Optimizing a spectacle lens taking account of a vision model

Abstract

A computer-implemented method for calculating or assessing a spectacles lens for an eye of a spectacles wearer. The method includes (a) providing an association of at least one imaging property or aberration of a spectacle lens system with the vision of the spectacles wearer, or of an average spectacles wearer, when observing an object through the spectacles lens system; (b) determining or prescribing a target function for the spectacles lens to be calculated or assessed, in which the association from step (a) is to be evaluated; and (c) calculating or assessing the spectacles lens to be calculated or assessed by evaluating the target function, wherein the target function is evaluated at least once.

Claims

1. A computer-implemented method for calculating or assessing a spectacles lens for an eye of a spectacles wearer, comprising: (a) providing a comparative association of at least one imaging property or aberration of a spectacle lens system with a visual acuity of the spectacles wearer when observing an object through the spectacle lens system, wherein the spectacle lens system is a combination of the spectacles lens and the eye or an eye model of the spectacles wearer, and the spectacles wearer is a specific spectacles wearer or an average spectacles wearer; (b) determining or prescribing a target function for the spectacles lens to be calculated or assessed, in which the association from step (a) is to be evaluated; and (c) calculating or assessing the spectacles lens to be calculated or assessed by evaluating the target function, wherein: V.sub.real(ΔU.sub.s,j(i)) designates the vision acuity, which is determined using the association and an actual value of the at least one imaging property of the spectacle lens to be calculated or assessed at the i-th assessment point, the subscript s designates an arbitrary evaluation surface of the at least one imaging property or aberration, and the subscript j,j≥1 designates a j-th imaging property or aberration, and wherein the target function that depends on the visual acuity V via the association of the at least one imaging property or aberration ΔU.sub.s,j with the visual acuity of the specific spectacles wearer or of the average spectacles wearer is represented as: $F_s={.Math.}_i\left[{G_{s,j,i}^V\left(V_{\mathrm{real}}\left(\Delta U_{s,j}\left(i\right)\right)-V_{\mathrm{target}}\left(\Delta U_{s,j}\left(i\right)\right)\right)}^2+.Math.\right],$ wherein: G.sub.s,j,i.sup.V designates weighting of the visual acuity at the i-th assessment point, prescribed by the association with the at least one imaging property or aberration ΔU.sub.s,j(i), and V.sub.target(ΔU.sub.s,j(i)) designates a target value of the visual acuity.

2. The computer-implemented method according to claim 1, wherein the calculating or assessing comprises optimizing the spectacles lens by minimizing or maximizing the target function.

3. The computer-implemented method according to claim 1, further comprising: calculating at least one light beam emanating from the object for at least one viewing direction, with the aid of wavetracing, raytracing, or wave field calculation through the spectacles lens system or through the spectacles lens alone up to an evaluation surface.

4. The computer-implemented method according to claim 3, further comprising: calculating the difference, present at the evaluation surface, of the light beam emanating from the object in comparison to a reference light beam converging on the retina of a model eye; and determining the at least one imaging property or aberration using the calculated difference.

5. The computer-implemented method according to claim 3, wherein the calculating at least one light beam emanating from the object takes place by means of wavetracing, and wherein the calculating the difference present at the evaluation surface comprises calculating the wavefront difference between the wavefront of the light beam emanating from the object and the wavefront of the reference light beam converging on the retina, wherein the wavefront difference is calculated at the evaluation surface.

6. The computer-implemented method according to claim 5, further comprising associating a geometric/optical angle or a quadratic form in space of a geometric/optical angle with the wavefront difference to be calculated, wherein the at least one imaging property or aberration depends on at least one component of the geometric/optical angle or the quadratic form.

7. The computer-implemented method according to claim 1, wherein the provision of the comparative association of the at least one imaging property or aberration of the spectacles lens system with the visual acuity of the spectacles wearer parametrically depends on a measured initial visual acuity or a measured sensitivity of the eye of the spectacles wearer, and wherein the measured sensitivity of the spectacles wearer corresponds to the visual acuity of the spectacles wearer which was measured given a predetermined faulty correction.

8. The computer-implemented method according to claim 1, wherein the provision of the comparative association of the at least one imaging property or aberration comprises using a value pair based on: a visual acuity value of one of the eyes of the spectacles wearer upon viewing through the spectacles lens system, and a spherical or astigmatic value of refractive power.

9. The computer-implemented method according to claim 8, wherein: the value of the refractive power is provided by the refraction value of one of the eyes of the spectacles wearer when observing the object through the spectacle lens system, or the refractive power is provided by the refraction value of one of the eyes of the spectacles wearer plus a spherical or astigmatic haze when observing the object through the spectacle lens system.

10. The computer-implemented method according to claim 9, wherein the refractive power is provided by the refraction value of one of the eyes of the spectacles wearer plus the spherical or astigmatic haze plus an additional dioptric spacing from the refraction value of a model eye, said dioptric spacing corresponding to a haze has a value of between 0.5 dpt and 3.0 dpt.

11. The computer-implemented method according to claim 1, wherein the spectacles lens system comprises a spectacles lens and a model eye, and the model eye is described with at least one of the following parameters: eye length, separations and curvatures of the refractive surfaces, refractive indices of the refractive media, pupil diameter, and position of the pupils.

12. The computer-implemented method according to claim 11, wherein at least one of the parameters of the model eye has been individually measured in the spectacles wearer, or at least one of the parameters of the model eye has been individually determined from individual measurement values.

13. An apparatus for calculating or assessing a spectacles lens for a spectacles wearer, comprising a calculator configured to calculate or assess the spectacles lens according to a method for calculating or assessing a spectacles lens according to claim 1.

14. A non-transitory computer program product which comprises a program code that is configured to implement the method for calculating or assessing a spectacles lens according to claim 1 when loaded and executed on a computer.

15. A method for producing a spectacles lens, comprising: calculating a spectacles lens according to the method for calculating a spectacles lens according to claim 1; and manufacturing the calculated spectacles lens.

16. An apparatus for producing a spectacles lens, comprising: a calculator or optimizer configured to calculate the spectacles lens according to the method for calculating a spectacles lens according to claim 1; and a manufacturing device configured to manufacture the spectacles lens according to the result of the calculation.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) Preferred embodiments of the invention are explained by way of example in the following, at least in part with reference to the drawings. Thereby shown are:

(2) FIG. 1 a schematic spectacles-eye system;

(3) FIG. 2 an example of a vision model;

(4) FIG. 3 the degrees of freedom of the parameterization of an example of a vision model;

(5) FIG. 4 the results of a standard optimization of a spectacle lens at the vertex sphere;

(6) FIG. 5 the results of an example of an optimization of a spectacle lens, taking into account the vision, according to the invention.

DETAILED DESCRIPTION

(7) In general, in this specification bold-faced lowercase letters should designate vectors, and bold-faced uppercase letters should designate matrices (such as the (2×2) vergence matrix S, for example). Italicized lowercase letters (such as d, for example) designate scalar variables.

(8) Furthermore, bold italicized uppercase letters should designate wavefronts or surfaces as a whole. For example, S designates the vergence matrix of the similarly named wavefront S; S alone also encompasses the entirety of all higher-order aberrations (HOAs) of the wavefront, except for the 2nd-order aberrations that are included in S. Considered mathematically, S stands for the set of all parameters that are necessary in order to describe a wavefront (sufficiently precisely) in relation to a given coordinate system. S preferably stands for a set of Zernike coefficients having a pupil radius, or a set of coefficients of a Taylor series. S particularly preferably stands for the set from a vergence matrix S to describe the 2nd-order wavefront properties and a set of Zernike coefficients (with a pupil radius) that serves to describe all remaining wavefront properties except those of the second order, or a set of coefficients according to a Taylor decomposition. Analogous statements apply to surfaces instead of wavefronts.

(9) Preferably, it is not the direct wavefront deviation in diopters, but rather the vision loss corresponding thereto relative to the maximum possible vision, that is utilized/used as a criterion for assessing the wavefront deviation. Either existing vision models or one of the vision models described in the following may thereby be used, and in fact preferably in combination with a rule as to how the vision model is to be incorporated into the target function of an optimization in conjunction with the transformation of the target specifications and weights.

(10) A first example of a method for calculating or optimizing a spectacle lens may include the following steps:

(11) Step S1: Calculate at least one light beam emanating from an object, with the aid of wavetracing or raytracing, through the optical elements of the eye up to an evaluation plane or evaluation surface in the eye, for example to behind the cornea, up to the leading surface of the eye lens, up to the rear surface of the eye lens, up to the exit pupil AP, or to the rear surface L2 of the lens.
Step S2: Calculate, at the evaluation plane or evaluation surface, the differences of the light beam relative to a reference light beam converging on the retina;
Step S3: Assess the differences of the light beam in comparison to a reference light beam, for example due to the size of the dispersion disc on the retina;
Step S4: Associate a vision value with the assessed difference of the light beam from step S3;
Step S5: Construct a target function that depends on the associated vision value.

(12) The individual steps may respectively be implemented in a more specialized form:

(13) Step S1: Calculate wavefronts through the optical elements of the eye, up to the exit pupil AP or to the rear surface L2 of the lens;

(14) Step S2: Calculate the differences via comparison of these wavefronts with spherical reference wavefronts, and calculation of the differential wavefront;

(15) Step S3: Assess the differences of the first light beam in comparison to a reference light beam, via association of geometric-optical angles (or of a quadratic form to describe the ellipse in the object-side space of the geometric-optical angle) relative to the differential wavefront at AP/L2;
Step S4: Associate a vision value with the quadratic form, wherein the association rule parametrically depends on the measured output vision (and the measured sensitivity) of the patient;
Step S5: Construct a target function that depends on the associated vision value.

(16) A further example of a method that in particular relates to the vision model uses the above step 4 as a starting point. The method may include the following steps:

(17) Step S1′: Provide an association of the effect of an optical system on a light beam emanating from an object with the vision of a person upon viewing the object through the optical system;

(18) Step S2′: Construct a target function for a spectacle lens to be optimized, in which the association from step (a) [sic] is to be evaluated;

(19) Step S3′: Calculate the spectacle lens by minimizing the target function, wherein the target function is evaluated at least once.

(20) In preferred embodiments, the steps may be refined:

(21) For step S1′:

(22) The provided association of the effect of the optical system with the vision may be determined using one or more provided value pairs from vision value of the eye of the person upon viewing through an optical system (for example of a spectacle lens of refraction spectacles) spherical and/or astigmatic refractive power of the optical system.

(23) Also: given one of the value pairs, the refractive power may be provided by the refraction value of the eye, and/or given one of the value pairs, the refractive power may be provided by the refraction value of the eye plus a spherical and/or astigmatic haze, wherein a dioptric distance corresponding to the haze preferably has a value of between 0.5 dpt and 3.0 dpt.

(24) The association of the effect of the optical system with the vision may be implemented using an eye model. The eye model may be described with at least one of the following parameters: eye length, distances and curvatures of the refractive surfaces, refractive indices of the refractive media, pupil diameter, position of the pupil, wherein at least one of the parameters of the eye model has preferably been individually measured at the person and/or has been determined from individual measurement values, for example as described in DE 10 2017 000 772.1.

(25) For step S3′:

(26) To evaluate the target function, a light beam emanating from an object point may be determined for at least one viewing direction with the aid of wavetracing or raytracing through the optical elements of the eye, up to an evaluation plane in the eye, for example to behind the cornea, up to the leading surface of the eye lens, up to the rear surface of the eye lens, up to the exit pupil AP, or to the rear lens surface L2.

(27) To evaluate the target function, the differences of the light beam that are present at the evaluation plane or evaluation surface in comparison with a reference light beam converging on the retina may be calculated, wherein the calculated differences are assessed in the evaluation of the target function, for example via the size of the dispersion disc on the retina.

(28) FIG. 1 shows a schematic depiction of a spectacle lens system comprising a model eye, and illustrates the determination of the geometric-optical angle, wherein the calculation of the residual astigmatism according to the prior art (see for example EP 2 499 534) is shown with “(1)”, and the calculation of the differential wavefront and of the geometric-optical angle is shown with “(2)”.

(29) In particular, in this regard it is assumed that a light beam emanates from an object point with a spherical wavefront and propagates up to the first spectacle lens surface. There, the light beam is refracted and subsequently propagates up to the second spectacle lens surface, where it is refracted again. The light beam exiting from the spectacle lens subsequently propagates in the direction of the eye until it strikes the cornea, where it is again refracted. After a further propagation within the anterior chamber of the eye up to the eye lens, the light beam is also refracted by the eye lens and propagates up to the retina.

(30) The effect of the optical system, consisting of the spectacle lens and the model eye, on the light beam emanating from the object may be determined by means of raytracing or by means of wavetracing. A wavetracing preferably takes place, wherein preferably only one ray (the principal ray, which preferably travels through the center of rotation of the eye) and the derivatives of the rise heights of the wavefront are calculated, per observation point of the spectacle lens, according to the transversal coordinates (orthogonal to the principal ray). These derivatives are taken into account up to the desired order, wherein the second derivatives describe the local curvature properties of the wavefront and coincide with the second-order imaging properties or aberrations. The higher derivatives of the wavefront coincide with the higher-order imaging properties or aberrations.

(31) In the calculation of light through the spectacle lens to the inside of the eye, the local derivatives of the wavefronts are determined at a suitable position in the beam path in order to compare them there with a reference wavefront which converges at a point on the retina of the eye. In particular, the two wavefronts (meaning the wavefront coming from the spectacle lens and the reference wavefront) are compared with one another at an evaluation plane (for example at an evaluation surface). A spherical wavefront whose center point of curvature lies on the retina of the eye may serve as a reference wavefront.

(32) At the vertex sphere SPK (also designated as SK), the vergence matrices S.sup.R and S.sup.BG of the formula (S.sup.R) and the wavefront from the spectacle lens (S.sup.BG) have the following form:

(33) $\begin{array}{cc}{S}^R=\left(\begin{array}{cc}{M}^R+J_0^R& J_{45}^R\\ J_{45}^R& M^R-J_0^R\end{array}\right);S^{BG}=\left(\begin{array}{cc}{M}^{BG}+J_0^{BG}& J_{45}^{BG}\\ J_{45}^{BG}& M^R-J_0^{BG}\end{array}\right)& \left(1\right)\end{array}$
with the astigmatic components of their power vectors

(34) $\begin{array}{cc}{J}^R=\left(\begin{array}{c}{J}_0^R\\ J_{45}^R\end{array}\right);J^{BG}=\left(\begin{array}{c}{J}_0^{BG}\\ J_{45}^{BG}\end{array}\right)& \left(2\right)\end{array}$

(35) The above vergence matrices, or the power vectors that contain second-order imaging properties or aberrations, may thereby occur as follows: either via a direct second-order wavetracing or via a wavetracing including higher-order aberrations (HOAs) that are then taken into account in the second-order errors or aberrations by means of a metric.

(36) Calculation of the Wavefronts

(37) Second-Order Wavetracing:

(38) For the sake of simplicity, the plane L2 (rear lens surface) is assumed as an evaluation plane in the following. However, instead of L2, an arbitrarily different evaluation plane or evaluation surface “s” in the eye may be used.

(39) If a wavefront enters into the eye, it is repeatedly propagated and refracted, which is described by the transfer matrix

(40) $\begin{array}{cc}T=\left(\begin{array}{cc}A& B\\ C& D\end{array}\right).& \left(4\right)\end{array}$
In order to calculate the wavefront in the eye, the vergence matrix S.sup.BG must be subjected [sic] corresponding to the application of T, such that:

(41) $\begin{array}{cc}{S}^{\mathrm{BG}}\stackrel{T}{.Math.}{S}^{BG}& \left(5\right)\end{array}$

(42) However, it is not a variable derived from the vergence matrix of the prescription S.sup.R that serves as a reference vergence, but rather a spherical reference vergence with the reference vergence matrix D.sub.LR.

(43) Instead of comparing S.sup.BG with S.sup.R as in the prior art, i.e. with the reference wavefront at the vertex sphere SPK or SK, the spectacle lens may be optimized on the basis of the spherical reference vergence matrix D.sub.LR and the transformed vergence matrix S.sup.BG, in that the transformed vergence matrix S.sup.BG is compared with the reference vergence matrix D.sub.LR.

(44) The second-order calculation from equation (5) corresponds in terms of content to the calculation in WO 2013/104548 A1, which in equation (2) there leads to the vergence matrix S′.

(45) Wavetracing Including the Higher-Order (Meaning of an Order Greater than 2) Imaging Errors or HOAs:

(46) A wavetracing including HOAs is described in WO 2013/104548 A1. Instead of being described by S′, the result of the calculation may then be described by a corresponding wavefront representation that also takes into account higher-order imaging errors. Zernike coefficients are preferably used for this, and particularly preferably the Taylor representation, so that the local derivations of the wavefront W.sub.xx, W.sub.xy, W.sub.yy, W′.sub.xxx, W′.sub.xxy, W′.sub.xyy, W′.sub.yyy, W′.sub.xxxx etc. may be directly used in the latter. The evaluation surface in the eye is generally designated by “s”, wherein the evaluation surface is preferably the exit pupil or the rear lens surface (meaning that “s”=“AP” or “s”=“L2”). An effective second-order wavefront may be associated with this wavefront by means of a metric. The metric may be a linear metric, for example.

(47) Calculation of the Differential Wavefront

(48) Second-Order Calculation

(49) In this instance, for the further procedure the starting point is the difference or differential wavefront which may be described in the second order by the differential vergence matrix ΔSD.sub.s:
ΔSD.sub.s=S′.sub.s.sup.BG−D.sub.LR.  (6a)
Calculation Including HOA:

(50) In the general instance, the difference of the wavefronts S′.sub.s and the reference wavefront R′.sub.s is calculated. This difference is preferably mapped by means of a metric in the space of the vergence matrices:
ΔSD.sub.s=Metric(S′.sub.s.sup.BG−R′.sub.s)  (6b)

(51) In the event that the metric is preferably linear, the result from equation (6b) is the same as that from equation (6a), if it is set there that:
S′.sup.BG=Metric(S′.sub.s)
D.sub.LR=Metric(R′.sub.s)  (6c)

(52) One possible metric relates to the representation of S′.sub.s.sup.BG−R′.sub.s in the form of Zernike coefficients. For example, what is known as the RMS metric may be used, which uses the pupil radius r.sub.0 and otherwise uses only the second-order Zernike coefficients, i.e. c.sub.2.sup.0,c.sub.2.sup.2,c.sub.2.sup.−2. The power vector components are then:

(53) $\begin{array}{cc}M=-\frac{4\sqrt{3}}{r_0^2}{c}_2^0,J_0=-\frac{2\sqrt{6}}{r_0^2}{c}_2^2{J}_{45}=-\frac{2\sqrt{6}}{r_0^2}{c}_2^{-2}& \left(6d\right)\end{array}$
and the differential matrix is then provided by:

(54) $\begin{array}{cc}\Delta S{D}_s=\left(\begin{array}{cc}M+J_0& J_{45}\\ J_{45}& M-J_0\end{array}\right)& \left(6e\right)\end{array}$

(55) Further examples of metrics are to be found in EP 2 115 527 B 1, and in J. Porter, H. Quener, J. Lin, K. Thorn and A. Awwal, Adaptive Optics for Vision Science (Wiley 2006). Assessment of the difference between the light beam and the reference light beam

(56) After a propagation through the spectacle lens and the eye, the wavefront is generally no longer spherical. For such an astigmatic wavefront that is not fully corrected, there is on the retina a dispersion disc that may be approximated with an ellipse (dispersion ellipse).

(57) The assessment of the differences of the light beam in comparison to the reference light beam may take place via the parameters (such as the size, for example) of the dispersion disc on the retina. In a preferred embodiment, the assessment of the differences takes place via the parameters of a dispersion disc in the object-side space of a geometric-optical angle which corresponds to the dispersion disc on the retina. The assessment of the differences of the light beam in comparison with the reference light beam may in particular include an association of i) geometric-optical angles or ii) of a quadratic form for describing the dispersion disc in object-side space of geometric-optical angles relative to the differential wavefront at the evaluation surface.

(58) Association of Geometric-Optical Angles

(59) In a preferred example, the variable ΔSD is not used directly for optimization; rather, first a variable that has yet to be further calculated is computed from ΔSD, namely the geometric-optical angle γ (see FIG. 1).

(60) As described above, for an astigmatic, not fully corrected wavefront, there is a dispersion disc on the retina that may be approximated with an ellipse (dispersion ellipse). The dispersion ellipse on the retina corresponds to an ellipse in the space of the object-side geometric-optical angle. A geometric-optical angle γ=(γ.sub.x,γ.sub.y) can be specified for each fixed point r.sub.s=(r.sub.sx,r.sub.sy) at the edge of the exit pupil (in the event that a: s=“A”), at the edge of the effective pupil on the rear lens surface (in the event that b: s=“L”), or at the edge of the effective pupil at an arbitrary evaluation plane “s” in the eye. If a circular orbit (r.sub.s=const.) is imagined around a point r.sub.s=r.sub.s(cos φ.sub.s, sin φ.sub.s).sup.t at the edge of the respective pupil, then γ describes an ellipse in γ-space. Two objects may then still be separately perceived (with regard to a preliminary and simple overlap criterion) if their dispersion ellipses do not overlap in γ-space.

(61) The differential wavefront ΔSD.sub.s at the evaluation surface “s” corresponds to a dispersion ellipse which may be described on the basis of the following correlation:
γ=ΔQ.sub.sr.sub.s  (7a)
with
ΔQ.sub.s=μ.sub.s(A.sub.s.sup.t−σ.sub.sC.sub.s.sup.t)ΔSD.sub.s  (7b)
wherein

(62) $\begin{array}{cc}{\mu }_s=\{\begin{array}{c}1\\ d_{\mathrm{LR}}/d_{\mathrm{AR}}\\ .Math.\end{array}{\sigma }_s=\{\begin{array}{c}0\\ {\tau }_{\mathrm{AL}}\\ .Math.\end{array}\Delta {\mathrm{SD}}_s=\{\begin{array}{c}\Delta {\mathrm{SD}}_A\\ \Delta {\mathrm{SD}}_L\\ .Math.\end{array}{r}_s=\{\begin{array}{c}{r}_{\mathrm{AP}},\mathrm{in}\mathrm{the}\mathrm{event}\mathrm{of}a)\\ r_L,\mathrm{in}\mathrm{the}\mathrm{event}\mathrm{of}b)\\ .Math.\end{array},& \left(7c\right)\end{array}$
with
ΔSD.sub.A=S′.sub.A.sup.BG−D.sub.AR
ΔSD.sub.L=S′.sub.L.sup.BG−D.sub.LR  (7d)

(63) In the above formulas:

(64) σ.sub.s designates a (reduced, i.e. relative to the optical index of refraction) length that characterizes the evaluation surface or evaluation plane from the exit pupil AP;

(65) r.sub.s designates the radius of the effective pupil at the evaluation plane or evaluation surface in the eye;

(66) r.sub.AP designates the radius of the exit pupil of the eye;

(67) τ.sub.AL designates the radius of the effective pupil at the rear lens surface.

(68) The actual dispersion ellipse may then be generated via the postulation |r.sub.s|.sup.2=r.sub.s.sup.tr.sub.s=r.sub.s.sup.2=const., since then the quadratic form
γ.sup.tΔQ.sub.s.sup.−1rΔQ.sub.s.sup.−1γ=r.sub.s.sup.2
γ.sup.tΔW.sub.sγ=1  (8)
with the symmetrical matrix
ΔW.sub.s=ΔV.sub.s.sup.−1tΔV.sub.s.sup.−1,  (9)
wherein
ΔV.sub.s=r.sub.sΔQ.sub.s,  (9a)
describes an ellipse in γ-space (i.e. in the space of the geometric-optical angle) whose semi-axes are provided by the roots from the inverse eigenvalues of the matrix ΔW.sub.s.

(69) The matrix ΔV.sub.s is generally not symmetrical, and therefore has one more degree of freedom than the symmetrical matrix ΔSD (the unit of ΔV.sub.s that of an angle (radians), and not the diopter of a wavefront metric). However, since the fourth, additional degree of freedom does not relate to the sharpness of an image, but rather only rotates the axial position of the blurriness, the fourth degree of freedom may be transformed away via a symmetrization rule.

(70) For this, a rotation matrix R.sub.s is determined

(71) 0$\begin{array}{cc}{R}_s=\left(\begin{array}{cc}\cos {\varphi }_s& -\sin {\varphi }_s\\ \sin {\varphi }_s& \cos {\varphi }_s\end{array}\right)& \left(10\right)\end{array}$
so that the matrix ΔU.sub.s

(72) $$\begin{gathered} \begin{array}{cc}\Delta U_s=\left(\begin{array}{cc}\Delta U_{s,\mathrm{xx}}& \Delta U_{s,\mathrm{xy}}\\ \Delta U_{s,\mathrm{xy}}& \Delta U_{s,\mathrm{yy}}\end{array}\right):=\Delta V_s{R}_s \\ ={\mu }_s{r}_s\left(A_s^t-{\sigma }_s{C}_s^t\right)\Delta S{D}_s{R}_s& \left(11\right)\end{array} \end{gathered}$$
is symmetrical, meaning that

(73) $\begin{array}{cc}{\phi }_s=\arctan \frac{\Delta Q_{\mathrm{xy}}-\Delta Q_{\mathrm{yx}}}{\Delta Q_{\mathrm{xx}}+\Delta Q_{\mathrm{yy}}}& \left(12\right)\end{array}$
must be set to zero.

(74) Because the symmetrical matrix ΔU.sub.s is sufficient to assess the visual acuity, this, or at least a variable derived therefrom, is preferably used in the target function used to calculate or optimize the lenses, and in fact as described below is not used directly but rather via the association of a vision value.

(75) The variables derived from the matrix ΔU.sub.s may be an anisotropic and an isotropic component of the matrix ΔU.sub.s. Suitable for this is a decomposition of ΔU.sub.s into an isotropic and an anisotropic portion, or into an isotropic and an anisotropic component, which are defined via the eigenvalues of ΔU.sub.s:

(76) $$\begin{gathered} \begin{array}{cc}\Delta u_{s1}=\frac{\Delta U_{s,\mathrm{xx}}+\Delta U_{s,\mathrm{yy}}+\sqrt{{\left(\Delta U_{s,\mathrm{xx}}-\Delta U_{s,\mathrm{yy}}\right)}^2+4\Delta U_{s,\mathrm{xy}}^2}}{2} \\ \Delta u_{s2}=\frac{\Delta U_{s,\mathrm{xx}}+\Delta U_{s,\mathrm{yy}}-\sqrt{{\left(\Delta U_{s,\mathrm{xx}}-\Delta U_{s,\mathrm{yy}}\right)}^2+4\Delta U_{s,\mathrm{xy}}^2}}{2}& \left(13\right)\end{array} \end{gathered}$$

(77) The isotropic portion or the isotropic components ΔU.sub.s,iso of ΔU.sub.s is defined as follows:

(78) $\begin{array}{cc}\Delta U_{s,\mathrm{iso}}:=\frac{\Delta u_{s1}+\Delta u_{s2}}{2}=\frac{\Delta U_{s,\mathrm{xx}}+\Delta U_{s,\mathrm{yy}}}{2}& \left(14\right)\end{array}$

(79) The anisotropic portion or the anisotropic components ΔU.sub.s,aniso of ΔU.sub.s is defined as follows:
ΔU.sub.s,aniso:=|Δu.sub.s1−Δu.sub.s2|=√{square root over ((ΔU.sub.s,xx−ΔU.sub.s,yy).sup.2+4ΔU.sub.s,xy.sup.2)}  (15)
Step S4: Association of a vision value with the assessed difference of the light beams

(80) The association of a vision value with the assessed difference of the light beams may include an association of a vision value with the quadratic form ΔU.sub.s describing the dispersion ellipse, or with the variables derived from the quadratic form.

(81) In one example, the variables ΔU.sub.s,iso, ΔU.sub.s,aniso are not directly utilized for optimization of the spectacle lens. Instead of this, the variables ΔU.sub.s,iso, ΔU.sub.s,aniso serve as a starting point in order to determine the vision belonging to ΔU.sub.s,iso, ΔU.sub.s,aniso in a manner defined by a given vision model. For this purpose, patient data or spectacles wearer data may be required, in particular the vision given full correction VA.sub.cc.

(82) What is understood by a vision model is in particular any function V(ΔU.sub.s) that has the following features: The argument ΔU.sub.s is the matrix defined in equation (11), or at least a variable derived from the matrix ΔU.sub.s, for example at least one of its components or a combination of components. That combination formed by the components ΔU.sub.s,iso, ΔU.sub.s,aniso is preferable. V(ΔU.sub.s) has a scalar value, and the calculated value stands for the vision. It is preferably to be specified in radians (thus in the meaning of the geometric-optical angle) or in arc minutes or decimal units (for example V=0.8; 1.0; 1.25; 1.6; 2.0), or in units of log MAR (for example V=−0.3; −0.2; −0.1; 0.0; 0.1; . . . ). The following association thereby preferably applies:

(83) TABLE-US-00001 TABLE 1 V [arc minutes] V [radians] V [decimal] V [logMAR] 0.5′ 0.000145 2.0 −0.3 0.63′ 0.00018 1.6 −0.2 0.8′ 0.00023 1.25 −0.1 1.0′ 0.00029 1.0 0.0 1.25′ 0.00036 0.8 +0.1

(84) Suitable vision models are known from the prior art. However, a new vision model is preferably proposed that is based on the following basic function:
V(ΔU)=(γ.sub.0.sup.k+(mΔU.sup.p).sup.k).sup.1/k  (16)

(85) It thereby applies that: The argument ΔU is generic and may be one of the variables ΔU.sub.s,iso, ΔU.sub.s,aniso, a combination of these variables, another variable derived from the matrix ΔU.sub.s, or a combination thereof; The parameter γ.sub.0 is directly provided by the value of the geometric-optical angle γ.sub.0 (in radians), which corresponds to the initial vision; The parameters k, m and p are (not necessarily whole number) parameters for describing the vision decline as a function of ΔU; The output value V of the function in equation (16) has the meaning of the geometric-optical angle (in radians) that corresponds to the current vision. All other vision measurements (thus geometric-optical angles in arc minutes, or vision decimally or vision in log MAR), may be converted according to Table 1.

(86) FIG. 2 shows an example of a vision model for V(ΔU.sub.s,iso, ΔU.sub.s,aniso).

(87) In a one-dimensional instance (i.e. if only one type of haze is present, for example a defocus), the basic function from equation (16) may be used directly. Namely, if all components of the eye are rotationally symmetrical, ΔU.sub.s,aniso=0 is then the case, and the vision decline is purely a function of ΔU.sub.s,iso alone.

(88) In a two-dimensional instance, it is possible to migrate from ΔU.sub.s,iso, ΔU.sub.s,aniso to polar coordinates and to define the following variables derived from the matrix ΔU.sub.s:

(89) $$\begin{gathered} \begin{array}{cc}\tan \phi =\frac{\Delta U_{s,\mathrm{aniso}}/2}{\Delta U_{s,\mathrm{iso}}} \\ \Delta U_{s,r}=\sqrt{\Delta U_{s,\mathrm{iso}}^2+1/4\Delta U_{s,\mathrm{aniso}}^2}& \left(17\right)\end{array} \end{gathered}$$

(90) According to the invention, the following simplifying model assumptions are made: a) The function γ.sub.meas(ΔU.sub.s,iso,ΔU.sub.s,aniso) is independent of the algebraic sign of the isotropic portion, γ.sub.meas(ΔU.sub.s,iso,ΔU.sub.s,aniso)=γ.sub.meas(+ΔU.sub.s,iso,ΔU.sub.s,aniso) b) The function γ.sub.meas(ΔU.sub.s,iso,ΔU.sub.s,aniso) is independent of the algebraic sign of the anisotropic portion, γ.sub.meas(ΔU.sub.s,iso,−ΔU.sub.s,aniso)=γ.sub.meas(ΔU.sub.s,iso,+ΔU.sub.s,aniso) c) For a fixed φ, the function γ.sub.meas(ΔU.sub.s,r,φ) is a function of the geometry as in equation (16)

(91) Assumption c) may, for example, be realized via the approach
V(ΔU.sub.s,r,φ)=(γ.sub.0.sup.k(φ)+(m(φ)ΔU.sub.s,r.sup.p(φ)).sup.k(φ)).sup.t/k(φ),  (18)
in which equation (16) is expanded in that the parameters k, p, m (but not γ.sub.0) are regarded as functions of the angle coordinate φ.

(92) Conditions a) and b) require
a).Math.γ.sub.meas(ΔU.sub.s,r,π−φ)=γ.sub.meas(ΔU.sub.s,r,φ)
b).Math.γ.sub.meas(ΔU.sub.s,r,−φ)=γ.sub.meas(ΔU.sub.s,r,+φ)  (19)
and imply a periodicity with the period π:
γ.sub.meas(ΔU.sub.s,rφ+π)=γ.sub.meas(ΔU.sub.s,r,φ)  (20)

(93) This leads to the approach of a Fourier series that is even at φ, with the terms 1, cos 2φ, cos 4φ, cos 6φ, . . . . It has proven to be expedient to instead use the equivalent base 1, sin.sup.2 φ, sin.sup.2 2φ, sin.sup.2 3φ, . . . because then practically all base functions except for the first disappear for φ=0. In the present instance, an expansion up to the order of sin.sup.2 2φ appears to be sufficient. Therefore, the following approximations may be made, for example:
k(φ)=k.sub.0(1+κ.sub.1 sin.sup.2 φ+κ.sub.2 sin.sup.2 2φ)
p(φ)=p.sub.0(1+π.sub.1 sin.sup.2 φ+π.sub.2 sin.sup.2 2φ)
m(φ)=m.sub.0(1+μ.sub.1 sin.sup.2 φ+μ.sub.2 sin.sup.2 2φ)  (21)

(94) k.sub.0, p.sub.0, m.sub.0 are thereby the parameters for φ=0, thus for the purely isotropic portion of ΔU.sub.s, and κ.sub.i, π.sub.i, μ.sub.i describe the vision model for the presence of anisotropic portions. The effect of these parameters is shown in FIG. 3.

(95) FIG. 3 shows the degrees of freedom of the φ-parameterization of the vision model from equation (21) in an example of m(φ), wherein m.sub.0 is the circle radius of the isotropic base φ=0, m.sub.0μ.sub.1 describes the deviation in the direction of the anisotropic axis (approximately elliptical, φ=90°), and m.sub.0μ.sub.2 describes the deviations from the ellipse in the direction φ=45°.

(96) The parameters of the vision model may thereby be freely established, or be obtained via data adaptation to vision tests of the spectacles wearer. Defined parameters are preferably identified that do not individually vary, or individually vary only weakly, and which may consequently be adapted to a representative ensemble in an advance study. Only the remaining parameters then need to be adapted to the current spectacles wearer.

(97) A construction of the vision model is particularly preferred in which some parameters are set equal to zero from the outset, and therefore do not need to be determined at all. One embodiment of this is defined by κ.sub.1=κ.sub.2=π.sub.1=π.sub.2=0, corresponding to the simplified model
k(φ)=k.sub.0
p(φ)=p.sub.0
m(φ)=m.sub.0(1+μ.sub.1 sin.sup.2 φ+μ.sub.2 sin.sup.2 2φ)  (22)
and the multi-dimensional vision model of the form
V(ΔU.sub.S,R,φ)=(γ.sub.0.sup.k.sup.0+)(m(φ)ΔU.sub.S,R.sup.p.sup.0).sup.K.sup.0).sup.1/K.sup.0  (23)

(98) This embodiment is particularly preferred in combination with the procedure that the parameters k.sub.0, p.sub.0, μ.sub.1, μ.sub.2 are adapted once to an assemblage of data, whereas the parameters m and γ.sub.0 are individually adapted to the spectacles wearer. For example, the parameter γ.sub.0 is provided directly by the log MAR value of the initial vision. The parameter m may be determined via the sensitivity, thus in that the vision V.sup.Neb is determined once given a distinct haze (for example ΔS.sup.Neb=1.5 dpt).

(99) Design of a target function that depends on the associated vision value

(100) In the prior art, a target function of the type

(101) $\begin{array}{cc}{F}_{\mathrm{SPK}}=\underset{i}{.Math.}\left[{G_{\mathrm{SPK},R,i}\left(R_{\mathrm{SPK},\mathrm{real}}\left(i\right)-R_{\mathrm{SPK},\mathrm{target}}\left(i\right)\right)}^2+{G_{\mathrm{SPK},A,i}\left(A_{\mathrm{SPK},\mathrm{real}}\left(i\right)-A_{\mathrm{SPK},\mathrm{target}}\left(i\right)\right)}^2+{G_{\mathrm{SPK},C,i}\left(C_{\mathrm{SPK},\mathrm{real}}\left(i\right)-C_{\mathrm{SPK},\mathrm{target}}\left(i\right)\right)}^2+{G_{\mathrm{SPK},S,i}\left(S_{\mathrm{SPK},\mathrm{real}}\left(i\right)-S_{\mathrm{SPK},\mathrm{target}}\left(i\right)\right)}^2+.Math.\right]& \left(24\right)\end{array}$
is minimized with regard to the optimization at the vertex sphere, wherein the first two terms G.sub.Ri(R.sub.real (i)−R.sub.target(i)).sup.2 and G.sub.A,i(A.sub.real(i)−A.sub.target(i)).sup.2 belong to the residuals of refraction errors and astigmatism at the vertex sphere, and the additional terms correspond to the residuals of further possible features of the vertex sphere that are to be optimized. The variables G.sub.SPK,R,i, G.sub.SPK,A,i, G.sub.SPK,C,i, G.sub.SPK,S,i, . . . are the weights that are utilized in the optimization at the vertex sphere.

(102) In the prior art, with regard to the optimization after the wavetracing in the eye (WO 2013/104548 A1), a target function of the same type as in equation (24) is minimized only in that the terms belong to the corresponding features of the wavefront after the calculation in the eye:

(103) $\begin{array}{cc}{F}_s=\underset{i}{.Math.}\left[{G_{s,R,i}\left(R_{s,\mathrm{real}}\left(i\right)-R_{s,\mathrm{target}}\left(i\right)\right)}^2+{G_{s,A,i}\left(A_{s,\mathrm{real}}\left(i\right)-A_{s,\mathrm{target}}\left(i\right)\right)}^2+{G_{s,C,i}\left(C_{s,\mathrm{real}}\left(i\right)-C_{s,\mathrm{target}}\left(i\right)\right)}^2+{G_{s,S,i}\left(S_{s,\mathrm{real}}\left(i\right)-S_{s,\mathrm{target}}\left(i\right)\right)}^2+.Math.\right]& \left(25\right)\end{array}$

(104) In contrast thereto, according to one aspect of the invention the optimization occurs directly at vision variables. An example of a target function may thus have the following structure:

(105) $\begin{array}{cc}{F}_s=\underset{i}{.Math.}.Math.{G_{s,\mathrm{iso},i}^V\left(V\left(\Delta V_{s,\mathrm{iso}}\left(\Delta {\mathrm{SD}}_{s,\mathrm{real}}\left(i\right)\right)\right)-V_{s,\mathrm{iso},\mathrm{target}}\left(i\right)\right)}^2+{G_{s,\mathrm{aniso},i}^V\left(V\left(\Delta V_{\mathrm{aniso},i}\left(\Delta {\mathrm{SD}}_{s,\mathrm{real}}\left(i\right)\right)\right)-V_{s,\mathrm{aniso},\mathrm{target}}\left(i\right)\right)}^2+.Math.]& \left(26\right)\end{array}$

(106) Preferably, no additional terms occur after the first two residuals.

(107) In equation (26), ΔSD.sub.s,real(i), stands for the real value of the variable ΔSD.sub.s according to equation (7c), according to which a spectacle lens is calculated at the i-th assessment point.

(108) The variables V.sub.s,iso,target(i) and V.sub.s,aniso,target(i) stand for the values of the target vision at the i-th assessment point for the isotropic or the anisotropic contribution. G.sub.iso,j.sup.V and G.sub.aniso,i.sup.N are the corresponding weightings.

Example 1

(109) In a first example, the values for target vision and weightings can be selected freely.

Example 2

(110) In a second example, only the weights are freely selectable, and the values for the target vision may be obtained via a transformation from target specifications that have already been proven by experience in the optimization at the vertex sphere.
V.sub.s,iso,target(i)=V(ΔU.sub.s,iso(ΔSD.sub.s,iso,target(i))
V.sub.s,aniso,target(i)=V(ΔU.sub.s,aniso(ΔSD.sub.s,aniso,target(i))  (27)
wherein ΔSD.sub.s,isonominal(i), ΔSD.sub.s,anisonominal(i) stand for the target values of the variable ΔSD.sub.s according to equation (7c) at the i-th assessment point and are functions of the target specifications at the vertex sphere.

Example 2.1

(111) In an example of a development of example 2.1 which does not take into account the HOAs, according to equation (5) it applies that

(112) $\begin{array}{cc}\begin{array}{c}\mathrm{\Delta S}{D}_{s,\mathrm{target}}\left(i\right)=S_s^{\prime BG}\left(S_{\mathrm{target}}^{BG}\left(i\right)\right)-D_{LR}\\ =S_s^{\prime BG}\left(S^R\left(i\right)+\Delta S_{\mathrm{target}}^{BG}\left(i\right)\right)-D_{LR}\end{array}& \left(29\right)\end{array}$
wherein ΔS.sub.target.sup.BG (i) is the vergence matrix that belongs to a selection of the target specification or to the entirety of the target specifications.

Example 2.1.2

(113) In another development of example 2.1 which takes into account the HOAs, it applies according to equation (6) that

(114) 0$\begin{array}{cc}\begin{array}{c}\Delta {\mathrm{SD}}_{s,\mathrm{target}}\left(i\right)=\mathrm{Metric}\left(S_s^{{\prime }^{\mathrm{BG}}}\left(S_{\mathrm{target}}^{\mathrm{BG}}\left(i\right)\right)-R_s^{\prime }\right)\\ =\mathrm{Metric}(S_s^{{\prime }^{\mathrm{BG}}}\left(S^R+\Delta S\left(S_{\mathrm{target}}^{\mathrm{BG}}\left(i\right)\right)-R_s^{\prime }\right)\end{array}& \left(30\right)\end{array}$
wherein ΔS.sub.target.sup.BG(i) is the vergence matrix that belongs to a selection of the target specification or to the entirety of the target specifications. Furthermore, ΔS(ΔS.sub.target.sup.BG(i)) is the wavefront associated therewith in the selected wavefront representation.

Example 2.2

(115) In a development of example 2, ΔSD.sub.s,iso,target(i), ΔSD.sub.s,anisotarget(i) are not provided by the same function.

Example 2.2.1

(116) In a development of example 2.2 which does not take the HOAs into account, according to equation (5) it applies that
ΔSD.sub.s,iso,nominal(i)=S′.sub.s.sup.BG(S.sup.R(i)+ΔS.sub.iso,nominal.sup.BG(i))−D.sub.LR
ΔSD.sub.s,aniso,nominal(i)=S′.sub.s.sup.BG(S.sup.R(i)+ΔS.sub.aniso,nominal.sup.BG(i))−D.sub.LR  (31)
wherein ΔS.sub.iso,target.sup.BG (i), ΔS.sub.aniso,target.sup.BG(i) are the vergence matrices that both belong to independent selections of the target specifications or to the entirety of the target specifications. Particularly preferred is
ΔS.sub.iso,target.sup.BG(i)=ΔS.sub.R,target.sup.BG(i)
ΔS.sub.aniso,target.sup.BG(i)=ΔS.sub.A,target.sup.BG(i),  (32)
wherein
ΔS.sub.R,target.sup.BG(i)=ΔS(R.sub.SPK,target(i))
ΔS.sub.A,target.sup.BG(i)=ΔS(A.sub.SPK,target(i))  (33)
are the vergence matrices that correspond to the target values of refraction errors or astigmatism.

Example 2.2.2

(117) In a development of example 2.2 which takes the HOAs into account, according to equation (6)
ΔSD.sub.s,iso,target(i)=Metric(S′.sub.s.sup.BG(S.sup.R+ΔS(ΔS(R.sub.SPK,target(i))))−R′.sub.s)
ΔSD.sub.s,aniso,target(i)=Metric(S′.sub.s.sup.BG(S.sup.R+ΔS(ΔS(A.sub.SPK,target(i))))−R′.sub.s)  (34)
Parameters of the Vision Model:

(118) The transformations in the instance without HOAs

(119) $\begin{array}{cc}\Delta S\stackrel{A}{.fwdarw.}\Delta {\mathrm{SD}}_s\stackrel{A,r_{\mathrm{EP}}}{.fwdarw.}\Delta U_s\stackrel{{\omega }_0}{.fwdarw.}V& \left(35\right)\end{array}$
and the transformations in the instance with HOAs

(120) $\begin{array}{cc}\Delta S.fwdarw.\Delta S\stackrel{A}{.fwdarw.}\Delta {\mathrm{SD}}_s\stackrel{A,r_{\mathrm{EP}}}{.fwdarw.}\Delta U_s\stackrel{{\omega }_0}{.fwdarw.}V& \left(36\right)\end{array}$
still depend on the following parameters: the transition of ΔS or ΔS to ΔSD.sub.s depends on the eye model whose parameters are summarized in a vector A; the transition from ΔSD.sub.s to ΔU.sub.s depends on the eye model A, and additionally on the entrance pupil r.sub.EP; and the transition from r.sub.EP to V depends on the vision model whose parameters are summarized in a vector ω.sub.0. For the preferred vision model, it applies that

(121) $\begin{array}{cc}{\omega }_0=\left(\begin{array}{c}{\gamma }_0\\ m_0\end{array}\right),& \left(37\right)\end{array}$
and for the preferred eye model in the purely spherical instance, without HOAs

(122) $\begin{array}{cc}A\left(C,M,\mathrm{Akk}\right)=\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}C\\ L_1\left(C,M,\mathrm{Akk}\right)\end{array}\\ L_2\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{CL}\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_L\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{LR}\left(M\right)\end{array}\right);& \left(38a\right)\end{array}$
in the sphero-cylindrical instance without HOAs

(123) $\begin{array}{cc}A\left(C,M,J,\mathrm{Akk}\right)=\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}C\\ L_1\left(C,M,J,\mathrm{Akk}\right)\end{array}\\ L_2\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{CL}\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_L\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{LR}\left(M\right)\end{array}\right);& \left(38b\right)\end{array}$
and in the general instance including HOAs

(124) $\begin{array}{cc}A\left(C,W,\mathrm{Akk}\right)=\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}C\\ L_1\left(C,W,\mathrm{Akk}\right)\end{array}\\ L_2\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{CL}\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_L\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{LR}\left(M\right)\end{array}\right)& \left(38c\right)\end{array}$
wherein (M, J).sup.T is the power vector of the subjective classification, and Akk is the accommodation.

(125) In the above formulas,

(126) C designates the cornea data set, including higher orders;

(127) L.sub.1 indicates the data set for leading lens surface, including higher orders;

(128) L.sub.2 indicates the data set for rear lens surface, including higher orders.

(129) The nomenclature that is used thereby corresponds to that of the publication WO 2013/104548 A1.

(130) Furthermore, standard populations of these models are provided that are preferably defined by average population values. The standard values of the parameters are characterized by a superscript ‘0’.

(131) The symbol r.sub.EP.sup.0 stands for a standard entrance pupil; for a standard vision model it applies that

(132) $\begin{array}{cc}{\omega }_0=\left(\begin{array}{c}{\gamma }_0^0\\ m_0^0\end{array}\right);& \left(39\right)\end{array}$
for the preferred standard eye model in the purely spherical instance without HOAs, it applies that

(133) $\begin{array}{cc}{A}^0\left(M,\mathrm{Akk}\right)=\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}C\left(L_1^0,M\right)\\ L_1\left(L_1^0,\mathrm{Akk}\right)\end{array}\\ L_2\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{CL}^0\left(\mathrm{Akk}\right)\end{array}\\ {\tau }_L\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{LR}\left(M\right)\end{array}\right);& \left(40a\right)\end{array}$
in the sphero-cylindrical instance without HOAs it applies that

(134) $\begin{array}{cc}{A}^0\left(M,\mathrm{Akk}\right)=\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}C\left(L_1^0,M,J=0\right)\\ L_1\left(L_1^0,\mathrm{Akk}\right)\end{array}\\ L_2\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{CL}^0\left(\mathrm{Akk}\right)\end{array}\\ {\tau }_L\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{LR}\left(M\right)\end{array}\right);& \left(40b\right)\end{array}$
and in the general instance including HOAs, it applies that

(135) 0$\begin{array}{cc}{A}^0\left(M,\mathrm{Akk}\right)=\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}C\left(L_1^0,W^0\right)\\ L_1\left(L_1^0,\mathrm{Akk}\right)\end{array}\\ L_2\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{CL}^0\left(\mathrm{Akk}\right)\end{array}\\ {\tau }_L\left(A\mathrm{kk}\right)\end{array}\\ {\tau }_{LR}\left(M\right)\end{array}\right),& \left(40c\right)\end{array}$
wherein the wavefront W.sup.0 associated with an ametropia M, J.sub.0, J.sub.45 with standard HOA is provided by

(136) $\begin{array}{cc}{W}^0\left(M\right)=\left(\begin{array}{c}\begin{array}{c}\begin{array}{c}\begin{array}{c}{c}_2^0\left(M\right)\\ c_2^2\left(J_0=0\right)\end{array}\\ c_2^{-2}\left(J_{45}=0\right)\end{array}\\ c_3^3\end{array}\\ \mathrm{.Math.}\end{array}\right)& \left(41\right)\end{array}$

(137) For the current calculation, the vision V is preferably performed with the individual parameters; by contrast, the calculation of the target vision is performed using standard parameters. If only subsets of the parameters are known (for example because, although the parameters of the eye model are individually present, those of the vision model are not), then the unknown parameters are preferably also replaced by standard values in the current calculation.

Example 3

(138) In a particularly preferred example, neither the weights nor the target specifications can be freely selected; rather, but may be obtained via a transformation from the weights and target specifications that have already been proved experimentally in the optimization to the vertex sphere.

(139) The target specifications may be determined as in conjunction with the above embodiments 2.1, 2.1, . . . , 2.2.2. With regard to the weights, possible embodiments differ in which model parameters are used in which transformation. The functions from equation (35) or equation (36) may be designated as follows:
ΔSD.sub.s(ΔS.sup.BG,A)
ΔU.sub.s(ΔSD.sub.s,A,r.sub.EP)
V(ΔU.sub.s,ω.sub.0)  (42)

(140) It is stipulated that, for a spectacles wearer for whom all parameters correspond to the standard parameters (ΔS.sup.BG, A=A.sup.0, r.sub.EP=r.sub.EP.sup.0,ω.sub.0=ω.sub.0.sup.0,J=0), an optimization by means of the target function F.sub.s from equation (26) leads to the same spectacle lens as an optimization by means of the target function F.sub.SPK from equation (24) according to the prior art. It is thereby ensured that improvements with respect to the prior art may be specifically controlled via the deviations of the parameters from their standard values.

(141) In one embodiment of the invention, the uniformity of the optimization results is ensured in that, for standard values, each term from the target function F.sub.s is equal to a corresponding term from the target function F.sub.SPK.

(142) In one embodiment, this is ensured by the stipulation
G.sub.s,iso,i.sup.V[V(ΔU.sub.s,iso(ΔSD.sub.s(ΔS.sup.BG(i),A.sup.0),A.sup.0,r.sub.EP.sup.0),ω.sub.0.sup.0)−V(ΔU.sub.s,iso(ΔSD.sub.s(ΔS.sub.iso,target.sup.BG(i),A.sup.0),A.sup.0,r.sub.EP.sup.0)ω.sub.0.sup.0)].sup.2=G.sub.SPK,R,i(ΔSPK,real(i)−A.sub.SPK,target(i)).sup.2
G.sub.s,aniso,i.sup.V[V(ΔU.sub.s,aniso(ΔSD.sub.s(ΔS.sup.BG(i),A.sup.0),A.sup.0,r.sub.EP.sup.0),ω.sub.0.sup.0)−V(ΔU.sub.s,aniso(ΔSD.sub.s(ΔS.sub.aniso,target.sup.BG(i),A.sup.0),A.sup.0,r.sub.EP.sup.0),ω.sub.0.sup.0)].sup.2=G.sub.SPK,R,i(R.sub.SPK,real(i)−R.sub.SPK,target(i)).sup.2  (43)
which for the weights means

(143) $\begin{array}{cc}{G}_{s,\mathrm{iso},i}^V=\frac{{G_{\mathrm{SPK},R,i}\left(A_{\mathrm{SPK},\mathrm{real}}\left(i\right)-A_{\mathrm{SPK},\mathrm{target}}\left(i\right)\right)}^2}{\begin{array}{c}V\left(\Delta U_{s,\mathrm{iso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S^{\mathrm{BG}}\left(i\right),A^0\right),A^0,r_{\mathrm{EP}}^0\right),{\omega }_0^0\right)-\\ {V\left(\Delta U_{s,\mathrm{iso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S_{\mathrm{iso},\mathrm{target}}^{\mathrm{BG}}\left(i\right),A^0\right),A^0,r_{\mathrm{EP}}^0\right),{\omega }_0^0\right)]}^2\end{array}}{G}_{s,\mathrm{aniso},i}^V=\frac{{G_{\mathrm{SPK},R,i}\left(R_{\mathrm{SPK},\mathrm{real}}\left(i\right)-R_{\mathrm{SPK},\mathrm{target}}\left(i\right)\right)}^2}{\begin{array}{c}V\left(\Delta U_{s,\mathrm{aniso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S^{\mathrm{BG}}\left(i\right),A^0\right),A^0,r_{\mathrm{EP}}^0\right),{\omega }_0^0\right)-\\ {V\left(\Delta U_{s,\mathrm{iso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S_{\mathrm{aniso},\mathrm{target}}^{\mathrm{BG}}\left(i\right),A^0\right),A^0,r_{\mathrm{EP}}^0\right),{\omega }_0^0\right)]}^2\end{array}}& \left(43a\right)\end{array}$

(144) In a further preferred embodiment, this is ensured by the stipulation
G.sub.s,iso,i.sup.V[V(ΔU.sub.s,iso(ΔSD.sub.s(ΔS.sup.BG(i),A.sup.0),A.sup.0,r.sub.EP.sup.0),ω.sub.0.sup.0)−V(ΔU.sub.s,iso(ΔSD.sub.s(ΔS.sub.iso,target.sup.BG(i),A.sup.0)A.sup.0,r.sub.EP.sup.0),ω.sub.0.sup.0)].sup.2=G.sub.SPK,R,i(R.sub.SPK,real(i)−R.sub.SPK,target(i)).sup.2,
G.sub.s,aniso,i.sup.V[V(ΔU.sub.s,aniso(ΔSD.sub.s(ΔS.sup.BG(i),A.sup.0),A.sup.0,r.sub.EP.sup.0),ω.sub.0.sup.0)−V(ΔU.sub.s,aniso(ΔSD.sub.s(ΔS.sub.aniso,target.sup.BG(i),A.sup.0)A.sup.0,r.sub.EP.sup.0),ω.sub.0.sup.0)].sup.2=G.sub.SPK,R,i(R.sub.SPK,real(i)−R.sub.SPK,target(i)).sup.2  (44)
which for the weights means

(145) $\begin{array}{cc}{G}_{s,\mathrm{iso},i}^V=\frac{{G_{\mathrm{SPK},R,i}\left(R_{\mathrm{SPK},\mathrm{Ist}}\left(i\right)-R_{\mathrm{SPK},\mathrm{target}}\left(i\right)\right)}^2}{\begin{array}{c}V\left(\Delta U_{s,\mathrm{iso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S^{\mathrm{BG}}\left(i\right),A^0\right),A^0,r_{\mathrm{EP}}^0\right),{\omega }_0^0\right)-\\ {V\left(\Delta U_{s,\mathrm{iso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S_{\mathrm{iso},\mathrm{target}}^{\mathrm{BG}}\left(i\right),A^0\right),A^0,r_{\mathrm{EP}}^0\right),{\omega }_0^0\right)]}^2\end{array}}{G}_{s,\mathrm{aniso},i}^V=\frac{{G_{\mathrm{SPK},R,i}\left(A_{\mathrm{SPK},\mathrm{Ist}}\left(i\right)-A_{\mathrm{SPK},\mathrm{target}}\left(i\right)\right)}^2}{\begin{array}{c}V\left(\Delta U_{s,\mathrm{aniso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S^{\mathrm{BG}}\left(i\right),A^0\right),A^0,r_{\mathrm{EP}}^0\right),{\omega }_0^0\right)-\\ {V\left(\Delta U_{s,\mathrm{iso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S_{\mathrm{aniso},\mathrm{target}}^{\mathrm{BG}}\left(i\right),A^0\right),A^0,r_{\mathrm{EP}}^0\right),{\omega }_0^0\right)]}^2\end{array}}& \left(44a\right)\end{array}$

(146) One advantage of the procedure according to the invention is that the target function

(147) $\begin{array}{cc}{F}_s=\underset{i}{.Math.}.Math.\begin{array}{c}{G}_{s,\mathrm{iso},i}^{V}V\left(\Delta U_{s,\mathrm{iso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S^{\mathrm{BG}}\left(i\right),A\right),A,r_{\mathrm{EP}}\right),{\omega }_0\right)-\\ \begin{array}{c}\begin{array}{c}{V\left(\Delta U_{s,\mathrm{iso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S_{\mathrm{iso},\mathrm{target}}^{\mathrm{BG}}\left(i\right),A^0\right),A^0,r_{\mathrm{EP}}^0\right),{\omega }_0^0\right)]}^2++\\ G_{s,\mathrm{aniso},i}^{V}V\left(\Delta U_{s,\mathrm{aniso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S^{\mathrm{BG}}\left(i\right),A\right),A,r_{\mathrm{EP}}\right),{\omega }_0\right)-\end{array}\\ {V\left(\Delta U_{s,\mathrm{aniso}}\left(\Delta {\mathrm{SD}}_s\left(\Delta S_{\mathrm{aniso},\mathrm{target}}^{\mathrm{BG}}\left(i\right),A^0\right),A^0,r_{\mathrm{EP}}^0\right),{\omega }_0^0\right)]}^2\end{array}\end{array}]& \left(45\right)\end{array}$

(148) for standard values reduces to F.sub.SPK; by contrast, for non-standard values it produces variations via which the aberrations of the spectacle lens distribute differently, in a way that leads to advantages for given parameters (for example vision model).

(149) FIG. 4 shows the results of a standard optimization of a spectacle lens at the vertex sphere (SPK) for a prescription of sphere Sph=−4.25 dpt, cylinder Cyl=0 dpt, and addition Add=2.5 dpt. FIG. 4a shows the distribution of the astigmatism (Asti), FIG. 4b shows the distribution of the vision, and FIG. 4c shows the curve of the refraction error (dashed line) and of the astigmatism (solid line) along the principal line on the leading surface of the spectacle lens. The spectacle lens is optimized with standard values for the cornea, the HOAs, and the vision model: initial vision=1.25 (decimal), by contrast to which only a vision=0.97 is optimized at the vertex sphere according to the prior art given haze with 1.3 dpt.

(150) FIG. 5 shows the result of an optimization of a spectacle lens with calculation in the eye, and with parameters of the vision model that deviate from the standard, namely with poorer initial vision. FIG. 5a shows the distribution of the astigmatism (Asti), FIG. 5b shows the distribution of the vision, and FIG. 5c shows the curve of the refraction error (dashed line) and of the astigmatism (solid line) along the principal line on the leading surface of the spectacle lens.

(151) If the spectacle lens shown in FIG. 4 having the values Sph=−4.25 dpt, Cyl=0 dpt, and Add=2.5 dpt is optimized for a spectacles wearer having deviating vision data (by contrast initial vision 1.00 (decimal) given a haze with 1.3 dpt, vision of only 0.9), then the result shown in FIG. 5 results. It is apparent that the spectacle lens obtains a peripheral astigmatism as a consequence of the adapted weight factors in equation (45). Although the zones of good seeing are slightly smaller in the spectacle lens (which, however, does not represent a severe disadvantage for a spectacle lens with poorer initial vision), the advantages of this predominate due to the slight peripheral astigmatism and the lessened shaking effect that is linked therewith.

REFERENCE LIST

(152) EP entrance pupil of the eye; AP exit pupil of the eye; SK vertex sphere; e corneal vertex distance; r.sub.0 pupil radius, here used only generically as a reference radius given the description via Zernike coefficients; r.sub.R radius of the dispersion disc; d.sub.LR distance of the rear lens surface from the exit pupil; d.sub.AR distance of the rear lens surface from the retina