Prescription-dependent and individualization-dependent modification of the temporal peripheral nominal astigmatism and adaptation of the object distance function to changed object distances for near and far vision

Abstract

Method for optimization of a progressive spectacle lens, including: defining a starting nominal astigmatism distribution for the spectacle lens; determining a transformed nominal astigmatism distribution and optimizing the spectacle lens on the basis of the transformed nominal astigmatism distribution, wherein the determination of a transformed nominal astigmatism distribution comprises multiplication of the maximum temporal nominal astigmatism of the starting nominal astigmatism distribution by a factor k as a result of which a modified maximum temporal astigmatism is obtained, wherein k is a function of a prescription value, and/or at least of one parameter of the spectacle lens or of the arrangement thereof in front of the eyes, and transformation of the starting nominal astigmatism distribution on the basis of the modified maximum temporal astigmatism.

Claims

1. A computer-implemented method for optimizing a progressive spectacle lens and forming the spectacle lens based on the method, comprising: specifying a starting object distance function A.sub.1G(y) that specifies a starting reciprocal object distance along the main line of sight as a function of the vertical coordinate y, obtaining a target object distance from at least one predetermined point D on the main line of sight, said predetermined point having a vertical coordinate y.sub.D; modifying the starting object distance function based on the obtained target object distance to produce a modified object distance function A.sub.1(y), said modified object distance function specifying a modified reciprocal object distance along the main line of sight as a function of the vertical coordinate y; optimizing the progressive spectacle lens, wherein in the optimization process of the spectacle lens the modified object distance function is taken into account, wherein: modifying the starting object distance function A.sub.1G(y) to produce a modified object distance function A.sub.1(y) comprises adding a correction function A.sub.1corr(y) to the starting object distance function A.sub.1G(y) in accordance with A.sub.1(y)=A.sub.1G(y)+A.sub.1corr(y), wherein the correction function has at least one variable parameter, which is determined based on the obtained target object distance from the at least one predetermined point D such that the condition A.sub.1(y=y.sub.D)=A.sub.1D is fulfilled, wherein A.sub.1(y=y.sub.D) is the value of the modified object distance function in the least one predetermined point D and A.sub.1D is the reciprocal value of the obtained target object distance for this point, and forming the optimized progressive spectacle lens based on the method.

2. The method according to claim 1, wherein the obtaining of a target object distance comprises obtaining a target object distance from a predetermined distance reference point on the main line of sight and a target object distance from a predetermined near reference point on the main line of sight.

3. The method according to claim 1, wherein the starting object distance function is a double asymptote function $A_{1 G} (y) = b_{G} + \frac{a_{G}}{{(1 +^{c (y + d)})}^{m}}$ with the parameters a.sub.G, b.sub.G, c, d, m, wherein: the two asymptotes respectively have values b.sub.G and (b.sub.G+a.sub.G), a vertical position can be controlled with the variable parameter d, and the parameter d is in a range of 10<d<10, the larger the value of the variable parameter c, the faster a transition from one of the two asymptotes to the other, an absolute value of the parameter c is <1.5, the parameter m, where m>0, describes the asymmetry of the double asymptote function, for m=1, the double asymptote function has a point symmetry with a center y=d, and the parameter m is in a range of 0.2<m<2, and if a negative sign (c<0) is selected for the parameter c, it holds that: a near portion asymptote A.sub.1G(y.fwdarw.)=A.sub.1Gnear=b.sub.G, and a distance portion asymptote A.sub.1G(y.fwdarw.+)=A.sub.1Gdistance=(b.sub.G+a.sub.G).

4. The method according to claim 3, wherein the obtaining of a target object distance comprises obtaining a target object distance from a predetermined distance reference point on the main line of sight y.sub.D.sub.F and a target object distance from a predetermined near reference point on the main line of sight; and wherein: the correction function is a double asymptote function $A_{1 corr} (y) = b_{corr} + \frac{a_{corr}}{{(1 +^{c_{corr} (y + d_{corr})})}^{m_{corr}}}$ with the parameters a.sub.corr, b.sub.corr, c.sub.corr, d.sub.corr, m.sub.corr, wherein the parameters c.sub.corr, d.sub.corr and m.sub.corr of the correction function are the same as the parameters c, d and m of the starting object distance function, respectively, such that c=c.sub.corr, d=d.sub.corr, m=m.sub.corr, and the parameters b.sub.corr and a.sub.corr of the correction function are determined based on the obtained target object distance from the distance reference point and target object distance from the near reference point such that the following conditions are fulfilled:
A.sub.1(y)=A.sub.1G(y)+A.sub.1corr(y)
A.sub.1(y.sub.D.sub.F)=A.sub.1distance, and
A.sub.1(y.sub.D.sub.N)=A.sub.1near, wherein: A.sub.1distance is the reciprocal value of the target object distance from the distance reference point; A.sub.1near is the reciprocal value of the target object distance from the near reference point; y.sub.D.sub.F is the vertical coordinate of the distance reference point; and y.sub.D.sub.N is the vertical coordinate of the near reference point.

5. The method according to claim 2, wherein the correction function is a linear function of the starting object distance function A.sub.corr(y)=c+mA.sub.1G(y) with the parameters c and m, wherein the parameters c and m are calculated from deviations of values of the starting object distance function A.sub.1G(y) from the values of the reciprocal target object distance in the distance and near reference points.

6. The method according to claim 5, wherein it holds for the parameters c and m that: $c = \frac{A_{1 F} A_{1 G} (y_{DN}) - A_{1 N} A_{1 G} (y_{DF})}{A_{1 G} (y_{DN}) - A_{1 G} (y_{DF})}$ $m = \frac{A_{1 N} - A_{1 F}}{A_{1 G} (y_{DN}) - A_{1 G} (y_{DF})},$ where
A.sub.1F=A.sub.1distanceA.sub.1G(y.sub.D.sub.F);
A.sub.1N=A.sub.1nearA.sub.1G(y.sub.D.sub.N); A.sub.1distance is the reciprocal value of the target object distance from the distance reference point; A.sub.1near is the reciprocal value of the target object distance from the near reference point; y.sub.D.sub.F is the vertical coordinate of the distance reference point; and y.sub.D.sub.N is the vertical coordinate of the near reference point.

7. The method according to claim 1, further comprising: overlaying the starting object distance function A.sub.1G(y) with a function that is a Gaussian bell curve $A_{1 Gauss} (y) = g_{a} + g_{b}^{- \frac{y - y_{0}}{}}$ with the parameters g.sub.a, g.sub.b, y.sub.0, , wherein: the parameter g.sub.b is determined according to a maximum A.sub.1-increase of a Gaussian function g.sub.b max, where: $g_{b} = \frac{g_{G}}{100} g_{bmax}$ based on a percentage weighting g.sub.G of the Gaussian function, where g.sub.G[0,100]%, a 90% weighting of the Gaussian function and a maximum A.sub.1-increase of the Gaussian function g.sub.b max=0.6 dpt, a value of 0.54 dpt results for g.sub.b, the parameter g.sub.a is in a range of 1<g.sub.a<1, the parameter y.sub.0 is in a range of 10<y.sub.0<5, and the parameter is in a range of 0<6<15.

8. A computer program product adapted, when loaded and executed on a computer, to perform a method for optimizing a progressive spectacle lens according to claim 1.

9. A storage medium with a computer program stored thereon, the computer program being adapted, when loaded and executed on a computer, to perform a method for optimizing a progressive spectacle lens according to claim 1.

10. A device for optimizing a progressive spectacle lens, comprising optimizing means adapted to perform an optimization of the spectacle lens according to the method of claim 1.

11. A method for producing a progressive spectacle lens, comprising: optimizing the spectacle lens according to the method of claim 1, providing surface data of the calculated and optimized spectacle lens; and manufacturing the spectacle lens according to the provided surface data of the spectacle lens.

12. A device for producing a progressive spectacle lens, comprising: optimizing means adapted to perform an optimization of the spectacle lens according to the method of claim 1; and processing means to produce the spectacle lens, which has been optimized by the optimization method.

Description

(1) Further objects, features, and advantages of the present invention will become apparent from the following detailed description of exemplary and preferred embodiments of the present invention with reference to the drawings, which show:

(2) FIG. 1 starting target astigmatism distribution for an addition of 2.5 dpt;

(3) FIG. 2 target astigmatism distribution for an addition of 2.5 dpt with a scaling of the temporal astigmatism;

(4) FIG. 3 the scaled target astigmatism distribution shown in FIG. 2, which is additionally scaled depending on the addition;

(5) FIG. 4 the starting target astigmatism distribution scaled depending on the addition;

(6) FIG. 5 a portion of a graphical user interface for setting the prefactor v;

(7) FIG. 6A an example of a starting target astigmatism distribution;

(8) FIG. 6B an example of a modified/transformed target astigmatism distribution calculated from the starting target astigmatism distribution shown in FIG. 6A;

(9) FIG. 7A the surface power of the progressive surface of a progressive spectacle lens optimized on the basis of the starting target astigmatism distribution shown in FIG. 6A;

(10) FIG. 7B the surface power of the progressive surface of a progressive spectacle lens optimized on the basis of the transformed target astigmatism distribution shown in FIG. 6B;

(11) FIG. 8A the gradient of the surface power of the progressive surface of the progressive spectacle lens optimized on the basis of the starting target astigmatism distribution shown in FIG. 6A;

(12) FIG. 8B the gradient of the surface power of the progressive surface of the progressive spectacle lens optimized on the basis of the transformed target astigmatism distribution shown in FIG. 6B;

(13) FIG. 9A the surface astigmatism of the progressive surface of the progressive spectacle lens optimized on the basis of the starting target astigmatism distribution shown in FIG. 6A;

(14) FIG. 9B the surface astigmatism of the progressive surface of the progressive spectacle lens optimized on the basis of the transformed target astigmatism distribution shown in FIG. 6B;

(15) FIG. 10A the gradient of the surface astigmatism of the progressive surface of the progressive spectacle lens optimized on the basis of the starting target astigmatism distribution shown in FIG. 6A;

(16) FIG. 10B the gradient of the surface astigmatism of the progressive surface of the progressive spectacle lens optimized on the basis of the transformed target astigmatism distribution shown in FIG. 6B;

(17) FIG. 11A the astigmatism in the wearing position of the progressive spectacle lens optimized on the basis of the starting target astigmatism distribution shown in FIG. 6A;

(18) FIG. 11B the astigmatism in the wearing position of the progressive spectacle lens optimized on the basis of the transformed target astigmatism distribution shown in FIG. 6B;

(19) FIG. 12A the mean refractive power in the wearing position of the progressive spectacle lens optimized on the basis of the starting target astigmatism distribution shown in FIG. 6A;

(20) FIG. 12B the mean refractive power in the wearing position of the progressive spectacle lens optimized on the basis of the transformed target astigmatism distribution shown in FIG. 6B;

(21) FIG. 13A,B the image formation of objects at different object distances through a spectacle lens;

(22) FIGS. 14A,B the reciprocal object distance (in dpt) along the main line of sight according to an example of the invention;

(23) FIGS. 15A-15H an example of an adjustment of a starting object distance function to a modified object distance model, wherein

(24) FIG. 15A is a further exemplary starting object distance function;

(25) FIG. 15B is the slope of the starting object distance function;

(26) FIG. 15C is an exemplary Gaussian function;

(27) FIG. 15D is the slope of the Gaussian function;

(28) FIG. 15E is the object distance function obtained by overlaying the starting object distance function with the Gaussian function;

(29) FIG. 15F is the slope of the object distance function;

(30) FIG. 15G is the object distance function modified by linear adjustment; and

(31) FIG. 15H is the slope of the object distance function modified by linear adjustment;

(32) FIGS. 16A-16C an example of a graphical user interface for visualizing and modifying the object distance function, wherein

(33) FIG. 16A is a portion for visualizing a starting object distance function;

(34) FIG. 16B is a portion for visualizing and changing the parameter of a correction function;

(35) FIG. 16C is a portion for visualizing the modified starting object distance function;

(36) FIGS. 17A-17D a further example of an adjustment of a starting object distance function to a modified object distance model, wherein

(37) FIG. 17A is a further exemplary starting object distance function;

(38) FIG. 17B is the slope of the starting object distance function;

(39) FIG. 17C is the new object distance function obtained by linear adjustment;

(40) FIG. 17D is the slope of the new object distance function;

(41) FIG. 18 an exemplary graphical user interface for visualizing and modifying the object distance function;

(42) FIG. 19 a further exemplary graphical user interface for visualizing and modifying the object distance function.

(43) On the abscissa of FIGS. 14A to 17D, the vertical coordinate y of the main line of sight is plotted in mm. On the ordinate of FIGS. 14 to 17, the reciprocal object distance (reciprocal object separation) is plotted in dpt. The coordinate system is the above-described coordinate system {u,y}.

(44) FIG. 1 shows the starting target astigmatism distribution based on a predetermined starting surface for an addition of 2.5 dpt. The maximum astigmatism for the periphery is 2.6 dpt. Based on the starting target astigmatism distribution, a spectacle lens with the following prescription values and parameters is to be calculated: sphere (sph)=5.0 dpt; cylinder (cyl)=0.0 dpt; addition (add)=2.5 dpt; base curve (BC)=3.0 dpt; refractive index n=1.579. The spectacle lens is calculated in a wearing position with the parameters: corneal vertex distance (CVD)=13 mm; forward inclination (FI)=7; interpupillary distance (ID)=64 mm; Y tilt angle=0.

(45) In one example, a factor k=0.58 is determined depending on the prescription data of the spectacle lens (in particular the prescription astigmatism, the prescribed axis of the prescription astigmatism, and the prescribed addition) and the tilt angle of the spectacle lens (cf. equations (7) to (13)). The factor k=0.58 is multiplied by the maximum temporal astigmatism of the starting target astigmatism distribution. Subsequently, an interpolation of the target astigmatism values between the 0.5 dpt base target isoastigmatism line and the periphery of the spectacle lens is performed taking the maximum temporal astigmatism multiplied by the factor k into consideration. The interpolation is performed for the peripheral target astigmatism according to the truncated cone method described in DE 10 2009 005 206 or DE 10 2009 005 214.

(46) In this example, the multiplication of the maximum temporal astigmatism by the factor k does not have any influence on the 0.5 dpt base target isoastigmatism line. The target astigmatism values between the main line and the 0.5 dpt base target isoastigmatism line thus remain unchanged. Between the temporal 0.5 dpt base target isoastigmatism line and the peak of the temporal astigmatism hill (i.e. the position of the maximum target astigmatism), however, an interpolation on the basis of the scaled maximum temporal astigmatism (in this case 2.6*0.58=1.508 dpt) is performed. FIG. 2 shows the target astigmatism distribution obtained after a multiplication of the maximum temporal astigmatism and a subsequent interpolation. The asymmetric target astigmatism distribution shown in FIG. 2 applies to a progressive spectacle lens having an addition of 2.5 dpt.

(47) As described in DE 10 2008 015 189, the total astigmatism specification resulting from a multiplication of the maximum temporal target astigmatism with subsequent interpolation of the target astigmatism values could be scaled depending on the addition as a whole, in order to obtain target astigmatism specifications for a different addition. For example, the target astigmatism distribution shown in FIG. 2 can be scaled with the factor 0.3 as a whole to obtain a new addition of 0.75 from the original addition of 2.5 dpt. Thereby, a temporal maximum astigmatism of 1.508*0.3=0.45 results. The target astigmatism distribution additionally scaled depending on the addition is shown in FIG. 3.

(48) FIG. 4 shows a comparative example of a target astigmatism distribution obtained from the target astigmatism distribution shown in FIG. 1 by means of a (global) scaling depending on the addition (as described in DE 10 2008 015 189). The example shown in FIG. 4 corresponds to a rescaling of the starting target astigmatism distribution from the original addition of 2.5 dpt to a new addition of 0.75 dpt.

(49) FIG. 5 shows a portion of a graphical user interface, which makes it possible to set the prefactor v. As described above, the asymptotic prefactor v can be specified e.g. depending on the mean distance power by a double asymptote function (cf. equation 7) with the parameters a=0.475; b=0.525; c=5.0; d=3.5 and m=1.

(50) FIG. 6A, B to 12A, B show the change of the target objectives in an exemplary transformation of the temporal target astigmatism distribution (FIGS. 6A and 6B) as well as the change of the results of the optimization of a progressive spectacle lens according to the respective target astigmatism objectives. The parameters of the prescription are as follows: sphere (sph)=8 dpt; cylinder (cyl)=6 dpt; axis 45; addition 0.75 dpt.

(51) The tilt angle, which in the case of flat base curves approximately corresponds to the face form angle, is 5.

(52) According to the above-described formulae (7) to (14), a factor k with a value of 0.58 results.

(53) FIGS. X-A (X=6, 7, . . . 12) relate to a comparative example with a symmetric target astigmatism distribution (starting target astigmatism distribution). FIGS. X-B (X=6, 7, . . . , 12) relate to an embodiment according to an aspect of the invention (manipulated target objectives) with a non-symmetric target astigmatism distribution.

(54) The target astigmatism distribution shown in FIG. 6B is obtained from the symmetric target astigmatism distribution shown in FIG. 6A by a multiplication of the temporal target astigmatism by the factor k=0.58 and a subsequent interpolation of the target astigmatism values. The interpolation is performed according to the truncated cone model disclosed in DE 10 2009 005 206 or DE 10 2009 005 214 for the peripheral astigmatism. The nasal target astigmatism is not affected by this modification. Consequently, the maximum temporal target astigmatism is lower than the maximum nasal target astigmatism by the factor 0.58.

(55) FIGS. 7A to 10A show the surface properties of the progressive surface of a spectacle lens optimized according to the symmetric target astigmatism objectives shown in FIG. 6A. FIGS. 7B to 10B show the surface properties of the progressive surface of a spectacle lens optimized according to the asymmetric manipulated target objectives shown in FIG. 6B. FIGS. 11A, B and 12A, B each show the astigmatism (FIG. 11A, B) and the refractive power (FIG. 12A, B) in the wearing position of the respective progressive spectacle lens. The following table 1 lists the target objectives and properties, shown in FIG. 6A, B to 12A, B, of a progressive surface optimized on the basis of the respective target objectives.

(56) TABLE-US-00001 TABLE 1 Symmetric Manipulated Property shown target objectives target objectives Target astigmatism [dpt] FIG. 6A FIG. 6B Surface power of the progressive FIG. 7A FIG. 7B surface [dpt] Surface power gradient of the FIG. 8A FIG. 8B progressive surface [dpt/mm] Surface astigmatism of the FIG. 9A FIG. 9B progressive surface [dpt] Surface astigmatism gradient of the FIG. 10A FIG. 10B progressive surface [dpt/mm] Wearing position astigmatism [dpt] FIG. 11A FIG. 11B Mean refractive power in wearing FIG. 12A FIG. 12B position [dpt]

(57) A comparison of FIGS. 6A and 6B clearly shows the asymmetry of the manipulated target astigmatism distribution shown in FIG. 6B. In FIG. 6B, the temporal target astigmatism is below 0.5 dpt.

(58) The progressive surface of the spectacle lens optimized according to the manipulated target objectives shown in FIG. 6B has clearly less surface power modifications temporally (cf. also FIG. 8A and FIG. 8B). For example, in a comparison of the gradients of the surface power of the progressive surface shown in FIG. 8A and FIG. 8, it can be clearly seen that the progressive surface optimized according to the manipulated target astigmatism objectives temporally has substantially smaller gradients than the surface optimized according to the symmetric target astigmatism objectives. In this example, the gradients are smaller by a factor 5.

(59) Moreover, a comparison of FIGS. 9A and 9B with FIGS. 10A and 10B shows that the progressive surface optimized according to the manipulated target astigmatism objectives temporally has clearly less modifications of the surface astigmatism and thus clearly smaller gradients of the surface astigmatism than the surface optimized according to the symmetric target astigmatism objectives. In this example, the gradients are smaller by a factor 4.5.

(60) Also, the properties in the wearing position (astigmatism and refractive power in the wearing position) of the spectacle lens optimized according to manipulated target astigmatism objectives have clearly less gradients, wherein the central viewing zones do not differ substantially in size and usability. In the specific example, the gradients change from 0.45 dpt/mm to 0.05 dpt/mm. For the mean refractive power in the wearing position, a reduction from 0.55 dpt/mm (cf. FIG. 12A) to 0.15 dpt/mm (cf. FIG. 12B) will be obtained.

(61) FIGS. 13A and 13B schematically show the image formation of objects at different object distances (object separations) through a spectacle lens 10. The spectacle lens 10 is disposed in a predetermined wearing position in front of the eyes 12 of the spectacles wearer. In FIGS. 13A and 13B:

(62) a1=1/A.sub.1 is the object distance (object separation);

(63) e is the corneal vertex distance (CVD);

(64) b is the ocular center of rotation distance;

(65) s.sub.Z is the distance corneal apexocular center of rotation

(66) sB.sub.G is the image separation/distance;

(67) Z is the ocular center of rotation;

(68) R is the far point sphere; and

(69) SK is the vertex sphere.

(70) The calculation and optimization of the spectacle lens 10 is performed completely in the wearing position of the spectacle lens 12, i.e. taking the predetermined arrangement of the spectacle lens in front of the eyes 12 of the spectacles wearer (defined by the corneal vertex distance, forward inclination, etc.) and a predetermined object distance model into consideration. The object distance model can comprise the objectives for an object surface 14, which specify different object distances or object zones for foveal vision. The object surface 14 is preferably defined by the objectives for the reciprocal object distance (the reciprocal object separation) A.sub.1(x,y) along the object-side main rays. The course of the reciprocal object distance A.sub.1(x=x.sub.0,y)=A.sub.1(u=0,y) along the main line of sight (i.e. with x=x.sub.0 and u=0) represents the object distance function. The object distance function A.sub.1(x=x.sub.0,y)=A.sub.1(u=0,y) determines the width of the viewing zones in the surrounding of the main line of sight (Minkwitz theorem). A point on the object surface is imaged to the far point sphere by the spectacle lens, as is schematically shown in FIGS. 13A and 13B. In the example shown in FIGS. 13A and 13B, the eye-side surface of the spectacle lens 10 is the progressive surface to be optimized.

(71) According to a first example, the object distance function A.sub.1(y) is represented as the sum of two double asymptote functions. FIGS. 14A and 14B show an exemplary starting object distance function A.sub.1G(y) (broken line) and a transformed object distance function A.sub.1(y) adjusted to the new object distance (solid line), which is obtained by means of overlaying the starting object distance function A.sub.1(y) with a correction function A.sub.1corr(y) (chain-dotted line).

(72) The parameters of the starting object distance function (which is described by a double asymptote function) are a.sub.G=2.606 dpt, b.sub.G=2.588 dpt, c=0.46/mm, d=2.2 mm and m=0.75.

(73) In this case, the distance reference point DF (design point distance) is at y=+8 mm (y.sub.DF=8 mm) and the near reference point DN (design point near) is at y=12 mm (y.sub.DN=12 mm). The object distance in the distance reference point is infinite and consequently A.sub.1distance=A.sub.1G(y)=0.00 dpt. The object distance in the near reference point is 40 cm and consequently A.sub.1near=A.sub.1G(y.sub.DN)=2.50 dpt.

(74) The object distances in the distance and near reference points for a specific spectacles wearer or for other designs and applications may be different from the above standard model though. For example, an object distance of 400 cm can be taken into consideration in the distance reference point DF, and an object distance of 50 cm in the near reference point. In this case, the modified specifications for the object distance in the distance and near reference points are A.sub.1distance=A.sub.1G(y.sub.DF)=0.25 dpt and A.sub.1near=A.sub.1G(y.sub.DN)=2.00 dpt, respectively.

(75) By overlaying the starting object distance function A.sub.1G(y) with a correction function A.sub.1corr(y) with the same coefficients c, d and m as that of the starting object distance function and with the coefficients b.sub.corr=0.526 and a.sub.corr=0.782, the adjusted course of the object distance function A.sub.1(y) shown in FIG. 14B results.

(76) FIG. 15A shows a further exemplary starting object distance function A.sub.1G(y). FIG. 15B shows the slope of the starting object distance function (i.e. the derivative of the starting object distance function according to y). The starting object distance function is described by a double asymptote function with the coefficients a.sub.G=2.100; b.sub.G=2.801; c=0.206; d=5.080; m=0.5. The starting object distance function has a very smooth transition from the distance to the near portions. In this example, the reciprocal object distance A.sub.1Gdistance in the distance reference point DF (at y=10 mm) is equal to 1.00 dpt (A.sub.1Gdistance=1.00 dpt), and the reciprocal object distance A.sub.1Gnear in the near reference point DN (at y=14 mm) is equal to 2.5 dpt (A.sub.1Gnear=2.5 dpt). Thus, the starting object distance function describes a tube design for a near-vision lens.

(77) FIG. 15C shows an exemplary Gaussian function A.sub.1Gauss(y) (i.e. the correcting reciprocal object distance along the main line of sight), which can be used for modifying the design characteristic, for example. The Gaussian function shown in FIG. 15C is described by a Gaussian bell curve

(78) $g (y) = g_{a} + g_{b}^{- \frac{y - y_{0}}{}}$
with the coefficients g.sub.a=0.00; g.sub.b=0.35; =5.56 and y.sub.0=3.47. FIG. 15D shows the slope (first derivative according to y) of the Gaussian bell curve shown in FIG. 15C.

(79) FIG. 15E shows an object distance function A.sub.1(y)(i.e. the modified reciprocal object distance along the main line of sight), which is obtained by overlaying the starting object distance function shown in FIG. 15A with the Gaussian function shown in FIG. 15C. FIG. 15F shows the slope (the first derivative according to y) of the object distance function A.sub.1(y) shown in FIG. 15E. By overlaying the starting object distance function with the Gaussian bell curve shown in FIG. 15C, a modified object distance function is obtained, which is particularly suitable for a for a lens design for computer work. The slope of the modified object distance function A.sub.1(y) has a maximum at y=7 mm, i.e. the modification of the object distance function A.sub.1(y) is greatest there. Accordingly, at a height of y=7 mm there is located the narrowest point in the progression range with respect to the viewing zone width, which is e.g. defined by the 0.5 dpt isoastigmatism line. At a height of y=0 mm, the slope of the object distance function A.sub.1(y) has a local minimum. At this height, the viewing zone is relatively wide and can be used for viewing at screens.

(80) Moreover, the object distance function A.sub.1(y) shown in FIG. 15E can be adjusted to the modified specifications for the object distance in the distance reference point and in the near reference point. FIG. 15G shows a modified object distance function A.sub.1new(y) obtained by adjusting the object distance function A.sub.1(y) shown in FIG. 15E to the objectives
A.sub.1(y=10)=0.50 dpt and
A.sub.1(y=14)=2.50 dpt.

(81) The modified and adjusted object distance function is obtained according to the formula A.sub.1new(y)=c+(1+m)A.sub.1(y), where c=0.836 and m=0.335.

(82) FIG. 15H shows the slope (derivative according to y) of the modified object distance function A.sub.1new(y) shown in FIG. 15G.

(83) FIG. 16A shows a portion of a graphical user interface, wherein the portion is adapted to visualize the starting object distance function (in the specific case a starting object distance function A.sub.1G(y) in the form of a double asymptote function of the form

(84) $A_{1 G} (y) = b + \frac{a}{(1 +^{c (y + d) m}}) .$
The graphical user interface can further comprise a portion (not shown in FIG. 16A) having a fields for inputting and optionally modifying the coefficients of the starting object distance function.

(85) FIG. 16B shows a graphical user interface adapted to visualize a correction function (in this case a Gaussian bell curve of the form

(86) $A_{1 Gauss} = a_{0} + b_{0}^{- {(\frac{y - y_{0}}{})}^{2}}) .$
Moreover, the graphical user interface comprises a further portion having input fields/masks in which the coefficients of the correction function are indicated and optionally changed. By the overlay with a correction function in the form of a Gaussian bell curve, the intermediate zone can be weighted new. FIG. 16C shows a graphical user interface with a portion adapted to visualize the object distance function put together by overlaying the starting object distance function with the correction function.

(87) FIGS. 17A and 17B show the course and the derivative of an exemplary starting object distance function (basic function): FIG. 17A shows the course of the function A.sub.1G(y) along the main line in dpt; FIG. 17B shows the first derivative

(88) $\frac{A_{1 G} (y)}{y}$
along the main line.

(89) In this example, the wearer specifications for the desired object distances are A.sub.1distance=0.5 dpt at the height y.sub.F=12 mm and A.sub.1near=2.75 dpt at the height y.sub.N=14 mm. The actual values of the starting object distance function A.sub.1G(y) in the reference point result for A.sub.1G(y.sub.F)=0.8896 dpt and A.sub.1G(y.sub.N)=2.4721 dpt.

(90) The starting object distance function shown in FIG. 17A is transformed linearly, wherein the straight line coefficients are calculated depending on the modified specifications for the object distances in the distance and near reference points as c=0.7648 and m=0.4212.

(91) FIGS. 17C and 17D show the course and the derivative of the new transformed object distance function A.sub.1 (A.sub.1-function), where: FIG. 17C shows the course of the new object distance function A.sub.1(y) along the main line on the front surface of the spectacle lens; and FIG. 17D shows the derivative

(92) $\frac{A_{1} (y)}{y}$
of the new object distance function A.sub.1(y) along the main line on the front surface of the spectacle lens.

(93) FIGS. 18 and 19 show an exemplary mask and an exemplary graphical user interface, respectively for indication and optionally modifying the parameters of the object distance function and for visualizing the thus calculated object distance function.

REFERENCE NUMERAL LIST

(94) 10 spectacle lens 12 eye of the spectacles wearer 14 object surface e corneal vertex distance (CVD) b ocular center of rotation distance sZ distance corneal vertexocular center of rotation sBG image distance Z ocular center of rotation R far point sphere SK vertex sphere

Prescription-dependent and individualization-dependent modification of the temporal peripheral nominal astigmatism and adaptation of the object distance function to changed object distances for near and far vision

Assignee

Inventors

Cpc classification

Classification Explorer

G02C7/065

PHYSICS

Classification Explorer

G02C7/061

PHYSICS

Classification Explorer

G02C7/063

PHYSICS

Classification Explorer

G02C7/028

PHYSICS

International classification

Classification Explorer

G02C7/02

PHYSICS

Classification Explorer

G02C7/06

PHYSICS

Abstract

Claims

Description