381] It obtains:

[0382]

[0383] To calculate D LR . Due to D LR is a scalar, so all quantities used in calculations must also be considered scalars. Preferably, S M , C, L1 and L2 are the spherical equivalents of the visual impairment, cornea, anterior lens surface and posterior lens surface respectively. LR (So ​​the length of the eye is d A =d C +d CL +d L +d LR ), one of the surfaces, preferably the anterior lens surface L1, can be modified again with respect to the cylinder and the HOA in order to conformably adapt it.

[0384] For the calculation, for the lens surface diopter, the so-called Bennett & Rabbetts eye values ​​can be used, which can be taken, for example, from Table 12.1 of the third edition of the book "Bennett & Rabbets' Clinical Visual Optics", Ronald B. Rabbetts, Butterworth-Heinemann, 1998, ISBN-10: 0750618175. The calculation described above leads to results that are in good agreement with population statistics, which show that myopic visual impairments tend to lead to large eye lengths and vice versa (see, for example, CWOyster: "The Human Eye", 1998). However, the calculation described is even more precise, since the direct use of correlations from population statistics leads to non-physical values ​​for the eye lens, which is avoided by the method according to the invention. Exact knowledge of the lens parameters is even more important for methods that assume given these parameters. For example, if a consumer had a visual impairment of -10 dpt before his cataract surgery, his eye length must be between 28 mm and 30 mm. However, postoperatively, due to his emmetropia, the ocular length was derived as 24 mm, which did not match the actual ocular length.

[0385] Preferred embodiments of the present invention will be explained below.

[0386] Examples using Bayesian statistics

[0387] The aim of the method using Bayesian statistics is to use, if possible, all available sources of information about an eye or a pair of eyes in a consistent manner in order to achieve the best correction for the eye or to have an ophthalmic lens (eg spectacle lens) based on this information.

[0388] Usually, this information is incomplete and / or imprecise, which has often led to the fact that only simplified eye models have been used to calculate the lenses of the eye. Such a simplified eye model is, for example, an eye that is characterized only by the diopter, since this can be determined with a certain accuracy (e.g., a spherical equivalent error of ± 0.75 dpt). However, if one wishes to use a more complex eye model to calculate the lenses of the eye, it makes sense to include information about the length of the eye and the position and curvature of the refractive surfaces of the cornea and the eye lens in the calculation, but this should only be taken into account as much as possible within its accuracy.

[0389] In Bayesian statistics (see DS Sivia: "Data Analysis - A Bayesian Tutorial", Oxford University Press, 2006, ISBN-13: 978-0198568322 or ET Jaynes: "Probability Theory", Cambridge University Press, 2003, ISBN-13: 978-0521592710), information is always described in the form of a probability distribution (in case of continuous parameters it is a probability density).

[0390] In this sense, a probability or probability density can be assigned to a single eye model with a given set of parameters. A single eye model that is consistent with the available information (e.g. objective wavefront measurements and biometrics of the eye) has a higher probability or probability density because, for example, the propagation and refraction of the wavefront generated on the retina after a point light source exits the eye reproduces the measured data well within the measurement accuracy of the objective wavefront measurements, and likewise the parameters of the single eye match the available information on the biometrics of the eye within a known distribution, e.g. from the literature. Single eye models that are inconsistent with the available information are correspondingly assigned a low probability or probability density. The probability or probability density of a single eye model can be written as

[0391] prob(θ i |d i ,I)

[0392] where θ i represents the parameters of a single eye model i, d iis the measured data (e.g. it may include the current refraction or the refraction measured before ophthalmological surgery, the measured corneal shape and / or refractive properties, the measured length of the eye measured on a single eye or other variables). Using I, the current state of knowledge after the evaluation of the data, i.e. the existing background information (e.g. about the measurement process of the refraction, the parameter distribution of the model of a single eye or other relevant variables in the population) is summarized. The vertical line "|" indicates that the variable distribution is on the left side of the "|" and the given (i.e. fixed) variable is on the right side of the "|".

[0393] The information obtained during the measurement process, where the measurement data d i , which can also be understood as data d i Given the parameters θ of a single eye model i i Probability distribution of the eye model:

[0394] prob(d i |θ i ,I)

[0395] The accuracy of the measurement process is reflected in the width of the distribution: precise measurements have narrower distributions than inaccurate measurements, which have wider or more extensive data spreads. i .

[0396] Now, if we wish to calculate the parameter distribution for a single eye using the given data and background information, we can use the following scale:

[0397] prob(θ i |d i ,I)∝prob(θ i |I)prob(d i |θ i ,I)

[0398] The term prob(θ i I) describes the background knowledge about the individual eye model parameters. This can be information from the literature, for example, or information from past measurement data. This can be data from the same person for whom the lenses for the eye were made, or data from measurements done for a large number of other people.

[0399] The probability here is used as a measure of consistency. In particular, in prob(θ i I) and prob(d i |θ i When , I) are both high, parameter values ​​of a single eye model can be found that are consistent with the measurement results.

[0400] Probability or probability density prob(θ i |d i, I) can also be properly normalized so that the ratio can be written as an equation.

[0401] The term prob(θ i |d i , I) may also include parameters of the eye lens. For example, some parameters θ i This may include the power of the eye's lens, its position and / or orientation in the eye, or other variables such as the refractive index and curvature or shape of the surface.

[0402] The eye lens may be a natural lens. In this case, literature data on parameters of natural human eye lenses may be used (e.g., curvature distribution of the front and / or back surfaces, refractive index, etc.).

[0403] If the eye lens is an artificial lens, the parameter distribution of the natural eye lens must not be used. Instead, the parameters of the artificial lens should be used, provided they are individually known. Otherwise, the distribution of these parameters from literature studies of eyes that have undergone surgery can be used. If such information is not available, a flat distribution within a reasonable range can be chosen. For parameters that are positive definite and define a length scale (such as radius of curvature or distance), a distribution that is flat in the logarithm of these parameters can also be chosen.

[0404] Formally, the situation of "natural eye lens" or "artificial lens as eye lens" will be described by different states of background knowledge I (i.e., I = I NL bzw.I=I IOL ).

[0405] Probability or probability density prob(θ i |d i , I) can have one or more factors. Here, each factor represents information about one or more parameters of a single eye model. For example, different independent parameters θ from different literature sources i 1 and θ i 2 The distribution of can be expressed as the product

[0406]

[0407] By prob(θ i |I), the parameters of the eye model may be inadvertently falsified. For example, if the "true" refraction is understood as a parameter of a single eye model, the most likely value of the "true" refraction may deviate from the measured refraction. If this is undesirable, then carefully chosen ranges should be chosen (e.g. between -30 dpt and +20 dpt for the spherical equivalent M, and between -30 dpt and +20 dpt for the astigmatism components J0 and J1). 45, which is ±5dpt) the corresponding parameters (e.g., equivalent spherical refraction) maintain a constant distribution.

[0408] If the parameters of the individual eye model or other variables related to the parameters or measurement data are known exactly or with high accuracy, their distribution can be approximated as a Dirac delta distribution. The equations in these parameters or variables can be integrated on both sides, which can simplify subsequent calculations.

[0409] Description of the method

[0410] Two possible approaches to calculating the ophthalmic lens (Bayesian A and Bayesian B) are presented below. In the Bayesian A approach, the available information is used to build a (single) individual eye model, with the help of which the ophthalmic lens best suited to the eye model is calculated. The eye model can be, for example, composed of a parameter set Given or assigned, it makes the probability or probability density prob(θ i |d i ,I) is maximized. Other parameter sets can also be selected, such as expected value <θ i > or about the distribution prob(θ i |d i ,I) parameter θ i the median of

[0411] Compared to Bayesian A, the Bayesian B approach is more advantageous - but computationally more demanding, since subsets of individual eye models with different sets of parameters may result in having very similar (or even identical) properties (e.g. the refractive power at a reference point of an ophthalmic lens, or the distribution of refractive defects in a given area of ​​an ophthalmic lens, or similar criteria for determining the quality of an ophthalmic lens). Overall, an ophthalmic lens that was not calculated with the most likely individual eye model may therefore represent the best correction for a subset of individual eye models that have a higher probability overall than the most likely individual eye model. Therefore, it is advantageous to search for an ophthalmic lens that best corrects the distribution of eye models, rather than just determining the most likely individual eye model and manufacturing an ophthalmic lens for it.

[0412] In both methods, an ophthalmic lens (eg, a spectacle lens) can be calculated that is consistent with the available information.

[0413] Bayesian A method

[0414] Specifically, you can perform one or more of the following steps:

[0415] - providing an initial distribution of the parameters of the eye model (ideally as a multivariate probability distribution of all parameters of the eye model, possibly also a marginal distribution; a probability distribution corresponds to information about the distribution of the parameters of the eye model in the population);

[0416] - Provides known (in the best case measured) data about the individual eye's characteristics (ideally with a probability distribution or measurement error; the probability distribution corresponds to the inaccuracy of the measurement)

[0417] The known data may include: known current subjective and / or objective refraction, known previous subjective and / or objective refraction (e.g. preoperatively), the power and / or shape of a determined refractive surface of the eye and / or the determined position (most importantly the axial position) of the refractive surface of the eye, the size and / or shape and / or position of the entrance pupil, the refractive index of the refractive medium, the refractive index distribution in the refractive medium, the opacity; these variables may be determined based on the accommodation of the eye on a fixation object (target) at a given near distance;

[0418] - Determining the parameters of the individual eye model based on the initial distribution of the parameters of the eye model and known or measured data of the individual eye using probability calculations. Ideally, a probability distribution or a set of parameters characterizing, for example, a maximum of a probability distribution is determined.

[0419] In particular, computational methods such as Markov chain Monte Carlo theory, variational inference, maximum likelihood, maximum a posteriori or particle filters can be used;

[0420] The goal here is to select parameters of the individual eye model that are consistent with the provided initial distribution of the eye model and the known data. The product of the probability or probability density of the data for the given parameters of the eye model and the probability or probability density of the eye model parameters is used as a consistency measure.

[0421] - Calculate / optimize / select an ophthalmic lens using at least one parameter of an individual eye model.

[0422] The initial distribution of the eye model parameters provided in the first step may be in a parameterized form, such as a (possibly multivariate) normal distribution, other distributions of the exponential family, a Cauchy distribution, a Dirichlet process, etc., or as a set of samples, i.e. one or more (possibly multidimensional) data sets. If the initial distribution of the parameters of the eye model is parameterized, the parameters of this distribution are called "hyperparameters".

[0423] The third step (i.e. determining the parameters of the individual eye models) may comprise determining a multivariate probability distribution comprising the parameters of the individual eye models and the hyperparameters of the initial distribution of the eye model parameters. In order to calculate the distribution of the parameters of the individual eye models therefrom, the distribution has to be marginalized, i.e. integrated over the hyperparameters. The integral may be solved using common numerical methods (e.g. using Markov chain Monte Carlo theory or hybrid Monte Carlo theory) and / or analytical methods. In this case, the probability or probability density of the eye model parameters may be calculated using the following equation:

[0424] prpb(θ i |d i ,I)∝prob(d i |θ i ,I)∫dλprpb(θ i ,λ|I)=prob(d i |θ i ,I)∫dλprob(θ i |λ,I)prob(λ|I)

[0425] Here, prob(θ i |λ,I) means finding an individual eye model θ in a population characterized by the hyperparameter λ i The probability or probability density of the parameter. The integration will be performed over the entire defined range of all hyperparameters λ.

[0426] Bayesian B method

[0427] As an alternative or in addition to the Bayesian A method, one or more of the following steps may be performed:

[0428] providing a distribution of at least one parameter of a single eye model;

[0429] Optimizing / calculating / selecting a virtual ophthalmic lens by using at least one parameter of the individual eye model, calculating a probability distribution of parameters of a virtual ophthalmic lens or calculating an ophthalmic lens set;

[0430] The ophthalmic lens is manufactured with the goal of making the manufacturing parameters of the ophthalmic lens most likely to reach the parameters of the virtual ophthalmic lens.

[0431] In a first step, a distribution similar to that calculated in steps 1 to 3 of the Bayesian A-method can be provided. In a second step, the most likely parameters L of the ophthalmic lens are determined i , that is, according to the probability distribution or probability density

[0432] prob(L i |d i ,I)=∫dθ i prob(θ i ,L i |d i ,I)=∫dθ i prob(L i |θ i ,I)prob(θ i |d i ,I)

[0433] =∫dθ i δ(L i -L(θ i ))prob(θ i |di ,I)

[0434] Identify ophthalmic lenses The parameters of prob(L i |d i ,I) is maximized. Here, L i Originally represents the parameters of any ophthalmic lens and is i =L(θ i ) is the case of using the parameter θ i The ophthalmic lens parameters created when the individual eye model of the ophthalmic lens is optimized. The Dirac function distribution is represented by δ(.).

[0435] The parameters of the ophthalmic lens may be, for example, vertex depth, diopter at an ophthalmic lens reference point, diopter distribution over an ophthalmic lens area, refractive error at an ophthalmic lens reference point or refractive error distribution over an ophthalmic lens area.

[0436] What is important is the function L(θ i ) can be nonlinear, so the probability density prob(θ i |d i ,I)(About θ i ) and L(θ i ) does not necessarily map to the maximum probability density prob(L i |d i ,I).

[0437] If the function L(θ i ) can be inverted one by one, and the above equation can also be solved with the help of partial integration. Other methods are also possible, such as numerical methods such as particle filters, Markov chain Monte Carlo, or parameter inference methods, which can calculate the ophthalmic lens L i Parameter distribution of .

[0438] In both Bayesian A and Bayesian B methods, the number and type of variables known by measurement (i.e., data d i and the likelihood is of the form prob(d i |θ i ,I)) and the number and type of parameters of the eye model θ i , will always produce a consistent eye model (Bayesian A and B methods) and may select ophthalmic lens parameters that match the set of possible consistent eye models (Bayesian B method).

[0439] Example of solving inconsistency problem based on probability considerations

[0440] Background of Maximum Likelihood

[0441] Basic Procedure

[0442] The initial situation is the N parameters x of the model i ,1≤i≤N is to be allocated, and the following information is available:

[0443] - the mean μ of these N parameters in the population i , standard deviation σ i and the correlation coefficient ρ ij (with 1≤i,j≤N);

[0444] - Either no measurements (k=0) or k measurements of these parameters 1≤i≤k(where 1≤k≤N). Each parameter x i The measured value The probability distribution of a random variable X i Description. A reliability measure is preferably available for each measurement, e.g., a random variable X i ,1≤i≤kStandard deviation

[0445] - For q=Nk of these parameters there are no measured values.

[0446] - In general, only K of the N parameters are independent, since the model requires consistency conditions that can be expressed by the Q=NK constraint.

[0447] Examples could be:

[0448] - Example without HOA

[0449] - Parameters (N=15): cornea (SZA), anterior lens surface (SZA), posterior lens surface (SZA), visual impairment (SZA), eye length, lens thickness, anterior chamber depth;

[0450] - Measurement data (k=13): cornea (SZA), anterior lens surface (SZA), posterior lens surface (SZA), visual impairment (SZA), anterior chamber depth;

[0451] - Constraint (Q=3): Visual impairment (SZA) = theoretical visual impairment (SZA) (calculated according to the specified eye model);

[0452] -Example using HOA (up to radial order)

[0453] - Parameters (N=103): cornea (SZA+HOA), anterior lens surface (SZA+HOA), posterior lens surface (SZA+HOA), visual impairment (SZA+HOA), eye length, lens thickness, anterior chamber depth;

[0454] - Measurement data (k=101): cornea (SZA+HOA), anterior lens surface (SZA+HOA), posterior lens surface (SZA+HOA), visual impairment (SZA+HOA), anterior chamber depth;

[0455] - Constraint (Q=25): Visual impairment (SZA+HOA) = theoretical visual impairment (SZA+HOA) (calculated according to the specified eye model).

[0456] The basic problem to be solved is that, in case of a deviation of a measurement from the population mean, it has to be decided whether the measurement has to be discarded (e.g. if it is not credible) or has to be adopted. If all the measurements are reasonable in themselves, but violate one of the consistency conditions, they are not necessarily all adopted. Instead, a balance between the various measurements has to be sought: those with very high measurement reliability should at least almost be retained, while uncertain measurements are more likely to be adjusted. Preferably, the best possible values ​​for all N parameters are identified from the known information.

[0457] The idea of ​​the invention is based in particular on the assumption that the parameters have certain (unknown but initially fixed) values. Under this assumption, based on the above information (statistical variables from the population, reliability measures of the measurements), the conditional probability density

[0458] P bed (X1,...,X N |x1,...,x N ) (1)

[0459] is established for the measurement results, where X1,...,X N is given by fixed real values ​​x1,...,x N Then, the observed measurement value P par The probability is then obtained by evaluating the function P of the measured value k bed And marginalize it to the remaining q=Nk (unmeasured) parameters to quantize:

[0460]

[0461] This probability density is understood as assuming N parameters x1,...,x N Those N parameter values ​​for which this function assumes a maximum are then preferably considered to be the best possible values ​​(maximum likelihood method):

[0462]

[0463] As an alternative to marginalization in Equation 2, the N parameter values ​​can also be defined by setting the last parameter equal to the population mean,

[0464] x i =μ i ,k+1≤i≤N (4)

[0465] The first k parameters x1,...,x k are determined so that their expected values ​​are equal to the measured values:

[0466]

[0467] As a further alternative, instead of the maximum value formation according to equation (3) or the expected value formation according to equation (5), the median value can also be used as the criterion.

[0468] As a further alternative, the maximum value formation according to equation (3) and the expected value formation according to equation (5) as well as the median value determination can also be combined as required in order to determine N parameter values.

[0469] Background of the Maximum Posterior Approach

[0470] Prior knowledge about the population is given by the distribution P pop (x1,...,x N ), which can correspond to a Bayesian prior. The overall probability density describing the distribution of measurements and model parameters is thus given by the distribution function

[0471] P ges (X1,...,X k ,x1,...,x N )=P mess (X1,...,X k |x1,...,x N )×P pop (x1,...,x N ) (6)

[0472] Except for a constant, it can correspond to the posterior described by Bayes. That is why this method is also called maximum a posteriori.

[0473] Preferably, P is described by a multivariate normal distribution pop

[0474]

[0475] where μ is the vector of means and C is the covariance matrix:

[0476]

[0477] Measurement through the distribution P mess (X1,...,X k |x1,...,x N)describe.

[0478] Preferably, the measurements are independent

[0479] P mess (X1,...,X k |x1,...,x N )=P1 mess (X1|x1)…P k mess (X k |x k ) (8)

[0480] The entire distribution function P ges (excluding the a posteriori factors) is given by

[0481] P ges (X1,...,X k ; x1,...,x N )=P1 mess (X1|x1)…P k mess (X k |x k )×P pop (x1,...,x N )(8a)

[0482] Particularly preferably, each measured value has an expected value x i and standard deviation Normal distribution

[0483]

[0484] Then by inserting the normal distribution from equation (8b) into equation (8a) we get the overall distribution function P ges .

[0485] Maximize P ges As parameters x1,...,x N The function is a creative idea. To apply the maximum a posteriori criterion, it is best to form the derivative of the logarithm

[0486]

[0487]

[0488] If the distribution is a multivariate normal distribution, as is particularly preferred, equation (9) or equation (10) represents an equation with N and N variables x1, ..., x2 to be solved. N A system of linear equations.

[0489] a) No constraints

[0490] If there are no constraints and equation (9) can be solved, then the result x1,..., x N is the unique solution. This is particularly preferred if the distribution is a multivariate normal distribution and if the measurement uncertainty is significantly less than the range of variation of the population, then the result is

[0491]

[0492] i.e., for all parameters for which measured values are available, one substantially trusts the measured values, and for the remaining values, the mean value μ of the population is obtained i plus the offset Δx due to the correlation with the measured values i . One embodiment of the invention then consists in directly taking the measured values 1 ≤ i ≤ k and ignoring their slight offset due to the underlying population.

[0493] b) Constraints

[0494] If there are constraints between the parameters, then each member of the population also satisfies these constraints.

[0495] The constraints can be described as

[0496]

[0497] i.e., through Q functions f N of the parameters x1,..., x j , which can be combined in a vector f, and by requiring that these functions should be equal to zero. The functions f j are preferably linear or linear approximations of the given constraints.

[0498] In the preferred case of a multivariate distribution, this has the consequence that the columns of the covariance matrix are linearly dependent, i.e., the covariance matrix has rank r < N and thus can no longer be inverted. Then the distribution density P pop (x1,..., x N ) can no longer be specified.

[0499] One possibility in practice is to regularize the covariance matrix C by shifting one or more of the correlations ρ ij contained therein by ε or the standard deviation σ i , and then determining x1,..., x N . The solution thus obtained then automatically satisfies the constraint for ε → 0.

[0500] In the context of the present invention, it has been found that this method has drawbacks. On the one hand, the distribution in the population must be known, and on the other hand, its covariance matrix is either singular or ill-conditioned. If the correlation ρ is studiedij and standard deviation σ i , then small inaccuracies or incomplete information may be sufficient to make the covariance matrix regular, but may then produce numerically unstable solutions for the parameters sought.

[0501] However, in the context of the present invention, it has been found that this problem can be circumvented by any calculation procedure based on the distribution (maximum likelihood method)

[0502]

[0503] Or based on distribution (maximum a posteriori method)

[0504]

[0505] For this purpose, substitution methods can preferably be used.

[0506] Maximum Likelihood with Constraints and Replacement

[0507] Assume that the first K parameter x u :=(x1,...,x K ) T are independent, equation (12) solves the remaining Q = NK related parameters x a :=(x K+1 ,...,x N ) T , which can then be understood as the independent parameter x u Function x a (x u ), and can be substituted into f. Then as x u The constraints of the function are:

[0508] f(x u ,x a (x u ))=0 (14).

[0509] In the context of the present invention, it is not necessary to know explicitly the function x a (x u ). In the context of the present invention, only its Jacobian matrix According to the implicit function theorem, it is given by

[0510]

[0511] in It's about x a The quadratic Jacobian matrix f, It's about x u The general rectangular Jacobian matrix f of . Therefore, the probability density P mess (xu ,x a (x u )) must be used as x u The function of maximizing is

[0512]

[0513] The system of equations (16) K can be solved for the parameter x independent of K. u The remaining parameters x a By inserting them into the context x a (x u ) is obtained.

[0514] Maximum Likelihood Method with Constraints and Lagrangian Parameters

[0515] As an alternative, within the scope of the invention, if the Lagrangian function instead of the function P mess (x1,...,x N ) is maximized, then the entire set of parameters can be considered independent

[0516] P mess,Lagrange (x1,...,x N ,λ)=P mess, (x1,...,x N )+λf(x1,...,x N ) (17)

[0517] where λ=(λ1,...,λ Q ) is a one-dimensional vector Q of Lagrange multipliers. Then the derivative N+Q is maximized by setting it to zero.

[0518]

[0519] Solve equation (18) for the unknowns (x1,...,x N ) and (λ1,...,λ Q ) to obtain the solution for the parameters.

[0520] In addition to handling constraints with substitution or long-range parameters, one can also use a damped Hamiltonian formalism with a friction term as an alternative (e.g. in the case of maximizing the local vanishing gradient of a function).

[0521] Similarly, the method of equations (16) to (18) can be applied to the function P ges (x1,...,x N ) instead of P mess (x1,...,x N ) and then express Constrained Maximum A Posteriori Method .

[0522] Embodiments with specific exemplary values

[0523] For simplicity, an eye that is rotationally symmetric about the optical axis and therefore has neither a cylindrical prescription, nor a cylindrical cornea, nor a cylindrical lens surface is considered as the starting case. Exemplary values ​​and parameters before IOL surgery are detailed below:

[0524] S = -7.0 dpt; visual impairment (measured)

[0525] C = 41.2 dpt; corneal diopter (measured)

[0526] L1 = 7.82 dpt; diopter of the anterior surface of the lens (literature)

[0527] L2 = 13.28 dpt; diopter of the posterior surface of the lens (literature)

[0528] d CL =3.6mm; Anterior chamber depth (measured) (19)

[0529] d L =3.7mm; Lens thickness (literature)

[0530] n CL =1.336; anterior chamber refractive index (literature)

[0531] n L =1.422; Lens refractive index (literature)

[0532] n LR =1.336; refractive index of glass (literature).

[0533] After IOL surgery, for example, the following values ​​or parameters are transmitted:

[0534] Visual impairment (measured) (20)

[0535] Posterior surface of lens (manufacturer's information).

[0536] For simplicity, all other parameters after IOL surgery were assumed to remain unchanged.

[0537] With help or equation

[0538]

[0539] The reduced inverse vitreous length (D LR =n LR / d LR , where the vitreous length is d LR ; Further, τ CL =dCL / n CL , τ L =d CLL / n L ), and thus calculate the eye length d A =d CL +d L +d LR The vitreous length and the eye length are directly related, so in the following the vitreous length may be considered instead of the eye length.

[0540] If equation (21) is applied to the pre- and post-operative conditions, the IOL pre-operative

[0541] D LR =64.69dpt (22a)

[0542] After artificial lens surgery

[0543]

[0544] However, since the vitreous length cannot be changed surgically, the inconsistency that exists here can be addressed within the scope of the present invention.

[0545] To choose the simplest example, the initial situation can be seen as one in which there is no variation and correlation in the underlying population and there is only uncertainty in the visual impairment measured later and in the IOL itself:

[0546] Visual impairment (standard deviation measurement method)

[0547] The diopter of the back surface of the lens (manufacturer tolerance) (23).

[0548] Now, within the scope of the present invention, it is possible to determine S IOL ,L 2,IOL As expected, they will all deviate from equation (20).

[0549] In the example case, P pop ≡1, and the S initially assumed based on the measured values IOL ,L 2,IOL The probability density of the distribution is

[0550]

[0551] However, now, the constraint is that S IOL ,L 2,IOL Inserting into equation (21) must produce the same postoperative value D as preoperative value LR Therefore, the equation for the constraint is

[0552]

[0553] When solving L 2,IOL As S IOL When the function is:

[0554]

[0555] This constraint means that only Figure 2 Movement on the cutting surface 30 is shown.

[0556] If L 2,IOL (S IOL ) into equation (24) and maximize S IOL , that is, if for S IOL , solve

[0557]

[0558] Its acquisition

[0559]

[0560] Therefore, compared with the measured values, the two variables S IOL ,L 2,IOL are both in the negative direction, but to different degrees. In contrast, this method seeks to balance the asymmetric position of the Gaussian bell for different standard deviations and constraints.

[0561] Inconsistencies in the eye model may arise not only in the calculated eye length (or calculated lens-retina distance), but also in, for example, measuring the eye length. Such inconsistencies may be resolved similarly to the example of calculated eye length described above. Of course, more complex examples may also be given, in which the eye length itself is not fixed or may be correlated.

[0562] First Example of Bayesian A Method

[0563] The eye model used in this example includes visual impairment Described as the 4th order Zernike order, involving a pupil diameter of 5 mm, and the natural logarithm of the pupil radius log r ph or log r mes exists under photopic or mesopic lighting conditions. In general, the model parameters of the eye model can be written as a vector

[0564]

[0565] Here, the Zernike coefficients of the 0th to 1st order (piston, horizontal and vertical prism) are not considered because they have no effect on the visual impairment of the eye and can be assumed to be constant at 0, for example.

[0566] For the known measurements of the individual eye d i Here are the axes of sphere, cylinder and (far) refraction Rx,

[0567] Rx=(S Rx ,Z Rx ,A Rx )=(2.5dpt,-1dpt,100°),

[0568] It is written as the diopter vector

[0569]

[0570] The measurement error of refraction is also known, as the standard deviation of the individual diopter vector components is

[0571]

[0572] Assuming the measurement error is normally distributed, the visual impairment can be identified from the model parameters p eye (θ i ) around the diopter vector, so that

[0573]

[0574] can be written as likelihood. Here, P eye (θ i ) is the diopter vector It is scaled from the Zernike wavefront to the photopic pupil radius r by means of the root mean square (RMS) metric according to known methods. ph In this case, P eye Depends only on a subset of the eye model's parameters:

[0575]

[0576] Likelihood can now be written

[0577]

[0578] In this example, the most likely eye model is given by the background knowledge I (model parameters θ i distribution in the population, the measurement accuracy of the refraction, the diopter vector determined from the visual impairment in the Zernike representation, etc.) and the known measurement data P Rx Sure.

[0579] As the prior prob(θi |I), approximated using a sample of model parameters identified for a large number of people with the aid of a measuring device (here an aberrometer). The actual prior has 14 partially dependent parameters, so it cannot be explained as a whole. However, in Figure 3a to Figure 3f In , the marginal density of the prior samples used for the calculation is shown.

[0580] The posterior consists of a likelihood-weighted sample of the prior. To do this, the likelihood of each element (sample) of the prior sample is evaluated and used as a weight. As an alternative, a smaller sample size can be used, in which case unweighted samples must be drawn from the weighted sample. The marginal posterior density is similar to Figures 4a to 4f The prior density in .

[0581] The maximum value of the posterior density is approximated with the aid of kernel density estimation (kernel: multivariate normal distribution with a standard deviation corresponding to 0.5 times the standard deviation of the posterior distribution of the eye model parameters). This yields the following values ​​for the most likely eye model (Zernike coefficients refer to a pupil with a diameter of 5 mm):

[0582]

[0583]

[0584] By scaling the Zernike coefficients Calculate the refractive power of the lens It optimally corrects the most likely eye model under mesopic lighting conditions. The Zernike coefficients relate to a pupil diameter of 5 mm for a pupil with a radius of 5 mm using methods known in the literature. Based on the visual impairment of this eye, still given in Zernike representation, the diopter vector is again determined using the RMS metric

[0585]

[0586] This can be used to produce a lens that is optimally corrected for the most likely eye model under mesopic lighting conditions (eg a single vision lens or a focal power as a distance reference point for a progressive lens).

[0587] Similarly, the visual impairment in the Zernike representation can be scaled to a radius of The most likely photopic pupil is used to calculate the refractive power of the lens for the most likely eye model that is best corrected under photopic lighting conditions. This yields

[0588]

[0589] Compared to other known methods (see for example WO2013087212A1), in the method presented here, a finite measurement error of the data (here the refraction) can be taken into account. This has the effect that the likelihood as a function of the data has a finite width. For this reason, in the case of a photopic pupil, the most likely refractive power vector It also moves more towards the a priori maximum than the refraction (also under photopic lighting conditions). This is an advantage compared to the method disclosed in WO2013087212A1, because in this way the best correction of the eye is statistically performed more often. It also does not erroneously assume (for example in a regression analysis) that parameters that are not actually known exactly have exact values ​​(this is true for the dependent variable in the regression analysis), but actual information (such as actual or estimated precision of the measured values) about the parameters is taken into account.

[0590] First example of Bayesian B method

[0591] The choice of eye model and measured data (here refraction) considered in this example is the same as in the Bayesian A example. However, now the goal is to calculate the most likely refractive power of the ophthalmic lens to be manufactured, rather than the refractive power of the ophthalmic lens for the most likely eye model. In the example of the Bayesian A method, the lens will be very suitable for intermediate vision. In this example, the parameters L of the ophthalmic lens are i Corresponding to its simplified form diopter: To this end, the mesopic Zernike wavefronts were calculated from the posterior samples of the example Bayes A by scaling to the corresponding mesopic pupil for the Zernike coefficients associated with the pupil diameter of 5 mm in this sample, using methods known in the literature. The power vectors for the mesopic pupil were determined from these mesopic Zernike wavefronts using the root mean square (RMS) metric. These in turn represent samples from the posterior distribution of the power of ophthalmic lenses optimized for mesopic pupils (see Figure 5a to Figure 5c ). The maximum value of the posterior distribution approximates the maximum value of the kernel density estimate of the sample (multivariate normal distribution as kernel with a standard deviation corresponding to 0.5 times the standard deviation of the posterior distribution of the power vector). This yields the following most likely power of the ophthalmic lens to be manufactured

[0592]

[0593] (e.g. the power of a spectacle lens such as a single vision lens, or the power of a progressive lens at a distance from a reference point), which allows to optimally exploit the available information about the eye model. This most likely power differs from the power calculated in the Bayesian A example for the most likely eye model due to the nonlinear transformation (here scaling) of the parameters of the eye model (here the 4th order Zernike orders and logarithms describing the visual impairment up to the mesopic pupil and the photopic pupil) into the parameters of the ophthalmic lens (here the power of the ophthalmic lens as a power vector) and correction Compared with the correction This represents a further improvement because corresponds to the most likely visual impairment given the information, and Only applies to the most likely eye model for visual impairment, but not usually the most likely eye impairment.

[0594] Other examples are readily available to a person skilled in the art, in which a Bayesian A-method or a Bayesian B-method is used, but in which a more complex eye model is used, which may, for example, include several refractive surfaces and media with different refractive indices. Each surface can be described, for example, as a Zernike representation, and the distribution of the coefficients can be described in part or in full in the literature or obtained by measurement (for example, with the aid of measurement methods for determining eye biometrics, such as scanning optical coherence tomography, ultrasound or magnetic resonance tomography). If such information is missing, the prior can be replaced by assumptions about the smoothness of the refractive surfaces or the local curvature properties of these surfaces (for example, the correlation length of the local curvature). The refractive index of the medium can also be included in the model as an imprecisely known parameter. Models with a refractive index gradient are also possible. The propagation and refraction of light through the model eye are selected according to the eye model used. Other known metrics (monochromatic or polychromatic) can also be used as metrics.

[0595] Other likelihood distributions may be chosen if motivated (e.g., other parameters of the eye model may be measured directly, or other measured variables that are indirectly related to the eye model parameters may be measured or otherwise determined, such as eye length and / or the distance between the eye refractive surfaces).

[0596] More complex lens descriptions (e.g., by processes of the front and back surfaces and thicknesses) can also be easily used. If the complexity (i.e., number of parameters) of the eye and / or lens model is very high, the posterior problem can be solved, e.g., by approximation methods such as parametric inference (e.g., variational inference), where the posterior itself is parameterized and its determination is understood as an optimization problem.

[0597] Second Example of Bayesian A Method

[0598] The eye model used in this example includes three refractive surfaces described in second-order order and not tilted to each other (the anterior surface of the cornea and the anterior and posterior surfaces of the eye lens, here numbered as surfaces k=1, 2 and 3) and the retina. The posterior surface of the cornea is neglected in this model (see Bennett-Rabbett's eye model). To parameterize the surface refraction of each surface, the surface refraction is used in sections at 0°, 45° and 90° to the horizontal (i.e., the elements of the surface refraction matrix, designated for this purpose as and The relative position of the refractive surface and the retina is calculated by the natural logarithm of the distance between the two directly adjacent surfaces (the logarithms of the distances from cornea to the anterior surface of the lens, the anterior surface of the lens to the posterior surface of the lens, and the posterior surface of the lens to the retina are respectively expressed as log d 12 、log d 23 and log d 34 , where the distance is in mm) is parameterized as a positive number. The refractive index of the medium between the refractive surfaces (i.e., in the anterior chamber, the lens of the eye, and the vitreous body) has n 12 、n 23 and n 34 Here, the parameter vector is summarized as

[0599]

[0600] For the known measurements of the individual eye d i Here are the axes of sphere, cylinder and (far) refraction Rx,

[0601] Rx=(S Rx ,Z Rx ,A Rx )=(2.5dpt,-1dpt,100°),

[0602] Writing the diopter vector as

[0603]

[0604] The measurement error of refraction is also known, as the standard deviation of the individual diopter vector components

[0605]

[0606] Assuming the measurement error is normally distributed, the visual impairment can be identified from the model parameters P eye (θ i ) around the diopter vector, so that

[0607]

[0608] can be written as likelihood. Here, Peye (θ i ) is the diopter vector It corresponds to the visual impairment of the eye model, and the repeated propagation and refraction of the wavefront, which originates from a point on the retina, through the eye to the vertex of the cornea according to the eye model parameters of the paraxial approximation, can be calculated by the following formula.

[0609] The likelihood can now be written as

[0610]

[0611] In this example, the most likely eye model is given by the background knowledge I (model parameters θ i distribution in the population, the measurement accuracy of refraction, the diopter vector determined from the visual impairment represented by Zernike, etc.) and the known measurement data P Rx Sure.

[0612] For the prior prob(θ i |I), assuming a multivariate normal distribution whose parameters are derived from a series of measurements of eye biometrics of a large number of people, literature values, and estimates of the scatter of each variable in the population (if no information on the range of scatter is found).

[0613] The following table shows the maximum value and standard deviation (in brackets) of a normal distribution:

[0614]

[0615]

[0616] The correlation matrix of a normal distribution has one diagonal filled with 1s and all other diagonal filled with 0s except for the following off-diagonal elements:

[0617]

[0618] The actual prior has 15 partially dependent parameters and therefore cannot be explained holistically. Figures 6a to 6e In , the marginal density of the prior samples used to calculate is shown as a scatter plot.

[0619] The posterior consists of a likelihood-weighted sample of the prior. To do this, the likelihood of each element (sample) of the prior sample is evaluated and used as a weight. As an alternative, a smaller sample size can be used, in which case unweighted samples must be drawn from the weighted sample. The marginal posterior density is similar to Figures 7a to 7e The prior density in .

[0620] The maximum value of the posterior density is approximated with the help of kernel density estimation (kernel: multivariate normal distribution with standard deviation corresponding to 0.5 times the standard deviation of the posterior distribution of the eye model parameters). This yields the following values ​​for the most likely eye model

[0621]

[0622]

[0623] It can be easily seen from the differences in the xx and yy components of the surface power that most of the astigmatism is in the cornea, since the cornea has the largest range of power fluctuations in the population (and therefore in the prior as well).

[0624] The power of the lens that best corrects the most likely eye model is also calculated. for

[0625]

[0626] This can be used to produce a lens that best corrects the most likely eye model (eg a single vision lens or a diopter as a distance reference point for a progressive lens).

[0627] Since the distance between the cornea and the corrective or refractive lens is usually different, the former is related to the corrective lens, while the latter is related to the diopter of the eye during refraction, the lens that best corrects the most likely eye model The diopter may differ from the most likely eye for visual impairment

[0628] Second Example of Bayesian B Method

[0629] The eye model considered in this example and the choice of measured data (here refraction) are the same as in the previous second Bayesian A example. However, now the goal is to calculate the most likely refractive power of the ophthalmic lens to be manufactured, rather than the refractive power of the ophthalmic lens of the most likely eye model. In this example, the parameters L of the ophthalmic lens are i Corresponding to its simplified form diopter:

[0630] To this end, the power vector is calculated from the posterior samples of the previous second Bayesian A example, which represent samples from the posterior distribution of the power of the best ophthalmic lens (see Figures 8a to 8c ). and the prior distribution given by the eye (see Figures 9a to 9c ) compared to the corresponding distribution of the density of the diopter of the ophthalmic lens produced by the posterior, the reduced scattering range based on the posterior compared to the prior can clearly identify the information obtained through the data.

[0631] The maximum value of the posterior distribution is approximated by the maximum value of the kernel density estimate of the sample (with a multivariate normal distribution as kernel and a standard deviation corresponding to 0.5 times the standard deviation of the posterior distribution of the power vector). This allows the following most likely powers of the ophthalmic lens to be manufactured (e.g. the power of a spectacle lens such as a single-vision lens, or the power at a distance from a reference point for a progressive lens), which optimally exploits the available information on the eye model:

[0632]

[0633] This most likely refraction differs from the refraction calculated in the Bayesian A example due to the nonlinear transformation of the parameters of the eye model (here the surface refraction and distance of the refractive surfaces and, to a lesser extent, the refractive index of the medium) (here mainly the propagation of the wavefront between the refractive surfaces) into the parameters of the ophthalmic lens (here the refraction of the ophthalmic lens as a refraction vector). Correction with the second example from the Bayesian B method Compared with the correction P L，max This represents a further improvement, because P L，max corresponds to the most likely visual impairment given the information, and Only applies to the most likely eye model for visual impairment, but not usually the most likely eye impairment.

[0634] Reference numerals list

[0635] 10 Principal Ray

[0636] 12 Eyes

[0637] 14 First surface of the lens (front surface)

[0638] 16 Second surface of the lens (back surface)

[0639] 18 Anterior surface of cornea

[0640] 20 Eye lens

[0641] 30 Cutting surface.

Claims

1. A computer-implemented method for identifying relevant individual parameters of at least one eye of a spectacle wearer for use in calculating or optimizing an ophthalmic lens for the at least one eye of the spectacle wearer, comprising the following steps: - providing individual data of characteristics of said at least one eye of said spectacles wearer; - constructing an individual eye model by defining a set of parameters of the individual eye model; - determining a probability distribution of values ​​of said parameters of said individual eye model based on said individual data, wherein constructing the individual eye model comprises an initial probability distribution of the parameters of the eye model; and Wherein the parameters of the eye model are determined by using a probability calculation based on the initial probability distribution of the parameters of the eye model and the provided individual data of characteristics of the at least one eye of the glasses wearer.

2. The computer-implemented method of claim 1 , wherein: - determining a probability distribution of values ​​of said parameters of said individual eye model, also based on said initial probability distribution of parameters of said eye model.

3. A computer-implemented method according to claim 1 or 2, wherein constructing the individual eye model and / or determining the probability distribution of the values ​​of the parameters of the individual eye model is performed using Bayesian statistics.

4. The computer-implemented method of claim 1 , wherein determining a probability distribution of values ​​of the parameter of the individual eye model comprises: A consistency measure is calculated, wherein what is used as the consistency measure is the product of the probability or probability density of the individual data for given parameters of the individual eye model and the probability or probability density of the parameters of the individual eye model given background knowledge.

5. The computer-implemented method according to claim 1 or 2, further comprising the steps of: - Using at least one parameter of said individual eye model, calculating a probability distribution of parameters of the ophthalmic lens to be calculated or to be optimized.

6. The computer-implemented method of claim 5, further comprising the steps of: - Determining the most probable value of said parameter of said ophthalmic lens to be calculated or to be optimized.

7. The computer-implemented method of claim 1 or 2, wherein: Providing individual data comprises: providing individual refractive data about the at least one eye of the eyeglass wearer; and Constraining the individual eye model comprises defining an individual eye model in which at least the following items can be determined based on individual measurements and / or standard values ​​of the eye of the spectacles wearer and / or based on the provided individual refractive data: - the shape and / or refractive power of the cornea of ​​the model eye (12); and / or -- the distance from the cornea to the lens; and / or -- parameters of the lens of the model eye; and / or - the distance from the lens to the retina; and / or - the size of the entrance pupil; and / or -- the size and / or position of the physical aperture stop; And wherein the method further comprises: - performing a consistency check on the defined eye model using the provided individual refractive data, and - Resolve any inconsistencies with the help of analytical and / or numerical and / or probabilistic methods.

8. The computer-implemented method of claim 7, wherein the shape and / or the refractive power of the anterior corneal surface (18) is determined.

9. The computer-implemented method of claim 7, wherein any inconsistency is resolved by: Adapting one or more parameters of the eye model, wherein a plurality of parameters of the eye model are adapted and the adaptation is divided between the plurality of parameters of the eye model; and / or adding at least one new parameter to the eye model and defining the new parameter such that the eye model becomes consistent; and / or The target diopter of the ophthalmic lens is adapted.

10. A computer-implemented method for calculating or optimizing an ophthalmic lens for at least one eye of a spectacle wearer, the method comprising: - A computer-implemented method for identifying relevant individual parameters of the at least one eye of the spectacle wearer according to one of the preceding claims; - specifying a first surface (14) and a second surface (16) for an ophthalmic lens to be calculated or to be optimized; - identifying the path of a chief ray (10) entering a model eye (12) through at least one viewpoint (i) of at least one surface (14; 16) of the ophthalmic lens to be calculated or optimized; - evaluating the aberration of a wavefront resulting from a spherical wavefront incident on said first surface of said ophthalmic lens along said principal ray on an evaluation surface, compared to a wavefront converging at a point on the retina of said eye model; - iteratively changing the at least one surface (14; 16) of the ophthalmic lens to be calculated or to be optimized until the evaluated aberration corresponds to a predetermined target aberration.

11. A method for manufacturing an ophthalmic lens, comprising: - calculating or optimizing an ophthalmic lens based on the computer-implemented method for calculating or optimizing an ophthalmic lens according to claim 10; - Manufacturing an ophthalmic lens calculated or optimized in the above manner.

12. A device for identifying relevant individual parameters of at least one eye of a spectacle wearer for calculating or optimizing an ophthalmic lens for said at least one eye of said spectacle wearer, comprising: - at least one data interface for providing individual data of the characteristics of said at least one eye of said spectacles wearer; - a modeling module for modeling and / or constructing an individual eye model by defining a set of parameters of the individual eye model; wherein The modeling module is configured to determine a probability distribution of values ​​of the parameters of the individual eye model based on the individual data, wherein modeling and / or constructing the individual eye model comprises providing an initial probability distribution of the parameters of the eye model; and Wherein the device is configured to determine the parameters of the eye model by using a probabilistic calculation based on the initial probability distribution of the parameters of the eye model and the provided individual data of characteristics of the at least one eye of the glasses wearer.

13. The apparatus of claim 12, wherein: Providing individual data comprises: providing individual refractive data of the at least one eye of the eyeglass wearer; Constructing the individual eye model comprises defining the individual eye model in which at least the following items are defined based on individual measurements and / or standard values ​​of the eye of the spectacle wearer and / or based on the provided individual refractive data: - the shape and / or refractive power of the cornea of ​​the model eye (12); and / or -- the distance from the cornea to the lens; and / or -- parameters of the lens of the model eye; and / or - the distance from the lens to the retina; and / or - the size of the entrance pupil; and / or -- the size and / or position of the physical aperture stop, And wherein the modeling module is configured to perform a consistency check on the defined eye model using the provided individual refractive data and to resolve any inconsistencies by means of analytical methods and / or numerical methods and / or probabilistic methods.

14. The device according to claim 12, wherein the shape and / or the refractive power of the anterior corneal surface (18) is determined.

15. An apparatus for calculating or optimizing an ophthalmic lens for at least one eye of a spectacle wearer, comprising: - a device for identifying relevant individual parameters of the at least one eye of the eyeglass wearer according to any one of claims 12 to 14; - a surface model database for specifying a first surface (14) and a second surface (16) for said ophthalmic lens to be calculated or to be optimized; - a chief ray identification module for identifying the path of a chief ray (10) entering a model eye (12) through at least one viewpoint (i) of at least one surface (14; 16) of the ophthalmic lens to be calculated or optimized; - an evaluation module for evaluating the aberration of a wavefront resulting from a spherical wavefront incident on said first surface of said ophthalmic lens along said principal ray on an evaluation surface, compared to a wavefront converging at a point on the retina of said eye model; as well as - an optimization module for iteratively varying said at least one surface (14; 16) of said ophthalmic lens to be calculated or to be optimized until said aberration evaluated corresponds to a predetermined target aberration.

16. An apparatus for producing an ophthalmic lens, comprising: a calculation or optimization device configured to calculate or optimize the ophthalmic lens based on the computer-implemented method for calculating or optimizing an ophthalmic lens according to claim 10; A processing device is configured to process the ophthalmic lens according to the calculated or optimized result.

17. A computer program product comprising a program code configured to, when loaded and executed on a computer, perform the computer-implemented method for identifying relevant individual parameters of at least one eye of a spectacle wearer according to one of claims 1 to 9 and / or the computer-implemented method for calculating or optimizing an ophthalmic lens according to claim 10.

18. An ophthalmic lens produced by the method according to claim 11 and / or using the apparatus according to claim 16.

19. The ophthalmic lens of claim 18, being a spectacle lens.

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