Combined determination of visual acuity for optimising a progressive lens

Abstract

The present invention relates to determining at least one individual visual acuity value for at least one eye of a subject, wherein a corresponding method comprises: determining at least one individual subjective visual acuity value for the at least one eye on the basis of an individual response of the subject to a set visual task; acquiring individual objective measurement data for the at least one eye from measurements performed on the at least one eye; and determining, from the at least one individual subjective visual acuity value and the individual objective measurement data, at least one combined visual acuity value as the at least one individual visual acuity value to be determined for the at least one eye of the subject.

Description

[0001] Applicant: Rodenstock GmbH

[0002] MB&P Mark: R03487WO - hb / hb

[0003] Combined visual acuity testing for optimizing progressive lenses: Description

[0004] The present invention relates to a method, a device and a computer program product for improved determination of visual acuity of at least one eye of a subject and a method for improved calculation, optimization or manufacture of a spectacle lens for the at least one eye.

[0005] Subjective refraction has always been an essential basis for determining the corrective power of a spectacle lens. More recently, subjective refraction has been complemented by objective refraction, particularly when measured using an autorefractor. The values ​​of the subjective and objective refractions provide the starting data for calculating the final refraction, which can then be used to determine the corrective power of a spectacle lens. This procedure is described, for example, in EP 2 171 525 A1, EP 3926390 A1, and EP 2079355 A2.

[0006] During subjective refraction testing, visual acuity (visual acuity) is typically determined based on the recognizability of optotypes. This is usually the visual acuity at full correction, representing the visual acuity achievable by the eye with full correction. Opticians primarily perform visual acuity testing to verify the endpoint of the refraction, in other words, the refractive result, or simply the refraction (of the person undergoing the refraction). At this point, the person should have the highest visual acuity (i.e., the best visual acuity). However, visual acuity can also be determined even with suboptimal corrections.

[0007] Methods for subjective visual acuity assessment include, for example, checking the recognizability of optotypes on a visual acuity chart, or psychophysical methods such as the Freiburg Visual Acuity Test (FrACT). German patent DE 102021 202442 A1 discloses how visual acuity can be determined both with and without full correction during refraction testing.

[0008] Numerous methods are also known that allow for objective visual acuity determination or estimation using models, without the need to determine subjective visual acuity based on optotypes or other visual impressions (Nestares et al., Bayesian model of Snellen visual acuity, JOSA A 2003, 20, 1371-1381, doi: 10.1364 / JOSAA.20.001371, Watson & Ahumada, Predicting visual acuity from wavefront aberrations; JoV 2008, 8(4): 17, 1 - 19, doi: 10.1167 / 8.4.17, Blendowske, Unaided Visual Acuity and Blur: A Simple Model, OVS 2015, 92(6) e121-e125, doi: 10.1097 / OPX.0000000000000592, Inoda et al., Graefe's Archive for Clinical and Experimental Ophthalmology (2023) 261:2775-2785, doi: 10.1007 / s00417-023-06054-9, Lee W. et al., Estimation of best corrected visual acuity based on deep neural network, Sei Rep. 2022 12: 17808, doi: 10.1038 / s41598-022-22586-2).Also known is the optimization of a spectacle lens from objective properties of an eye by simulating a method of determining visual acuity (e.g. EP 3586721 B1).

[0009] Apart from the contributions of, for example, the lens design, numerical calculation, material selection and the manufacturing of the lens itself, the quality of the individual adaptation of a lens always depends very significantly on the quality of the refraction determination and its verification, especially by means of visual acuity.

[0010] Against this background, the object of the present invention is therefore to improve the individual fitting of a spectacle lens. This object is achieved by an improved visual acuity determination according to the independent claims. Preferred embodiments are the subject of the dependent claims.

[0011] Thus, in one aspect, the invention provides a (particularly at least partially computer-implemented) method for determining at least one individual visual acuity value for at least one eye of a subject, wherein the method comprises determining at least one individual subjective visual acuity value for the at least one eye based on an individual response of the subject to a visual task; acquiring individual objective measurement data for the at least one eye from (individual) measurements on the at least one eye; and determining at least one combined visual acuity value from the at least one individual subjective visual acuity value and the individual objective measurement data as the at least one individual visual acuity value to be determined for the at least one eye of the subject.

[0012] Visual acuity, or angular resolution, is a measure of an eye's sharpness of vision. Generally, and specifically within the context of this description, visu is understood as the numerical reciprocal of the angle of vision, in arcminutes, that can still be resolved by at least one eye. In other words, visu is the reciprocal of the smallest angle that can be resolved by the eye, or a derived value thereof, for a given refraction (e.g., sphere, cylinder, axis values, or power vector components M, JO, J45). This function has an optimum at the so-called "full correction" (often simply referred to as "refraction" in the literature), at which high image sharpness is achieved.

[0013] While the minimum resolvable angle of view in arcminutes is often referred to as "MAR" (minimum angle of resolution), the following applies to visual acuity: Visual acuity = 1 / MAR. The sharper the vision, i.e., the smaller the resolvable angle, the higher the visual acuity. Visual acuity can be characterized in various units, such as MAR (the resolvable angle in arcminutes), visual acuity = 1 / MAR, or logMAR = log(1 / visual acuity), i.e., the base-10 logarithm of the reciprocal of visual acuity. Since the units can be uniquely converted into one another, each of these units is essentially equally suitable for characterizing visual acuity. Therefore, the visual acuity value within the meaning of this invention (especially where this description refers to a subjective and / or objective and / or combined visual acuity value) can be specified in any of these units.In the implementation examples described below, we will indicate the unit used where applicable.

[0014] The acquisition of individual objective measurement data is carried out in particular either by direct measurement of at least one eye or by retrieving data from one or more previous measurements stored in a data memory. The measurement data can include directly measured values ​​and / or data derived from direct measurements.

[0015] To determine at least one subjective visual acuity value, the subject is presented with a visual task that allows for the differentiation of various visual acuity levels, and the subject's reaction to this task is recorded. Specifically, the subject's individual reaction to a visual task can be recorded as feedback regarding their perceived visual acuity. This can be done, for example, by having the subject identify a visual symbol presented with the task. A visual acuity value (or a minimum visual acuity value) can then be determined from the accuracy and, in particular, the speed of the (correct) identification of the visual symbol. By comparing the visual tasks that the subject can (correctly) complete with those that they cannot, the threshold visual acuity can be determined as a subjective visual acuity value.Alternatively or additionally, it is also possible to record a (descriptive or evaluative) statement from the test subject as to whether he can clearly or indistinctly (or no longer) recognize the visual task or the optotype.

[0016] In other words, the present invention thus combines, in a sense, a subjective visual acuity value individually determined for at least one eye of the subject with objective measurement data that were measured for or on this at least one eye of the subject in order to obtain more accurate information about the visual acuity for the at least one eye of the subject.

[0017] The recording of individual objective measurement data is carried out primarily without evaluating the subjective visual impressions (e.g., the subjective recognizability of optotypes) of the subject in question, but possibly using objective measurement data collected for that subject (e.g., fundus image, wavefront measurement, etc.). The (at least one) subjective visual acuity value, on the other hand, is determined from the subjective visual impressions of the subject in question, possibly also using other data sources (e.g., distance of optotypes, current correction, existing optical fogging, etc.).

[0018] The combined visual acuity can then be used to further optimize a spectacle lens, as is done, for example, in EP 2499534 A1 (Visual acuity-dependent lens design) or EP 3669230 A1 (Optimization of a spectacle lens using a visual acuity model). The subjective and / or combined visual acuity and / or an objective visual acuity described later can be expressed as one or more values ​​or as a visual acuity model that describes the subjective or combined visual acuity or objective visual acuity of the subject, particularly depending on other parameters (e.g., depending on optical fogging), as will be described in more detail below.

[0019] Like subjective refraction, subjective visual acuity determination is dependent on the individual refractive error and can therefore be systematically flawed. Based on the principle of comparing subjective refraction with an objective measurement, objective refraction, to verify and improve subjective refraction, the present invention proposes using individual objective measurement data for at least one eye to more accurately determine a (combined) visual acuity value, particularly to consider these data together for determining, calculating, or optimizing a spectacle lens. This is advantageous because the measurement error of the combined visual acuity is generally lower than the measurement error of subjective visual acuity measurements.If one were to attempt to improve accuracy solely through subjective visual acuity testing, more frequent or longer measurements would be necessary, which, due to the measurement being taken at the threshold of perceptibility, can be perceived as very strenuous. Furthermore, this approach would likely fail to correct or mitigate the consequences of systematic measurement errors by the refractionist.

[0020] If the individual objective measurement data are already available or can be collected without much effort, then the combination of subjective visual acuity value and this objective measurement data offers the advantage of requiring shorter and / or less strenuous measurements overall in order to achieve a required or desired accuracy in determining visual acuity.

[0021] Preferably, the individual objective measurement data comprise one or more measured values ​​for one or more of the following measured quantities:

[0022] The individual objective measurement data particularly preferably comprise one or more measured values ​​from at least one wavefront measurement of the subject's eye. In particular, the acquisition of the individual objective measurement data includes determining a wavefront aberration of the at least one eye, especially using a wavefront aberrometer. Higher-order aberration terms are preferably characterized in the individual objective measurement data. For example, a wavefront measurement is particularly preferably performed on the at least one eye, and a radius r is determined. EE50The energy of the circle around the center of the dispersion disk without nebulization (i.e., especially when compensating for the eye's refraction for sphere and astigmatism), in which 50% of the intensity of the point spread function (PSF) is located (encircled energy), is evaluated. In this evaluation, radial Zernike coefficients of orders n = 3 and n = 4 are particularly favored as higher-order aberrations.

[0023] Alternatively or additionally, it is preferred if the individual objective measurement data include one or more measurements from at least one measurement for the biometry of the eye (e.g. shape of the cornea, size and / or shape of the pupil, eye length, anterior chamber depth, lens thickness, corneal thickness, vitreous length, etc.).

[0024] Preferably, the individual objective measurement data includes one or more measurements of at least one pupil size and / or shape in at least one eye of the subject. This is particularly advantageous when combined with wavefront measurements and / or other information about higher-order aberrations of the at least one eye. The latter can, in turn, be derived from direct individual measurements (e.g., a wavefront and / or the shape of a corneal surface and / or a lens surface) in the at least one eye and / or from statistical correlations with other measurement data (e.g., a refraction measurement).

[0025] Alternatively or additionally, it is preferred if the individual objective measurement data comprise one or more measurements of at least one corneal shape of the subject's at least one eye. In particular, in this case, the acquisition of the individual objective measurement data includes determining a corneal topography of the at least one eye, especially using a corneal topographer. Particularly preferably, higher-order aberrations of the corea (especially the anterior surface of the corea) of the at least one eye are determined.

[0026] Alternatively or additionally, it is preferred if the individual objective measurement data includes one or more measured values ​​for one or more of the following quantities:

[0027] one or more measurements of at least one measurement of the length of at least one eye of the subject (in particular eye length or vitreous body length); and / or

[0028] one or more measurements of at least one anterior chamber depth of at least one eye of the subject; and / or

[0029] one or more measurements of at least one lens thickness measurement of the subject's eye (lens thickness); and / or

[0030] one or more measurements of at least one corneal thickness of the subject's eye; and / or

[0031] one or more measurements of at least one refractive error (including HOA); and / or

[0032] one or more measured values ​​of at least one measurement of the opacity of one or more components of the at least one eye, in particular the opacity of the lens (and / or the cornea and / or the vitreous body) of the at least one eye.

[0033] In general, at least one visual acuity model is provided. This at least one visual acuity model can be analytical and / or numerical. In particular, the at least one visual acuity model can be a trained model (for example, in the form of an AI model, especially an artificial neural network).

[0034] The visual acuity model can, for example, assign a combined visual acuity value to each individual (especially technically plausible) combination of subjective visual acuity value and objective measurement data.

[0035] In a preferred embodiment, the visual acuity model is or comprises an objective visual acuity model such that it (explicitly) determines an objective visual acuity value, which is then considered or used together with the subjective visual acuity value to determine the combined visual acuity value. The at least one objective visual acuity value is determined, in particular, based on individual measurements (i.e., data from individual measurements) of at least one eye of the subject, especially without requiring or utilizing feedback from the subject regarding individually perceived visual acuity.

[0036] Thus, determining at least one combined visual acuity value preferably comprises determining at least one individual objective visual acuity value for at least one eye from the recorded individual objective measurement data; and determining at least one combined visual acuity value from at least one individual subjective visual acuity value and at least one individual objective visual acuity value. The objective determination of visual acuity, i.e., determining at least one objective visual acuity value, is performed in particular without evaluating subjective visual impressions (e.g., the subjective recognizability of optotypes) of the subject in question, but possibly using objective measurement data collected for this subject (e.g., fundus image, wavefront measurement, etc.). The (at least one) subjective visual acuity value, on the other hand, is determined from the subjective visual impressions of the subject in question, but possibly also using other data sources (e.g.,Removal of optotypes, current correction, existing optical fogging, etc.).

[0037] Preferably, determining the at least one combined visual acuity value in this case involves comparing the deviation of the at least one individual subjective visual acuity value from the at least one individual objective visual acuity value with a predefined tolerance threshold; and weighting the individual subjective visual acuity value and / or the individual objective visual acuity value when determining the at least one combined visual acuity value, depending on the comparison performed. In particular, less plausible data (sources) are given correspondingly less weight and / or outliers (i.e., implausible measurements) are even completely removed. Alternatively or additionally, a user is notified or warned if a data value (especially a measured value) is implausible.In this process, a decision regarding plausibility is made, in particular based on a threshold determined using statistical methods as a tolerance threshold. This threshold is derived from a dataset containing many values ​​for the same individuals for both subjective and objective visual acuity. Preferably, the threshold is chosen as a (generally non-integer) multiple of the measurement uncertainty of the difference, assuming an approximately normal distribution of the differences between objective and subjective visual acuity values ​​(especially visual acuity values ​​in logMAR).

[0038] Preferably, determining the at least one combined visual acuity value comprises calculating a weighted average between the at least one objective visual acuity value and the at least one subjective visual acuity value. Particularly preferably, determining the at least one objective visual acuity value and / or determining the at least one subjective visual acuity value comprises calculating at least one accuracy measure for the at least one objective or subjective visual acuity value, respectively. In this case, it is particularly preferred if calculating the weighted average includes calculating a weighting factor for the objective and / or subjective visual acuity value based on the calculated accuracy measure for the objective and / or subjective visual acuity value. This makes it particularly efficient to give less weight to less plausible or reliable data (sources) and / or even to completely eliminate outliers (i.e., implausible measurements).

[0039] To determine at least one subjective visual acuity value, the subject is preferably presented with at least one visual task, particularly in the form of optotypes (e.g., comprising letters and / or numbers and / or Landolt C and / or Snellen E) as optotypes, which the subject answers by providing active and / or passive feedback. In particular, the implementation of the present invention can also utilize known methods for determining a subjective visual acuity value, such as the Freiburg Visual Acuity Test FrACT (see, e.g., Bach (1996) The “Freiburg Visual Acuity Test” - Automatic measurement of visual acuity, Optometry and Vision Science 73: 49-53; Bach (2007) The Freiburg Visual Acuity Test - Variability unchanged by post-hoc reanalysis. Graefe's Arch Clin Exp Opthalmol 245:965-971); and / or a visual acuity test according to DIN 58220 or EN-ISO 8596.

[0040] To derive the objective or combined visual acuity value from the specific individual measurement of at least one eye, a visual acuity model is provided, which preferably assigns an objective or combined visual acuity value to each (especially technically plausible) specification or set of objective measurement data. Such a visual acuity model is, in particular, an analytical and / or statistical model of such a general relationship between objective measurement data and an objective or combined visual acuity value. A trained artificial neural network can also be used as the statistical model. The statistical relationship or the training data for the trained artificial neural network can be derived from population data.

[0041] In a preferred embodiment, the individual objective measurement data (each) comprise at least one evaluation condition x and at least one measured value u. Determining the at least one individual objective visual acuity value preferably includes providing a visual acuity model that can be applied to any (in particular, technically meaningful or plausible) combination of at least one evaluation condition x and at least one measured value u according to a function

[0042] y = f(x,u)

[0043] assigns an estimated value y for the combined or objective visual acuity value.

[0044] The combined or individual objective visual acuity value is then determined for a specific evaluation condition by evaluating the visual acuity model against the individual objective measurement data as the resulting estimated value. The estimated value y for the visual acuity is preferably expressed in logMAR. If this model depends on adjustable (free) parameters 0, the (above) function can equivalently be expressed as f(x,u, 0). The procedure can therefore include:

[0045] Determining a (specific or individual) estimated value by evaluating the provided visual acuity model against the individual objective measurement data for an evaluation condition and outputting the determined estimated value as the combined or the individual objective visual acuity value.

[0046] In other words, the provided visual acuity model is evaluated against the objective data values ​​(e.g., a given wavefront from an objective measurement), with the result of the evaluation being a combined or individual objective (e.g., predicted) visual acuity. It is possible to use the visual acuity model to determine only an objective visual acuity, or a visual acuity derived from objective measurements (such as a wavefront measurement), which is then later combined with the subjective value. It is also possible for the visual acuity model to receive the subjectively determined visual acuity in addition to objective measurements (e.g., from a wavefront measurement), and for a combined visual acuity to be calculated from these values. For example, the visual acuity model could be a (trained) neural network with the objective data and the subjective visual acuity as inputs and the combined visual acuity as the output.Another preferred, somewhat more specific form involves separating essential contributions that depend on only one type of these variables using an additive separation approach.

[0047] f(x,u) = g(x,u) + / i(x) + fc(u)

[0048] This form is particularly preferred when g(x,u) is small compared to / i(x) and / or k(u). Specifically, if g(x,u) = 0, then the additive separation is complete.

[0049] Alternatively, a multiplicative separation approach can be used:

[0050] f(x,u) = gx, u) * / i(x) * k(u)

[0051] In this case, the separation is complete if g(x,u) = const. Hybrid forms of additive and multiplicative separations can also be used.

[0052] In a particularly preferred embodiment of a corresponding visual acuity model, the at least one measured value u comprises a pupil radius and coefficients of higher-order aberrations of the eye. Alternatively or additionally, the evaluation condition x preferably defines a nebulization for which the combined or individual objective visual acuity value is to be determined as the estimated value y.

[0053] Coefficients for higher-order aberrations of the eye are primarily measured values ​​from a wavefront aberrometer or values ​​derived from them. These coefficients can be, for example, Zernike coefficients or other parameters capable of characterizing or quantifying aberrations of the eye that go beyond purely spherical and cylindrical (i.e., astigmatic) refraction. An example of a suitable coefficient for higher-order aberrations is a measured individual visual acuity r. EE5Q of at least one eye without fogging. r EE5QThis can be, in particular, in the aforementioned form, the radius of the circle around the center of mass of the scattering disk in a (real or simulated) wavefront measurement without fogging, in which 50% of the intensity of the point spread function (PSF) is located (Encircled Energy). Preferably, this value is obtained from the wavefront measured with a wavefront sensor using FFT, taking only monochromatic aberrations of higher Zernike order into account. Particularly preferably, the radial Zernike coefficients of orders n = 3 and n = 4 are considered as higher-order aberrations in this evaluation.

[0054] In general, as well as in the context of this description, "fogging" is understood as a deliberate deviation of the presentation of a visual impression of an object or (virtual) target from a fully corrected presentation. In this context, "fully corrected" refers specifically to the correction of the spherical and cylindrical components of the eye's (especially subjective) refraction. Therefore, if at least one eye looks through an optical element (e.g., corrective lenses) that compensates for at least the spherical and cylindrical components of the eye's refractive error, and thus specifically the subjective refraction, this state is considered fully corrected in this sense. In this state, the (at least approximately) best visual acuity achievable with a spectacle lens for that eye should be attained.A deliberate deviation from this state, in particular through an additional spherical component (AM) and / or an additional cylindrical component (A / 0, A / . 45 This is understood as nebulization. It leads to a deterioration of visual acuity, i.e., in particular to a reduction in visual acuity. Using a visual acuity model for the objective and / or combined visual acuity value, which incorporates nebulization as an evaluation condition, the influence of a deviation from full correction on the visual acuity of an individual eye can be determined particularly reliably. This is especially advantageous when calculating or optimizing spectacle lenses.

[0055] Spectacle lenses generally cannot provide full correction at all points of vision simultaneously. Therefore, local deviations from full correction are intentionally accepted or even introduced into the lenses. These deviations are carefully distributed across the lens during the calculation or optimization process to minimize their impact. To assess these deviations and their influence on the effectiveness and comfort of spectacles, it is preferable to determine their effect on visual acuity individually for each eye and to incorporate this information into the lens calculation or optimization.

[0056] In a particular embodiment, x thus includes the fogging ( M, J0, J 45 ) and u includes the pupil radius r pup as well as the HOA (higher-order imaging errors) for the formation of r EE5Q. A very special embodiment is of the form f(x,u) = g(x,u) + / i(x) + fc(u) with

[0057] g(x,u) = bJ(AM 2 + A / Q +

[0058]

[0059] k(u) = a + clogr EE50 + e t

[0060] h(x) = 0

[0061] According to a preferred embodiment, the provided visual model thus has each combination of at least one evaluation condition x and at least one measured value u according to a function

[0062] y(x f ) = a + + AJ% + AJl5)r pup + c log r EE50 +

[0063]

[0064] the estimated value y for the combined or objective visual acuity, where r pup a measured individual pupil radius;

[0065] x = AM 2 + AJo + AJl ) a nebulization with the spherical component AM and the cylindrical components (4 / 0,4 / 45 );

[0066] r EE50 a measured individual visual acuity of at least one eye without blurring;

[0067] a, b and c are adjustment parameters of the visual model; and

[0068] e t a particularly individual residual value.

[0069] Again, the estimated value y for visual acuity is given here, specifically in logMAR. The fitting parameters of the visual acuity model are defined when the model is deployed. They are primarily adapted by statistically fitting the model to available population data or determined by training the model with such available data.

[0070] In the simplest case, the provided model can have a fixed residual value, in particular a residual value.

[0071]

[0072] The value = 0 can be used. This alone allows for the creation of a visual acuity model for an individual objective visual acuity value. However, it is also possible to individually adjust the residual value, for example, based on individual subjective visual acuity values ​​of at least one eye. This allows the visual acuity model to be further improved and, in particular, makes it possible to create a visual acuity model for a combined visual acuity value.

[0073] As measured individual visual acuity r EE5Q of at least one eye without nebulization, in particular the already mentioned radius of the circle around the center of gravity of the dispersion disk in a (real or simulated) wavefront measurement without nebulization.

[0074] In another aspect, the invention relates to a device for determining at least one individual visual acuity value for at least one eye of a subject, wherein the device is designed to carry out a method according to the invention, in particular in one of the preferred implementations described herein.

[0075] The invention is described in more detail below with reference to exemplary embodiments shown in the figures. Here, identical or similar reference numerals may denote identical or similar features of the embodiments. Individual features shown in the figures may be implemented in other exemplary embodiments. The figures show:

[0076] Fig. 1 AD Subjective visual acuity values ​​for a large number of people at different conditions

[0077] Nebelungen; Fig. 2A-D Deviations of a simple visual acuity model from subjective visual acuity values ​​for a large number of people under different Nebelungen conditions; and

[0078] Fig. 3A-D Comparison of adapted visual acuity models with a simple visual acuity model.

[0079] In simple terms, one idea of ​​the present invention is to combine a person's subjective visual acuity measurement with objective measurements to obtain more accurate information about that person's visual acuity. Both the individually determined subjective visual acuity and the individually determined objective measurement data are used to derive a more reliable individual visual acuity value. As described below, with a suitable visual acuity model, it is not only possible to improve the reliability and reproducibility of individual visual acuity determination. It can also be used to determine individual visual acuity values ​​for very different evaluation conditions (e.g., different fog levels) with comparatively little measurement effort.

[0080] A visual acuity model, if used, can be structured in various ways. For example, such a model may implicitly or explicitly determine an objective visual acuity value from individual objective measurement data. This objective value is then compared and / or calculated with the individual subjective visual acuity value to determine the individual visual acuity value (e.g., as a combined visual acuity value). Such objective visual acuity models can be universally applicable to different test subjects. The individual objective visual acuity value is then derived by applying this objective visual acuity model to the individual objective measurement data.

[0081] However, it is also possible to directly provide and use a combined or (individually) adapted visual acuity model, which is specifically tailored based on at least one individual subjective visual acuity value of the respective test subject. In one embodiment, the resulting individual visual acuity value can be understood and used as an objective visual acuity value, which is compared and / or calculated with a corresponding subjective visual acuity value of the test subject to obtain a corresponding combined visual acuity value. It is also possible to use the visual acuity value determined by this combined or adapted visual acuity model as such a combined visual acuity value. In particular, it already incorporates both the at least one individual subjective visual acuity value and the individual objective measurement data. In this case, a separate objective visual acuity value would not need to be explicitly determined.

[0082] These different approaches are described below using examples, starting with an objective visual acuity model, and then outlining possibilities for individual adaptation or a fusion of such a visual acuity model with individual subjective visual acuity values ​​or subjective visual acuity models.

[0083] Subjective visual acuity is preferably determined using conventional methods (e.g., with a visual acuity chart or FrACT). The accuracy of the measurement is determined by the method used, or can be estimated from it. While with FrACT the measurement error is part of the result, the measurement error of visual acuity determination using a visual acuity chart can be determined from the size increments of the optotypes (typically + / - 1 to 2 visual acuity levels).

[0084] For determining objective visual acuity, aberrometer measurements can be used, for example. Higher-order refractive errors, which cannot be corrected by spectacle lenses, are of particular interest here. From these higher-order measurements, especially in conjunction with an (individual) pupil measurement, a measure of visual acuity can be defined. Visual acuity correlates with the imaging properties of the eye. Therefore, corresponding metrics of the eye's imaging properties can be used to determine objective visual acuity from the higher-order errors of an incident wavefront. Possible metrics include, for example: the sum of squared errors of the higher-order errors, the Strehl ratio of the point spread function of the higher-order errors, the encircled energy radius of the point spread function, as well as other more complex methods known from the prior art.

[0085] The sum of squared errors of the coefficients of the Zernike polynomial of the wavefront is a readily calculable quantity for objective visual acuity. The Strehl ratio, comparing the point spread function derived from higher-order aberrations with a standardized point spread function, is an alternative measure. The radius of encircled energy is defined as the portion of the point spread function that lies within a certain radius around the center. This measure is also suitable for accurately determining optical image quality even with larger aberrations, as it optimally accounts for the radially asymmetric spread of the point spread function across the surface. More complex methods are described, for example, in the aforementioned works "Predicting visual acuity from wavefront aberrations" by Andrew B. Watson and Albert J. Ahumada Jr., and "Bayesian model of Snellen visual acuity" by Oscar Nestares, Rafael Navarro, and Beatriz Antona.

[0086] There are various ways to determine overall visual acuity from objective visual acuity and subjective visual acuity: e.g., simple plausibility checks and / or a weighted average of subjective and objective values ​​and / or enriching an objective or subjective visual acuity model with further subjective or objective visual acuity measurements (e.g., using Gaussian processes) and / or merging a visual acuity model for subjective visual acuity and a visual acuity model for objective visual acuity.

[0087] In simple plausibility checks, for example, subjective and objective visual acuity values ​​are compared. If there are large discrepancies, such as exceeding certain thresholds, a warning is issued to the refractionist indicating a possible measurement error. Alternatively, large discrepancies between subjective and objective visual acuity may indicate eye diseases such as retinal damage or amblyopia. The subjective and objective visual acuity values ​​to be checked should preferably be obtained under comparable conditions (e.g., with full correction or the same optical fogging). In weighted averaging, the subjective and objective visual acuity values ​​are preferably averaged, with the values ​​being weighted differently in the calculation. The subjective and objective visual acuity values ​​to be averaged should preferably be obtained under comparable conditions (e.g.,(with full correction or with the same optical nebulization).

[0088] If (subjective) visual acuity measurements have been carried out under different fog conditions for a large number of people for whom further parameters (e.g. biometric parameters) are known as objective measurement data, a visual acuity model can be adapted to the data set, with which the visual acuity of people who have not yet been (subjectively) measured, but whose further parameters (individual objective measurement data) are known, can be determined from these (objectively, i.e. in particular without subjective visual acuity assessment by this person).

[0089] In the following example, three or more FrACT measurements from subjects were initially fitted with the following visual acuity model under each measurement condition (here a given spherical and / or astigmatic nebulization - including no nebulization - as well as the individual wavefront of the subjects at full correction and a pupil diameter):

[0090] = a + bj (AM 2 + + AJ^ s )r pup + clogr EE50 + (1)

[0091]

[0092] The model determines the base-10 logarithm of visual acuity in arcminutes with the estimator y(%) as a function of the evaluation condition x. One component of the evaluation condition is the nebulization (AM, A / 0, A / 45 ), which represents the deviation of the effect placed in the refraction glasses from the subjective refraction. The radius r EE50The area of ​​the circle around the center of the dispersion disk without nebulization, in which 50% of the intensity of the point spread function (PSF) is located, is preferably determined from the wavefronts measured with a wavefront sensor using standard FFT-based methods (e.g., wavelength 550 nm, mesopic pupil, here pixel size: 0.0625 arcmin), whereby only monochromatic aberrations of higher radial Zernike order were considered (3 < n < 4 for mesopic pupil). The residuals

[0093]

[0094] In the following analysis, the parameters were assumed to be statistically independent and normally distributed. They can be understood as individual (and adjustable) parameters of the visual acuity model.

[0095] It has been found that particularly reliable results can be obtained when the Encircled Energy Term (i.e., r) is used. EE50) or its logarithm is calculated from a wavefront containing radial Zernike orders of n = 3 and n = 4. Adding higher orders may, under certain circumstances, lead to a poorer fit due to the reduced measurement accuracy of the higher wavefront orders, or correspondingly high demands would have to be placed on the measuring instruments.

[0096] The adjusted coefficients a, b and c are shown in the following table.

[0097] Coefficient Value Standard Unit

[0098] Mistake

[0099] a -0.158 0.066 logMAR

[0100] b 0.303 0.0062 logMAR dpt -1 mm -1 / 2

[0101]

[0102] c -0.011 0.016 logMAR pixel sizeps F

[0103] Figures 1 and 2 provide an overview of the individual prediction of the visual acuity model compared to the actual individual subjective visual acuity measurements for different individuals (a) to (n). Figure 1A-D first plots the corresponding subjectively determined visual acuity values ​​for different nebulae. For each individual, the upper figure shows cylindrical nebulae with different cylinder axes, and the lower figure shows spherical nebulae. The nebulae were varied between 0 and 2 diopters. The respective subjective visual acuity values ​​were determined using FrACT. Figure 2A-D then shows the residuals (also referred to as "residual values") corresponding to the respective visual acuity values ​​for the different individuals (a) to (n), which represent an adjustment of the above visual acuity model to the subjective visual acuity values.These residuals are plotted against the visual acuity values ​​predicted by the model, which in turn result from the different nebulizations. The standard deviation of the residuals was 0.11 logMAR for this fit. Analysis revealed that the residuals deviate significantly from 0 within the measurement accuracy of a FrACT measurement, meaning that the model does not explain all systematic deviations. Another observation is that, for the same individual, the residuals as a function of the nebulizations and the predicted visual acuities show a significant correlation with each other (see Fig. 2).

[0104] The visual acuity model can therefore be improved by individually adjusting the residuals through the use of individual measurements of subjective visual acuity, at least provided that these have a measurement accuracy comparable to or better than the accuracy of the prediction.

[0105] For this purpose, the correlation structure of the residuals is preferably modeled. Therefore, in a further analysis, it was assumed that the residuals can be modeled as a Gaussian process depending on the predicted visual acuity y(%). From this assumption, it follows that the distribution of a person's actual visual acuity is normally distributed multivariately around the expected value y(%) predicted by the visual acuity model:

[0106] yx)~Multi.vari.atNormal y(x), K"0(y(x ))) (2)

[0107] The elements of the covariance matrix 0(y(x)) were modeled as Gaussian functions:

[0108] = a 2 exp(-(y(x i ) - y(x j )) 2 / (2p 2 ))

[0109]

[0110] This represents a special form of a Gaussian process and means, in the present case, that the systematic deviations of the residuals from the prediction are described by smooth functions.

[0111] The parameter a is the standard deviation of the actual visual acuity in the population of subjects from the respective (individual) estimated value y(%), and p is the correlation length (here in units of the predicted visual acuity) over which the deviation of the actual visual acuity from the prediction persists.

[0112] To estimate the parameters a and p of the Gaussian process from the visual acuity measurements, the measured visual acuity was also modeled as a Gaussian process as a function of the estimated visual acuity:

[0113] y mess (x)~MultivariateNormal(y(x), K mess (y(x))) (3)

[0114]

[0115] where the covariance matrix has an additional term for the uncertainty of a single measurement, which shows no correlations between measurements and corresponds to the measurement accuracy of a single visual acuity measurement:

[0116] = K0(y(x i )) + δ ij σ

[0117]

[0118] 2

[0119] '-J '-J

[0120] This involves

[0121]

[0122] the Kronecker delta is denoted, and o is the standard deviation of the measurement uncertainty of a single visual acuity measurement.

[0123] Equations (2) and (3) reveal a distinction between actual visual acuity (as a property of the subjects) and measured visual acuity. Equation (2) can be used to model visual acuity and its variation as a function of measurement conditions in the same individual. Equation (3), on the other hand, was used to determine the parameters of the population mean visual acuity y (%) (i.e., a, b, c), the parameters of the correlation matrix p and a, and the measurement uncertainty o.

[0124] The results of the data fitting for the correlation parameters are summarized in the following table:

[0125] Parameter exp(value) Value Standard deviation

[0126] logp 0.456 -0.786 0.185

[0127] log« 0.111 -2.19 0.230

[0128]

[0129] log ff 0.077 -2.56 0.057

[0130] Preferably, the visual acuity model is enriched with additional individual measurements. In the following, N additional measurements of visual acuity y with ie {1,...,7V} of a person, which is represented in the vector y, are assumed. mess = (y1,y2, -,yN). The i-th measurement is taken under the measurement conditions (evaluation condition) x. t carried out, whereby x mess =

[0131]

[0132] -,x N ') is the vector of all measurement conditions (evaluation conditions). The measurement condition of the j-th measurement can itself be a tuple, e.g.

[0133]

[0134] x t = would be the tuple consisting of the (spherical) nebulization AM;, the pupil radius r present at the time of measurement t as well as the individual wavefront in full correction WF.

[0135] After modeling the dataset using the Gaussian process, this information about visual acuity in the subject population can be combined with the additional measurements. In the exemplary procedure presented here, it is assumed that the visual acuity measurements y mess a multivariate normal distribution with a maximum at the actual value under the measurement conditions x mess present visual acuity yx mess ) is expected, where the measurement inaccuracies are expressed by the covariance matrix 2:

[0136] y mess ~MultivariateNormal(y(x) mess ), Σ) ■

[0137] In the simplest case, the individual measurements are independent, so the covariance matrix 2 of the additional measurements consists solely of a diagonal matrix of the standard deviations Ay representing the measurement uncertainty. mess = (Ay1, Ay2,..., Ay w ) consists of:Σ ij = δ ij Δy i 2

[0138] Due to the discretization of subjectively determined visual acuity levels, the assumption of a normal distribution is not strictly valid for visual acuity determined using vision charts. However, a more suitable form of distribution could be chosen (e.g., a uniform distribution centered around the visual acuity with a width of one visual acuity level). Strictly speaking, treatment with a Gaussian process is not exact, since the measurement error is not normally distributed. Therefore, the model parameters (in the example, a, b, c) and the parameters of the correlation matrix p and a can be determined numerically, e.g., within the framework of a maximum likelihood analysis or, preferably, a Bayesian analysis. The probability distribution to be maximized is then the likelihood (in the case of ML analysis), or the probability distribution to be sampled is the posterior probability density function, composed of the likelihood and the prior. In both cases, the measured visual acuity is distributed according to:

[0139] y mess (x)~ MultivariateNormal(y(x), K mess (y(x))) ⊗ Uniform(-Δ VA / 2,+Δ VA / 2)

[0140]

[0141] with

[0142] K mess (y(x)) = K0(y(x)) + σ 2 mess I

[0143] where Uniform(-Δ VA / 2, +Δ VA / 2) represents the uniform distribution (i.e. a distribution with constant probability density) in a range of + / - 0.5 visual acuity levels (i.e. + / - 0.05 logMAR) around 0.

[0144] In the case that the measured values ​​are modeled multivariately normally distributed around the actual visual acuity, the combined visual acuity y can be expressed as a mean weighted with the inverse covariance matrices (see completing the square):

[0145] y s = (K0(y(x mess )) -1 + Σ -1 ) -1 (K0(y(x mess )) -1 y(x mess ) + Σ -1 y mess)with the covariance matrix of the combined visual acuity s =

[0146]

[0147] (K0(y( x mess)) 1 + S“ 1 )

[0148] An example calculation involving model fitting (fusion) based on one or two additional visual acuity measurements is shown in Fig. 3A-D, each in comparison to the simple, i.e., unfitted, visual acuity model. If the measurement deviates from the visual acuity predicted by the original (simple) model, the combined visual acuity is changed locally on the scale of parameter p of the Gaussian process. For deviations that are far removed on this scale from the measurement conditions of the additional measurements, the prediction of the original visual acuity model remains virtually unchanged. The change is greater the higher the weight of the measurement, i.e., the lower the measurement inaccuracy. It can also be seen that the additional measurements should preferably have an accuracy comparable to parameter a so that they carry the same weight as the original prediction.

[0149] The visual acuity measurements combined in this way can be used to determine the model parameters of the visual acuity model used for optimization in ATOP. This is particularly useful when it is essential to ensure that visual acuity increases monotonically with increasing fog, as this is no longer guaranteed with additional measurements that deviate significantly from the original prediction.

[0150] A person's subjective visual acuity may be known in the form of a subjective visual acuity model, meaning that an individual visual acuity model has already been fitted to several visual acuity measurements of that person. If the number of visual acuity measurements is small, errors in the model parameters can lead to unintended deviations in the lens design during subsequent lens calculations. To avoid this, the individual visual acuity model can be fused with a visual acuity model derived from data of a larger population (see equation (1)). This fusion has the effect of limiting improbable deviations in the model parameters of the individual visual acuity model, which may arise due to measurement errors, by using the population visual acuity model. Such a fusion of visual acuity models can be achieved by weighted averaging the respective parameter values. The weights of the individual parameters are...

[0151] Similarly, a maximum likelihood method can be used to combine the parameter values ​​by multiplying the likelihood of the respective models together and determining the position of the maximum of the product in the space of the model parameters (e.g., by summing the quadratic approximation of the respective maxima of the log likelihood using completing the square).

[0152] As already mentioned, in a preferred embodiment, less plausible data sources can be given correspondingly less weight, or outliers (implausible measurements) can even be completely removed. This decision can preferably be made based on a threshold determined using statistical methods. Assuming an approximately normal distribution of the differences between the objective and subjective measurements (visual acuity values ​​in logMAR), the threshold can be set as a (generally non-integer) multiple of the measurement uncertainty of the difference. One can rely here on the analysis of the data above and use a multiple of √K. mess,ii Choose a threshold value. Preferably, choose a value between two and three times the threshold. For example, in the present case, the measurement uncertainty of the difference under the same conditions (e.g., measurements of visual acuity with full correction) would be σ. 2 + σ 2 = 0.077 2 + 0.111 2= 0.135 logMAR. Therefore, a threshold value in the range between 0.27 and 0.405 can preferably be chosen.

Claims

Applicant: Rodenstock GmbH MB&P Mark: R03487WO - hb / hb Patent claims 1. A method for determining at least one individual visual acuity value for at least one eye of a subject, comprising: Determining at least one individual subjective visual acuity value for at least one eye based on the subject's individual response to a visual task; Acquisition of individual objective measurement data for at least one eye from measurements on at least one eye; Determine at least one combined visual acuity value from at least one individual subjective visual acuity value and the individual objective measurement data as the at least one individual visual acuity value to be determined for at least one eye of the subject.

2. The method of claim 1, wherein the individual objective measurement data comprise one or more measured values ​​for one or more of the following measured quantities: one or more measurements of at least one wavefront measurement at at least one eye of the subject; and / or one or more measurements of at least one pupil size and / or shape in at least one eye of the subject; and / or one or more measurements of at least one form of the cornea of ​​at least one eye of the subject; and / or one or more measurements of at least one length of at least one eye of the subject; and / or one or more measurements of at least one anterior chamber depth of at least one eye of the subject; and / or one or more measurements of at least one lens thickness measurement of the subject's eye; and / or one or more measurements, at least one measurement of corneal thickness of at least one eye of the subject; and / or one or more measurements of at least one refractive error (including HOA); and / or one or more measured values ​​of at least one measurement of the opacity of one or more components of at least one eye, in particular the opacity of the lens of at least one eye.

3. Method according to claim 1 or 2, wherein determining the at least one combined visual acuity value comprises: Determine at least one individual objective visual acuity value for at least one eye from the recorded individual objective measurement data; and Determining at least one combined visual acuity value from at least one individual subjective visual acuity value and at least one individual objective visual acuity value.

4. The method of claim 3, wherein determining the at least one combined visual acuity value comprises: Comparing a deviation of at least one individual subjective visual acuity value from at least one individual objective visual acuity value with a predetermined tolerance threshold; and Weighting of the individual subjective visual acuity value and / or the individual objective visual acuity value when determining at least one combined visual acuity value depending on the comparison made.

5. Method according to claim 3 or 4, wherein determining the at least one combined visual acuity value comprises: Determining a weighted mean between at least one objective visual acuity value and at least one subjective visual acuity value.

6. Method according to claim 5, wherein determining the at least one objective visual acuity value and / or determining the at least one subjective visual acuity value comprises determining at least one accuracy measure for the at least one objective or subjective visual acuity value, and wherein determining the weighted mean value comprises determining a weighting factor for the objective and / or subjective visual acuity value based on the determined accuracy measure for the objective and / or subjective visual acuity value.

7. Method according to one of the preceding claims, wherein the subject is presented with at least one visual task, in particular in the form of optotypes, to determine at least one subjective visual acuity value, which the subject answers by providing active and / or passive feedback.

8. Method according to any one of the preceding claims, wherein the optotypes comprise one or more of the following optotypes: letters; and / or numbers; and / or Landolt-C; and / or Snellen-E.

9. Method according to one of the preceding claims, wherein the individual objective measurement data comprise at least one evaluation condition x and at least one measured value u, and wherein determining the at least one individual objective visual acuity value comprises: Providing a visual model that can represent any combination of at least one evaluation condition x and at least one measurement u according to a function y =fx,u) assigns an estimated value y for the combined or objective visual acuity value; and determines the estimated value by evaluating the visual acuity model on the individual objective measurement data for an evaluation condition and outputs the determined estimated value as the combined or individual objective visual acuity value.

10. Method according to claim 9, wherein the at least one measured value u comprises a pupil radius and coefficients of higher-order aberrations of the eye, and wherein the evaluation condition x defines a nebulization for which the combined or individual objective visual acuity value is to be determined.

11. Method according to claim 9 or 10, wherein the provided visual model of each combination of at least one evaluation condition x and at least one measured value u according to a function y(x i ) = a + b√(ΔM 2 + ΔJ0 2 + ΔJ 45 2 )r pup + c log r EE50 + assigns the estimated value y for the combined or objective visual acuity value, where r pup a measured individual pupil radius; x = (ΔM 2 + ΔJ0 2 + ΔJ 45 2) a nebulization with the spherical component ΔM and the cylindrical components (ΔJ0, ΔJ 45 ); r EE50 a measured individual visual acuity of at least one eye without blurring; a, b and c are adjustment parameters of the visual model; and e t a particularly individual residual value.

12. Device for determining at least one individual visual acuity value for at least one eye of a subject, wherein the device is designed to perform a method according to any one of claims 1 to 11.

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