US20220413319A1 - Method and apparatus for optimizing spectacle lenses, in particular for wearers of implanted intraocular lenses - Google Patents

Method and apparatus for optimizing spectacle lenses, in particular for wearers of implanted intraocular lenses Download PDF

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Publication number
US20220413319A1
US20220413319A1 US17/623,993 US202017623993A US2022413319A1 US 20220413319 A1 US20220413319 A1 US 20220413319A1 US 202017623993 A US202017623993 A US 202017623993A US 2022413319 A1 US2022413319 A1 US 2022413319A1
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eye
lens
individual
model
parameters
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Stephan Trumm
Wolfgang Becken
Adam Muschielok
Anne Seidemann
Helmut Altheimer
Gregor Esser
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Rodenstock GmbH
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Rodenstock GmbH
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Assigned to RODENSTOCK GMBH reassignment RODENSTOCK GMBH ASSIGNMENT OF ASSIGNORS INTEREST (SEE DOCUMENT FOR DETAILS). Assignors: SEIDEMANN, ANNE, ALTHEIMER, HELMUT, BECKEN, WOLFGANG, ESSER, GREGOR, MUSCHIELOK, Adam, TRUMM, STEPHAN
Publication of US20220413319A1 publication Critical patent/US20220413319A1/en
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    • 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
    • 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, and to a corresponding method, a device, and a computer program product for the calculation (optimization) and manufacture 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 have been implanted in the at least one eye during surgery.
  • the spectacle wearer can in particular be a wearer of an implanted intraocular lens.
  • the present invention relates to a method, a device and a corresponding computer program product for the calculation (optimization) and manufacture of a spectacle lens, in particular for a wearer of an implanted intraocular lens, with the help of a partially individual eye model.
  • each spectacle lens is manufactured such that for each desired viewing direction or each desired object point the best possible correction of a refractive error of the respective eye of the spectacle wearer is achieved.
  • 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 upon passing the vertex sphere conform to the values for sphere, cylinder and axis of the prescription for the eye having the vision disorder.
  • dioptric values in particular sphere, cylinder, cylinder axis—i.e.
  • sphero-cylindrical deviations for a far (usually infinite) distance and optionally (for multifocal lenses or progressive lenses) an addition or a complete near refraction for a near distance (e.g. according to DIN 58208) are determined.
  • object distances deviating from the norm, which are used in the refraction determination can also be specified.
  • the prescription in particular sphere, cylinder, cylinder axis, and optionally addition or near refraction
  • the spectacle lenses are manufactured such that they cause a good correction of vision disorders of the eye and only small aberrations particularly in the main zones of use, especially in the central visual zones, while larger aberrations are permitted in peripheral zones.
  • the spectacle lens surfaces or at least one of the spectacle lens surfaces is first calculated such that the desired distribution of the unavoidable aberrations is effected thereby.
  • This calculation and optimization is usually performed by means of an iterative variation method by minimizing a target function.
  • a target function particularly a function F having the following functional relationship to the spherical power S, the magnitude of the cylindrical power Z, and the axis of the cylinder ⁇ (also referred to as “SZA” combination) is taken into account and minimized:
  • the target function F at the evaluation points i of the spectacle lens, at least the actual refractive deficits of the spherical power S ⁇ ,i and the cylindrical power Z ⁇ ,i as well as target specifications for the refractive deficits of the spherical power S ⁇ ,i,target and the cylindrical power Z ⁇ ,i,target are taken into consideration.
  • the respective refractive deficits at the respective evaluation points are preferably taken into consideration with weighting factors g i.S ⁇ and g i,Z ⁇ .
  • the target specifications for the refractive deficits of the spherical power S ⁇ ,i,target and/or the cylindrical power Z ⁇ ,i,target form the so-called spectacle lens design.
  • particularly further residues, especially further parameters 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 consideration, which is particularly implied by the expression “+. . . ” in the above-mentioned formula for the target function F.
  • consideration not only of aberrations up to the second order (sphere, magnitude of the astigmatism, and cylinder axis) but also of higher order (e.g. coma, trefoil, spherical aberration) may in some cases contribute to a clear improvement particularly of an individual adaptation of a spectacle lens.
  • the local derivatives of the wavefront are calculated at a suitable position in the beam path in order to compare them with desired values obtained from the refraction of the spectacle lens wearer.
  • the vertex sphere or e.g. the principal plane of the eye for the corresponding direction of sight is considered.
  • a spherical wavefront emanates from the object point and propagates up to the first spectacle lens surface.
  • the wavefront is refracted and subsequently propagates to the second spectacle lens surface, where it is refracted again.
  • the last propagation takes place from the second boundary surface to the vertex sphere (or the principal plane of the eye), where the wavefront is compared with the predetermined values for the correction of the refraction of the eye of the spectacle wearer.
  • the refractive deficit is considered to be the lack or excess of refractive power of the optical system of the eye having the vision disorder compared with an equally long eye having normal vision (residual eye).
  • the refractive power of the refractive deficit is in particular approximately equal to the distance point refraction with negative sign.
  • the spectacle lens and the refractive deficit together from a telescopic system (afocal system).
  • the residual eye eye having the vision disorder without added refractive deficit
  • a spectacle lens is said to be fully correcting for distance if its image-side focal point coincides with the distance point of the eye having the vision disorder and thus also with the object-side focal point of the refractive deficit.
  • IOL implanted intraocular lenses
  • model-based properties are assumed for the eye lens, so that possibly the eye model used for the optimization in these cases no longer corresponds to the actual structure of the eye with an IOL, e.g. if a length ametropia is at least partially compensated for by the IOL due to the power (mean sphere) of the IOL.
  • a spectacle lens preferably a progressive spectacle lens.
  • it can be an object to provide patients with specially designed spectacle lenses after cataract surgery.
  • it can be an object to improve the calculation or optimization of a spectacle lens, preferably a progressive spectacle lens, with regard to patients having 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 object relates to a computer-implemented method for identifying relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of an ophthalmic lens (in particular a spectacle lens) for the at least one eye of the spectacle wearer, comprising the steps of:
  • the individual data on properties of the at least one eye of the spectacle wearer include, in particular, measurement data on properties of the at least one eye of the spectacle wearer.
  • These known individual data can e.g. include: 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 prior to surgery, for example), the power 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 is to include and/or by which parameters the individual eye model is to be defined or characterized.
  • the parameters defined for the eye model can initially be variables (i.e. 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 be determined or defined (e.g. as the most likely parameters of the individual eye model).
  • constructing an individual eye model comprises providing an initial probability distribution of the parameters of the eye model. Furthermore, determining a probability distribution (or a probability density) of values of the parameters of the individual eye model takes place 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 general public or in the population of certain people.
  • the method according to the invention is thus based on probability calculation, in which in particular Bayesian statistics can be used for.
  • 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 comprises calculating a consistency measure, wherein 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 with given background knowledge, is used as the consistency measure.
  • the background knowledge i.e. the current state of knowledge when evaluating the data
  • the probability or probability density of the parameters of the individual eye model with given 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(d i
  • i , I) can in particular correspond to the “posterior” of Bayesian statistics.
  • the method further comprises the steps of:
  • the probability distribution (or the probability density) of parameters L i of the ophthalmic lens to be calculated or optimized can in particular be specified as follows:
  • providing individual data comprises providing individual refraction data on the at least one eye of the spectacle wearer.
  • constricting an individual eye model comprises defining an individual eye model in which at least
  • 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.
  • the position or the size of either the aperture diaphragm or of the entrance pupil is used as a (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, the at least one eye of the spectacle wearer having an implanted intraocular lens can in particular comprise the following steps of:
  • the parameters of the lens of the model eye is carried out on the basis of the provided intraocular lens data.
  • at least defining the lens-retina distance is carried out 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 surgery (but no longer the natural lens).
  • a phakic intraocular lens in contrast, 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 surgery.
  • the term “lens of the model eye” can refer not only to a single real lens (e.g. the natural eye lens or an intraocular lens), but also to a lens system.
  • the lens system can include one or more lenses, in particular two lenses (namely the natural lens of the eye 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 and/or describes both the properties of the natural eye lens and the properties of an additional intraocular lens.
  • the term “lens of the model eye” is understood to mean a “lens system of the model eye”.
  • the term “lens-retina distance” is understood to mean in particular a “lens system-retina distance”.
  • the terms “lens of the model eye” and “lens-retina distance” will be used in the following.
  • a phakic intraocular lens can e.g. be considered as an own/separate or additional element in the eye model.
  • the power of a phakic intraocular lens can influence the power (or one of the surfaces or both surfaces) of the cornea.
  • the intraocular lens can be an anterior chamber lens, for example.
  • the power of a phakic intraocular lens can influence the power (or 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 power, surfaces and/or thickness) can be taken into account in the eye model as additional parameters of the eye model.
  • the position of this additional lens can either be defined as a known position or taken into account as an additional parameter (e.g. measured or model-based) in the eye model.
  • the defined position can (in the case of an anterior chamber lens) e.g. be directly or at 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 tracing into the eye.
  • the eye model required for this is assigned individual values, with the known properties of the IOL, e.g. from the manufacturer's information, being included in 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 or WO 2018/138140 A2 are not necessarily consistent with the properties of the lens actually implanted. This can be the case, for example, when a length myopia is at least partially compensated for by an IOL with less refraction. In this case, the method 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 set of parameters of these components.
  • Parameters of the eye model are e.g. the shape of a corneal front surface of the model eye, the cornea-lens distance, the parameters of the lens of the model eye, the lens-retina distance, etc.
  • the distance lens-retina (hereinafter DLR or d LR ) is calculated from the defocus term of the entire eye, the defocus term of the corneal surface, the distance cornea-lens (hereinafter DCL or d CL ) and the data on the IOL with one of the formalisms described in DE 10 2017 007 975 A1 or WO 2018/138140 A2.
  • the term defocus term will be used below for the value of the symmetrical second term (c 2,0 ) of the Zernike decomposition of the refractive power or the surface of an optical element.
  • a second-order term such as the power in the main section with the highest or lowest refractive power or in a meridian with a defined position (e.g. horizontal or vertical) can be used.
  • the eye model can be supplemented by the astigmatism (magnitude and axis, or the other second-order variables according to the previous paragraph) as well as higher-order components (see DE 10 2017 007 975 A1 or WO 2018/138140 A2) of the entire eye and the components.
  • astigmatism magnitude and axis, or the other second-order variables according to the previous paragraph
  • higher-order components see DE 10 2017 007 975 A1 or WO 2018/138140 A2
  • these can be taken e.g. from the IOL data, measurements (e.g. topography/topometry or aberrometry/autorefraction), model assumptions and/or calculated values (e.g. optimized refraction).
  • IOLs information about asphericity or higher-order aberrations is given for IOLs. These can be used when higher-order aberrations are assigned to the eye model.
  • individual refraction data on the at least one eye of the spectacle wearer are provided.
  • This individual refraction data is based on an individual refraction determination.
  • the refraction data includes at least the spherical and astigmatic vision disorder of the eye.
  • the acquired refraction data also describes higher-order aberrations (HOA).
  • the refraction data (also referred to as aberrometric data in particular if they include higher-order aberrations) is measured by an optician, for example, using an autorefractometer or an aberrometer (objective refraction data).
  • a subjectively determined refraction can be used as well.
  • the refraction data will preferably be communicated to a lens manufacturer and/or provided to a calculation or optimization program.
  • the data is therefore available to be acquired, in particular to be read out and/or received in digital form for the method according to the invention.
  • providing the individual refraction data comprises providing or identifying the vergence matrix S M of the vision disorder of the at least one eye.
  • the vergence matrix describes a wavefront in front of the eye of the light emanating from a point on the retina or converging in a point on the retina.
  • such refraction data can be determined e.g. by illuminating a point on the retina of the spectacle wearer by means of a laser, from which point light then propagates. While the light from the illuminated point initially diverges substantially spherically in the vitreous body of the eye, the wavefront can change when passing through the eye, in particular at optical boundary surfaces in the eye (e.g. the eye lens and/or the cornea). The refraction data on the eye can thus be measured by measuring the wavefront in front of the eye.
  • the method can comprise defining 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 which in particular at least partially define the optical power of the lens of the model eye
  • a lens-retina distance d LR this distance between the lens, in particular the lens back surface, and the retina of the model eye is also referred to as the vitreous body length
  • the vitreous body length is defined in a specific way, namely in such a way that the model eye has the provided individual refraction data, i.e.
  • parameters of the lens of the model eye for example either geometric parameters (shape of the lens surfaces and their distance) and preferably material parameters (e.g. refractive indices of the individual components of the model eye) can be defined so completely that they at least partially define an optical power of the lens.
  • parameters directly describing the optical power of the lens of the model eye can also be defined as lens parameters.
  • the shape of the corneal front surface is usually measured, but alternatively or in addition the power of the cornea as a whole (no differentiation between front and back surfaces) can be specified.
  • a corneal back surface and/or a corneal thickness can possibly also be specified as well.
  • the parameters of the lens of the model eye can be defined (exclusively) on the basis of the provided intraocular lens data.
  • the parameters of the lens of the model eye correspond to the individual provided intraocular lens data.
  • the provided intraocular lens data is defined as the parameters of the lens of the model eye.
  • the refraction of the eye is determined by the optical system consisting of the corneal front surface, the eye lens, and the retina.
  • the refraction of light on the corneal front surface and the refractive power of the eye lens preferably including the spherical and astigmatic aberrations and higher-order aberrations
  • the refractive power of the eye lens preferably including the spherical and astigmatic aberrations and higher-order aberrations
  • the individual variables (parameters) of the model eye are defined accordingly on the basis of the provided intraocular lens data and further on the basis of individual measurement values for the eye of the spectacle wearer and/or on the basis of standard values and/or on the basis of the provided individual refraction data.
  • some of the parameters e.g. the topography of the corneal front surface and/or the anterior chamber depth and/or at least a curvature of a lens surface, etc.
  • Other values can also be taken over from values of standard models for a human eye, especially if the parameters involved are very complex to measure individually.
  • 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 performing a calculation taking into account the predefined parameters such that the then-resulting model eye has the provided individual refraction data.
  • a corresponding number of (free) parameters of the eye model can be individually adapted (fitted). Deviating from a model proposed e.g. in WO°2013/104548°A1, at least the lens-retina distance can be defined by calculation in the context 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 back surface of the spectacle lens.
  • a corresponding starting surface is preferably specified for both the front surface and the back surface of the spectacle lens.
  • only one surface is iteratively changed or optimized during the optimization process.
  • the other surface of the spectacle lens can be a simple spherical or rotationally symmetrical aspherical surface, for example. However, it is also possible to optimize both surfaces.
  • the method for calculating or optimizing comprises determining the path of a main ray through at least one visual point (i) of at least one surface of the spectacle lens to be calculated or optimized into the model eye.
  • the main ray describes the geometric beam path emanating from an object point through the two spectacle lens surfaces, the corneal front surface, and the lens of the model eye preferably up to the retina of the model eye.
  • the method for calculating or optimizing can comprise evaluating an aberration of a wavefront resulting from a spherical wavefront incident on the first surface of the spectacle lens along the main ray on an evaluation surface in particular in front of or within the model eye compared to a wavefront (reference light) converging in one point on the retina of the eye model.
  • a spherical wavefront (w 0 ) incident on the first surface (front surface) of the spectacle lens along the main ray is specified for this purpose.
  • This spherical wavefront describes the light emanating from an object point (object light).
  • the curvature of the spherical wavefront when incident on the first surface of the spectacle lens corresponds to the reciprocal of the object distance.
  • the method thus preferably comprises specifying an object distance model that 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 wearing situation in which the spectacle lens to be manufactured is to be used.
  • the wavefront incident on the spectacle lens is now refracted on the front surface of the spectacle lens preferably for the first time.
  • the wavefront then propagates along the main ray within the spectacle lens from the front surface to the back surface, where it is refracted for the second time.
  • the wavefront transmitted through the spectacle lens now propagates along the main ray up to the corneal front surface of the eye, where it is preferably refracted again.
  • the wavefront is also refracted again there in order to finally propagate preferably up to the retina of the eye.
  • each refraction process also leads to a deformation of the wavefront.
  • the wavefront would preferably have to leave the eye lens as a converging spherical wavefront, the curvature of which corresponds exactly to the reciprocal value of the distance to the retina.
  • a comparison of the wavefront emanating from the object point with a wavefront (reference light) converging in 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 path of the main ray, in particular between the second surface of the optimizing spectacle lens and the retina.
  • the evaluation surface can thus be at different positions, in particular between the second surface of the spectacle lens and the retina.
  • the refraction and propagation of the light emanating from the object point is calculated accordingly in the individual eye model, preferably for each visual point.
  • the evaluation surface can either relate to the actual beam path or to a virtual beam path such as is used to construct the exit pupil AP, for example.
  • the light In the case of the virtual beam path, the light must be propagated back through the back surface of the eye lens after refraction up to a desired level (preferably up to the level of the AP), wherein the refractive index used must correspond to the medium of the vitreous body and not to the eye lens.
  • the resulting wavefront of the object light can preferably simply be compared to a spherical wavefront of the reference light.
  • the method thus preferably comprises specifying a spherical wavefront incident on the first surface of the spectacle lens, identifying a wavefront resulting from the spherical wavefront due to the power at least of the first and second surfaces of the spectacle lens, the corneal front surface, and the lens of the model eye in the at least an eye, and evaluating the aberration of the resulting wavefront in comparison to a spherical wavefront converging on the retina.
  • an evaluation surface is to be provided within the lens or between the lens of the model eye and the spectacle lens to be calculated or optimized, a reverse propagation from a point on the retina through the individual components of the model eye up to the evaluation surface is simulated as the reference light, in order to make a comparison of the object light with the reference light there.
  • the at least one surface of the spectacle lens to be calculated or optimized is varied iteratively until an aberration of the resulting wavefront corresponds to a specified target aberration, i.e. in particular deviates from the wavefront of the reference light (e.g. a spherical wavefront whose center of curvature is on the retina) by specified values.
  • the wavefront of the reference light is also referred to as a reference wavefront here.
  • the method comprises minimizing a target function F, in particular analogous to the target function described at the beginning. Further preferred target functions, in particular when taking higher-order aberrations into account, will be 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-retina distance (vitreous body length) can already be carried out e.g. in an aberrometer or a topograph with a correspondingly expanded functionality.
  • the length of an eye is identified individually.
  • the measured and/or calculated vitreous body length and/or the identified (measured and/or calculated) eye length is 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 back surface of the intraocular lens, and a thickness of the intraocular lens.
  • the individual intraocular lens data includes at least a defocus of the refractive power of the intraocular lens or an optical power of the intraocular lens.
  • the intraocular lens data can therefore either be the defocus of the refractive surfaces (front and back surfaces) and a propagation length (thickness of the lens, hereinafter DLL) or the defocus of the refractive power of the IOL.
  • 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 formulae with different names. It is also known as the IOL constant or “surgeon factor”. Each IOL from each manufacturer has a different A constant that is specified for each calculation formula. This constant represents the intraocular lens in the various calculation formulae.
  • IOL constants can be converted into one another, there is in principle only one constant (number) that is to characterize a given intraocular lens in the entire available power range, regardless of form factor, optical material, IOL diameter, etc.
  • a constant particularly reflects any adaptations in the power and can be part of the lens prescription or IOL prescription.
  • the individual intraocular lens data is provided on the basis of type or serial number information, in particular by the manufacturer of the IOL. This information can be indicated e.g. directly when ordering or be obtained from a database.
  • the method further comprises the steps of:
  • the procedure according to the invention provides a consistent model with regard to the defocus (or the other variables used in the calculation of the eye length).
  • the consistency of the model is no longer ensured already with other second-order variables (e.g. magnitude 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, which can occur e.g 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 power of the entire eye.
  • a consistent eye model is understood to mean an eye model in which an incident wavefront that corresponds to the aberrations of the entire 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 solved e.g. by determining a maximum of the probability.
  • the present invention thus generally provides a computer-implemented method for identifying 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 of:
  • “Defining an individual eye model” can mean defining model parameters to be specific values. Additionally or alternatively, however, “defining an individual eye model” can also comprise defining at least one consistency measure (or at least one probability). In particular, a plurality of values of the model parameters can exist. A consistency measure or probability can be defined for each combination of these values. For example, such consistency measures or probabilities can be defined using Bayes' method.
  • the term “calculation” in the context of the present invention can include not only the 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. With the Bayes' method, it is possible, for example, that only a likely or most likely lens-retina distance is selected or defined by an optimization problem (which then still has to be solved).
  • the term “calculation” in the context of the present invention can thus in particular also include the selection of likely or most likely values of one or more parameters and/or the definition of an optimization problem.
  • the term “calculation” also includes a selection, determination and/or definition in the context of a statistical procedure, e.g. in the context of or using the Bayes' method.
  • the term “calculation” can in particular also include optimization.
  • the computer-implemented method can also comprise defining or constructing a consistent eye model, in particular using Bayes' method and/or a maximum likelihood method.
  • the individual eye model used or to be defined is a consistent eye model, with the consistency being made possible or established by statistical or probabilistic methods, in particular using Bayes' method and/or a maximum likelihood method.
  • a computer-implemented method and a corresponding device for performing such a method for identifying 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:
  • one or more of the information or parameters and/or at least partially the provided individual refraction data is or are initially defined in the form of a probability distribution
  • defining the individual eye model comprises identifying the model eye by identifying values for information or parameters within the defined probability distribution by a probabilistic method.
  • a model eye is first created by defining parameter values in order to then possibly modify the model eye on the basis of a consistency check using a probabilistic method so that the eye model is consistent
  • a probability distribution is started for at least one parameter in order to then consistently identify the most likely parameter value and thus the most probably model eye using a probabilistic method.
  • Parameters of the probability distribution(s) such as mean values and/or standard deviations, can in particular be determined on the basis of individual measurement values for the eye of the spectacle wearer and/or standard values and/or on the basis of the provided individual refraction data. Further details and specific exemplary embodiments of such methods will be 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, back surface of the IOL, refractive power of the IOL).
  • the back 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 (e.g. according to the method described in DE°10°2017°007°975°A1 or WO°2018/138140°A2) can be defined so that the eye model becomes consistent in terms of astigmatism.
  • higher-order components of this surface e.g.
  • the corneal surface could be adapted accordingly. This is particularly useful if only model-based information on the cornea or no information on astigmatism or higher-order components are available due to topometric measurements.
  • any inconsistencies are solved by adapting or redefining one or more parameters of the eye model.
  • several parameters of the eye model are adapted and the adaptation is divided among the plurality of parameters of the eye model.
  • known deviations can be divided among several elements or components and/or several parameters of the eye model, e.g. the cornea, the front surface of the IOL, the back surface of the IOL, and/or the refractive power of the IOL.
  • fixed or predetermined factors or proportions can be assumed, e.g. 33% on the cornea and 67% on the lens.
  • a physiologically based distribution can be used as well.
  • a further or new parameter can be added to the eye model and defined such that the eye model becomes consistent.
  • the shape of the corneal back surface of a model eye can be such a further parameter.
  • the cylinder axis 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 power of the entire eye can also be adjusted. Here, the target power of the spectacle lens can be changed accordingly in order to render 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.
  • Bayesian statistics and/or a maximum likelihood algorithm can be used.
  • input parameters can be combined and the parameters of the eye model (hereinafter output parameters) can be determined with the aid of statistical methods such as maximum likelihood and Bayes.
  • output parameters parameters of the eye model
  • one or more of the following information on at least individual input parameters can be used:
  • 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-retina distance.
  • the identified eye length is displayed on a display device or display.
  • the method described above relates in particular to the case that properties or data on an implanted intraocular lens, i.e. the intraocular lens data, are known. However, if this data is not known, an alternative approach is proposed in the context of this invention, which will be described below. According to this alternative approach of the present invention, i.e. if there is no direct knowledge of the properties of the implanted lens, conclusions are drawn regarding the properties of the implanted IOLs by measurements on the patient.
  • An alternative approach to solving the object relates to a computer-implemented method for identifying 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 having been implanted in the at least one eye of the spectacle wearer as part of surgery, comprising the steps of:
  • a computer-implemented method for identifying 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 having been implanted in the at least one eye of the spectacle wearer as part of surgery the method in particular comprising the following steps of:
  • parameters of the individual eye model are defined as parameters of the individual eye model, wherein defining the parameters of the individual eye model takes place on the basis of data on visual acuity correction of the at least one eye having the intraocular lens and further on the basis of individual measurement values for the eye of the spectacle wearer and/or standard values and/or on the basis of the provided individual refraction data such that the model eye has the provided individual refraction data.
  • parameters of the individual eye model wherein defining the parameters of the individual eye model takes place on the basis of data on visual acuity correction of the at least one eye having the intraocular lens and further on the basis of individual measurement values for the eye of the spectacle wearer and/or standard values and/or on the basis of the provided individual refraction data such that the model eye has the provided individual refraction data.
  • the data for the visual acuity correction of the at least one eye having the intraocular lens include (in particular individual) intraocular lens data.
  • the parameters of the individual eye model are defined on the basis of intraocular lens data and further on the basis of individual measurement values for the eye of the spectacle wearer and/or standard values and/or on the basis of the provided individual refraction data so that the model eye has the provided individual refraction data, with the parameters of the lens of the model eye being defined on the basis of the intraocular lens data.
  • a lens-retina distance of the eye of the spectacle wearer is identified, and the parameters of the individual eye model are defined on the basis of the identified lens-retina distance and further on the basis of individual measurement values for the eye of the spectacle wearer and/or standard values and/or on the basis of the provided individual refraction data such that the model eye has the provided individual refraction data, with the lens-retina distance of the model eye being defined by the identified lens-retina 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 includes an identified lens-retina distance.
  • the data for the visual acuity correction of the at least one eye having the intraocular lens can include an identified lens-retina distance and/or intraocular lens data.
  • a computer-implemented method for identifying 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 having been implanted in the at least one eye of the spectacle wearer as part of surgery or the at least one eye of the spectacle wearer (in particular instead of or in addition to the natural eye lens) having an implanted intraocular lens.
  • the method can in particular comprise the following steps of:
  • a) defining the parameters of the individual eye model takes place on the basis of intraocular lens data and further on the basis of individual measurement values for the eye of the spectacle wearer and/or standard values and/or on the basis of the provided individual refraction data such that the model eye has the provided individual refraction data, wherein the parameters of the lens of the model eye are defined on the basis of the intraocular lens data;
  • a lens-retina distance of the eye of the spectacle wearer is identified and defining the parameters of the individual eye model takes place on the basis of the identified lens-retina distance and further on the basis of individual measurement values for the eye of the spectacle wearer and/or standard values and/or on the basis of the provided individual refraction data such that the model eye has the provided individual refraction data, wherein the lens-retina distance of the model eye is defined by the identified lens-retina distance of the eye of the spectacle wearer.
  • the term surgery (German: Operation) is generally abbreviated as OP.
  • the term “post-surgery” (German: Nach-OP) refers to a situation after surgery, while the term “pre-surgery” (German: Vor-OP) refers to a situation before surgery.
  • the surgery is a cataract surgery in which the natural eye lens is replaced by an intraocular lens.
  • it can also be a surgery 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 has been replaced by an intraocular lens during surgery.
  • 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 tracing into the eye.
  • the eye model required for this is assigned individual values. In this case, however, no information about the IOL is available and model-based values are not necessarily consistent with the actually implanted lens. 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, based on data that corresponds to a situation in which the original lens was located in the eye, the eye length or a lens-retina distance, as described in DE 10 2017 007 975 A1 or WO 2018/138140 A2, will be calculated.
  • the other parameters i.e. the parameters of the eye lens, in this case the implanted IOL
  • the other parameters will be determined on the basis of the thus-calculated eye length (or the calculated lens-retina distance) and the post-surgery values for the aberrations of the entire eye, the surface of the cornea, and the distance cornea-lens such that the power of this eye model corresponds to the aberrations of the entire eye.
  • the following data is preferably used specifically:
  • the data on the last two points can be either from measurements before the surgical procedure (operation) or after the surgical procedure.
  • the use of data determined after the surgical procedure is particularly useful if no corresponding measurements have been carried out before the surgical procedure.
  • the data on the last two points can be either from measurements before the surgical procedure (operation) or after the surgical procedure.
  • the use of data determined before the surgical procedure is particularly useful if no corresponding measurements have been carried out after the surgical procedure.
  • Providing the individual intraocular lens data can in particular comprise the following steps of:
  • the determination of a lens-retina distance or an eye length of the eye of the spectacle wearer can take place by direct measurement, for example.
  • the method further comprises providing individual pre-surgery refraction data on the at least one eye of the spectacle wearer, wherein the determination of a lens-retina distance or an eye length of the eye of the spectacle wearer on the basis of an individual pre-surgery eye model takes place using the provided individual pre-surgery refraction data.
  • the corneal front surface is preferably measured individually and the eye lens of the individual pre-surgery eye model is calculated accordingly in order to meet the individually determined pre-surgery refraction data.
  • the corneal front surface (or its curvature) is measured individually along the main sections (topometry).
  • the topography of the corneal front surface i.e. the complete description of the surface
  • the cornea-lens distance is defined on the basis of individual measurement values for the cornea-lens distance.
  • defining the parameters of the lens of the pre-surgery model eye comprises defining the following parameters:
  • defining the lens thickness and the shape of the lens back surface takes place on the basis of predetermined values (standard values, for example from the technical literature), wherein defining the shape of the lens front surface further preferably comprises:
  • defining the shape of the lens front surface comprises:
  • defining the lens thickness and the shape of the lens back surface take place on the basis of standard values, and even more preferably defining the shape of the lens front surface comprises:
  • defining the lens parameters can include defining an optical power of the lens.
  • at least one position of at least one main plane and a spherical power (or at least one focal length) of the lens of the model eye are defined.
  • a cylindrical power (magnitude and axial position) of the lens of the model eye is also particularly preferred.
  • optical higher-order aberrations of the lens of the model eye can also be identified.
  • Another independent aspect for solving the object relates to a computer-implemented method for calculating or optimizing an ophthalmic lens (in particular a spectacle lens) for at least one eye of a spectacle wearer, comprising:
  • Another independent aspect for solving the object relates to a computer-implemented method for calculating or optimizing an ophthalmic lens (in particular a spectacle lens) for at least one eye of a spectacle wearer, comprising:
  • the evaluation surface is located between the corneal front surface and the retina.
  • the evaluation surface is located between the lens and the retina of the model eye.
  • the evaluation surface is located on the exit pupil (AP) of the model eye.
  • the exit pupil can be located in front of the lens back surface of the model eye. With this positioning, a particularly precise, individual adaptation of the spectacle lens can be achieved.
  • Another independent aspect for solving the object relates to a method for producing an ophthalmic lens (in particular a spectacle lens), comprising:
  • Another independent aspect for solving the object relates to a device for identifying relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of an ophthalmic lens for the at least one eye of the spectacle wearer, comprising:
  • providing individual data comprises providing individual refraction data on the at least one eye of the spectacle wearer.
  • constructing an individual eye model comprises defining an individual eye model in which at least
  • the modeling module is also configured to carry out a consistency check of the defined eye model with the provided individual refraction data and to solve any inconsistencies, in particular with the aid of analytical and/or probabilistic methods.
  • the invention thus offers a device for identifying relevant individual parameters of at least one eye of a spectacle wearer for the calculation or optimization of an ophthalmic lens (in particular a spectacle lens) for the at least one eye of the spectacle wearer, comprising:
  • the modeling module is configured to carry out a consistency check of the defined eye model with the provided individual refraction data and to solve any inconsistencies, in particular with the aid of analytical and/or probabilistic methods.
  • the invention provides a device for identifying 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 having an implanted intraocular lens (in particular instead of or in addition to the natural eye lens), comprising:
  • defining the parameters of the lens of the model eye is carried out on the basis of the provided intraocular lens data.
  • defining the lens-retina distance is carried out by measuring and/or calculating.
  • the modeling module is configured to identify an eye length of the model eye taking into account the measured and/or calculated lens-retina distance.
  • the device preferably also comprises a display device for displaying the measured and/or calculated lens-retina distance and/or the determined eye length.
  • the device is particularly preferably designed as an aberrometer and/or as a topograph.
  • the modeling module is configured to carry out a consistency check of the identified eye model, in particular the identified pre-surgery eye model and/or the identified post-surgery eye model. Furthermore, the modeling module is preferably configured to solve 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 provides a device for identifying 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 surgery, comprising:
  • the lens-retina distance of the model eye of the post-surgery eye model is defined by the identified lens-retina distance of the spectacle wearer's eye.
  • Another independent aspect for solving the object relates to a device for calculating or optimizing a spectacle lens for at least one eye of a spectacle wearer, comprising:
  • Another independent aspect for solving the object relates to a device for producing a spectacle lens, comprising:
  • the device for producing a spectacle lens can be designed in one piece or as an independent machine, i.e. all components of the device (in particular the calculation or optimization means and the machining means) can be part of one and the same system or one and the same machine.
  • the device for producing a spectacle lens is not designed in one piece, but is realized by different (in particular independent) systems or machines.
  • the calculation or optimization means can be realized as a first system (in particular comprising a computer) and the machining means as a second system (in particular a machine comprising the machining means).
  • the different systems can be located in different places, i.e. they can be locally separated from one another.
  • one or more systems can be located in the front end and one or more other systems in the back end.
  • the individual systems can e.g. 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 communicate with one another directly, in particular via a network (e.g. 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 several devices (possibly locally separated) configured to carry out individual method steps of a corresponding method.
  • the invention offers a computer program product or a computer program article, in particular in the form of a storage medium or a data stream containing program code that is designed, when loaded and executed on a computer, to execute a method according to the invention for identifying relevant individual parameters of at least one eye of a spectacle wearer and/or to execute a method according to the invention for calculating or optimizing a spectacle lens.
  • a computer program 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 that, when loaded into a memory of a computer and executed by the computer, cause the computer to execute a method according to the invention.
  • the invention provides a spectacle lens produced by a method according to the invention and/or using a device according to the invention.
  • the invention provides a use of a spectacle lens produced by the production method according to the present invention, in particular in a preferred embodiment, in a predetermined average or individual wearing position of the spectacle lens in front of the eyes of a specific spectacle wearer for correcting a vision disorder of the spectacle wearer.
  • the invention can in particular comprise one or more of the following aspects:
  • 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-surgery and/or post-surgery refraction data) of the at least one eye of the spectacle wearer, can be acquired and/or transmitted.
  • the intraocular lens data can be transmitted e.g. 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 e.g.
  • the optician and/or ophthalmologist or surgeon may retrieve this data from a database, in particular with the help of a type and/or serial number of the implanted IOL or with the help of a patient code (e.g. customer or patient number, name, etc.).
  • Measurement or refraction data can also be called up directly from a measuring device, for example.
  • 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 input, at least in part, manually via an input unit. In this way, an ophthalmologist or surgeon can e.g. transmit the so-called A constant or IOL constant of the intraocular lens used.
  • a lens or IOL prescription 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 can in particular comprise a computer and/or data server configured to communicate via a network (e.g. Internet).
  • the computer is in particular configured to execute a computer-implemented method, e.g. ordering software for ordering at least one spectacle lens, and/or transmission software for transmitting relevant data (in particular intraocular lens data and/or prescription data and/or refraction data), and/or identification software for identifying relevant individual parameters of at least one eye of a spectacle wearer, and/or calculation or optimization software for calculating and/or optimizing a spectacle lens to be produced, according to the present invention.
  • a computer-implemented method e.g. ordering software for ordering at least one spectacle lens, and/or transmission software for transmitting relevant data (in particular intraocular lens data and/or prescription data and/or refraction data), and/or identification software for identifying relevant individual parameters of at least one eye of a spectacle wearer, and/or calculation or optimization software for calculating and/or optimizing
  • FIG. 1 a schematic representation of the physiological and physical model of a spectacle lens and an eye together with a beam path in a predetermined wearing position;
  • FIG. 2 a graph with an exemplary dependency of P mess on S IOL and L 2,IOL to illustrate and explain a method for identifying parameters under constraint conditions according to a preferred embodiment of the present invention
  • FIGS. 3 a - 3 f 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 method according to Bayes A;
  • FIGS. 4 a - 4 f 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 method according to Bayes A;
  • FIGS. 5 a - 5 c histograms of marginal probability densities of M, J 0 , and J 45 , which represent a sample from the posterior distribution of the power of the ophthalmic lens, for the first example for the method according to Bayes A or Bayes B;
  • FIGS. 6 a - 6 e marginal prior probability densities as scatter diagrams of a sample from the prior distribution for the second example for the method according to Bayes A;
  • FIGS. 7 a - 7 e marginal posterior probability densities as scatter diagrams of a sample from the posterior distribution for the second example for the method according to Bayes A;
  • FIGS. 8 a - 8 c histograms of marginal probability densities of M, J 0 , and J 45 , which represent a sample from the posterior distribution of the power of the ophthalmic lens, for the second example for the method according to Bayes A or Bayes B;
  • FIGS. 9 a - 9 c histograms of marginal probability densities of M, J 0 , and J 45 , which result from a prior distribution, for the second example for the method according to Bayes A or Bayes B.
  • FIG. 1 shows a schematic representation of the physiological and physical model of a spectacle lens and an eye in a predetermined wearing position 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 ocular center of rotation Z′), but also the derivatives of the vertex depths 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 higher-order aberrations.
  • the local derivatives of the wavefronts are ultimately identified at a suitable position in the beam path in order to compare them there with a reference wavefront that converges in a point on the retina of the eye 12 .
  • the two wavefronts i.e. the wavefront coming from the spectacle lens and the reference wavefront
  • the two wavefronts are compared with one another in an evaluation surface.
  • “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 surfaces through which refraction took place before reaching the evaluation surface.
  • refraction takes place through all refractive surfaces including the lens back surface.
  • the reference wavefront is preferably a spherical wavefront whose center of curvature is located on the retina of the eye 12 .
  • the radius of curvature of this reference wavefront does correspond to the distance between the lens back surface and the retina.
  • propagation is still carried out after the last refraction, preferably up to the exit pupil AP of eye 12 .
  • the reference wavefront is spherical with the center of curvature on the retina, but has a radius of curvature 1/d AR .
  • a spherical wavefront w 0 emanates from the object point and propagates up to the first spectacle lens surface 14 . There it is refracted and then it propagates to the second lens surface 16 , where it is refracted again.
  • the wavefront w g1 exiting the spectacle lens then propagates along the main ray in the direction of the eye 12 (propagated wavefront w g2 ) until it hits the cornea 18 , where it is refracted again (wavefront w c ).
  • the wavefront is also refracted again by the eye lens 20 , whereby the resulting wavefront we arises on the back surface of the eye lens 20 or on the exit pupil of the eye, for example.
  • This is compared with the spherical reference wavefront w s and the deviations are evaluated for all visual points in the target function (preferably with corresponding weightings for the individual visual points).
  • the vision disorder is no longer described only by a thin sphero-cylindrical lens, as was customary in many conventional methods, 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 cylinder axis—as well as preferably including the higher-order aberrations) are directly taken into account in the eye.
  • the vitreous body length d LR is calculated individually in the eye model according to the invention.
  • An aberrometer measurement preferably provides the individual wavefront deformations of the real eye having the visual defect for distance and near (deviations, no absolute refractive indices) and the individual mesopic and photopic pupil diameters.
  • an individual real corneal front 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 corneal back surface. It is preferably described by an adaptation of the refractive index of the cornea and not by a separate refractive surface due to the small refractive index difference compared to the aqueous humor and because of the small cornea thickness in a good approximation.
  • S is the vergence matrix of the wavefront S of the same name, except that S besides the 2nd order aberrations summarized in S, also comprises the entirety of all higher-order aberrations (HOA) of the wavefront.
  • HOA higher-order aberrations
  • S stands for the set of all parameters necessary to describe a wavefront (with sufficient accuracy) in relation to a given coordinate system.
  • S stands for a set of Zernike coefficients with a pupil radius or a set of coefficients of a Taylor series.
  • S stands for the set of a vergence matrix S for describing the wavefront properties of the 2nd order 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 Taylor decomposition. Analogous statements apply to surfaces instead of wavefronts.
  • the modeling of the passage of the wavefront through the eye model used according to the invention i.e. after passage through the surfaces of the spectacle lens, can be described as follows in a preferred embodiment in which the lens is described via a front and a back surface, with the transformations the vergence matrices is explicitly being specified:
  • steps 2, 4, 6, in which the distances ⁇ CL , ⁇ CL , and ⁇ CL are propagated can be divided into two partial propagations 2a, b), 4a, b) or 6a, b) according to the following scheme, which explicitly reads for step 6a, b):
  • steps 6a and 6b offer advantages, however, and the intermediate plane can preferably be placed in the plane of the exit pupil AP, which preferably is located in front of the lens back surface.
  • ⁇ LR (a) ⁇ 0 and ⁇ LR (b) >0.
  • steps 2, 4 can be analogous to the division of step 6 in 6a, b).
  • the plane of the AP (which normally is located between the lens front surface and the lens back surface) is formally passed by the light for the first time after an imaginary step 4a, in which propagation takes place from the lens front surface by the length ⁇ L (a) >0.
  • the same plane is reached for the second time after step 6a when, after the refraction through the lens back surface, propagation back to the AP plane takes place, i.e.
  • the wavefront S AP S LR that is the result of step 6a should preferably always be meant (unless explicitly stated otherwise).
  • 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 described later takes into account and also uses higher orders of aberrations.
  • the eye model in a preferred embodiment, has twelve parameters as degrees of freedom of the model that have to undergo assignment. 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 1 and L 2 for the front and back surfaces of the lens, as well as respectively one for the length parameters anterior chamber depth d CL , lens thickness d L , and the vitreous body length d LR .
  • the total number df 2 of degrees of freedom of the eye model in the second order (df stands for ‘degree of freedom’, index ‘2’ for second order) is thus composed of
  • df 2 df 2 ( i )+df 2 ( ii )+df 2 ( iii )
  • the objective refraction of the relevant eye is also defined, so that an objective refraction determination no longer has to be carried out in addition.
  • a central aspect of the invention relates precisely to the airm 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), be assigned with other given data.
  • L 1 is adapted to the measurements in particular by calculating the measured vergence matrix S M by means of steps 1, 2 through the likewise measured matrix C and propagating it up to the object-side side of the lens front surface.
  • a spherical wave is calculated back to front from an imaginary point-like light source on the retina by means of steps 6, 5, 4 carried out backward by refracting this spherical wave at the previously defined surface power matrix L 2 of the lens back surface and propagating the then-obtained wavefront from the lens back surface up to the image-side side of the lens front surface.
  • L 2 D LR - ( S M + C 1 - ⁇ CL ( S M + C ) + L 1 ) ⁇ ( 1 - ⁇ L ( S M + C 1 - ⁇ CL ( S M + C ) + L 1 ) ) - 1 ( 1 ⁇ b )
  • the central idea of the invention is to calculate at least the length parameter d LR (or D LR ) from other measurement data and a priori assumptions about other degrees of freedom and not to assume it a priori itself, as is conventional.
  • d LR the length parameter d LR
  • D LR the length parameter
  • the data on the vergence matrix S M and particularly preferably also the data on C are preferably available from individual measurements.
  • a spherical back surface i.e. a back surface without astigmatic components is taken as a basis.
  • measurement data up to the second order are available for the cornea C, which corresponds to the data on the surface power matrix C.
  • df 2 3+6+3.
  • six parameters from ⁇ L 1 , L 2 , d L , d CL ⁇ have to undergo assignment by assumptions or literature values. The other two result in addition to d LR from the calculation.
  • the parameters of the lens back surface, the mean curvature of the lens front surface, and the two length parameters d L and d CL undergo assignment a priori (as predetermined standard values).
  • the anterior chamber depth d CL i.e. the distance between the cornea and the lens front surface
  • the measured parameters thus include ⁇ C, d CL , S M ⁇ .
  • the problem is therefore still underdetermined mathematically, so five parameters from ⁇ L 1 , L 2 , d L ⁇ have to be deformed a priori through assumptions or literature values.
  • these are the parameters of the lens back surface, the mean curvature of the lens front surface, and the lens thickness.
  • the parameters of the lens back surface and the lens thickness are involved. The exact calculation will be described below.
  • This embodiment is particularly advantageous if a pachymeter is used, the measuring depth of which allows the lens back surface 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 lens front surface can be obtained by an individual measurement.
  • This additional information can be exploited in two ways in particular:
  • the anterior chamber depth, two or three parameters of the lens front surface, and the lens thickness are measured individually.
  • the other variables 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 lens front surface, the lens thickness, and at least one parameter of the lens back surface are provided.
  • the respective additionally measured parameters can be carried out analogously to the step-by-step expansions of the above sections.
  • L 2 D LR - ( S M + C 1 - ⁇ CL ( S M + C ) + L 1 ) ⁇ ( 1 - ⁇ L ( S M + C 1 - ⁇ CL ( S M + C ) + L 1 ) - 1
  • D LR L 2 + ( S M + C 1 - ⁇ CL ( S M + C ) + L 2 ) ⁇ ( 1 - ⁇ L ( S M + C 1 - ⁇ CL ( S M + C ) + L 2 ) ) - 1
  • D LR is a scalar
  • S M , C, L 1 and L 2 are each the spherical equivalents of the vision disorder, the cornea, the lens front surface, and the lens back surface, respectively.
  • the values of the so-called Bennett & Rabbetts eye for the refractive powers of the lens surfaces can be used, which can be taken from Table 12.1 of the book “Bennett & Rabbets' Clinical Visual Optics”, third edition, by Ronald B. Rabbetts, Butterworth-Heinemann, 1998, ISBN-10: 0750618175, for example.
  • the calculation described above leads to results that are very compatible with the population statistics, which state that short-sighted vision disorders tend to lead to large eye lengths and vice versa (see e.g. C. W. Oyster: “The Human Eye”, 1998).
  • the aim of the method using Bayesian statistics is to use, if possible, all available information sources 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 (e.g. a spectacle lens) in the light of this information.
  • an ophthalmic lens e.g. a spectacle lens
  • a probability or probability density can be assigned to an individual eye model with a given set of parameters.
  • Individual eye models that are consistent with the available information e.g. objective wavefront measurement and biometrics of the eye
  • have a higher probability or probability density because e.g. the propagation and refraction of a wavefront that a point light source would generate on the retina after exiting the eye reproduces the measured data well within the scope of the measurement accuracy of the objective wavefront measurement, and likewise the parameters of the individual eye match with the available information about the biometry of the eye within the scope of the distributions known e.g. from the literature.
  • i denotes the parameters of the individual eye model i
  • d i are the measured data (it can e.g. include the current refraction or the refraction measured prior to eye surgery, the measured shape and/or refractive properties of the cornea, the measured eye length or other variables measured on the individual eye).
  • I the current state of knowledge upon evaluation of the data, i.e. the existing background information (e.g. about the measurement process of the refraction, the distribution of the parameters of the individual eye model or other related variables in the population) is summarized.
  • ′ means that the distribution of the variables to the left of ,
  • the information obtained in the measurement process, in which the data d i is measured, can also be understood as the probability distribution of the data d i with given parameters i of the individual eye model i:
  • the accuracy of the measurement process is reflected in the width of the distribution: an exact measurement has a narrower distribution than an imprecise measurement, which has a wide or wider distribution of the data d i .
  • 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 for a large number of other people.
  • the probability here serves as a measure of consistency. Parameter values of the individual eye model that are consistent with the measurements can be found in particular where both prob( i
  • d i , I) can also be suitably normalized in order to write the proportionality as an equation.
  • d i , I) can also include parameters of the eye lens.
  • some of the parameters i can include 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 eye lens can be a natural lens.
  • literature data on the parameters of natural eye lenses can be used (e.g. 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, provided they are individually known. Otherwise, distributions of these parameters can be used from literature studies of eyes that underwent surgery. If such information is not available, a flat distribution within reasonable limits can be selected.
  • parameters that are positively definite and define length scales e.g. radii of curvature or distances
  • d i , I) can have one or more factors.
  • ach factor represents the information about one or more parameters of the individual eye model.
  • the distribution of different independent parameters i 1 and i 2 from different literature sources can be represented as a product
  • d i ,I ) prob( i 1 , i 2
  • d i ,I ) prob( i 1
  • parameters of the eye model can inadvertently be falsified. For example, if 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, a distribution that is constant in the corresponding parameter (e.g. spherical equivalent of refraction) within carefully selected limits (e.g. between ⁇ 30 dpt and +20 dpt for the spherical equivalent M, ⁇ 5 dpt for the astigmatic components J 0 and J 45 ) should be chosen.
  • spherical equivalent of refraction e.g. spherical equivalent of refraction
  • parameters of the individual eye model or other variables related to the parameters or measurement data is 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 variables can be integrated on both sides, which may simplify subsequent calculations.
  • Bayes A and Bayes B Two possible methods for calculating an ophthalmic lens will be presented below (Bayes A and Bayes B).
  • the eye model can e.g. be given by or assigned the set of parameters i max , which maximizes the probability or probability density prob( i
  • Other sets of parameters can also be selected, e.g. the expected value ⁇ i > or the median i med of the parameters i with regard to the distribution prob( i
  • the Bayes B method is more advantageous—but computationally more demanding—compared to Bayes A, since a subset of individual eye models with different sets of parameters can lead to ophthalmic lenses that have very similar (even identical) properties (e.g. refractive power in a reference point of the ophthalmic lens, or the distribution of the refractive deficit across 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, instead of just determining the most likely individual eye model and manufacturing an ophthalmic lens for it.
  • an ophthalmic lens e.g. a spectacle lens
  • a spectacle lens consistent with the information available
  • 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, i.e. 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 (i.e. determining the parameters of an individual eye model) can include determining a multivariate probability distribution that includes 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, i.e. it is integrated via the hyperparameters.
  • the integrals can be solved with common numerical methods (e.g. using Markov Chain Monte Carlo or Hybrid Monte Carlo) and/or analytical methods.
  • the probability or the probability density of the parameters of the eye model can in this case be calculated using the following equation:
  • ⁇ ,I) denotes the probability or probability density to find the parameters of the individual eye model i in the population characterized by the hyperparameters ⁇ .
  • the integrals are to be carried out over the entire definition ranges of all hyperparameters ⁇ .
  • the distribution calculated analogously to steps 1 to 3 of the Bayes A method can be provided.
  • the most likely parameters L i of the ophthalmic lens are determined, i.e. on the basis of the probability distribution or probability density
  • L i max are determined, which maximize prob(L i
  • L i initially denotes the parameters of any ophthalmic lens
  • L i L( i ) the parameters of the ophthalmic lens created when an ophthalmic lens is optimized with the aid of an individual eye model with the parameters i .
  • the Dirac delta distribution is denoted by ⁇ (.).
  • the parameters of the ophthalmic lens can be e.g. vertex depth, refractive power at a reference point of the ophthalmic lens, refractive power distribution over an area of the ophthalmic lens, refractive errors at a reference point of the ophthalmic lens, or the distribution of the refractive errors over an area of the ophthalmic lens.
  • the equation described above can also be solved with the help of partial integration.
  • Other methods are also possible, e.g. numerical methods such as Particle Filter, Markov Chain Monte Carlo, or methods of parametric inference, with which a distribution of the parameters of the ophthalmic lens L i can be calculated.
  • the basic problem to be solved is that in the case of measurement 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 adopted. If all measurement values are plausible in themselves, but violate one of the consistency conditions, then they must not all be adopted. Instead, a balance between the various measurement values must then be sought: those that have a very high measurement reliability should at least almost be retained, while uncertain measurement values are more likely to be adapted. Preferably, the best possible values for all N parameters are identified from the known information.
  • the inventive idea is based in particular on the assumption that the parameters have certain (unknown but initially fixed) values. Under this assumption, in the light of the above-mentioned information (statistical variables from the population, reliability measures of the measurements), the conditional probability density
  • This probability density is understood as a function P par (x 1 , . . . , x N ) of the assumed N parameters x 1 , . . . , x N .
  • Those N parameter values for which this function assumes a maximum are then preferably considered to be the best possible values (maximum likelihood approach):
  • the N parameter values can also be defined by setting the last parameters equal to the mean values of the population
  • the medians can be used as a criterion as well.
  • 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 ges ( X 1 , . . . ,X k ,x 1 , . . . ,x N ) P mess ( X 1 , . . . ,X k
  • P pop is described by the multivariate normal distribution
  • the measurement is described by the distribution P mess (X 1 , . . . , X k
  • the measurements are independent
  • each of the measurements is normally distributed with expected value x i and standard deviation ⁇ i mess
  • equation (9) or equation (10) represents a linear system of equations with N equations and N variables that can be solved for x 1 , . . . , x N .
  • One embodiment of the invention then consists in adopting the measurement values for 1 ⁇ i ⁇ k directly and neglecting their slight shift due to the underlying population.
  • One possibility in practice is to regularize the covariance matrix C by shifting one or more of the correlations ⁇ ij or standard deviations ⁇ i contained in it by ⁇ and then determining x 1 , . . . , x N .
  • the solutions thus obtained then automatically satisfy the constraints for ⁇ 0.
  • the substitution method can preferably be used for this purpose.
  • the constraints as a function of x u are:
  • the system of equations (16) is K equations that can be solved for the parameters x u independent for K.
  • the remaining parameters x a are obtained by inserting them into the context x a (x u ).
  • the entire set of parameters can be considered independent if, instead of the function P mess (x 1 , . . . , x N ), the Lagrange function is maximized
  • ⁇ ( ⁇ 1 , . . . , ⁇ Q ) is a Q-dimensional vector of Lagrange multipliers. It is then to be maximized by setting the derivatives N+Q to zero
  • the method of Eqs. (16) to (18) can be applied to the function P ges (x 1 , . . . , x N ) instead of P mess (x 1 , . . . , x N ) and then represents a maximum-posterior method with constraints.
  • n CL 1.336;refractive index anterior chamber (literature)
  • n L 1.422;refractive index lens (literature)
  • n LR 1.336;refractive index vitreous body (literature) (19).
  • D LR L 2 + ( L 1 + S + C 1 - ⁇ CL ( S + C ) ) ⁇ ( 1 - ⁇ L ( L 1 + S + C 1 - ⁇ CL ( S + C ) ) ) - 1 ( 21 )
  • Vitreous body length and eye length are so directly related that in the following the vitreous body length can be considered instead of the eye length.
  • the initial situation can be regarded as the case that there are no variations and no correlations in the basic population, and that only the vision disorder measured afterward as well as the IOL itself are subject to uncertainties:
  • D LR L 2 , IOL + ( L 1 + S IOL + C 1 - ⁇ CL ( S IOL + C ) ) ⁇ ( 1 - ⁇ L ( L 1 + S IOL + C 1 - ⁇ CL ( S IOL + C ) ) ) - 1 ( 25 )
  • IOL ( S IOL ) D LR - ( L 1 + S IOL + C 1 - ⁇ CL ( S IOL + C ) ) ⁇ ( 1 - ⁇ L ( L 1 + S IOL + C 1 - ⁇ CL ( S IOL + C ) ) ) - 1 . ( 26 )
  • the constraint means that one may only move on the cutting surface 30 shown in FIG. 2 .
  • Both variables S IOL , L 2,IOL are therefore in the negative direction compared to the measurement values, but not to the same extent. Rather, 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 for a calculated eye length (or a calculated lens-retina distance), but also e.g. when measuring the eye length. Such inconsistencies can be solved analogously to the example of a calculated eye length described above. Of course, more complex examples in which the eye length itself is also not fixed or where possibly correlations occur, can also be given.
  • the eye model that is used in this example consists of a vision disorder, c n m , described up to the 4 th Zernike order, which relates to a pupil diameter of 5 mm, as well as the natural logarithm of a pupil radius log r ph or log r mes present under photopic or mesopic lighting conditions.
  • the model parameters of the eye model can be written as a vector
  • the Zernike coefficients of the 0 th to 1 st order were not considered here, as they do not play a role in the vision disorder of the eye and can be assumed to be constantly 0, for example.
  • the measurement data d i known for an individual eye are here sphere, cylinder and axis of the (far) refraction Rx,
  • the measurement error of the refraction is also known and as the standard deviation in the individual power vector components is
  • the measurement error is normally distributed as a power vector around the power vector of the vision disorder P eye ( i ) that can be identified from the model parameters, so that
  • P eye ( i ) is the power vector (M eye ,J 0 Rx ,J 45 eye ), which with the help of the Root-Mean-Squared (RMS) metric results from a Zernike wavefront scaled to the photopic pupil radius r ph according to known methods.
  • RMS Root-Mean-Squared
  • P eye ( i ) P eye (log r ph ,c 2 ⁇ 2 ,C 2 0 ,C 2 +2 ,C 4 ⁇ 2 ,C 4 0 ,C 4 +2 ).
  • the most likely eye model is identified for given background knowledge I (distribution of the model parameters i in the population, measurement accuracy of the refraction, determination of the power vector from a vision disorder in Zernike representation, etc.) and the known measurement data P Rx .
  • the posterior consists of the likelihood-weighted sample of the prior. To this end, the likelihood for each element (sample) of the sample of the prior was evaluated and used as a weight. Alternatively, a smaller sample size can be used, in which case an unweighted sample must be taken from the weighted sample. Marginal posterior densities are to be seen analogously to the prior in FIGS. 4 a to 4 f.
  • i max The maximum of the posterior density, was approximated by means of a kernel density estimation (kernel: 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 5 mm diameter):
  • the power of the lens, P mes ( ⁇ i max ), which optimally corrects the most likely eye model under mesopic lighting conditions, was calculated by scaling the Zernike coefficients c 2 ⁇ 2,max , c 2 0,max , c 2 +2,max , c 3 ⁇ 3,max , c 3 ⁇ 1,max , c 3 +1,max , c 3 +3,max , c 4 ⁇ 4,max , c 4 ⁇ 2,max , c 4 0,max , c 4 +2,max , c 4 +4,max , related to the pupil diameter of 5 mm to the most likely mesopic pupil with the radius r mes max with the aid of the method known from the literature. From this vision disorder of the eye, still given in the Zernike representation, the power vector was again identified with the RMS metric
  • mesopic lighting conditions e.g. a single vision lens or as a power in the distance reference point of a progressive lens.
  • the power of a lens that optimally corrects the most likely eye model under photopic lighting conditions can be calculated by scaling the vision disorder in Zernike representation to the most likely photopic pupil with radius r ph max . This yields
  • the eye model considered in this example and the measurement data (here the refraction) are chosen as in the Bayes A example. Now, however, the aim is to calculate the most likely power of an ophthalmic lens to be manufactured, and not the power of the ophthalmic lens for the most likely eye model. As in the example of the Bayes A method, the lens is to 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 related to a pupil diameter of 5 mm in this sample using the method known from the literature.
  • Power vectors for the mesopic pupil were identified from these mesopic Zernike wavefronts using the root-mean-squared (RMS) metric. These in turn represent a sample from the posterior distribution of the power of an ophthalmic lens optimized for a mesopic pupil (cf. FIGS. 5 a to 5 c ).
  • the maximum of the posterior distribution was approximated by the maximum of a kernel density estimation of the sample (multivariate normal distribution as kernel with a standard deviation corresponding to 0.5 times the standard deviation of the posterior distribution of the power vector). This yielded the following most likely power
  • an ophthalmic lens to be manufactured e.g. the power of a spectacle lens such as a single vision lens, or the power in the distance reference point of a progressive lens
  • This most likely power differs from the power P mes ( i max ) calculated in the Bayes
  • the most likely eye model due to the non-linear transformation (here scaling) of the parameters of the eye model (here the vision disorder described up to the 4 th Zernike order and the logarithms the mesopic and photopic pupils) into the parameters of the ophthalmic lens (here the power of the ophthalmic lens as a power vector).
  • P mes L, max in turn represents a further improvement compared to the correction P mes ( i max ), since P mes L, max corresponds to the most likely vision disorder for the given information, and P mes ( i max ) only to the vision disorder of the most likely eye model but generally not the most likely vision disorder.
  • Bayes A or Bayes B methods are used, but in which a much more complex eye model is used, which e.g. can consist of several refractive surfaces and media with different refractive indices.
  • Each of the surfaces can be described e.g. in a Zernike representation, the distribution of the coefficients can be partially or fully 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, 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.
  • the refractive indices of the media can also be included in the model as parameters that are not precisely known. Models with refractive index gradients are also 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 e.g. by approximation methods such as parametric inference (e.g. variational inference), in which the posterior itself is parameterized and its determination is understood as an optimization problem.
  • parametric inference e.g. variational inference
  • the corneal back surface is neglected in this model (see Bennett-Rabbett's eye model).
  • the surface power is used in the cross-section 0°, 45° and 90° to the horizontal (i.e. the elements of the surface power matrix, designations for this are D xx k , D xy k und D yy k ).
  • the mutual position of the refractive surfaces and the retina is parameterized as a positive quantity by the natural logarithms of the distances between two directly adjacent surfaces (logarithms of the distances cornea-lens front surface, lens front surface-lens back surface, and the lens back surface-retina are designated with log d 12 , log d 23 and log d 34 , respectively, wherein the distances are used in mm).
  • the refractive indices of the media between the refractive surfaces i.e. in the anterior chamber, eye lens, and vitreous body
  • n 12 , n 23 und n 34 respectively.
  • the measurement data d i known for an individual eye are here sphere, cylinder and axis of the (far) refraction Rx,
  • the measurement error of the refraction is also known and as the standard deviation in the individual power vector components is
  • the measurement error is normally distributed as a power vector around the power vector of the vision disorder P eye ( i ) that can be identified from the model parameters, so that
  • P eye ( ⁇ i ) is the power vector (M eye )( i ), J 0 eye ( i ), J 45 eye ( i )), which corresponds to the vision disorder of the eye model and can be calculated by repeated propagation and refraction of a wavefront, emanating from a point on the retina, through the eye to the vertex of the cornea from the parameters of the eye model in a paraxial approximation.
  • the most likely eye model is identified for given background knowledge I (distribution of the model parameters i in the population, measurement accuracy of the refraction, determination of the power vector from a vision disorder in Zernike representation, etc.) and the known measurement data P Rx .
  • the correlation matrix of the normal distribution had a diagonal occupied by 1 and was occupied by zero everywhere except for the following non-diagonal elements:
  • the posterior consists of the likelihood-weighted sample of the prior. To this end, the likelihood for each element (sample) of the sample of the prior was evaluated and used as a weight. Alternatively, a smaller sample size can be used, in which case an unweighted sample must be taken from the weighted sample. Marginal posterior densities are to be seen analogously to the prior in FIGS. 7 a to 7 e.
  • i max The maximum of the posterior density, was approximated by means of a kernel density estimation (kernel: 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 i max for the most likely eye model
  • the power of the lens P( i max ) that optimally corrects the most likely eye model can differ from the vision disorder of the most likely eye, P eye (( i max )), since the former relates to the corrective lens and the latter to the power of the eye during refraction, since the distances between the cornea and the corrective lens or refractive lens generally differ.
  • the eye model considered in this example as well as the measurement data (here the refraction) are chosen as in the previous second Bayes A example. Now, however, the aim is to calculate the most likely power of an ophthalmic lens to be manufactured, and not the power of the ophthalmic lens for the most likely eye model.
  • the parameters of the ophthalmic lens, L i correspond to their power in simplified form:
  • power vectors were calculated from the posterior sample of the previous second Bayes A example, which represent a sample from the posterior distribution of the power of the optimal ophthalmic lens (cf. FIGS. 8 a to 8 c ).
  • the information gain through the data is clearly recognizable on the basis of the reduced scattering range of the posterior compared to the prior.
  • the maximum of the posterior distribution was approximated by the maximum of a kernel density estimation of the sample (multivariate normal distribution as kernel with a standard deviation corresponding to 0.5 times the standard deviation of the posterior distribution of the power vector).
  • This resulted in the following most likely power of an ophthalmic lens to be manufactured e.g. the power of a spectacle lens such as a single vision lens, or the power in the distance reference point of a progressive lens, which makes optimal use of the information available about the eye model:
  • This most likely power differs from the power P( i max ) calculated in the Bayes
  • the non-linear transformation here mainly the propagation of the wavefronts between the refracting surfaces
  • the parameters of the eye model here the surface powers and distances of the refractive surfaces and, to a lesser extent, the refractive indices of the media
  • the power of the ophthalmic lens as a power vector
  • P L, max in turn represents a further improvement compared to the correction P( i max ) from the second example for the Bayes B method, since P L, max corresponds to the most likely corrective power for the given information, and P mes ( i max ) only to the power correcting the most likely eye model but generally not the most likely corrective power.

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