Classifications

• • A—HUMAN NECESSITIES
  • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
  • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
  • A61B3/00—Apparatus for testing the eyes; Instruments for examining the eyes
  • A61B3/0016—Operational features thereof
• • G—PHYSICS
  • G02—OPTICS
  • G02C—SPECTACLES; SUNGLASSES OR GOGGLES INSOFAR AS THEY HAVE THE SAME FEATURES AS SPECTACLES; CONTACT LENSES
  • G02C7/00—Optical parts
  • G02C7/02—Lenses; Lens systems ; Methods of designing lenses
  • G02C7/024—Methods of designing ophthalmic lenses
  • G02C7/027—Methods of designing ophthalmic lenses considering wearer's parameters
• • A—HUMAN NECESSITIES
  • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
  • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
  • A61B3/00—Apparatus for testing the eyes; Instruments for examining the eyes
  • A61B3/0016—Operational features thereof
  • A61B3/0025—Operational features thereof characterised by electronic signal processing, e.g. eye models
• • A—HUMAN NECESSITIES
  • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
  • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
  • A61B3/00—Apparatus for testing the eyes; Instruments for examining the eyes
  • A61B3/02—Subjective types, i.e. testing apparatus requiring the active assistance of the patient
  • A61B3/028—Subjective types, i.e. testing apparatus requiring the active assistance of the patient for testing visual acuity; for determination of refraction, e.g. phoropters
  • A61B3/04—Trial frames; Sets of lenses for use therewith
• • G—PHYSICS
  • G02—OPTICS
  • G02C—SPECTACLES; SUNGLASSES OR GOGGLES INSOFAR AS THEY HAVE THE SAME FEATURES AS SPECTACLES; CONTACT LENSES
  • G02C7/00—Optical parts
  • G02C7/02—Lenses; Lens systems ; Methods of designing lenses
  • G02C7/024—Methods of designing ophthalmic lenses
  • G02C7/028—Special mathematical design techniques
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
  • G06F17/10—Complex mathematical operations
  • G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F30/00—Computer-aided design [CAD]
  • G06F30/20—Design optimisation, verification or simulation
  • G06F30/27—Design optimisation, verification or simulation using machine learning, e.g. artificial intelligence, neural networks, support vector machines [SVM] or training a model
• • G—PHYSICS
  • G02—OPTICS
  • G02C—SPECTACLES; SUNGLASSES OR GOGGLES INSOFAR AS THEY HAVE THE SAME FEATURES AS SPECTACLES; CONTACT LENSES
  • G02C2202/00—Generic optical aspects applicable to one or more of the subgroups of G02C7/00
  • G02C2202/06—Special ophthalmologic or optometric aspects
• • G—PHYSICS
  • G02—OPTICS
  • G02C—SPECTACLES; SUNGLASSES OR GOGGLES INSOFAR AS THEY HAVE THE SAME FEATURES AS SPECTACLES; CONTACT LENSES
  • G02C2202/00—Generic optical aspects applicable to one or more of the subgroups of G02C7/00
  • G02C2202/22—Correction of higher order and chromatic aberrations, wave front measurement and calculation
• • G—PHYSICS
  • G06—COMPUTING OR CALCULATING; COUNTING
  • G06F—ELECTRIC DIGITAL DATA PROCESSING
  • G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
  • G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]

Definitions

• 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 the at least one eye of the spectacle wearer or a corresponding method, a device and a computer program product for Calculation (optimization) and production of a spectacle lens with the help of a partially individual eye model.
• the at least one eye of the spectacle wearer has an implanted intraocular lens (IOL).
• IOL intraocular lens
• an intraocular lens can be implanted into the at least one eye during an operation.
• the spectacle wearer can in particular be a wearer of an implanted intraocular lens.
• the present invention also relates to a method, a device and a corresponding computer program product for calculating (optimizing) and manufacturing a spectacle lens, in particular for a wearer of an implanted intraocular lens, with the aid of a partially individual eye model.
• each spectacle lens is manufactured in such a way that the best possible correction of a refraction error of the respective eye of the spectacle wearer is achieved for each desired viewing direction or each desired object point.
• a spectacle lens is considered to be fully correcting for a given viewing direction if the values for sphere, cylinder and axis of the wavefront when passing the vertex sphere match the values for sphere, cylinder and axis of the Regulation for the ametropolitan eye match.
• dioptric values in particular sphere, cylinder, axis position - i.e.
• sphero-cylindrical deviations are used for a long (usually infinite) distance and possibly (for multifocal lenses or progressive lenses) an addition or a complete near-range fraction intended for a close distance (e.g. according to DIN 58208).
• object distances that deviate from the norm and that were used in the refraction determination can also be specified. This defines the regulation (in particular the sphere, cylinder, axis position and, if necessary, addition or close fraction) that is transmitted to a lens manufacturer.
• Knowledge of a special or individual anatomy of the respective eye or the actually present refractive index of the ametropic eye are not required for this.
• the spectacle lenses are manufactured in such a way that they cause good correction of ametropia of the eye and only minor imaging errors, especially in the main areas of use, in particular in the central vision areas, while larger imaging errors are permitted in peripheral areas.
• the spectacle lens surfaces or at least one of the spectacle lens surfaces is first calculated in such a way that the desired distribution of the unavoidable imaging errors is effected. This calculation and optimization usually takes place using an iterative variation method by minimizing an objective function.
• a function F with the following functional relationship to the spherical effect S, the amount of the cylindrical effect Z and the axis position of the cylinder a (also referred to as a “SZA” combination) is taken into account and minimized as the objective function: At least the actual refraction deficits of the spherical power SA and the cylindrical power ZA; as well as target values for the refraction deficits of the spherical power SA, SOII and the cylindrical power ZA; SOII are taken into account in the objective function F at the evaluation points / of the spectacle lens.
• the respective Refr disordersdefizite at the respective evaluation points g are preferably with weighting factors: sA and g: zA considered.
• further residuals in particular further variables to be optimized, such as coma and / or spherical aberration and / or prism and / or magnification and / or anamorphic distortion, etc., can be taken into account, which is particularly indicated by the expression “+. .. ”is indicated in the above formula for the objective function F.
• it can contribute to a significant improvement, in particular an individual adjustment of a spectacle lens, if during the optimization of the spectacle lens not only imaging errors up to the second order (sphere, magnitude of the Astigmatism and axial position), but also of a higher order (e.g. coma, three-leaf defect, spherical aberration).
• a higher order e.g. coma, three-leaf defect, spherical aberration
• the local derivatives of the wave fronts are calculated at a suitable position in the beam path in order to compare them there with the desired values that result from the refraction of the spectacle lens wearer.
• the vertex sphere or, for example, the main plane of the eye in the corresponding viewing direction is generally used as the position at which the wave fronts are evaluated. It is assumed here that a spherical wavefront emanates from the object point and propagates to the first lens surface. There the wave front is broken and then propagates to the second lens surface, where it is broken again.
• the last propagation then takes place from the second boundary surface to the vertex sphere (or the main plane of the eye), where the wavefront is compared with predetermined values for the correction of the refraction of the eye of the spectacle wearer.
• the evaluation of the wave front at the vertex sphere is based on an established model of the ametropic eye, in which an ametropia (refraction deficit) is superimposed on a right-sighted basic eye. This has proven to be particularly useful, since further knowledge of the anatomy or optics of the respective eye (eg distribution of the refractive index, eye length, length ametropy and / or refractive index ametropy) is not required for this.
• the refraction deficit is the lack or excess of the refractive power of the optical system of the ametropic eye compared to a right-sighted eye of the same length (residual eye).
• the refractive power of the refraction deficit is in particular approximately equal to the far point refraction with a negative sign.
• the spectacle lens and the refraction deficit together form a telescope system (afocal system).
• the residual eye (defective eye without inserted refraction deficit) is assumed to be right-sighted.
• a spectacle lens is therefore considered to be fully correcting for the distance if its image-side focal point coincides with the far point of the ametropic eye and thus also with the object-side focal point of the refraction deficit.
• IOLs have a changed spherical effect to at least partially compensate for a corneal or length ametropia and / or a changed cylindrical effect to at least partially compensate for a
• the object of the present invention is to improve the calculation or optimization of a spectacle lens, preferably a progressive spectacle lens.
• a spectacle lens preferably a progressive spectacle lens.
• it can be a task to provide patients with specially adapted spectacle lenses after a cataract operation.
• it can be an object to improve the calculation or optimization of a spectacle lens, preferably a progressive spectacle lens, with regard to patients with an implanted intraocular lens.
• 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 with the features specified in the independent claims.
• Preferred embodiments are the subject of the dependent claims.
• a first aspect for solving the problem relates to a computer-implemented one
• the individual data on properties of the at least one eye of the spectacle wearer include, in particular, measurement data of properties of the at least one eye of the spectacle wearer.
• These known individual data can include, for example: refraction data (in particular a current subjective and / or objective refraction and / or an earlier subjective and / or objective refraction, the term earlier referring to a point in time before an operation, for example), the effect and / or shape and / or position (in particular the axial position) of certain refractive surfaces of the eye, the size and / or shape and / or position of the entrance pupil, the refractive index of the refractive media, the refractive index profile in the refractive media, the opacity, etc. .
• Defining a set of parameters of the individual eye model is understood in particular to mean that the eye model is set up or defined via or by a specific set of parameters. In other words, it is established which parameters the eye model should include and / or which parameters should define or characterize the individual eye model.
• the parameters that are defined for the eye model can initially be variables (ie parameters without a specific value). With the aid of the method described in the context of the invention, the parameters or values of the parameters can then can be determined or established (e.g. as the most likely parameters of the individual eye model).
• Eye model providing an initial probability distribution of the parameters of the eye model. Furthermore, a probability distribution (or a probability density) of values of the parameters of the individual eye model is determined on the basis of the initial probability distribution of 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 population or in the population of certain people.
• the method according to the invention is thus based on probability calculation, with Bayesian statistics (also called Bayesian statistics) being able to be used for this purpose.
• Bayesian statistics also called Bayesian statistics
• an individual eye model is constructed and / or a probability distribution of values of the parameters of the eye model is determined using Bayesian statistics.
• determining a probability distribution of values of the parameters of the individual eye model includes calculating a consistency measure, the consistency measure being in particular the product of the probability or probability density of the individual data for given parameters of the individual eye model with the probability or probability density of the parameters of the individual Eye model, especially given background knowledge, is used.
• the background knowledge ie the current state of knowledge when evaluating the data
• Parameters of the individual eye model given the background knowledge can in particular correspond to the “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
• the consistency measure prob (ß i ⁇ d i , l), which is proportional to probissß) prob ⁇ di ⁇ u /), can in particular correspond to the "posterior" of Bayesian statistics.
• the method further comprises the steps:
• the probability distribution (or the probability density) of parameters Li of the ophthalmic lens to be calculated or optimized can in particular be specified as follows:
• the provision of individual data comprises provision of individual refraction data of the at least one eye of the spectacle wearer.
• the construction of an individual eye model comprises a definition of an individual eye model in which at least
• a shape and / or effect of a cornea in particular a corneal front surface (18), of a model eye (12); and or
• the method also includes the following steps:
• the position and size of the aperture diaphragm of the eye can be converted into the position and size of the entrance pupil, and vice versa, since the entrance pupil represents the aperture diaphragm imaged by the cornea. It can therefore be sufficient in particular if in this case the position or the size of either the aperture diaphragm or the entrance pupil is used as an (possibly additional) parameter of the eye model.
• a computer-implemented method for determining relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of a spectacle lens for the at least one eye of the spectacle wearer, wherein the at least one eye of the spectacle wearer has an implanted intraocular lens can in particular comprise the following steps: Providing intraocular lens data of the intraocular lens implanted in the eye of the spectacle wearer;
• a shape and / or effect of a cornea in particular a corneal front surface, of a model eye
• the setting of the parameters of the lens of the model eye based on the intraocular lens data provided.
• at least the setting of the lens-retinal distance takes place by calculation.
• the intraocular lens can in particular be an aphakic intraocular lens or a phakic intraocular lens.
• An aphakic intraocular lens replaces the natural eye lens, i.e. the at least one eye of the spectacle wearer only has the intraocular lens after the operation (but no longer the natural eye lens).
• a phakic intraocular lens is inserted or implanted in 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 the intraocular lens and the natural eye lens after the operation.
• the term “lens of the model eye” can refer not only to a single real lens (for example the natural eye lens or an intraocular lens), but also to a lens system.
• the lens system can have one or more lenses, in particular two lenses (namely the natural eye lens and also an intraocular lens).
• the “lens of the model eye” can be a lens, in particular a model-based or virtual lens, which describes the natural eye lens or an (aphakic) intraocular lens.
• the “lens of the model eye” can also be a, in particular model-based or virtual, lens system which describes the natural eye lens and additionally a (phakic) intraocular lens.
• the “lens of the model eye” can be understood as a thick lens of the model eye (or the “lens of the model eye” can be a thick lens of the model eye), which combines both the properties of the natural eye lens and the properties of an additional intraocular lens / or describes.
• the term “lens of the model eye” is understood to mean a “lens system of the model eye”.
• the term “lens-retinal distance” is understood to mean, in particular, a “lens system-retinal distance”.
• a “lens system-retinal distance” For the sake of simplicity, however, only the terms “lens of the model eye” and “lens-retinal distance” are used below.
• a phakic intraocular lens can, for example, be considered as a separate or additional element in the eye model.
• the effect of a phakic intraocular lens can influence the effect (or one of the surfaces or both surfaces) of the cornea.
• the intraocular lens can be, for example, an anterior chamber lens.
• the effect of a phakic intraocular lens can be incorporated into the effect (or in one of the surfaces or in both surfaces) of the natural eye lens.
• the intraocular lens can be a posterior chamber lens, for example. If the intraocular lens is introduced as an additional element, its properties (in particular effect, areas and / or thickness) can be taken into account as additional parameters of the eye model in the eye model.
• the position of this additional lens can either be established as a known position or taken into account as an additional parameter (eg measured or model-based) in the eye model.
• the fixed position can, for example (in the case of an anterior chamber lens) directly or with a certain distance behind the cornea, or e.g. (in the case of a posterior chamber lens) directly or at a certain distance in front of the eye lens.
• the ophthalmic lens or the spectacle lens can be optimized according to one of the methods described in WO 2013/104548 A1 or DE 10 2017 007 974 A1 by calculating into the eye.
• the eye model required for this is assigned individual values as described in DE 10 2017 007 975 A1 or WO 2018/138140 A2, the known properties of the IOL, e.g. from the manufacturer's information, being included for the lens of the eye model.
• the intraocular lens data includes data on properties of the implanted intraocular lens. These can be specified directly when ordering or obtained from a database by specifying the type or the individual serial number.
• model-based values used in DE 10 2017 007 975 A1 and WO 2018/138140 A2 are not necessarily in accordance with the properties of the lens actually implanted. This can be the case, for example, if a length myopia is at least partially compensated for by an IOL with less refraction. In this case, the procedure described in DE 10 2017 007 975 A1 or WO 2018/138140 A2 would result in too short an eye length.
• the eye model preferably comprises various components such as cornea, lens, retina etc. and parameters or a parameter set of these components.
• the parameters of the eye model are, for example, the shape of the anterior corneal surface of the model eye, the corneal-lens distance, the parameters of the lens of the model eye, the lens-retinal distance, etc.
• one of the formalisms described in DE 10 2017 007 975 A1 or WO 2018/138140 A2 consisting of the defocus term of the overall eye, the defocus term of the corneal surface, the corneal-lens distance (hereinafter DCL or da.) And the IOL data of the lens-retina distance (hereinafter DLR or di_R) calculated.
• the term defocus term is used for the value of the symmetrical second term (c2, o) according to the decomposition Zernike used the refractive effect or the surface of an optical element.
• - Defocus mode of the total eye The result of an aberrometric measurement or an autorefraction, a subjective refraction or another determination (e.g. retinoscopy) can be used here.
• a so-called "optimized refraction" i.e. the result of a calculation from several components (e.g. subjective refraction and aberrometry) can be used. Examples of such an optimization are compiled in DE 10 2017 007 975 A1 and WO 2018/138140 A2.
• the individual refraction data of the at least one eye of the spectacle wearer include a defocus or defocus term of the (overall) eye.
• - Defocus term of the cornea This can e.g. be taken from a topography or topometry measurement or it can be assumed based on a model.
• - Corneal-lens distance This can be determined with a measurement (e.g. Scheimpflug image or OCT) or assumed based on a model.
• another variable preferably a term of the second order such as the wrung, can also be used in the main section the highest or lowest refractive index or in a meridian with a defined position (e.g. horizontal or vertical).
• the eye model can be based on the astigmatism (magnitude and axis, or the other second-order quantities according to the previous paragraph) as well as higher-order components (see DE 102017 007 975 A1 or WO 2018/138140 A2) of the overall eye and the components can be added. These can be taken, for example, from the IOL data, measurements (e.g. topography / topometry or aberrometry / auto refraction), model assumptions and / or calculated values (e.g. optimized refraction).
• measurements e.g. topography / topometry or aberrometry / auto refraction
• model assumptions e.g. optimized refraction
• IOLs Often information about asphericity or higher order aberrations is given for IOLs. These can be used when covering the eye model with higher-order aberrations.
• individual refraction data of the at least one eye of the spectacle wearer are provided. These individual refraction data are based on an individual refraction determination.
• the refraction data include at least the spherical and astigmatic ametropia of the eye.
• the acquired refraction data also describe higher-order imaging errors (HOA).
• the refraction data (in particular if they include higher-order imaging errors, also called aberrometric data) are preferably measured, for example, by the optician using an autorefractometer or an aberrometer (objective refraction data). Alternatively or additionally, a subjectively determined refraction can also be used.
• the refraction data are then preferably transmitted to a lens manufacturer and / or made available to a calculation or optimization program. They are thus available to be recorded for the method according to the invention, in particular to be read out and / or received in digital form.
• the provision of the individual refraction data preferably includes provision or determination of the vergence matrix S M of the ametropia of the at least one eye.
• the vergence matrix describes a wavefront in front of the eye of the light exiting from a point on the retina or converging in a point on the retina.
• such refraction data can be determined, for example, by using a laser to illuminate a point on the retina of the spectacle wearer, from which point light then propagates.
• the wavefront can change when passing through the eye, in particular at optical interfaces in the eye (eg the lens of the eye and / or the cornea).
• the refraction data of the eye can thus be measured by measuring the wavefront in front of the eye.
• the method can include the definition of an individual eye model, which individually defines at least certain specifications about geometric and optical properties of a model eye.
• an individual eye model which individually defines at least certain specifications about geometric and optical properties of a model eye.
• parameters of the lens of the model eye for example, either geometric parameters (shape of the lens surfaces and their spacing) and preferably material parameters (for example refractive indices of the individual Components of the model eye) can be completely defined so that they at least partially define an optical effect of the lens.
• parameters can also be specified as lens parameters that directly describe the optical effect of the lens of the model eye.
• the shape of the front surface of the cornea is usually measured, but alternatively or additionally the effect of the cornea as a whole (no differentiation between front and back surface) can be specified.
• a corneal posterior surface and / or a corneal thickness can possibly also be specified.
• the parameters of the lens of the model eye can be determined (exclusively) on the basis of the intraocular lens data provided.
• the parameters of the lens of the model eye correspond to the individual intraocular lens data provided.
• the intraocular lens data provided are set as the parameters of the lens of the model eye.
• the refraction of the eye is determined by the optical system consisting of the front surface of the cornea, the eye lens and the retina.
• the refraction of light on the front surface of the cornea and the refractive power of the eye lens preferably including the spherical and astigmatic aberrations and higher order aberrations
• the individual sizes (parameters) of the model eye are determined accordingly on the basis of the intraocular lens data provided and also on the basis of individual measured values for the eye of the spectacle wearer and / or on the basis of standard values and / or on the basis of the individual refraction data provided.
• some of the parameters for example the topography of the anterior corneal surface and / or the anterior chamber depth and / or at least a curvature of a lens surface, etc.
• Other values can also be derived from values of, especially if the parameters involved are parameters whose individual measurement is very complex Standard models for a human eye can be adopted.
• not all (geometric) parameters of the model eye have to be specified from individual measurements or from standard models.
• an individual adaptation is carried out for one or more (free) parameters by calculation taking into account the specified parameters in such a way that the then resulting model eye has the individual refraction data provided.
• a corresponding number of (free) parameters of the eye model can be individually adapted (fitted).
• at least the lens-retinal distance can be determined by calculation within the scope of the present invention.
• a first surface and a second surface of the spectacle lens are specified in particular as starting surfaces with a predetermined (individual) position relative to the model eye.
• only one of the two surfaces is optimized.
• This is preferably the rear surface of the spectacle lens.
• a corresponding starting area is preferably specified for both the front surface and the rear surface of the spectacle lens.
• only one area is iteratively changed or optimized during the optimization process.
• the other surface of the spectacle lens can be, for example, a simple spherical or rotationally symmetrical aspherical surface. However, it is also possible to optimize both surfaces.
• the method for calculating or optimizing includes determining the course of a main ray through at least one visual point () of at least one surface of the spectacle lens to be calculated or optimized into the model eye.
• the main beam describes the geometric beam path starting from an object point through the two spectacle lens surfaces, the front surface of the cornea and the lens of the model eye, preferably up to the retina of the model eye.
• the method for calculating or optimizing can evaluate an aberration of a wave front resulting along the main ray from a spherical wave front impinging on the first surface of the spectacle lens on an evaluation surface, in particular in front of or within the model eye, compared to one at a point on the retina of the eye model include converging wavefront (reference light).
• a spherical wave front (wo) impinging on the first surface (front surface) of the spectacle lens along the main ray is specified for this purpose.
• This spherical wave front describes the light emanating from an object point (object light).
• the curvature of the spherical wave front when it hits the first surface of the spectacle lens corresponds to the reciprocal value of the object distance.
• the method thus preferably includes specifying an object distance model which assigns an object distance to each viewing direction or to each visual point of the at least one surface of the spectacle lens to be optimized. This preferably describes the individual usage situation in which the spectacle lens to be manufactured is to be used.
• the wave front impinging on the spectacle lens is now refracted, preferably for the first time, on the front surface of the spectacle lens.
• the wavefront then propagates along the main ray within the spectacle lens from the front surface to the rear surface, where it is refracted for the second time.
• the wavefront transmitted through the spectacle lens now preferably propagates along the main beam as far as the anterior corneal surface of the eye, where it is preferably refracted again.
• the wavefront is preferably also refracted there again in order to finally propagate preferably to the retina of the eye.
• each refraction process also leads to a deformation of the wave front.
• the wavefront should preferably leave the lens of the eye as a converging spherical wavefront, the curvature of which corresponds exactly to the reciprocal of the distance to the retina.
• a comparison of the wavefront exiting from the object point with a wavefront (reference light) converging (in the ideal case of a perfect image) at a point on the retina thus allows the evaluation of a mismatch.
• This comparison and thus the evaluation of the wavefront of the object light in the individual eye model can take place at different points along the course of the main ray, in particular between the second surface of the optimizing spectacle lens and the retina.
• the evaluation area can thus lie at different positions, in particular between the second area of the spectacle lens and the retina.
• the refraction and propagation of the light exiting from the object point is calculated accordingly in the individual eye model, preferably for each visual point.
• the evaluation area can either relate to the actual beam path or to a virtual beam path such as is used, for example, to construct the exit pupil AP.
• the light In the case of the virtual beam path, the light must be propagated back through the rear surface of the eye lens after refraction up to a desired level (preferably up to the level of the AP), whereby the refractive index used must correspond to the medium of the vitreous body and not the eye lens.
• the resulting wavefront of the object light can preferably simply be spherical wavefront of the reference light are compared.
• the method thus preferably comprises specifying a spherical wavefront impinging on the first surface of the spectacle lens, determining a wavefront resulting from the spherical wavefront in the at least due to the action of at least the first and second surfaces of the spectacle lens, the corneal front surface and the lens of the model eye an eye, and an evaluation of the aberration of the resulting wavefront in comparison to a spherical wavefront converging on the retina.
• an evaluation area is to be provided within the lens or between the lens of the model eye and the spectacle lens to be calculated or optimized, a reverse propagation from a point on the retina through the individual components of the model eye to the evaluation area is simulated as reference light, to make a comparison of the object light with the reference light.
• the at least one surface of the spectacle lens to be calculated or optimized is iteratively varied until an aberration of the resulting wavefront corresponds to a specified target aberration, i.e. in particular by specified values of the aberration from the wavefront of the reference light (e.g. a spherical wavefront whose center of curvature lies on the retina) deviates.
• the wave front of the reference light is also referred to here as a reference wave front.
• the method preferably comprises minimizing an objective function F, in particular analogously to the objective function already described at the beginning. Further preferred objective functions, in particular when taking higher-order imaging errors into account, are also described further below. If a propagation of the object light up to the retina is calculated, an evaluation can be carried out there instead of a comparison of wavefront parameters for example by means of a so-called “point spread function”.
• the individual calculation of the eye model in particular the lens-retinal distance (vitreous body length) can already be carried out, for example, in an aberrometer or a topograph with a correspondingly expanded functionality.
• the length of an eye is preferably determined individually.
• the measured and / or calculated vitreous body length and / or the determined (measured and / or calculated) eye length is particularly preferably displayed to the user.
• a corresponding device in particular an aberrometer or topograph
• the individual intraocular lens data comprise at least a defocus of the front surface of the intraocular lens, a defocus of the rear surface of the intraocular lens and a thickness of the intraocular lens.
• the individual intraocular lens data include at least a defocus of the refractive power of the intraocular lens or an optical effect of the intraocular lens.
• the intraocular lens data can therefore either be the defocus of the refractive surfaces (front and rear surfaces) and a propagation length (thickness of the lens, hereinafter DLL) or the defocus of the refractive power of the IOL. While a model based on the areas and the distance can deliver more precise results during optimization, optimization requires more calculation steps (refraction-propagation-refraction instead of just refraction) and correspondingly detailed information about the IOL, which may not be available.
• the individual intraocular lens data can include information, in particular a value, relating to a so-called A constant.
• the A constant is an individual lens constant, in particular a type of correction factor that can appear in IOL calculation formulas with different names.
• the intraocular lens is represented by this constant in the various calculation formulas. Since all IOL constants can be converted into one another, there is in principle only one constant (number) that should characterize a given intraocular lens in the entire available strength range, regardless of form factor, optic material, IOL diameter, etc. By using A - or IOL constants, the effects of individual surgical technology, the measurement and surgical equipment used and individual physiological differences in the operated patient cohort on the IOL calculation are minimized.
• the A constant particularly reflects any adjustments in the power and can be part of the lens passport or IOL passport.
• the individual intraocular lens data are based on type or serial number information, in particular provided by the manufacturers of the IOL. This information can, for example, be given directly when ordering or obtained from a database.
• the method further comprises the steps:
• the procedure according to the invention provides a consistent model with regard to the defocus (or the other variables used when calculating the eye length).
• the consistency of the model is no longer guaranteed even with other second-order quantities (e.g. amount and direction of the astigmatism).
• the eye model can be overdetermined and consequently no longer consistent.
• this can be due to manufacturing inaccuracies of the IOL and measurement inaccuracies that can occur, for example, in the topography or topometry, aberrometry or autorefraction and / or the measurement of the anterior chamber depth.
• inconsistencies can in principle arise if the subjective or optimized refraction does not correspond to the objective optical effect of the overall eye.
• a consistent eye model is understood to mean an eye model in which an incident wave front, which corresponds to the aberrations of the overall eye, converges at a point on the retina. This is synonymous with the fact that the wavefront emanating from a point of light on the retina corresponds to the aberrations of the entire eye after it has passed through the entire eye.
• a consistency check can in particular be carried out using probabilistic methods.
• a consistency measure could be given as a probability.
• Any inconsistencies could be resolved, for example, by determining a maximum of the probability.
• Carrying out a consistency check and resolving any inconsistencies improves, in particular, the calculation or optimization of spectacle lenses that are intended for a patient with IOLs.
• carrying out a consistency check and resolving any inconsistencies are advantageous even with spectacle lenses that are not specifically intended for a patient with IOLs.
• the present invention therefore generally offers a computer-implemented method for determining relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of a spectacle lens for the at least one eye of the spectacle wearer, comprising the steps:
• a shape and / or effect of a cornea in particular one
• a size and / or position of a physical aperture stop can be determined based on individual measured values for the eye of the spectacle wearer and / or standard values and / or based on the individual refraction data provided,
• the "definition of an individual eye model” can mean setting model parameters to specific values. Additionally or alternatively, the “definition of an individual eye model” can also at least be a definition a consistency measure (or at least a probability). In particular, there can be a large number of values of the model parameters. For every
• a consistency measure or a probability can be determined by combining these values.
• consistency measures or probabilities can be specified using Bayes' method.
• the term “calculate” in the context of the present invention can not only include calculation using an equation, but also steps that are carried out in a statistical method, such as the selection of values on the basis of statistical considerations or probabilities.
• a statistical method such as the selection of values on the basis of statistical considerations or probabilities.
• the term “calculating” in the context of the present invention can thus in particular also include the selection of probable or most probable values of one or more parameters and / or the definition of an optimization problem.
• the term “calculate” also includes a selection, determination and / or definition in the context of a statistical method, e.g. in the context of or using the Bayesian method.
• the term “calculation” can in particular also include optimization.
• the computer-implemented method can also include the definition or construction of a consistent eye model, in particular using the Bayesian method and / or a maximum likelihood method.
• the individual eye model used or to be determined is a consistent eye model, the consistency being enabled or established by statistical or probabilistic methods, in particular using the Bayesian method and / or a maximum likelihood method.
• this aspect provides a computer-implemented method and a corresponding device for executing such a method for determining relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of a spectacle lens for the at least one eye of the spectacle wearer, comprising one or more of the following steps or functions:
• a shape and / or effect of a cornea in particular one
• Corneal anterior surface, of a model eye Corneal anterior surface, of a model eye.
• a size and / or position of a physical aperture stop can be determined in particular on the basis of individual measured values for the eye of the spectacle wearer and / or of standard values and / or on the basis of the individual refraction data provided,
• one or more of the information or parameters and / or at least partially the provided individual refraction data is or are initially determined in the form of a probability distribution
• the determination of the individual eye model involves determining the model eye by determining values for information or parameters within the defined probability distribution by a probabilistic method.
• a model eye is first created by specifying parameter values in order to then modify the model eye on the basis of a consistency check using a probabilistic method if necessary so that the eye model is consistent
• instead of possibly inconsistent parameter values started with a probability distribution for at least one parameter in order to then consistently determine the most likely parameter value and thus the most likely model eye by means of a probabilistic method.
• Parameters of the probability distribution such as mean values and / or standard deviations, can in particular be determined on the basis of individual measured values for the eye of the spectacle wearer and / or standard values and / or on the basis of the individual refraction data provided. Further details and specific exemplary embodiments of such methods are described below.
• the simplest possibility is to transfer the deviations to an element or a component of the eye model (e.g. cornea, front surface of the IOL, rear surface of the IOL, refractive effect of the IOL).
• the rear surface of the IOL could (contrary to the manufacturer's instructions) be chosen so that the model is consistent.
• the astigmatism in particular according to magnitude and direction (for example according to the method described in DE 10 2017 007 975 A1 or WO 2018/138140 A2) can be determined so that the eye model becomes consistent in terms of astigmatism.
• components of a higher order of this area can, for example, be specified in subsequent steps so that the eye model is also consistent in these components.
• the corneal surface could be adapted accordingly. This is particularly useful if there is only model-based information from the cornea or no information on astigmatism or higher-order components is available on the basis of topometric measurements.
• any inconsistencies are resolved by adapting or redefining one or more parameters of the eye model. A number of parameters of the eye model are preferably adapted and the adaptation is divided among the several parameters of the eye model.
• known deviations can be divided into several elements or components and / or several parameters of the eye model, for example the cornea, the front surface of the IOL, the rear surface of the IOL, and / or the refractive effect of the IOL.
• fixed or predetermined factors or proportions can be assumed, for example 33% on the cornea and 67% on the lens.
• a physiologically based distribution can also be used.
• a further or new parameter can be added to the eye model and specified in such a way that the eye model becomes consistent.
• the shape of the back surface of the cornea of a model eye can be such a further parameter.
• the axis position and / or a lateral shift or tilt can be selected so that the resulting astigmatism of the model eye corresponds to the specification (as best as possible).
• the lengths DCL, DLL and / or DLR can be adapted. If necessary, the effect of the overall eye can also be adjusted. The target effect of the spectacle lens can be changed accordingly in order to make the eye model consistent.
• the parameters of the eye model are determined with the aid of probabilistic methods, i.e. using probability calculations.
• probabilistic methods i.e. using probability calculations.
• a Bayesian statistic and / or a maximum likelihood algorithm can be used.
• Input parameters parameters of known parameters
• output parameters parameters of the eye model
• an initial distribution of parameters of the eye model and individual data on properties of the at least one eye are provided, the parameters of the individual eye model being determined on the basis of the initial distribution of parameters of the eye model and the individual data using probability calculations.
• an initial eye model and individual data on properties of the at least one eye are provided, the parameters of the individual eye model being determined on the basis of the initial eye model and the individual data using probability calculations.
• an eye length of the model eye is determined taking into account the measured and / or calculated lens-retinal distance.
• the determined eye length is preferably displayed on a display device or display.
• the method described above relates in particular to the case that properties or data of an implanted intraocular lens, that is to say the intraocular lens data, are known. However, if these data are not known, an alternative approach is proposed within the scope of this invention, which is described below. According to this alternative approach to the present Invention, ie in the absence of direct knowledge of the properties of the implanted
• the properties of the implanted IOLs are deduced from measurements on the patient.
• An alternative approach to solving the problem concerns a computer-implemented method for determining relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of a spectacle lens for the at least one Eye of the spectacle wearer, an intraocular lens being implanted in the at least one eye of the spectacle wearer as part of an operation, comprising the steps:
• a shape and / or effect of a cornea in particular one
• the lens-retinal distance of the post-OP eye model is determined by the determined lens-retinal distance of the eye of the spectacle wearer.
• a computer-implemented method for determining relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of a spectacle lens for the at least one eye of the spectacle wearer, with an intraocular lens being implanted in the at least one eye of the spectacle wearer during an operation are provided, wherein the method comprises in particular the following steps:
• a shape and / or effect of a cornea in particular a corneal front surface, of a model eye
• the model eye has the individual refraction data provided.
• a device for determining relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of 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 can be provided, the Device in particular comprises: at least one data interface for providing individual
• a modeling module for determining an individual eye model which at least
• a shape and / or effect of a cornea in particular a corneal front surface (18), of a model eye;
• the data for the visual acuity correction of the at least one eye having the intraocular lens comprise (in particular individual) intraocular lens data.
• the parameters of the individual eye model are set on the basis of intraocular lens data and furthermore on the basis of individual measured values for the eye of the spectacle wearer and / or standard values and / or on the basis of the individual refraction data provided so that the model eye has the individual refraction data provided, the parameters of the lens of the model eye being determined using the intraocular lens data.
• a lens-retinal distance of the eye of the spectacle wearer is determined, and the parameters of the individual eye model are determined based on the determined lens-retinal distance and furthermore on the basis of individual measured values for the eye of the spectacle wearer and / or of standard values and / or based on the provided individual Refraction data that the model eye has the provided individual refraction data, the lens-retinal distance of the model eye being determined by the determined lens-retinal distance of the eye of the spectacle wearer.
• the data for the visual acuity correction of the at least one eye having the intraocular lens comprise a determined lens-retinal distance.
• the data for the visual acuity correction of the at least one eye having the intraocular lens can include a determined lens-retinal distance and / or intraocular lens data.
• a computer-implemented method for determining relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of a spectacle lens for the at least one eye of the spectacle wearer, with an intraocular lens in the at least an eye of the spectacle wearer has been implanted or the at least one eye of the spectacle wearer has an intraocular lens (in particular instead of or in addition to the natural eye lens).
• the method can in particular comprise the following steps:
• a shape and / or effect of a cornea in particular one
• a lens-retinal distance of the eye of the spectacle wearer is determined and the setting of the parameters of the individual eye model based on the determined lens-retinal distance and furthermore on the basis of individual measured values for the eye of the spectacle wearer and / or standard values and / or The individual refraction data provided are used to ensure that the model eye has the individual refraction data provided, the lens-retinal distance of the model eye being determined by the determined lens-retinal distance of the wearer's eye.
• the term surgery is generally abbreviated to OP.
• post-op refers to a situation after the operation, while the term “pre-op” refers to a situation before the operation.
• the operation is a cataract operation in which the natural lens of the eye is replaced by an intraocular lens.
• it can also be an operation on an aphakic eye (eye without a lens) in which an intraocular lens is inserted or implanted in the patient's eye.
• the intraocular lens can therefore in particular represent a replacement for the natural eye lens.
• the natural lens of the wearer's eye was replaced by an intraocular lens during the operation.
• the spectacle lens is preferably optimized according to one of the methods described in WO 2013/104548 A1 or DE 10 2017 007 974 A1 by performing calculations into the eye.
• the eye model required for this is assigned individual values analogously to the description in DE 10 2017 007 975 A1 or WO 2018/138140 A2.
• no information about the IOL is available and model-based values are not necessarily consistent with the actual lens implanted.
• This can be the case, for example, if a length myopia is at least partially compensated for by an IOL with less refraction.
• the eye length would be assumed to be too short according to the procedure described in DE 10 2017 007 975 A1 or WO 2018/138140 A2. Therefore, starting with Data that correspond to a situation in which the original lens was in the eye, the eye length or a lens-retinal distance, as described in DE 10 2017 007 975 A1 and WO 2018/138140 A2, is calculated.
• the other parameters ie the parameters of the eye lens, in this case the implanted IOL
• the surface the cornea and the distance between the cornea and the lens are determined in such a way that the effect of this eye model corresponds to the imaging errors of the entire eye.
• a second-order term e.g. defocus
• the following data are preferably used:
• - Defocus of the entire eye before replacing the lens This can be the result of an aberrometric measurement or an autorefraction, a subjective refraction or another determination (e.g. retinoscopy) before the procedure.
• a so-called "optimized refraction" i.e. the result of a calculation from several components (e.g. subjective refraction and aberrometry) can be used. Examples of such an optimization are compiled in DE 10 2017 007 975 A1 and WO 2018/138140 A2.
• the defocus of the computer can be used by virtue of older glasses worn before the procedure;
• the data of the last two points can come either from measurements before the procedure (operation) or after the procedure.
• the use of data obtained after the procedure is particularly useful if no corresponding measurements have been carried out before the procedure.
• - Image errors of the entire eye after replacing the lens can be the result of an aberrometric measurement or an autorefraction, a subjective refraction or another determination (e.g. skiascopy) after the procedure.
• a so-called "optimized refraction" i.e. the result of a calculation from several components (e.g. subjective refraction and aberrometry) can be used. Examples of such an optimization are compiled in DE 10 2017 007 975 A1 and WO 2018/138140 A2.
• the data of the last two points can come either from measurements before the procedure (operation) or after the procedure.
• the use of data obtained before the procedure is particularly useful if no corresponding measurements have been carried out after the procedure.
• the provision of the individual intraocular lens data can in particular comprise the following steps:
• the determination of a lens-retina distance or an eye length of the eye of the spectacle wearer can be done, for example, by a direct measurement.
• the method further comprises providing individual pre-op refraction data of the at least one eye Glasses wearer, determining a lens-retinal distance or a
• Eye length of the eye of the spectacle wearer based on an individual pre-op eye model using the provided individual pre-op refraction data.
• a shape and / or effect of a cornea in particular a front surface of the cornea, of a model eye of the pre-OP eye model;
• a lens-retinal distance of the model eye of the pre-op eye model based on individual measured values for the eye of the spectacle wearer (determined before or after the operation) and / or from standard values and / or on the basis of the individual pre-op refraction data provided stipulated that the model eye has the provided individual pre-op refraction data, wherein at least the stipulation of the lens-retinal distance is preferably carried out by measuring and / or calculating.
• the anterior corneal surface is preferably measured individually and the eye lens of the individual pre-op eye model is calculated accordingly in order to meet the individually determined pre-op refraction data.
• the front surface of the cornea (or its curvature) is measured individually along the main slices (topometry).
• the topography of the anterior corneal surface i.e. the complete description of the surface
• the corneal-lens distance is established on the basis of individual measured values for the corneal-lens distance.
• Specifying the parameters of the lens of the pre-op model eye particularly preferably includes setting the following parameters:
• the lens thickness and the shape of the rear surface of the lens are determined on the basis of predetermined values (standard values, for example from the specialist literature), with the determination of the shape of the front surface of the lens further preferably comprising:
• determining the shape of the lens front surface comprises:
• the definition of the lens thickness and the shape of the rear surface of the lens also take place on the basis of standard values, and even more preferably the definition of the shape of the front surface of the lens includes:
• the definition of the lens parameters can include a definition of an optical effect of the lens.
• at least one position of at least one main plane and a spherical effect (or at least one focal length) of the lens of the model eye are established.
• a cylindrical effect is also particularly preferred (Amount and axis position) of the lens of the model eye.
• optical imaging errors of higher orders of the lens of the model eye can also be determined.
• Another independent aspect for solving the problem 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:
• Another independent aspect for solving the problem 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:
• Viewpoint of at least one surface of the spectacle lens to be calculated or optimized into the model eye
• the evaluation area is preferably located between the anterior corneal surface and the retina. In a particularly preferred embodiment, the evaluation area lies between the lens and the retina of the model eye. In another particularly preferred embodiment, the evaluation area lies on the exit pupil (AP) of the model eye. The exit pupil can lie in front of the rear surface of the lens of the model eye. With these positions, a particularly precise, individual adaptation of the spectacle lens can be achieved.
• Another independent aspect for solving the problem relates to a method for producing an ophthalmic lens (in particular a spectacle lens) comprising:
• Another independent aspect for solving the problem relates to a device for determining relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of an ophthalmic lens for the at least one eye of the spectacle wearer, comprising:
• At least one data interface for providing individual data on properties of the at least one eye of the spectacle wearer; and 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;
• the modeling module is designed to determine a probability distribution of values of the parameters of the individual eye model on the basis of the individual data, in particular using probability calculation.
• providing individual data comprises providing individual refraction data of the at least one eye of the spectacle wearer.
• construction of an individual eye model comprises a definition of an individual eye model in which at least
• a shape and / or effect of a cornea in particular one
• a size and / or position of a physical aperture stop can be determined in particular on the basis of individual measured values for the eye of the spectacle wearer and / or of standard values and / or on the basis of the individual refraction data provided.
• the modeling module is also designed to carry out a consistency check of the established eye model with the provided individual refraction data and to resolve any inconsistencies, in particular with the aid of analytical and / or probabilistic methods.
• the invention thus offers a device for determining 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 the at least one eye of the spectacle wearer, comprising: at least one data interface for providing individual
• a modeling module for defining an individual eye model which in particular at least
• a shape and / or effect of a cornea in particular one
• the modeling module is designed to carry out a consistency check of the specified eye model with the provided individual refraction data and to resolve any inconsistencies, in particular with the aid of analytical and / or probabilistic methods.
• the invention offers a device for determining relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of a spectacle lens for the at least one eye of the spectacle wearer, with the at least one eye of the spectacle wearer (in particular instead of or in addition to the natural eye lens) having an implanted one Having intraocular lens comprising:
• At least one data interface for providing individual intraocular lens data of the intraocular lens implanted in the eye of the spectacle wearer and for providing individual refraction data of the at least one eye of the spectacle wearer;
• a modeling module for defining an individual eye model, which in particular at least a shape and / or effect of a cornea, in particular a corneal front surface, of a model eye;
• the lens-retinal distance is preferably established by measuring and / or calculating.
• the modeling module is preferably designed to determine an eye length of the model eye taking into account the measured and / or calculated lens-retinal distance.
• the device preferably also comprises a display device for displaying the measured and / or calculated lens-retinal distance and / or the determined eye length.
• the device is particularly preferably designed as an aberrometer and / or as a topograph.
• the modeling module is preferably designed to carry out a consistency check of the specified eye model, in particular the specified pre-OP eye model and / or the specified post-OP eye model. Furthermore, the modeling module is preferably designed to resolve any inconsistencies, in particular with the aid of analytical and / or probabilistic methods (probability calculation, e.g. using Bayesian statistics and / or a maximum likelihood approach).
• the invention offers a device for determining relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of a spectacle lens for the at least one eye of the spectacle wearer, wherein an intraocular lens was implanted in the at least one eye of the spectacle wearer as part of an operation, comprising:
• At least one data interface for providing individual post-op refraction data for the at least one eye of the spectacle wearer
• a modeling module for determining a lens-retinal distance of the eye of the spectacle wearer and for establishing an individual post-op eye model, which in particular at least
• a shape and / or effect of a cornea in particular a front surface of the cornea, of a model eye of the post-OP eye model;
• the lens-retinal distance of the model eye of the post-op eye model being determined by the determined lens-retinal distance of the wearer's eye.
• Another independent aspect for solving the problem relates to a device for calculating or optimizing a spectacle lens for at least one eye of a spectacle wearer comprising:
• a device for determining relevant individual parameters of the at least one eye of the spectacle wearer
• a surface model database for specifying a first surface and a second surface for the spectacle lens to be calculated or optimized; a main ray determination module for determining the course of a main ray through at least one visual point of at least one surface of the spectacle lens to be calculated or optimized into the model eye;
• an evaluation module for evaluating an aberration of a wave front resulting along the main ray from a spherical wave front impinging on the first surface of the spectacle lens on an evaluation surface in comparison with a wave front converging at a point on the retina of the eye model;
• an optimization module for iteratively varying the at least one area of the spectacle lens to be calculated or optimized until the evaluated aberration corresponds to a predetermined nominal aberration.
• Another independent aspect for solving the problem relates to a device for producing a spectacle lens, comprising:
• Calculation or optimization means which are designed to calculate or optimize the spectacle lens according to a method according to the invention for calculating or optimizing a spectacle lens
• Processing means which are designed to process the spectacle lens in accordance with the result of the calculation or optimization.
• the device for producing a spectacle lens can be designed in one piece or as an independent machine, ie all components of the device (in particular the calculation or optimization means and the processing means) can be part of one and the same system or one and the same machine. In a preferred embodiment, however, the device for producing a spectacle lens is not designed in one piece, but is implemented by different (in particular independent) systems or machines.
• the calculation or optimization means can be implemented as a first system (in particular comprising a computer) and the processing means as a second system (in particular a machine comprising the processing means).
• the various systems can be located at different locations, ie they can be spatially separated from one another. For example, a or several systems are in the front end and one or more other systems are in the back end.
• the individual systems can, for example, be located at different company locations or operated by different companies.
• the individual systems in particular have communication means in order to exchange data with one another (for example via a data carrier).
• the various systems of the device can preferably communicate with one another directly, in particular via a network (for example via a local network and / or via the Internet).
• a device described herein can be designed as a system.
• the system can in particular comprise a plurality of devices (possibly locally separated) which are designed to carry out individual method steps of a corresponding method.
• the invention offers a computer program product or a computer program product, in particular in the form of a storage medium or a data stream that contains program code that is designed when loaded and executed on a computer, a method according to the invention for determining relevant individual parameters of at least one eye of a spectacle wearer and / or to carry out a method according to the invention for calculating or optimizing a spectacle lens.
• a Com puterprogram m product is to be understood as a program stored on a data carrier.
• the program code is stored on a data carrier.
• the computer program product comprises computer-readable instructions which, when loaded into a memory of a computer and executed by the computer, cause the computer to carry out a method according to the invention.
• the invention offers a spectacle lens which was produced by a method according to the invention and / or by means of a device according to the invention.
• the invention offers a use of a spectacle lens manufactured by the manufacturing method according to the present invention, in particular in a preferred embodiment, in a predetermined average or individual position of use of the spectacle lens in front of the eyes of a particular spectacle wearer for correcting ametropia of the spectacle wearer.
• the invention can in particular comprise one or more of the following aspects:
• the spectacle lens as a product
• a method, a device and / or a system for recording the relevant data e.g. in the form of or as part of order and / or industry software, in particular for manual input and / or for importing from measuring devices and / or databases;
• a computer-implemented method according to the invention can be provided in the form of ordering and / or industry software.
• the data required for the calculation and / or optimization and / or manufacture of a spectacle lens in particular the intraocular lens data and / or the prescription data and / or the individual refraction data (pre-OP and / or post-OP refraction data) of the at least one eye of the spectacle wearer can be detected and / or transmitted.
• the intraocular lens data can be transmitted, for example, from the manufacturer of the intraocular lens data to the calculator and / or manufacturer of the spectacle lens.
• the prescription data and / or individual refraction data can be transmitted, for example, from the optician and / or ophthalmologist or surgeon to the calculator and / or manufacturer of the spectacle lens.
• a database in particular with the aid of a type and / or serial number of the implanted IOL or with the aid of a patient code (for example customer or patient number, name, etc.).
• Measurement or refraction data can, for example, also be called up directly from a measuring device.
• a common transmission protocol or a transmission protocol specially developed for the method according to the invention can be used for the transmission of the data.
• the data to be transmitted can also be entered, at least in part, manually via an input unit.
• an ophthalmologist or surgeon can transmit the so-called A constant or IOL constant of the intraocular lens used in this way.
• a lens or IOL passport can also be created semi- or fully automatically on the basis of the transmitted data.
• a device according to the invention and / or a system according to the invention, for example for ordering a spectacle lens can in particular comprise a computer and / or data server which is designed to be able to communicate via a network (eg Internet).
• the computer is designed in particular, a computer-implemented method, e.g. ordering software for ordering at least one spectacle lens, and / or transfer software for transferring relevant data (in particular intraocular lens data and / or prescription data and / or refraction data), and / or determination software to determine more relevant individual parameters of at least one eye of a spectacle wearer, and / or one
• FIG. 1 shows a schematic representation of the physiological and physical model of a spectacle lens and an eye together with a beam path in a specified position of use
• FIG. 2 shows a graph with an exemplary dependency of P mess on S I0L and L 1 10L to illustrate or explain a method for
• FIGS. 3a-3f marginal prior probability densities as a contour representation of a sample from the prior distribution with equidistant lines of the same probability density for the first example for the Bayes A method;
• Figures 4a-4f marginal posterior probability densities as a contour representation of a sample from the posterior distribution with equidistant lines of the same probability density for the first example for the Bayes A method;
• FIGS. 5a-5c show histograms of marginal probability densities of M, Jo and
• FIGS. 7a-7e marginal posterior probability densities as scatter diagrams of a sample from the posterior distribution for the second example for the Bayes A method
• FIGS. 8a-8c show histograms of marginal probability densities of M, Jo and
• FIGS. 9a-9c histograms of marginal probability densities of M, Jo and
• FIG. 1 shows a schematic representation of the physiological and physical model of a spectacle lens and an eye in a predetermined position of use together with an exemplary beam path on which an individual spectacle lens calculation or optimization according to a preferred embodiment of the invention is based.
• a single ray is preferably calculated for each visual point of the spectacle lens (the main ray 10, which preferably runs through the eye pivot point Z), but also the derivatives of the arrow heights of the wavefront according to the transverse coordinates (perpendicular to the main ray). These derivatives are taken into account up to the desired order, the second derivatives describing the local curvature properties of the wavefront and the higher derivatives being related to the aberrations of higher orders.
• the local derivatives of the wave fronts are ultimately determined at a suitable position in the beam path in order to compare them there with a reference wave front which is at a point on the retina of the eye 12 converges.
• the two wave fronts i.e. the wave front coming from the spectacle lens and the reference wave front
• the two wave fronts are compared with one another in an evaluation area.
• “Position” does not simply mean a certain value of the z-coordinate (in the direction of light), but such a coordinate value in combination with the specification of all areas that were broken through before reaching the evaluation area.
• all refractive surfaces including the rear surface of the lens are refracted.
• a spherical wave front whose center of curvature lies on the retina of the eye 12 is preferably used as the reference wave front.
• the radius of curvature of this reference wavefront corresponds precisely to the distance between the rear surface of the lens and the retina.
• the reference wavefront is spherical with the center of curvature on the retina, but has a radius of curvature 1 / d AR .
• a spherical wave front originates from the object point and propagates to the first spectacle lens surface 14. There it is broken and then it propagates to the second lens surface 16, where it is broken again.
• the wavefront w gi emerging from the spectacle lens then propagates along the main beam in the direction of the eye 12 (propagated wavefront w g 2) until it hits the cornea 18, where it is again refracted (wavefront w c ).
• the wave front is also refracted again by the eye lens 20, whereby the resulting wave front w e arises, for example, on the rear surface of the eye lens 20 or on the exit pupil of the eye.
• This is compared with the spherical reference wavefront w s and the deviations are evaluated for all visual points in the objective function (preferably with corresponding weightings for the individual visual points).
• the ametropia is no longer just described by a thin sphero-cylindrical lens, as was usual in many conventional procedures, but rather the corneal topography, the eye lens, the distances in the eye and the deformation of the wavefront (including the low-order aberrations - i.e. sphere, cylinder and axis position - and preferably also including the higher-order imaging errors) directly taken into account in the eye.
• the vitreous body length CILR is calculated individually in the eye model according to the invention.
• An aberrometer measurement preferably supplies the individual wavefront deformations of the real ametropic eye for distance and near (deviations, no absolute refractive index) and the individual mesopic and photopic pupil diameters.
• an individual real corneal anterior surface is preferably obtained, which generally makes up almost 75% of the total refractive power of the eye.
• it is not necessary to measure the rear surface of the comea. Because of the small difference in refractive index to the aqueous humor and because of the small corneal thickness, it is preferably not described by a separate refractive surface, but by an adaptation of the refractive index of the cornea.
• bold lowercase letters are intended to denote vectors and bold capital letters denote matrices, such as the (2 x 2) vergence matrices or refractive index matrices and italics like d scalar quantities.
• 5 stands for the set of all parameters that are necessary to describe a wavefront (with sufficient accuracy) in relation to a given coordinate system.
• S preferably stands for a set of Zernike coefficients with a pupil radius or a set of coefficients of a Taylor series.
• S particularly preferably stands for the set of a vergence matrix S for describing the 2nd order wavefront properties and a set of Zernike coefficients (with a pupil radius), which is used to describe all remaining wavefront properties except the 2nd order or a set of coefficients according to a Decomposition according to Taylor.
• Analogous statements apply to surfaces instead of wavefronts.
• the following data can in principle be measured directly:
• This variable can also be determined indirectly by measuring the distance between the cornea and the iris; correction values can be applied if necessary. Such corrections can be the distance between the front surface of the lens and the iris from known eye models (e.g. literature values).
• Curvature of the lens front surface in a direction L lxx (by pachymetry)
• the x-plane can be defined, for example, such that this section lies in the x-plane. If the coordinate system is defined in such a way that this plane is inclined, the derivation must be supplemented by the functions of the corresponding angle. It is not required that this be a main cut. For example, it can be the cut in the horizontal plane.
• n CL Refractive indices n CL of the cornea and anterior chamber as well as the aqueous humor n LR and that of the lens n L
• Retina and the components L l yy and L l xy L l yx of the lens front surface as unknown parameters.
• Spectacle lenses in a preferred embodiment, in which the lens has a
• steps 2, 4, 6, in which the distances T cl , T cl , or T CL are propagated can be divided into two partial propagations 2a, b), 4a, b) or 6a, b) after the following scheme, which is explicitly for step 6a, b):
• the division into steps 6a and 6b offers advantages, and the
• steps 2, 4 can also take place analogously to the division of step 6 in 6a, b).
• steps 1 to 6 are referred to again and again in the further course of the description. They describe a preferred relationship between the Vergenzmatrix S of a wave front S on the cornea and the Vergenzmatrizen all resulting therefrom between wave fronts of the refracting interfaces of the eye, in particular the Vergenzmatrix S 'L2 of a wave front S' L2 to the eye lens (or even a wave front S R on the retina).
• These relationships can be used both to calculate parameters that are not known a priori (e.g. d LR or L t ) and thus to assign values to the model either individually or generically, as well as to determine the propagation of the wavefront in the eye with models that are then assigned to simulate the optimization of spectacle lenses.
• the surfaces and wavefronts are treated up to the second order, for which a representation by means of vergence matrices is sufficient.
• Another preferred embodiment which will be described later, takes into account and also uses higher orders of imaging errors.
• the eye model in a preferred embodiment has twelve parameters as degrees of freedom of the model which must be verified. These preferably include the three degrees of freedom of the surface power matrix C of the cornea C, the three degrees of freedom of the surface power matrices L x and l 2 for the front and rear surfaces of the lens, as well as one each for the length parameters of the anterior chamber depth d CL , the lens thickness d L and the vitreous body length d LR .
• ii Value of a parameter given a priori, e.g. as a literature value or from an estimate, e.g. through the presence of a measured value for another variable that correlates in a known manner with the parameter to be determined on the basis of a previous population analysis
• a central aspect of the invention relates precisely to the goal of not having to measure all parameters directly.
• it is significantly easier to measure the refraction of the relevant eye or to determine it objectively and / or subjectively than to measure all parameters of the model eye individually.
• these values can be taken from aberrometric measurements or autorefractometric measurements or, according to (ii) data provided elsewhere, can be documented.
• L t is adapted to the measurements in particular by calculating the measured vergence matrix S M using steps 1, 2 through the likewise measured matrix C and up to the object-side side propagated along the front surface of the lens.
• one calculates a spherical wave from an imaginary point light source on the retina by means of steps 6, 5, 4 carried out backwards from back to front by refracting this spherical wave at the previously determined surface power matrix L 2 of the lens back surface and then removing the wavefront obtained from the Lens back surface propagated to the image side of the lens front surface.
• the data of the vergence matrix S M and particularly preferably also the data on C from individual measurements are preferably available.
• data on the rear surface of the lens is assumed to be a spherical rear surface, ie a rear surface without astigmatic components.
• df 2 3 + 6 + 3.
• six parameters from ⁇ L 1; l 2 , d L , d CL ⁇ can be substantiated by assumptions or literature values. The other two result from the calculation in addition to d LR .
• the parameters of the rear surface of the lens, the mean curvature of the front surface of the lens and the two length parameters d L and d CL are assigned a priori (as predefined standard values).
• the anterior chamber depth d CL that is to say the distance between the cornea and the anterior surface of the lens
• the measured parameters include ⁇ C, d CL , S M ⁇ .
• df 2 4 + 5 + 3.
• the problem is therefore still mathematically underdetermined, so five parameters from ⁇ L 1 L 2 , d L ⁇ must be determined a priori by assumptions or literature values. In a preferred embodiment, these are the parameters of the rear surface of the lens, the mean curvature of the front surface of the lens and the lens thickness.
• the parameters of the rear surface of the lens and the lens thickness are involved. The exact calculation is described below.
• the lens thickness can also be made available from an individual measurement.
• This embodiment is particularly advantageous when a pachymeter is used, the measuring depth of which allows the rear surface of the lens to be recognized, but not a sufficiently reliable determination of the lens curvatures.
• one (e.g. measurement in two normal sections) or two further parameters (measurement of both main sections and the axial position) of the front surface of the lens can be recorded by an individual measurement.
• This additional information can be exploited in two ways in particular:
• D LR (and possibly the missing parameter from L x ) is determined (“fit”) in such a way that the distance between the L x resulting from the equations and the measured L x (or the measured L x supplemented by the missing parameter) becomes minimal. This procedure can - obviously - reduce the measurement uncertainty.
• the anterior chamber depth, two or three parameters of the lens anterior surface and the lens thickness are measured individually.
• the other quantities are calculated in the same way, whereby the a priori assumption of the lens thickness can be replaced by the corresponding measurement.
• individual 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.
• the respective additionally measured parameters can be carried out analogously to the step-by-step extensions of the above sections.
• SM, C, LI and L2 are each the spherical equivalents of the ametropia, the cornea, the front surface of the lens and the rear surface of the lens.
• the values of the so-called Bennett & Rabbetts eye for the refractive powers of the lens surfaces can be used, for example from Table 12.1 of the book “Bennett &Rabbets” Clinical Visual Optics “, third edition, by Ronald B. Rabbetts, Butterworth-Heinemann, 1998, ISBN-10: 0750618175 can be found.
• the calculation described above leads to results that are very well compatible with the population statistics, which state that nearsighted ametropia tends to lead to large eye lengths and vice versa (see eg CW Oyster: "The Human Eye", 1998).
• the aim of the method using Bayesian statistics is to use all available sources of information about an eye or a pair of eyes in a consistent manner in order to achieve an optimal correction of the eye or the eyes with an ophthalmic lens in the light of this information (e.g. a spectacle lens).
• this information is incomplete and / or inaccurate, which so far has often led to only simplified eye models being used to calculate ophthalmic lenses.
• Such a simplified eye model is, for example, an eye that is characterized solely by its refraction, since this can be determined with a certain accuracy (e.g. with an error of ⁇ 0.75 D in the spherical equivalent).
• a certain accuracy e.g. with an error of ⁇ 0.75 D in the spherical equivalent.
• you want to use more complex eye models to calculate ophthalmic lenses it makes sense to include information about the length of the eye, as well as the position and curvature of the refracting surfaces of the cornea and eye lens, in the calculation, but this should only be taken into account as much as is possible within their accuracy.
• a probability or probability density can be assigned to an individual eye model with a given set of parameters.
• Individual eye models that are based on the information available e.g. Objective wavefront measurement and biometry of the eye
• Individual eye models that are based on the information available are consistent, have a higher probability or probability density, since, for example, the propagation and refraction of a wave front, which a point light source would generate on the retina after exiting the eye, are measured within the scope of the measurement accuracy of the objective wave front measurement Reproduces data well, and at the same time the parameters of the individual eye agree with the available information about the biometry of the eye within the framework of the distributions known, for example, from the literature.
• Individual eye models that are not consistent with the available information are assigned correspondingly low probabilities or probability densities.
• the probability or probability density of an individual eye model can be written as prob (i ⁇ di, /), where denote the parameters of the individual eye model i, and di are the measured data (these can include, for example, the current refraction or the refraction measured before an eye operation, the measured shape and / or refractive properties of the cornea, the measured eye length or other variables measured on the individual eye) .
• the existing background information eg about the measuring process of the refraction, the distribution of the parameters of the individual eye model or other related variables in the population
• ' means that the distribution of quantities to the left of 'j' for given (ie fixed) quantities to the right of '
• the information obtained in the measuring process, in which the data d t are measured, can also be used as a probability distribution of the data d ⁇ with given parameters of the individual eye model i: prob (di ⁇ di, /)
• prob (di ⁇ di, /) The accuracy of the measurement process is reflected in the breadth of the distribution: an accurate measurement has a narrower distribution than an imprecise measurement, which has a broad or broader distribution of the data d t .
• prob (ßi ⁇ I) describes the background knowledge about the parameters of the individual eye model. This can be information from literature, for example, but also information from data from past measurements. This can be data from the same person for whom the ophthalmic lens is to be manufactured, as well as data from measurements made by a large number of other people.
• the probability serves as a measure of consistency. Parameter values of the individual eye model that are consistent with the measurements can be found particularly where both prob (ßi ⁇ I) and prob (di ⁇ d ir I) are high.
• the probability or probability density prob (ßi ⁇ d ir I) can also be suitably normalized in order to write the proportionality as an equation.
• prob ⁇ di ⁇ d u / can also contain parameters of the eye lens. So can be part of the parameters eg the refractive power of the eye lens, its position and / or orientation in the eye, or other variables such as the refractive index and curvatures or shape of the surfaces.
• the lens of the eye can be a natural lens.
• literature data on the parameters of natural eye lenses can be used (eg distributions of the curvatures of the front and / or back surface, refractive index, etc.).
• the eye lens is an intraocular lens, the distributions of the parameters of natural eye lenses must not be used. Instead, the parameters of the intraocular lens should be used if they are known individually. Otherwise distributions of these parameters from literature studies of operated eyes can be used. If such information is not available, a flat distribution within reasonable limits can be selected. For parameters that are positive definite and define length scales (eg radii of curvature or distances), distributions can also be selected that are flat in the logarithm of these parameters.
• Prob (ßi ⁇ I) can unintentionally falsify parameters of the eye model.
• the “true” refraction is understood as a parameter of the individual eye model, the most likely value of the “true” refraction can deviate from the measured refraction. If this is not desired, one should be included in the corresponding parameter (e.g. spherical equivalent of refraction) within sensibly chosen limits (e.g. between -30 D and + 20 D for the spherical equivalent M, ⁇ 5 D for the astigmatic components Jo and J45) constant distribution can be chosen.
• sensibly chosen limits e.g. between -30 D and + 20 D for the spherical equivalent M, ⁇ 5 D for the astigmatic components Jo and J45
• parameters of the individual eye model or other quantities related to the parameters or measurement data are known exactly or with a high degree of accuracy, their distribution can be approximated as a Dirac delta distribution.
• the equations in these parameters or quantities can be integrated on both sides, which may simplify subsequent calculations.
• Bayes A and Bayes B Two possible methods for calculating an ophthalmic lens are presented below (Bayes A and Bayes B).
• the available information is used to set up a (single) individual eye model, with the help of which an ophthalmic lens is calculated that is optimal for this eye model.
• the eye model can be given or occupied, for example, by the parameter set i9 TM a , which maximizes the probability or probability density prob (i ⁇ di, I).
• Other sets of parameters can also be selected, for example the expected value ⁇ ß t ) or the median ⁇ TM b ⁇ of the parameters with regard to the distribution prob (di ⁇ d i /).
• the Bayes B method is more advantageous - but more computationally demanding - compared to Bayes A because a subset of individual eye models with different parameter sets can lead to ophthalmic lenses that have very similar (even identical) properties (e.g. B calc power at a reference point of the ophthalmic lens, or the distribution of the refraction deficit over a given area of the ophthalmic lens, or similar criteria for determining the quality of an ophthalmic lens).
• an ophthalmic lens that was not calculated with the most likely individual eye model can therefore represent an optimal correction for a subset of individual eye models which overall have a higher probability than the most likely individual eye model. It is therefore advantageous to search for the ophthalmic lens that optimally corrects the distribution of eye models, rather than just determine the most likely individual eye model and manufacture an ophthalmic lens for it.
• an ophthalmic lens e.g. a spectacle lens
• a spectacle lens consistent with the available information
• the already known data can include: already known current subjective and / or objective refraction, already known earlier subjective and / or objective refraction (e.g. before an operation), effect and / or shape and / or position (most important is the axial position ) certain refractive surfaces of the eye, size and / or shape and / or position of the entrance pupil, refractive index of the refractive media, refractive index profile in the refractive media, opacity; if necessary, determination of these variables depending on the accommodation of the eye on a fixation object (target) at a given close distance;
• calculation methods such as Markov Chain Monte Carlo, Variational Inference, Maximum Likelihood, Maximum Posterior, or Particle Filter can be used;
• the aim here is to select the parameters of the individual eye model that are consistent both with the initial distribution of eye models provided and with the already known data provided.
• the product of the probability or probability density of the data for given parameters of the eye model with the probability or probability density of the parameters of the eye model is used as the consistency measure.
• the initial distribution of the parameters of eye models provided in the first step can be in a parameterized form, e.g. (possibly multivariate) normal distribution, other distribution of the exponential family, Cauchy distribution, Dirichlet process, etc., or as a set of samples , ie one or more (possibly multidimensional) data sets. If the initial distribution of the parameters of eye models is parameterized, the parameters of this distribution are called “hyperparameters”.
• the third step can include the determination of a multivariate probability distribution which contains both the parameters of the individual eye model and the hyperparameters of the initial distribution of the parameters of the eye model.
• the distribution In order to calculate the distribution of the parameters of the individual eye model from this, the distribution must be marginalized, ie it is integrated via the hyperparameters.
• the integrals can be solved with common numerical methods (eg by means of the Markov Chain Monte Carlo or Hybrid Monte Carlo) and / or analytical methods.
• the probability or the In this case, the probability density of the parameters of the eye model can be calculated using the following equation:
• the distribution calculated analogously to steps 1 to 3 of the Bayes A method can be provided.
• the most likely parameters L t of the ophthalmic lens are determined, ie on the basis of the probability distribution or probability density the parameters of the ophthalmic lens L "are determined, which maximize prob (Li ⁇ di, l.
• L t denotes the parameters of any ophthalmic lens
• L (i9 ; ) the parameters of the ophthalmic lens, when optimizing an ophthalmic lens with the help of an individual eye model with the parameters arises.
• the Dirac Delta distribution is denoted by ⁇ 5 (.).
• the parameters of the ophthalmic lens can, for example, arrow heights, refractive power at a reference point of the ophthalmic lens, refractive power over an area of the ophthalmic lens, refraction errors at a reference point of the ophthalmic lens, or the distribution of refraction errors over an area the ophthalmic lens.
• L (ßi) can be non-linear, and therefore the maximum of the probability density rtoB ( ⁇ i ⁇ ⁇ 0 1) (with respect to tf £ ) with L (ßi) not necessarily to the maximum of the probability density prob (Li ⁇ d i I is mapped.
• the result is independent of the number and type of quantities known through measurement (ie the data di and the form of the likelihood prob ⁇ di ⁇ u l)) as well as of the number and type the Parameters of the eye model always a consistent eye model (procedure
• Bayes A and B Bayes A and B and, if necessary, a choice of the parameters of the ophthalmic lens that matches the ensemble of possible consistent eye models (Bayes B method).
• the initial situation is that a total of N parameters x ,, l ⁇ i ⁇ N of a model are to be assigned and the following information is available:
• the probability distribution for the measured value x TM ess of each parameter x is described by a random variable X t .
• a reliability measure is preferably present for each measured value, for example a standard deviation a TM ess of the random variable X t , 1 ⁇ i ⁇ k
• Rear surface of the lens SZA
• ametropia SZA
• eye length lens thickness
• anterior chamber depth SZA
• SZA Ametropia
• SZA + HOA rear surface of the lens
• SZA + HOA ametropia
• eye length lens thickness, anterior chamber depth
• SZA + HOA rear surface of the lens
• SZA + HOA ametropia
• anterior chamber depth anterior chamber depth
• the basic problem to be solved is that in the case of measured values that deviate from the population mean, a decision must be made as to whether the measurement must be discarded (e.g. if it is implausible) or must be accepted. If all measured values are plausible in themselves, but violate one of the consistency conditions, then they must not all be adopted. Rather, a balance must then be sought between the various measured values: those that have a very high measurement reliability should at least almost be retained, while uncertain measured values are more likely to be adapted.
• the best possible values for all N parameters are preferably determined from the known information.
• the concept of the invention is based in particular on the assumption that the N parameters have certain (unknown but initially fixed) values. Under this In the light of the above information (statistical values from the population, reliability measures of the measurements), the conditional probability density is assumed
• This probability density is assumed as a function P par ⁇ x x , ..., x N ) of the
• the medians can also be used as a criterion.
• the maximum formation according to equation (3) and the expected value formation according to equation (5) as well as the median determination can also be combined as desired in order to determine the N parameter values.
• P pop is preferred due to the multivariate normal distribution where m is the vector of the means and C is the covariance matrix:
• the measurement is described by the distribution P mess (X 1 , ..., X k ⁇ c ⁇ ,.., C ⁇ .
• each of the measurements is normally distributed with the expected value x and the standard deviation er ""
• the idea of the invention is to maximize P tot as a function of the parameters x ⁇ , ..., x N.
• the derivatives of the logarithm are preferably formed
• Equation (9) and equation (10) represent a linear system of equations with N equations and N variables, which according to can be resolved. a) No constraints
• the system of equations (16) are K equations, which can be solved for the parameters x "which are independent of K.
• the remaining parameters x" are obtained by inserting them into the context x "( x ").
• n CL 1,336; Refractive index anterior chamber (literature)
• n L 1,422; Refractive index lens (literature)
• n LR 1,336; Refraction index vitreous (literature)
• the initial situation can be regarded as the case that there are no fluctuations and no correlations in the basic population, and that only the ametropia measured afterwards and the IOL itself are subject to uncertainties: (23).
• the constraint means that one may only move on the cutting surface 30 shown in FIG.
• the method seeks a balance in the light of the different standard deviations and the asymmetrical position of the constraint relative to the Gaussian bell.
• Inconsistencies in the eye model can occur not only with a calculated eye length (or a calculated lens-retina distance), but also, for example, when measuring the eye length. Such inconsistencies can be resolved analogously to the example of a calculated eye length described above. Of course, more complex examples can also be given, in which the eye length itself is also not fixed, or where correlations occur.
• the eye model used in this example consists of an ametropia described up to the 4th Zernike order, c, which relates to a pupil diameter of 5mm, as well as the natural logarithm of a photopic or mesopic lighting condition Pupil radius, log r ph or logr mes .
• the model parameters of the eye model can be used as a vector
• the measurement data di known for an individual eye are here the sphere, cylinder and axis of the (far) refraction Rx,
• the measurement error of the refraction is also known and is as
• the measurement error is normally distributed as a power vector around the power vector of the ametropia P eye (ßi) which can be determined from the model parameters, so that for the likelihood
• the most likely eye model is determined.
• the posterior consists of the sample of the prior, weighted with the likelihood.
• the likelihood for each element (sample) of the sample of the prior was evaluated and used as a weight.
• Marginal posterior densities can be seen analogously to the prior in FIGS. 4a to 4f.
• kernel density estimate multivariate normal distribution with a standard deviation that corresponds to 0.5 times the standard deviation of the posterior distribution of the parameters of the eye model. This resulted in the following values for the most likely eye model (Zernike coefficients are related to a pupil of 5mm diameter):
• the effect of a lens that optimally corrects the most probable eye model under photopic lighting conditions can also be calculated by scaling the ametropia in Zernike representation to the most probable photopic pupil with radius r ⁇ ax .
• the eye model considered in this example as well as the measurement data (here the refraction) are chosen as in the Bayes A example. Now, however, we want to calculate the most likely effect of an ophthalmic lens to be manufactured, and not the effect of the ophthalmic lens for the most likely eye model. As in the example of the Bayes A method, the lens should be ideally suited for mesopic vision.
• mesopic Zernike wavefronts were calculated from the posterior sample of Example Bayes A by scaling to the respective mesopic pupil for the Zernike coefficients based on a pupil diameter of 5mm in this sample using the method known from the literature.
• power vectors for the mesopic pupil were in turn determined using the root-mean-squared (RMS) metric.
• RMS root-mean-squared
• the maximum of the posterior distribution was replaced by the maximum one Kernel density estimation of the sample approximated (multivariate normal distribution as kernel with a standard deviation which corresponded to 0.5 times the standard deviation of the posterior distribution of the power vector). This gave the following most likely effect
• P mes (ßi iax ) calculated in the Bayes
• P mes ax again represents a further improvement over the correction P meS (ßf iax ) , corresponds to the most probable ametropia for the given information, and P mes iß 1 ⁇ ) only corresponds to the ametropia of the most probable eye model but generally not the most probable ametropia.
• Bayes A or Bayes B method is used, but in which a much more complex eye model is used, which can consist of several refractive surfaces and media with different refractive indices.
• Each of the surfaces can, for example, be described in a Zernike representation, the distribution of the coefficients can be partially or completely described in the literature or accessible through measurements (e.g. with the help of measuring methods for determining eye biometry such as scanning optical coherence tomography, ultrasound or magnetic resonance tomography ). If such information is missing, then priors can be replaced with the help of assumptions about the smoothness of the refracting surfaces or the local curvature properties of these surfaces (e.g. correlation lengths of the local curvatures).
• the refractive indices of the media can also be included in the model as parameters that are not precisely known. There are also models with Refractive index gradients possible. The propagation and refraction of the light through the model eye is selected according to the eye model used. Other known metrics (monochromatic or polychromatic) can also be used as metrics.
• the posterior can be solved, for example, by approximation methods such as parametric inference (e.g. variational inference), in which the posterior itself is parameterized and its determination is optimized ation problem is perceived.
• parametric inference e.g. variational inference
• the rear surface of the cornice is neglected in this model (see Bennett-Rabbett's eye model).
• the surface power in the cross-section 0 °, 45 ° and 90 ° to the horizontal is used (ie the elements of the surface power matrix, designations for this are D xx , D xy and D yy ).
• the mutual position of the refractive surfaces and the retina is parameterized as a positive variable by the natural logarithms of the distances between two directly adjacent surfaces (logarithms of the distances between the cornea and the front of the lens, the front of the lens and the rear of the lens, and the rear of the lens and the retina are each with log d 12 , log d 23 and log d 34 , where the distances are used in mm).
• the Refractive indices of the media between the refractive surfaces ie in the anterior chamber, eye lens and vitreous
• the parameter vector is here as
• -di (log d 12 , log d 23 , log d 34 , D X D xy , D y , D xx , D y , D yy , D x , D y , D y , n 12 , n 23 , n 34 ) summarized.
• the measurement data d t known for an individual eye are here the sphere, cylinder and axis of the (far) refraction Rx,
• P Auee (di) is the power vector for the ametropia of the eye model
• the most likely eye model is determined.
• the correlation matrix of the normal distribution had a diagonal occupied by 1 and was occupied by zero everywhere except for the following off-diagonal elements:
• the posterior consists of the sample of the prior, weighted with the likelihood.
• the likelihood for each element (sample) of the sample of the prior was evaluated and used as a weight.
• Marginal posterior densities can be seen analogously to the prior in FIGS. 7a to 7e.
• kernel density estimate multivariate normal distribution with a standard deviation that corresponds to 0.5 times the standard deviation of the posterior distribution of the parameters of the eye model. This resulted in the following values d - ax for the most likely eye model:
• the effect of the lens P d ia x), which optimally corrects the most probable eye model, can differ from the ametropia of the most probable eye, P 4tlfi, e ((i9 t max )), since the former relates to the corrective lens and the latter to the effect of the eye during refraction, since the distances between the cornea and the corrective lens or refraction lens generally differ.
• the eye model considered in this example and the measurement data (here the refraction) are chosen as Bayes A in the second example above. Now, however, the most likely effect of an ophthalmic lens to be manufactured is to be calculated, and not the effect of the ophthalmic lens for the most likely eye model.
• Bayes A power vectors were calculated from the posterior sample from the previous second example, which represent a sample from the posterior distribution of the effect of the optimal ophthalmic lens (cf. FIGS. 8a to 8c).
• the gain in information through the data is clearly recognizable from the reduced spread of the posterior compared to the prior.
• the maximum of the posterior distribution was approximated by the maximum of a kernel density estimate of the sample (multivariate normal distribution as kernel with a standard deviation that corresponded to 0.5 times the standard deviation of the posterior distribution of the power vector).
• This resulted in the following most likely effect of an ophthalmic lens to be manufactured e.g. the effect of a spectacle lens such as a single vision lens, or the effect at the distance reference point of a progressive lens, which makes optimal use of the information available about the eye model:
• This most likely effect differs from the effect Piß 1 ) calculated in the Bayes A example for the most likely eye model due to the non-linear transformation (here mainly the propagation of the wave fronts between the refracting surfaces) of the parameters of the eye model (here the Surface power and distances between the refracting surfaces and, to a lesser extent, the refractive indices of the media) into the parameters of the ophthalmic lens (here the effect of the ophthalmic lens as a power vector).
• the non-linear transformation here mainly the propagation of the wave fronts between the refracting surfaces
• the parameters of the eye model here the Surface power and distances between the refracting surfaces and, to a lesser extent, the refractive indices of the media
• p L ' max again represents a further improvement over the correction P (ß TM ax ) from the second example for the Bayes B method, since p L ' max corresponds to the most likely corrective effect for the given information, and P m es ( ⁇ ax only the corrective effect of the most likely eye model but generally not the most likely corrective effect.

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• 2020
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