Method for designing a lens shape and spectacle lens

Abstract

The current invention is directed to a computer-implemented method for providing a lens shape for an ophthalmic lens. Further, there is provided a method for angular smoothing of a surface determined by carrier lines radially outwards of a prescription zone bordered by a first boundary line. Further, there is provided an ophthalmic lens, in particular a spectacle lens. Further, a method for minimizing the difference in thickness between two ophthalmic lenses for the same spectacles. A computer program product and a machine readable storage medium are provided as well.

Claims

1. A method for manufacturing an ophthalmic lens, wherein the ophthalmic lens comprises a shape determined by the following steps: a) providing a predetermined lens shape of an ophthalmic lens having a front surface and a back surface, wherein the predetermined lens shape comprises a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone of the back surface bordered by a first boundary line, such that the ophthalmic lens satisfies predetermined optical properties within the prescription zone; b) determining a carrier point on the back surface within the prescription zone and a plurality of carrier lines each extending from the carrier point into a respective direction; c) determining a transition zone of the back surface, wherein the transition zone extends radially outwards from the first boundary line towards the outer edge of the ophthalmic lens and ends at a second boundary line bordering the transition zone radially outwards; d) for each carrier line, setting a desired constant curvature gradient over the transition zone; e) for each carrier line, determining a curvature profile of the back surface between the first boundary line and an outer edge the ophthalmic lens along the carrier line, and wherein the curvature profile in the transition zone is determined based on the respective desired constant curvature gradient; f) angular smoothing the back surface radially outwards of the first boundary line; and g) manufacturing the ophthalmic lens comprising the shape defined by steps a) through f).

2. The method of claim 1, wherein a curvature along the carrier line between the second boundary line and the outer edge is essentially constant and equals the curvature along the carrier line in the transition zone at the second boundary line.

3. The method of claim 1, wherein the desired constant curvature gradient is set based on the curvature of the prescription zone at the first boundary line and a boundary condition for the curvature within the transition zone.

4. The method of claim 3, wherein the curvature gradient is further set based on a desired thickness reduction of the ophthalmic lens along the carrier line.

5. The method of claim 1, wherein the desired constant curvature gradient is set based on the curvature of the prescription zone at the first boundary line and a curvature target to be reached at the second boundary line, and wherein the curvature target is at least one of zero and a curvature of the front surface.

6. The method of claim 5, wherein the curvature of the front surface is determined in the same coordinate system as the curvature of the back surface.

7. The method of claim 5, wherein the front surface is a spherical surface.

8. The method of claim 1, wherein the curvature gradient is set to be negative in case the ophthalmic lens is a minus lens and the curvature gradient is set to be positive in case the ophthalmic lens is a plus lens.

9. The method of claim 1, wherein the curvature profile is determined by determining a cubic spline from the first boundary line to the second boundary line, wherein the cubic spline is comprised of a plurality of sections each described by a cubic polynomial, and wherein the cubical polynomials are determined section-wise from the first boundary line to the second boundary line.

10. A method for manufacturing an ophthalmic lens, wherein the ophthalmic lens comprises a shape determined by: a) providing a predetermined lens shape of an ophthalmic lens having a front surface and a back surface, wherein the predetermined lens shape comprises a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone of the back surface bordered by a first boundary line, such that the ophthalmic lens satisfies predetermined optical properties within the prescription zone; b) determining a carrier point on the back surface within the prescription zone and a plurality of carrier lines each extending from the carrier point into a respective direction; c) determining a transition zone of the back surface, wherein the transition zone extends radially outwards from the first boundary line towards the outer edge of the ophthalmic lens and ends at a second boundary line bordering the transition zone radially outwards; d) for each carrier line, setting a desired constant curvature gradient over the transition zone: e) for each carrier line, determining a curvature profile of the back surface between the first boundary line and an outer edge the ophthalmic lens along the carrier line, and wherein the curvature profile in the transition zone is determined based on the respective desired constant curvature gradient f) angular smoothing the back surface radially outwards of the first boundary line; and g) manufacturing the ophthalmic lens comprising the shape defined by steps a) through f), wherein the curvature profile is determined by determining a cubic spline from the first boundary line to the second boundary line, wherein the cubic spline is comprised of a plurality of sections each described by a cubic polynomial, and wherein the cubical polynomials are determined section-wise from the first boundary line to the second boundary line, and wherein the cubical polynomials are determined section-wise from the first boundary line to the second boundary line such that a sagittal height, a slope and a curvature of the back surface along the carrier line are continuous and the curvature along the carrier line changes over each section resulting in an approximated constant curvature gradient over the transition zone.

11. A method for manufacturing an ophthalmic lens, wherein the ophthalmic lens comprises a shape determined by: a) providing a predetermined lens shape of an ophthalmic lens having a front surface and a back surface, wherein the predetermined lens shape comprises a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone of the back surface bordered by a first boundary line, such that the ophthalmic lens satisfies predetermined optical properties within the prescription zone; b) determining a carrier point on the back surface within the prescription zone and a plurality of carrier lines each extending from the carrier point into a respective direction; c) determining a transition zone of the back surface, wherein the transition zone extends radially outwards from the first boundary line towards the outer edge of the ophthalmic lens and ends at a second boundary line bordering the transition zone radially outwards; d) for each carrier line, setting a desired constant curvature gradient over the transition zone; e) for each carrier line, determining a curvature profile of the back surface between the first boundary line and an outer edge the ophthalmic lens along the carrier line, and wherein the curvature profile in the transition zone is determined based on the respective desired constant curvature gradient; f) angular smoothing the back surface radially outwards of the first boundary line; and g) manufacturing the ophthalmic lens comprising the shape defined by steps a) through f, wherein the curvature profile is determined by determining a cubic spline from the first boundary line to the second boundary line, wherein the cubic spline is comprised of a plurality of sections each described by a cubical polynomial, and wherein the cubical polynomials are determined section-wise from the first boundary line to the second boundary line such that a sagittal height, a slope and a curvature of the back surface along the carrier line are continuous and the curvature gradient is reset to the desired constant curvature gradient for each polynomial at the radially inwards end of each section.

12. The method of claim 1, wherein a length of the transition zone along each carrier line is constant resulting in the second boundary line bordering the transition zone radially outwards and the second boundary line being radially offset from the first boundary line by the length.

13. The method of claim 8, wherein the length of the transition zone is within a range of at least 10 mm up to and including 20 mm.

14. The method of claim 1, wherein the constant curvature gradient has a magnitude in range from and including 0.05 diopters/mm to and including 1.5 diopters/mm.

15. The method of claim 9, wherein the length of each section is within a range of at least 0.5 mm up to and including 2 mm.

16. The method of claim 1, wherein the method comprises a further step of checking, for each carrier line, whether a thickness of the spectacle lens at an outer edge and/or at an intended frame line along which the ophthalmic lens is to be edged is above a predefined threshold and, if not, reducing or increasing the magnitude of the desired constant curvature gradient.

17. The method of claim 1, wherein the ophthalmic lens is an uncut finished spectacle lens.

18. The method of claim 1, wherein a curvature profile of the predetermined lens shape of the back surface is preserved within the first boundary line.

19. The method of claim 1, wherein at least a sagittal height of the prescription zone of the back surface transitions continuously at the first boundary line into each carrier line.

20. The method of claim 19, wherein further a slope of the prescription zone of the back surface in the direction along the carrier lines transitions continuously at the first boundary line into each carrier line.

21. The method of claim 20, wherein further a curvature of the prescription zone of the back surface in the direction along the carrier lines transitions continuously at the first boundary line into each carrier line.

22. The method of claim 12, wherein the length is to be measured within a plane parallel to a tangential plane oriented tangentially to the carrier point of the back surface.

23. The method of claim 1, wherein the carrier point is offset nasally from a prism reference point of the ophthalmic lens.

24. The method of claim 1, wherein first boundary line is circular and the second boundary line is circular.

25. The method of claim 1, wherein the curvature profile along each carrier line radially outwards of the second boundary line is determined via a circular arc.

26. The method of claim 1, wherein a further step of angular smoothing of the back surface radially outwards of the first boundary line is conducted by flattening a profile of the curvature of the prescription zone in the direction of the carrier lines along the first boundary line via approximation by a polynomial or a spline function or a Fourier series to obtain a flattened curvature profile, and wherein the flattened curvature profile is used as a radially inward starting curvature value for each carrier line.

27. The method of claim 1, wherein the method further comprises the following steps to provide for angular smoothing of the back surface radially outwards of the first boundary line: i) forming a series of coefficient values of corresponding coefficients of a respective function describing each carrier line in the transition zone; and, ii) determining, for each corresponding coefficient, a first Fourier series of a first order approximating the series of coefficient values, to obtain a first set of Fourier series each dependent on an angle around the carrier point, the first set of Fourier series describing any carrier line in a radial direction for a given angle.

28. The method of claim 27 further comprising the steps of: iii) determining, for each coefficient, a second Fourier series of a second order approximating the series of coefficient values, to obtain a second set of Fourier series each dependent on an angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction for the given angle, wherein the second order is higher than the first order, and wherein the second set of Fourier series is applied at the first boundary line; and, iv) blending the second set of Fourier series into the first set of Fourier series radially outwards over a blending zone.

29. The method of claim 28, wherein the step of blending is conducted via the following formula:
Z=Z.sub.2(A,R)+W(R).Math.(Z.sub.1(A,R)Z.sub.2(A,R)), wherein Z is the resulting sagittal height, A is the angle around the carrier point, R is the radial distance from the carrier point, Z.sub.1(A,R) is the sagittal height at the angle A and the radial distance R based on the first set of Fourier series, and Z.sub.2(A,R) is the sagittal height at the angle and the radial distance based on the second set of Fourier series, and wherein W(R) is a quintic blending polynomial.

30. The method of claim 29, wherein
W(R)=10.Math.t.sup.315.Math.t.sup.4+6.Math.t.sup.5, wherein $t = \frac{(R - RD)}{delta},$ wherein RD is the radial distance between the first boundary line and the carrier point at the angle A, and wherein delta is the width of the blending zone.

31. The method of claim 30, wherein delta is 0.6 times the radial distance between the first boundary line and the carrier point at the angle A.

32. A method for manufacturing an ophthalmic lens, wherein the ophthalmic lens comprises a shape defined by a surface determined by carrier lines extending radially outwards of a prescription zone, the method comprising the following steps: aa) providing a plurality of carrier lines each extending from a carrier point in the prescription zone into a respective direction, wherein a curvature profile of the surface along each carrier line radially outwards of the prescription zone is provided by a cubic spline; bb) forming a first set of truncated Fourier series of a definite high order each approximating corresponding coefficients of a first spline for all carrier line directions, cc) forming a second set of truncated Fourier series of a definite low order each approximating corresponding coefficients of a second spline for all carrier line directions, dd) determining a third spline sufficient to determine a surface height at any radial location within the range of the carrier lines for any specified carrier line direction by a weighted average of the first spline and second spline for that direction, where the weighting function is a polynomial function of the radial distance from the first boundary, and ee) manufacturing the ophthalmic lens comprising the shape defined by steps aa) through dd).

33. A method for manufacturing an ophthalmic lens, wherein the ophthalmic lens comprises a shape defined by a surface determined by carrier lines extending radially outwards of a prescription zone bordered by a first boundary line, the method comprising the following steps: i) providing a plurality of carrier lines each extending from a carrier point in the prescription zone into a respective direction, wherein a curvature profile of the surface in a direction along each carrier line extending radially outwards of the prescription zone has at least one section, wherein the curvature profiles of corresponding sections of each carrier line are provided by respective polynomials, ii) forming a series of coefficient values of corresponding coefficients of the polynomials of each carrier line, iii) determining, for each corresponding coefficient, a first Fourier series of a first order approximating the series of coefficient values, to obtain a first set of Fourier series each dependent on an angle around the carrier point, iv) determining, for each coefficient, a second Fourier series of a second order approximating the series of coefficient values, to obtain a second set of Fourier series each dependent on an angle around the carrier point, the second set of Fourier series describing any carrier line extending in a radial direction for a given angle, wherein the second order is higher than the first order, and wherein the second set of Fourier series is applied at the first boundary line, v) blending the second set of Fourier series into the first set of Fourier series radially outwards over a blending zone, and vi) manufacturing the ophthalmic lens comprising the shape defined by steps i) through v).

34. A method for manufacturing an ophthalmic lens, wherein the ophthalmic lens comprises a shape defined by a surface determined by carrier lines extending radially outwards of a prescription zone bordered by a first boundary line, the method comprising: i) providing a plurality of carrier lines each extending from a carrier point in the prescription zone into a respective direction, wherein a curvature profile of the surface in a direction along each carrier line extending radially outwards of the prescription zone has at least one section, wherein the curvature profiles of corresponding sections of each carrier line are provided by respective polynomials, ii) forming a series of coefficient values of corresponding coefficients of the polynomials of each carrier line, iii) determining, for each corresponding coefficient, a first Fourier series of a first order approximating the series of coefficient values, to obtain a first set of Fourier series each dependent on an angle around the carrier point, iv) determining, for each coefficient, a second Fourier series of a second order approximating the series of coefficient values, to obtain a second set of Fourier series each dependent on an angle around the carrier point, the second set of Fourier series describing any carrier line extending in a radial direction for a given angle, wherein the second order is higher than the first order, and wherein the second set of Fourier series is applied at the first boundary line v) blending the second set of Fourier series into the first set of Fourier series radially outwards over a blending zone, and vi) manufacturing the ophthalmic lens comprising the shape defined by steps i) through v), wherein the step of blending is conducted via the following formula:
Z=Z.sub.2(A,R)+W(R).Math.(Z.sub.1(A,R)Z.sub.2(A,R)), wherein Z is the resulting sagittal height, A is the angle around the carrier point, R is the radial distance from the carrier point, Z.sub.1(A,R) is the sagittal height at the angle A and the radial distance R based on the first set of Fourier series, and Z.sub.2(A,R) is the sagittal height at the angle A and the radial distance R based on the second set of Fourier series, and wherein W(R) is a quintic blending polynomial.

35. The method of claim 34, wherein
W(R)=10.Math.t.sup.315.Math.t.sup.4+6.Math.t.sup.5, wherein $t = \frac{(R - RD)}{delta},$ wherein RD is the radial distance between the first boundary line and the carrier point at the angle A, and wherein delta is the width of the blending zone.

36. The method of claim 35, wherein delta is 0.6 times radial distance between the first boundary line and the carrier point at the angle A.

37. A non-transitory computer program product comprising program code for carrying out the steps of a method for providing a lens shape for an ophthalmic lens, when the computer program product is run on a data processing device, the method for providing comprising the steps of: providing a predetermined lens shape of an ophthalmic lens having a front surface and a back surface, wherein the predetermined lens shape comprises a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone of the back surface bordered by a first boundary line, such that the ophthalmic lens satisfies predetermined optical properties within the prescription zone; determining a carrier point on the back surface within the prescription zone and a plurality of carrier lines each extending from the carrier point into a respective direction; determining a transition zone of the back surface, wherein the transition zone extends radially outwards from the first boundary line towards the outer edge of the ophthalmic lens and ends at a second boundary line bordering the transition zone radially outwards; for each carrier line, setting a desired constant curvature gradient over the transition zone; for each carrier line, determining a curvature profile of the back surface between the first boundary line and an outer edge the ophthalmic lens along the carrier line, wherein the curvature profile in the transition zone is determined based on the respective desired constant curvature gradient; and angular smoothing of the back surface radially outwards of the first boundary line.

38. A non-transitory computer program product comprising program code for carrying out the steps of a method for constructing a surface determined by carrier lines extending radially outwards of a prescription zone, when the computer program product is run on a data processing device, the method for constructing comprising: providing a plurality of carrier lines each extending from a carrier point in the prescription zone into a respective direction, wherein a curvature profile of the surface along each carrier line extending radially outwards of the prescription zone is provided by a cubic spline; forming a first set of truncated Fourier series of a definite high order each approximating corresponding coefficients of a first spline for all carrier line directions; forming a second set of truncated Fourier series of a definite low order each approximating corresponding coefficients of a second spline for all carrier line directions; determining a third spline sufficient to determine a surface height at any radial location within the range of the carrier lines for any specified carrier line direction by a weighted average of the first spline and second spline for that direction, where the weighting function is a polynomial function of the radial distance from a first boundary line; and manufacturing the ophthalmic lens according to the lens shape.

39. A non-transitory computer program product comprising program code for carrying out the steps of a method for providing a surface determined by carrier lines extending radially outwards of a prescription zone bordered by a first boundary line, when the computer program product is run on a data processing device, the method comprising: providing a plurality of carrier lines each extending from a carrier point in the prescription zone into a respective direction, wherein a curvature profile of the surface in a direction along each carrier line extending radially outwards of the prescription zone has at least one section, wherein the curvature profiles of corresponding sections of each carrier line are provided by respective polynomials; forming a series of coefficient values of corresponding coefficients of the polynomials of each carrier line; determining, for each corresponding coefficient, a first Fourier series of a first order approximating the series of coefficient values, to obtain a first set of Fourier series each dependent on an angle around the carrier point; determining, for each coefficient, a second Fourier series of a second order approximating the series of coefficient values, to obtain a second set of Fourier series each dependent on an angle around the carrier point, the second set of Fourier series describing any carrier line extending in a radial direction for a given angle, wherein the second order is higher than the first order, and wherein the second set of Fourier series is applied at the first boundary line; blending the second set of Fourier series into the first set of Fourier series radially outwards over a blending zone; and manufacturing the ophthalmic lens according to the lens shape.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The invention will now be described with reference to the drawings wherein:

(2) FIG. 1 shows an embodiment of a method for providing a lens shape for an ophthalmic lens;

(3) FIG. 2 shows a simplified diagram showing and illustrating an embodiment of the different steps of the method in FIG. 1;

(4) FIG. 3 shows a further general simplified diagram showing and illustrating the different steps of the method for plus lenses and for minus lenses;

(5) FIG. 4 shows an embodiment of an ophthalmic lens, in particular an uncut finished spectacle lens;

(6) FIG. 5 shows the uncut finished spectacle lens of FIG. 4 along a section line X-X;

(7) FIG. 6 shows another embodiment of an ophthalmic lens, in particular an uncut finished spectacle lens;

(8) FIG. 7 shows the embodiment of FIG. 6 and the different zones of the design;

(9) FIG. 8 shows an example of the development of the curvature in a radial direction at a certain angle of the embodiment in FIGS. 6 and 7;

(10) FIG. 9A shows another embodiment of an ophthalmic lens, in particular an uncut finished spectacle lens;

(11) FIG. 9B shows an example of the development of the curvature in a radial direction at a 180 degree meridian of the embodiment in FIG. 9A;

(12) FIG. 9C shows an example of the development of the thickness in a radial direction at a 180 degree meridian of the embodiment in FIG. 9A;

(13) FIG. 10A shows surface and optical astigmatism in an example minus lens provided according to the method for angular smoothing of a surface determined by carrier lines;

(14) FIG. 10B shows surface and optical astigmatism in an example plus lens provided according to the method for angular smoothing of a surface determined by carrier lines;

(15) FIG. 11 shows an embodiment of a method for angular smoothing of a surface determined by carrier lines;

(16) FIG. 12 shows an embodiment of a method for minimizing the difference in thickness between two ophthalmic lenses for the same spectacles; and,

(17) FIG. 13 shows a block diagram of an embodiment of a manufacturing method.

DESCRIPTION OF THE PREFERRED EMBODIMENTS OF THE INVENTION

(18) FIG. 1 shows an embodiment of the method according to the first aspect of the invention. The method is generally designated by reference numeral 100.

(19) The conduction of the method, in the following, is explained viewing both FIGS. 1 and 2.

(20) At first, a step 102 is conducted of providing a predetermined lens shape 10 of an ophthalmic lens, in particular an uncut finished spectacle lens, having a front surface and a back surface, wherein the predetermined lens shape comprises a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone of the back surface bordered by a first boundary line, such that the ophthalmic lens satisfies predetermined optical properties within the prescription zone.

(21) In FIG. 2, the uncut finished spectacle lens 10 is schematically shown with a view on the back surface in the upper left. The method 100 then follows the arrows to the bottom line. The uncut finished spectacle lens has a periphery or outer edge 16 of the ophthalmic lens, which may be an uncut finished spectacle lens. For example, a minimum eye rotation angle 12 that shall be preserved concerning the optical properties of the back surface may be provided, however, that is not necessary. Further, a carrier point or design reference point is determined on the back surface. Just as an example, the carrier point may be the geometrical center of the ophthalmic lens. The carrier point may also be at or behind the fitting cross of the ophthalmic lens. The carrier point may also be shifted nasally. Just as an example, when viewed in a direction corresponding to that of a standard boxed system the carrier point may be shifted nasally from the prism reference point, in particular by 10 mm. The plane in which the nasal shift is measured may alternatively be defined as a plane tangential to the geometric center of the back surface of the lens. The periphery of the uncut finished spectacle lens may have the form of a circle or an ellipse.

(22) Then, in a step 104, a first boundary line 18 is determined. In particular, a curvature profile of the original shape of the back surface is to be preserved within the first boundary line 18. Further in particular, the carrier point 14 is set on the back surface, in the given example in the geometrical center, and a first boundary line 18 on the back surface is determined, in particular when a curvature profile of the original shape of the back surface is to be preserved within the first boundary line 18. Hence, as shown in the upper right to FIG. 2, the first boundary line 18 will usually be drawn to enclose the intended minimum eye rotation angle 12. The first boundary line 18 encloses a domain of transition points at the back surface of rays for the viewing eye. More exactly the points of this domain refer to all rays for a viewing angle of the eye of up to 12 degree. The shape of the boundary line may be chosen to be identical to the shape of the frame into which the final lens is to be inserted. However, it may also be a circle as shown in further examples. Within the first boundary line 18, the curvature profile of the original lens shape 10 is to be preserved. The rest of the original lens shape of the back surface can be considered cut off. Hence, only a dashed line 26 of the original periphery is shown. The lens shape will now be determined by adding carrier lines or carrier curves extending radially outwards from the prescription zone 20. In a transition portion or transition zone 24, a desired constant curvature gradient is set in later step 108 for each carrier line so that the curvature will transition from the curvature of the preserved lens shape within boundary line 18 towards a constant curvature in the margin portion 28. Hence, a second boundary line 22 can be considered to be the outer boundary of the transition zone 24 with the boundary line 18 being the inner boundary line of the transition zone 24. Hence, in step 106, there is determined a carrier point on the back surface within the prescription zone and a plurality of carrier lines each extending from the carrier point straight into a respective radial direction. Each straight carrier line 30 to 37 runs in a different angle . As in the given example the periphery of the uncut finished spectacle lens 10 has the form of a circle, each carrier line runs in a plane that cuts through the full diameter of this circle. As in the given example the front surface has a spherical shape, and the carrier point 14 as in the geometrical center, each carrier line 30 to 37 runs in a meridian of the front surface. In the provided example, eight carrier lines are used so that a separation angle between them is 45 degrees. However, any different number of carrier lines could be used, for example 128, 180 or 360.

(23) However, the transition zone 24, the margin portion 28 and that outer boundary line 22 are fixedly determined by a constant width of transition zone 24 or length of the transition zone along each carrier line. Each carrier line extends straight from the carrier point radially outwards.

(24) In a next step 108, for each carrier line, a desired constant curvature gradient in the transition zone is set. This constant curvature gradient is in the direction of the respective carrier line.

(25) In step 110, for each carrier line, a curvature profile of the back surface between the first boundary line and an outer edge the lens blank along the carrier line is determined, wherein a curvature along the carrier line between the second boundary line and the outer edge is constant and equals the curvature along the carrier line in the transition zone at the second boundary line, and wherein the curvature profile in the transition zone is determined based on the respective desired constant curvature gradient. In FIG. 2, a mere resulting example surface is shown in the picture in the middle right.

(26) On the first boundary line 18, the curvature of the new curvature profile within the plane of the straight carrier line, that is, in the given example the tangential or radial curvature, equals the curvature of the optically preserved surface area of the original lens shape 10 within the boundary line 18. That means that curvatures inside and outside the boundary line equal each other approaching the boundary line 18. Hence, the curvature along the first boundary line 18 is preferably determined to be continuous. That means preferably no kink is provided at the boundary line 18.

(27) The curvature profile of the predetermined shape within the boundary line 18 is fixed with the new curvature profiles outside the boundary line 18 attached to it. In the straight view in the back surface, hence in this stage the determined and fixed back surface profile looks like a spider with the optically preserved curvature profile within the boundary line 18 being the body and each new curvature profile along a carrier line forming one leg. This description of the back surface may already be sufficient for manufacturing the ophthalmic lens.

(28) However, in an optional further step, for subsequent manufacturing and to provide for angular smoothing, a complete description of the back surface may be provided. Hence, the method may further comprise steps to provide for angular smoothing of the back surface radially outwards of the first boundary line. First, a series of coefficient values of corresponding coefficients of a respective function describing each carrier line in the transition zone may be formed, in particular of the cubic polynomials of each carrier line. Then, for each corresponding coefficient, a first Fourier series of a first order approximating the series of coefficient values may be determined to obtain a first set of Fourier series each dependent on an angle around the carrier point, the first set of Fourier series describing any carrier line in a radial direction for given angle. Even further, for each coefficient, a second Fourier series of a second order approximating the series of coefficient values may be determined, to obtain a second set of Fourier series each dependent on an angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction for given angle, wherein the second order is higher than the first order, and wherein the second set of Fourier series is applied at the first boundary line. Then, the second set of Fourier series may be blended into the first set of Fourier series radially outwards over a blending zone, in particular so that only the first set of Fourier series is applied beyond the blending zone. In particular, blending may be conducted via the following formula Z=Z.sub.2 (A,R)+W(R).Math.(Z.sub.1(A,R)Z.sub.2 (A,R)), wherein Z is the resulting sagittal height, A is the angle around the carrier point, R is the radial distance from the carrier point, Z.sub.1(A,R) is the sagittal height at the angle A and the radial distance R based on the first set of Fourier series, and Z.sub.2(A,R) is the sagittal height at the angle and the radial distance based on the second set of Fourier series, and wherein W(R) is a quintic blending polynomial, in particular wherein W(R)=10.Math.t.sup.315.Math.t.sup.4+6.Math.t.sup.5, wherein

(29) $t = \frac{(R - RD)}{delta},$
and wherein RD is the radial distance between the first boundary line and the carrier point at the angle A, and wherein delta is the width of the blending zone, in particular wherein delta is 0.6 times the radial distance between the first boundary line and the carrier point at the angle A.

(30) For minus-lenses, the method could then already end here. However, it may be necessary to further readjust the sagittal height of the fixed curvature profile within the boundary line in case of a plus lens. In case the reduced lens thickness should be considered significant so that, due to the reduced thickness and the conditions of a real lens, the optical properties within the boundary line 18 may be deteriorated, an optimization step may be conducted that starts on the original lens shape of the back surface and readjusts it to restore the optical properties of the original lens shape.

(31) FIG. 3 shows further simplified illustrations to generally show the development of the lens shape through the method. FIG. 3 is generally independent of FIG. 2. In the left column, the development of a shape of a plus lens is shown. In the right column, the development of a shape of a minus lens is shown.

(32) Concerning the plus lens, from top to bottom, a predetermined lens shape 10 of an uncut finished spectacle lens 60 having a front surface 70 and a back surface 72 is provided, wherein the predetermined lens shape 10 comprises an predetermined shape of the front surface 70 and an predetermined shape of the back surface 72 of the uncut finished spectacle lens 60, such that the uncut finished spectacle lens 60 satisfies predetermined optical properties. Then, a first boundary line 18 on the back surface 72 is determined, wherein a curvature profile 20 of the predetermined shape of the back surface 72 is to be preserved within the first boundary line 18. Then, a carrier extension 38 of the back surface 72 between the first boundary line 18 and an outer edge 16 of the uncut finished spectacle lens 60 is determined, wherein a curvature of the carrier extension 38 at the first boundary line 18 may equal the boundary curvature. In case of the plus lens, the predetermined lens shape 10 provides for a positive focal power. Hence, a lens shape 40 of the uncut finished spectacle lens 60 is determined, wherein the modified lens shape 40 comprises the predetermined shape of the front surface 70, and a modified shape of the back surface 72. This leads to the new curvature profile of the back surface being determined which then may be moved towards the front surface until a thickness requirement is fulfilled.

(33) Concerning the minus lens, from top to bottom, an predetermined lens shape 10 of an uncut finished spectacle lens 60 having a front surface 70 and a back surface 72 is provided, wherein the predetermined lens shape 10 comprises an predetermined shape of the front surface 70 and an predetermined shape of the back surface 72 of the uncut finished spectacle lens 60, such that the uncut finished spectacle lens 60 satisfies predetermined optical properties within the prescription zone. Then, a first boundary line 18 on the back surface 72 is determined, wherein a curvature profile of the predetermined shape of the back surface 72 is to be preserved within the first boundary line 18. Then, a new curvature profile 38 of the back surface 72 between the first boundary line 18 and an outer edge 16 of the uncut finished spectacle lens 60 is determined, wherein a curvature of the new curvature profile 38 at the first boundary line 18 may equal the boundary curvature. In case of the minus lens, the predetermined lens shape 10 provides for a negative focal power. A sagittal height of the fixed curvature profile of the predetermined lens shape 10 of the back surface 72 within the first boundary line 18 is maintained or preserved. Hence, the thickness of the modified shape is reduced. Hence, a modified lens shape 40 of the uncut finished spectacle lens 60 is determined, wherein the modified lens shape 40 comprises the predetermined shape of the front surface 70, and a modified shape of the back surface 72 with carrier extensions. This leads to the new curvature profile of the back surface being determined.

(34) FIG. 4 shows an uncut finished spectacle lens or ophthalmic lens 60. It has a periphery or outer edge 16 which can be circular or elliptical, in the example of FIG. 4 it is circular. The carrier point can then be the geometrical center 14 as explained above. On the back surface shown in FIG. 4, the first boundary line 18 covers a preserved area 62 which is surface area of the back surface within the first boundary line 18 which has a free-form surface, that is, a surface curvature profile that has no symmetries. It is neither point nor plane nor rotationally symmetric. Between a margin portion 66 and the prescription zone 20, there is a transition zone 64 having a length or width 68. The length or width of the transition zone is set to be constant, that is, the length is the same in any radial direction from carrier point 14.

(35) FIG. 5 shows a section along line X-X in FIG. 4. A front surface of the uncut finished spectacle lens is spherical. Hence, it is rotationally symmetric with respect to the geometrical center and has a single curvature. The back surface is designated with reference numeral 72. The first boundary line 18 is chosen so that the minimum eye rotation angle 12 is within the boundary line 18. In other words, the first boundary line 18 is chosen so that for all rays through the eye for a viewing angle of the eye of less or equal 12 degree the corresponding intersection points of the rays through the back surface are within the boundary line 18. The eye 74 may be determined with its center of rotation according to the standard eye used for calculations. The ophthalmic lens 60 comprises a front surface and a back surface, wherein the front surface is a convex rotationally symmetric surface, and wherein the back surface comprises a prescription zone which is asymmetric, a margin portion and a transition zone located between the prescription zone and the margin portion, and wherein a curvature gradient of the back surface along a straight line emanating from a point on the back surface is constant within the transition zone, and wherein the transition zone has the same length along any straight line emanating from the point, in particular wherein the length is measured parallel to a plane tangential to a vertex point of the front surface or a plane tangential to the back surface at the geometric center of the back surface of the lens.

(36) With reference to FIGS. 6 to 8, further principles of the determination of the carrier lines within the transition zone are described.

(37) In general, it may be started with the back surface of the ophthalmic lens, a frame outline 19, and the location of a fitting cross 15. First, the radius and center of the inner boundary line 18 may be determined. It may be provided that the first boundary line 18 does not intersect the frame line 19 on the nasal side as shown in FIG. 6. A distance 13 to the first boundary line 18 may be measured from the fitting cross 15 along the 180 meridian. A center and radius of a circle describing the inner boundary line 18 may be determined to satisfy a distance requirement to the inner boundary from the fitting cross and should not intersect the frame line 19 on the nasal side.

(38) Once the first boundary line 18 is defined the change to the surface in the transition zone 64 has to be determined and applied. Then from the second boundary line 22 of the transition zone 64 until at least the edge of the frame the radial curvature should be held constant. This circular extension can continue to the edge of the uncut finished spectacle lens. FIG. 7 shows the relevant regions and boundaries.

(39) A general approach to providing the desired constant curvature gradient is to construct a piece-wise cubic polynomial for the transition zone, rather than a single global single cubic polynomial. This removes the difficulty of achieving the desired gradient, and can be determined directly. The one-dimensional curvature is given by

(40) $C = \frac{Z_{xx}}{{(1 + Z_{x}^{2})}^{3 / 2}}$
where Z.sub.x, and Z.sub.xx are the first and second derivatives of the surface height in the direction of the respective carrier line. Then the gradient G is just the derivate of C

(41) $G = \frac{Z_{xxx}}{{(1 + Z_{x}^{2})}^{3 / 2}} - \frac{3 Z_{x} Z_{xx}^{2}}{{(1 + Z_{x}^{2})}^{5 / 2}} .$

(42) For the initial condition one can use the slope S, curvature C, and gradient G, and set Z to zero. The corresponding value of the optical zone at the first boundary line may be used as an alternative. Then for the first interval it is
Z=a.sub.0+b.sub.0x+c.sub.0x.sup.2+d.sub.0x.sup.3
where
a.sub.0=0, b.sub.0=s, c.sub.0=C(1+b.sub.0.sup.2).sup.3/2/2

(43) Further, in the first interval
Z.sub.x=b.sub.0, Z.sub.xx=2c.sub.0, Z.sub.xxx=6d.sub.0.

(44) So the equation for G becomes

(45) $G = \frac{6 d_{0}}{{(1 + b_{0}^{2})}^{3 / 2}} - \frac{12 b_{0} c_{0}^{2}}{{(1 + b_{0}^{2})}^{5 / 2}}$ $or$ $d_{0} = ({G (1 + b_{0}^{2})}^{3 / 2} + 12 b_{0} c_{0}^{2} / (1 + b_{0}^{2})) / 6.$

(46) Now, the carrier line function can be developed in small steps. So if in general it is written for the i.sup.th interval
Z.sub.i=a.sub.i+b.sub.ix+c.sub.ix.sup.2+d.sub.ix.sup.3
where x=xx.sub.i, then
a.sub.i+1=a.sub.i+b.sub.ix+c.sub.ix.sup.2+d.sub.ix.sup.3
b.sub.i+1=b.sub.i+2c.sub.ix+3d.sub.ix.sup.2,
c.sub.i+1=c.sub.i+3d.sub.ix
d.sub.i+1(G(1+b.sub.i+1.sup.2).sup.3/2+12b.sub.i+1c.sub.i+1.sup.2/(1+b.sub.i+1.sup.2))/6.

(47) This may be solved by numerical integration. The idea being that the output series would be represented by a standard cubic spline. Past the end and radially outwards of the transition zone the curvature gradient may be set to zero, which produces a constant curvature function past the second boundary line. Optionally, if the slope of the function exceeds a boundary value, the function may be extended with a quadratic polynomial past that point, to prevent the curve from becoming too step.

(48) FIG. 8 shows the one-dimensional curvature for a carrier line that starts at 13 diopters with a gradient of 4 diopters/mm over a length of 5 mm. The function is a cubic spline made from 1 mm steps of the numerically integrated function. The final curvature after the transition zone is about 6.97 diopters.

(49) FIGS. 9A to 9C show a simple example of an ophthalmic lens 60 which may be an uncut finished spectacle lens. This example is intended to be a simple single vision example of the carrier extension. The lens prescription is 5 diopters, the front surface is a 3.5 diopter in refractive index 1.530 sphere, the material index is 1.586, and the back surface at the geometric center is 8.02 diopters in index 1.530. In general, throughout the application, the curvatures in diopters are given with a refractive index of 1.53 as a reference value and independent of the refractive index of the material actually used. Hence, in case a curvature is given in diopters, the corresponding curvature in radius can be calculated by

(50) $r = \frac{1.53 - 1}{diopters} .$
This will provide for the radius in meters. This recalculation is well known to persons skilled in the art with a known refractive index which is 1.53 throughout the application. The full diameter of the blank shown is 80 mm. The first boundary line 18 is an inner radius of the extension R.sub.in is 25 mm, and the second boundary line 22 is an outer radius R.sub.out is 35 mm. The center of the circular extension boundaries are displaced by 10 mm to the nasal side of the geometric center of the lens blank. The gradient of the tangential curvature in the ring between R.sub.in and R.sub.out is 0.8 diopters/mm. This gradient takes the tangential curvature from just over eight diopter at the inner boundary down to just over zero diopters at the outer boundary. The thickness of the lens normal to the front surface at the temporal edge of the blank would be about 8 mm without the extension; with the carrier extension that is reduced to under 5.0 mm.

(51) The example in FIG. 10A illustrates an implementation of the carrier extension on a single progressive lens design having distance prescription of 3.00 diopters with addition power of +2.50 diopters. The center of the carrier extension ring (x.sub.o, y.sub.o) is at (10,0), decentered 10 mm nasally from the prism reference point. The inner radius of the first boundary line is 25 mm and the outer radius of the second boundary line is 40 mm. The rate of change of curvature variation or curvature gradient in the ring is fixed to 0.25 D/mm. The contour plots in FIG. 10A illustrate the surface astigmatism and the residual optical astigmatism with the frame outline overlayed. The frame box dimensions are 6436 mm, bridge width 18 mm, pantoscopic tilt is 5, frame wrap angle 15, wearer monocular pupil distance is 32 mm, fitting height of 21 mm. The thick ring shows the location of the first boundary line.

(52) The example in FIG. 10B illustrates an implementation of the carrier extension on a single progressive lens design having distance prescription of +3.00 diopters with addition power of +2.50 diopters. The center of the carrier extension ring (x.sub.o, y.sub.o) is at (10,0), decentered 10 mm nasally from the prism reference point. The inner radius of the first boundary line is 25 mm and the outer radius of the second boundary line is 40 mm. The rate of change of curvature variation or the curvature gradient in the ring is fixed to 0.507 D/mm. The contour plots in FIG. 10B illustrate the surface astigmatism and the residual optical astigmatism with the frame outline overlayed. The frame box dimensions are 6436 mm, bridge width 18 mm, pantoscopic tilt is 5, frame wrap angle 15, wearer monocular pupil distance is 32 mm, fitting height of 21 mm. The thick ring shows the location of the first boundary line. The center thickness of this lens is 4.21 mm and the edge thickness around the perimeter of the frame shown in FIG. 10B varies from 1.0 mm to 3.5 mm. For comparison, the same lens without the carrier curve is shown. It has the center thickness of 7.21 mm, while the edge thickness around the perimeter of the same size and shape frame varies from 1.0 mm to 6.5 mm. The carrier curve had the effect of reducing the center thickness by 3 mm, as well as reducing the maximum edge thickness by the same amount with a much more uniform edge thickness profile.

(53) In FIG. 11, a method 150 for angular smoothing of a surface determined by carrier lines radially outwards of a prescription zone bordered by a first boundary line.

(54) In step 152, a plurality of carrier lines each extending from a carrier point in the prescription zone, in particular straight, into a respective radial direction may be provided, wherein a curvature profile of the surface in a direction along each carrier line radially outwards of the prescription zone has at least one section, wherein the curvature profiles of corresponding sections of each carrier line are provided by corresponding polynomials,

(55) In step 154, a series of coefficient values of corresponding coefficients of the polynomials of each carrier line may be formed.

(56) In step 156, for each corresponding coefficient, a first Fourier series of a first order approximating the series of coefficient values may be determined to obtain a first set of Fourier series each dependent on an angle around the carrier point, the first set of Fourier series describing any carrier line in a radial direction for a given angle.

(57) In further refinements, for each coefficient, a second Fourier series of a second order approximating the series of coefficient values may be determined to obtain a second set of Fourier series each dependent on an angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction for given angle, wherein the second order is higher than the first order, and wherein the second set of Fourier series is applied at the first boundary line. The second set of Fourier series may then be blended into the first set of Fourier series radially outwards over a blending zone, in particular so that only the first set of Fourier series is applied beyond the blending zone.

(58) In particular, blending may be conducted via the following formula:
Z=Z.sub.2(A,R)+W(R).Math.(Z.sub.1(A,R)Z.sub.2(A,R)),
wherein Z is the resulting sagittal height, A is the angle around the carrier point, R is the radial distance from the carrier point, Z.sub.1(A,R) is the sagittal height at the angle A and the radial distance R based on the first set of Fourier series, and Z.sub.2(A,R) is the sagittal height at the angle A and the radial distance R based on the second set of Fourier series, and wherein W(R) is a quintic blending polynomial, in particular wherein
W(R)=10.Math.t.sup.315.Math.t.sup.4+6.Math.t.sup.5,
wherein

(59) $t = \frac{(R - RD)}{delta},$
and wherein RD is the radial distance between the first boundary line and the carrier point at the angle A, and wherein delta is the width of the blending zone, in particular wherein delta is 0.6 times radial distance between the first boundary line and the carrier point at the angle A.

(60) In FIG. 12, a method 200 for minimizing the difference in thickness between two ophthalmic lenses for the same spectacles is shown. It comprises providing 202, for each ophthalmic lens, an original lens shape satisfying predetermined optical properties over the complete back surface and a modified lens shape having a front surface and a back surface, wherein the modified lens shape comprises a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone of the back surface bordered by a first boundary line, such that the ophthalmic lens satisfies the predetermined optical properties within the prescription zone, and an extension of the back surface radially outwards of the prescription zone by carrier lines.

(61) Then, in step 204, the modified lens shape of the ophthalmic lens having a smaller maximum thickness is adapted by replacing the back surface by a combination of the original lens shape and the modified lens shape according to
CS=OS+A.Math.(MSOS)
wherein CS is the sagittal height of the combined back surface, OS is the sagittal height of the back surface of the original lens shape, MS is the sagittal height of the back surface of the modified lens shape and A is a value from and including 0 to and including 1.

(62) Then, in step 206, parameter A may be optimized so that the difference in thickness between the two ophthalmic lenses is minimized.

(63) In practice, carriers extensions could be applied for both lenses of the spectacle frame if for either lens the edge thickness exceeds, for example, 5 mm at any point outside the first boundary line or outside the frame line or frame boundary. When carrier lines have been determined for minus lenses, then the maximum edge thickness may be determined for both lenses. If the difference is greater than a specified threshold (for example, 1 mm), then, to balance the edge thickness of the lenses for the right and left eyes, the extension for the thinner lens is modified as explained above.

(64) The determination may result in lens edge thicknesses maps for a pair of lenses having very different prescriptions in the right and left eyes, for example, right eye 4.00 diopters sphere, left eye: 2.00 diopters sphere/2.00 diopters cylinder at 150 and +2.50 diopters addition with maximum temporal edge thickness balancing may result in both lenses having a maximum temporal edge thickness of 7.55 mm.

(65) Finally, FIG. 13 shows a method for manufacturing generally designated by reference numeral 300. After the start, a method 100 according to the first aspect and/or a method 150 according to the third aspect is conducted in step 302. Afterwards, based on the modified lens shape, a manufacturing step 304 would take place that manufactures the uncut finished spectacle lens 60. Subsequently, the uncut finished spectacle lens 60 could be further processed, in particular in an edging process that cuts the lens out of the uncut finished spectacle lens towards its final shape that in particular may then be shipped towards an ophthalmic dispenser. The method may then end.

(66) Further, the current invention comprises embodiments according to the following clauses: Clause 1. A computer-implemented method (100) for providing a lens shape for an ophthalmic lens (60), comprising the following steps: a) providing (102) a predetermined lens shape of an ophthalmic lens (60), in particular an uncut finished spectacle lens, having a front surface and a back surface, wherein the predetermined lens shape comprises a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone (20) of the back surface bordered by a first boundary line (20), such that the ophthalmic lens (60) satisfies predetermined optical properties within the prescription zone (20); b) determining (104) a carrier point on the back surface within the prescription zone (20) and a plurality of carrier lines each extending from the carrier point into a respective direction; c) determining (106) a transition zone (24) of the back surface, wherein the transition zone (24) extends radially outwards from the first boundary line (18) towards the outer edge (60) of the ophthalmic lens (60) and ends at a second boundary line (22) bordering the transition zone radially outwards; d) for each carrier line (30-37), setting (108) a desired constant curvature gradient in the transition zone (24), in particular wherein the desired constant curvature gradient is different from zero; e) for each carrier line (30-37), determining (110) a curvature profile of the back surface between the first boundary line (18) and an outer edge the ophthalmic lens (60) along the carrier line (30-37), and wherein the curvature profile in the transition zone (24) is determined based on the respective desired constant curvature gradient. Clause 2. The method according to clause 1, characterized in that a curvature along the carrier line (30-37) between the second boundary line (22) and the outer edge is essentially constant, in particular constant, and equals the curvature along the carrier line (30-37) in the transition zone (24) at the second boundary line (22). Clause 3. The method according to clause 1 or 2, characterized in that the desired constant curvature gradient is set based on the curvature of the prescription zone (20) at the first boundary line (18) and a boundary condition for the curvature within the transition zone (24), in particular wherein the curvature gradient is further set based on a desired thickness reduction of the ophthalmic lens (60) along the carrier line (30-37). Clause 4. The method according to clause 1 or 2, characterized in that the desired constant curvature gradient is set based on the curvature of the prescription zone (20) at the first boundary line (18) and a curvature target to be reached at the second boundary line (22), and wherein the curvature target is zero and/or a curvature of the front surface, in particular wherein the curvature of the front surface is determined in the same coordinate system as the curvature of the back surface, and in particular wherein the front surface is a spherical surface. Clause 5. The method according to any of clauses 1 to 4, characterized in that the curvature gradient is set to be negative in case the ophthalmic lens (60) is a minus lens and the curvature gradient is set to be positive in case the ophthalmic lens (60) is a plus lens. Clause 6. The method according to any of clauses 1 to 5, characterized in that the curvature profile is determined by determining a cubic spline from the first boundary line (18) to the second boundary line (22), wherein the cubic spline is comprised of a plurality of sections each described by a cubic polynomial, and wherein the cubical polynomials are determined section-wise from the first boundary line (18) to the second boundary line (22), in particular such that a sagittal height, a slope and a curvature of the back surface along the carrier line (30-37) are continuous and the curvature along the carrier line (30-37) changes over each section resulting in an approximated constant curvature gradient over the transition zone (24). Clause 7. The method according to any of clauses 1 to 5, characterized in that the curvature profile is determined by determining a cubic spline from the first boundary line (18) to the second boundary line (22), wherein the cubic spline is comprised of a plurality of sections each described by a cubical polynomial, and wherein the cubical polynomials are determined section-wise from the first boundary line (18) to the second boundary line (22) such that a sagittal height, a slope and a curvature of the back surface along the carrier line (30-37) are continuous and the curvature gradient is reset to the desired constant curvature gradient for each polynomial at the radially inwards end of each section. Clause 8. The method of any of clauses 1 to 7, characterized in that a length (68) of the transition zone (24) along each carrier line (30-37) is constant resulting in the second boundary line (22) bordering the transition zone (24) radially outwards and the second boundary line (22) being radially offset from the first boundary line (18) by the length. Clause 9. The method according to clause 8, characterized in that the length of the transition zone (24) is within a range of at least 10 mm up to and including 20 mm, in particular 10 mm, 15 mm or 17.5 mm. Clause 10. The method according to any of clauses 1 to 9, characterized in that the constant curvature gradient has a magnitude in range from and including 0.05 diopters/mm to and including 1.5 diopters/mm. Clause 11. The method according to any of clauses 6 to 10, characterized in that the length of each section is within a range of at least 0.5 mm up to and including 2 mm, in particular 1 mm. Clause 12. The method according to any of clauses 1 to 11, characterized in that the method comprises a further step of checking, for each carrier line (30-37), whether a thickness of the spectacle lens at an outer edge and/or at an intended frame line along which the ophthalmic lens (60) is to be edged is above a predefined threshold and, if not, changing, in particular reducing or increasing, the magnitude of the desired constant curvature gradient. Clause 13. The method according to any of clauses 1 to 12, characterized in that the ophthalmic lens (60) is an uncut finished spectacle lens. Clause 14. The method according to any of clauses 1 to 13, characterized in that a curvature profile of the predetermined lens shape of the back surface is preserved within the first boundary line (18). Clause 15. The method according to any of clauses 1 to 14, characterized in that at least a sagittal height of the prescription zone (20) of the back surface transitions continuously at the first boundary line (18) into each carrier line (30-37), preferably wherein further a slope of the prescription zone (20) of the back surface in the direction along the carrier lines (30-37) transitions continuously at the first boundary line (18) into each carrier line (30-37), more preferably wherein further a curvature of the prescription zone (20) of the back surface in the direction along the carrier lines (30-37) transitions continuously at the first boundary line (18) into each carrier line (30-37). Clause 16. The method according to any of clauses 8 to 15, characterized in that the length is to be measured within a plane parallel to a tangential plane in the carrier point of the back surface. Clause 17. The method according to any of clauses 1 to 16, characterized in that the carrier point is offset nasally from a prism reference point of the ophthalmic lens (60). Clause 18. The method according to any of clauses 1 to 17, characterized in that first boundary line (18) is circular and the second boundary line (22) is circular. Clause 19. The method according to any of clauses 1 to 17, characterized in that the curvature profile along each carrier line (30-37) radially outwards of the second boundary line (22) is determined via a circular arc. Clause 20. The method according to any of clauses 1 to 19, characterized in that the method comprises a further step of angular smoothing of the back surface radially outwards of the first boundary line (18). Clause 21. The method according to any of clauses 1 to 20, characterized in that a further step of angular smoothing of the back surface radially outwards of the first boundary line (18) is conducted by flattening a profile of the curvature of the prescription zone (20) in the direction of the carrier lines (30-37) along the first boundary line (18) via approximation by a polynomial or a spline function or a Fourier series to obtain a flattened curvature profile, and wherein the flattened curvature profile is used as a radially inward starting curvature value for each carrier line (30-37). Clause 22. The method according to any of clauses 1 to 20, characterized in that the method further comprises the following steps to provide for angular smoothing of the back surface radially outwards of the first boundary line (18): i) forming a series of coefficient values of corresponding coefficients of a respective function describing each carrier line (30-37) in the transition zone (24), in particular of the cubic polynomials of each carrier line (30-37), ii) determining, for each corresponding coefficient, a first Fourier series of a first order approximating the series of coefficient values, to obtain a first set of Fourier series each dependent on an angle around the carrier point, the first set of Fourier series describing any carrier line (30-37) in a radial direction for given angle. Clause 23. The method according to clause 22, characterized in that the method comprises the further steps of: iii) determining, for each coefficient, a second Fourier series of a second order approximating the series of coefficient values, to obtain a second set of Fourier series each dependent on an angle around the carrier point, the second set of Fourier series describing any carrier line (30-37) in a radial direction for given angle, wherein the second order is higher than the first order, and wherein the second set of Fourier series is applied at the first boundary line (18), iv) blending the second set of Fourier series into the first set of Fourier series radially outwards over a blending zone, in particular so that only the first set of Fourier series is applied beyond the blending zone. Clause 24. The method according to clause 23, characterized in that the step of blending is conducted via the following formula:
Z=Z.sub.2(A,R)+W(R).Math.(Z.sub.1(A,R)Z.sub.2(A,R)), wherein Z is the resulting sagittal height, A is the angle around the carrier point, R is the radial distance from the carrier point, Z.sub.1(A,R) is the sagittal height at the angle A and the radial distance R based on the first set of Fourier series, and Z.sub.2(A,R) is the sagittal height at the angle and the radial distance based on the second set of Fourier series, and wherein W(R) is a quintic blending polynomial, in particular wherein
W(R)=10.Math.t.sup.315.Math.t.sup.4+6.Math.t.sup.5, wherein

(67) 0 $t = \frac{(R - RD)}{delta},$
and wherein RD is the radial distance between the first boundary line (18) and the carrier point at the angle A, and wherein delta is the width of the blending zone, in particular wherein delta is 0.6 times the radial distance between the first boundary line (18) and the carrier point at the angle A. Clause 25. A method for providing a smoothed extension surface from a plurality of carrier lines (30-37) extending radially outwards of a prescription zone (20), the method comprising the following steps: I) providing (152) a plurality of carrier lines (30-37) each extending from a carrier point in the prescription zone (20) into a respective direction, wherein a curvature profile of the surface along each carrier line (30-37) radially outwards of the prescription zone (20) is provided by a cubic spline; II) forming (154, 156) a set of truncated Fourier series of a definite order each approximating corresponding spline coefficients for all carrier line directions. Clause 26. A method for constructing a surface determined by carrier lines (30-37) radially outwards of a prescription zone (20), the method comprising the following steps: aa) providing a plurality of carrier lines each extending from a carrier point in the prescription zone into a respective direction, wherein a curvature profile of the surface along each carrier line radially outwards of the prescription zone is provided by a cubic spline; bb) forming a first set of truncated Fourier series of a definite high order each approximating corresponding coefficients of a first spline for all carrier line directions, cc) forming a second set of truncated Fourier series of a definite low order each approximating corresponding coefficients of a second spline for all carrier line directions, dd) determining a third spline sufficient to determine a surface height at any radial location within the range of the carrier lines for any specified carrier line direction by a weighted average of the first spline and second spline for that direction, where the weighting function is a specified polynomial function of the radial distance from the first boundary. Clause 27. A method (150) for providing a surface determined by carrier lines (30-37) radially outwards of a prescription zone (20) bordered by a first boundary line (18), the method comprising the following steps: i) providing (152) a plurality of carrier lines (30-37) each extending from a carrier point in the prescription zone (20) into a respective direction, wherein a curvature profile of the surface in a direction along each carrier line (30-37) radially outwards of the prescription zone (20) has at least one section, wherein the curvature profiles of corresponding sections of each carrier line (30-37) are provided by respective polynomials, ii) forming (154) a series of coefficient values of corresponding coefficients of the polynomials of each carrier line (30-37), iii) determining (156), for each corresponding coefficient, a first Fourier series of a first order approximating the series of coefficient values, to obtain a first set of Fourier series each dependent on an angle around the carrier point. Clause 28. The method according to clause 27, characterized in that the method comprises the further steps of: iv) determining, for each coefficient, a second Fourier series of a second order approximating the series of coefficient values, to obtain a second set of Fourier series each dependent on an angle around the carrier point, the second set of Fourier series describing any carrier line (30-37) in a radial direction for given angle, wherein the second order is higher than the first order, and wherein the second set of Fourier series is applied at the first boundary line (18), v) blending the second set of Fourier series into the first set of Fourier series radially outwards over a blending zone, in particular so that only the first set of Fourier series is applied beyond the blending zone. Clause 29. The method according to clause 28, characterized in that the step of blending is conducted via the following formula:
Z=Z.sub.2(A,R)+W(R).Math.(Z.sub.1(A,R)Z.sub.2(A,R)), wherein Z is the resulting sagittal height, A is the angle around the carrier point, R is the radial distance from the carrier point, Z.sub.1(A,R) is the sagittal height at the angle A and the radial distance R based on the first set of Fourier series, and Z.sub.2(A,R) is the sagittal height at the angle A and the radial distance R based on the second set of Fourier series, and wherein W(R) is a quintic blending polynomial, in particular wherein
W(R)=10.Math.t.sup.315.Math.t.sup.4+6.Math.t.sup.5, wherein

(68) $t = \frac{(R - RD)}{delta},$
and wherein RD is the radial distance between the first boundary line (18) and the carrier point at the angle A, and wherein delta is the width of the blending zone, in particular wherein delta is 0.6 times radial distance between the first boundary line (18) and the carrier point at the angle A. Clause 30. A method (300) for manufacturing an ophthalmic lens (60), comprising the steps of providing (302) a lens shape for an ophthalmic lens (60) according to any of clauses 1 to 29, and manufacturing (304) the ophthalmic lens (60) according to the lens shape. Clause 31. An ophthalmic lens (60), comprising a front surface and a back surface, wherein the front surface is a convex rotationally symmetric surface, and wherein the back surface comprises a prescription zone (20) which is asymmetric, a margin portion (28) and a transition zone (24) located between the prescription zone (20) and the margin portion (28), and wherein a curvature gradient of the back surface along a straight line emanating from a point on the back surface is constant within the transition zone (24). Clause 32. The ophthalmic lens of clause 31, characterized in that the transition zone (24) has the same length along any straight line emanating from the point, in particular wherein the length is measured parallel to a plane tangential to the point of the back surface. Clause 33. The ophthalmic lens of clause 32, characterized in that the length of the transition zone (24) is within a range of at least 10 mm up to and including 20 mm, in particular 10 mm, 15 mm or 17.5 mm. Clause 34. A method (200) for minimizing the difference in thickness between two ophthalmic lenses (60) for the same spectacles, comprising the following steps: A) providing (202), for each ophthalmic lens (60), an original lens shape satisfying predetermined optical properties over the complete back surface and a modified lens shape having a front surface and a back surface, wherein the modified lens shape comprises a predetermined shape of the front surface and a predetermined shape of the back surface within a prescription zone (20) of the back surface bordered by a first boundary line (18), such that the ophthalmic lens (60) satisfies the predetermined optical properties within the prescription zone (20), and an extension of the back surface radially outwards of the prescription zone (20) by carrier lines (30-37); B) adapting (204) the modified lens shape of the ophthalmic lens (60) having a smaller maximum thickness by replacing the back surface by a combination of the original lens shape and the modified lens shape according to
CS=OS+A.Math.(MSOS) wherein CS is the sagittal height of the combined back surface, OS is the sagittal height of the back surface of the original lens shape, MS is the sagittal height of the back surface of the modified lens shape and A is a value from and including 0 to and including 1, and C) optimizing A so that the difference in thickness between the two ophthalmic lenses (60) is minimized. Clause 35. A computer program product comprising program code for carrying out the steps of a method according to any of clauses 1 to 29 or according to clause 34, in particular when the computer program product is run on a data processing device. Clause 36. A machine readable storage medium having stored thereon a computer program comprising program code for carrying out the steps of a method according to any of clauses 1 to 29 or according to clause 34, in particular when the computer program or the program code is run on a data processing device.
It is understood that the foregoing description is that of the preferred embodiments of the invention and that various changes and modifications may be made thereto without departing from the spirit and scope of the invention as defined in the appended claims.

Method for designing a lens shape and spectacle lens

Assignee

Inventors

Cpc classification

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G02C7/027

PHYSICS

Classification Explorer

G02C2202/04

PHYSICS

Classification Explorer

G02C7/063

PHYSICS

Classification Explorer

G02C7/028

PHYSICS

International classification

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G02C7/02

PHYSICS

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G02C7/06

PHYSICS

Abstract

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Description