Method for designing lens shape and spectacle lens

Abstract

Method for designing a lens shape and a spectacle lens. The invention relates to a computer-implemented method for providing a lens shape for an ophthalmic lens. Further, a method for angular smoothing of a surface determined from a carrier line radially outwards from a prescription area bounded by a first boundary line is provided. Further, an ophthalmic lens, in particular a spectacle lens, is provided. Further, a method for minimizing the thickness difference between two ophthalmic lenses of the same spectacle is provided. A computer program product and a machine-readable storage medium are also provided.

Description

[0001] This application is a divisional application of a divisional application with a filing date of November 18, 2016, application number 201810722997.X, and invention name “Method for designing lens shape and eyeglass lens”. Technical Field

[0002] The present invention relates to a computer-implemented method for providing an ophthalmic lens with a lens shape; a method for angular smoothing of a surface defined by a carrier line radially outward from a prescription area bounded by a first boundary line; a method for manufacturing an ophthalmic lens; an uncut finished spectacle lens for manufacturing an ophthalmic lens, in particular a spectacle lens, a computer program product and a machine-readable storage medium. Background Art

[0003] In recent years, the number of so-called individually designed spectacle lenses has increased significantly. These individually designed spectacle lenses take into account many personal parameters of the intended wearer. This has led to more and more lenses being designed with "free-form surfaces", i.e. surfaces for which no symmetry is inhibited or restricted by any symmetry requirements. The full surface profile is determined, for example, by providing a sagittal height for each surface over the entire area and forwarded to the manufacturing site, for example for grinding, polishing, coating and / or edging.

[0004] Prescription sunglasses for large wrap-around frames are limited in appearance for stronger prescriptions, and the delivery range is limited by the thickness limitations of the puck, i.e., the uncut finished spectacle lens. This is particularly a problem for myopic prescriptions, where the temporal edge thickness can be very large for fairly moderate negative prescriptions, for example, a spherical power of less than -2.00 diopters may produce a maximum edge thickness of more than 5 mm in a large frame. It is also a problem for higher positive prescriptions, where the need to have a specific minimum edge thickness may result in higher center thickness values. In addition, in some half-frame style wrap-around frames (e.g., so-called "leaf-type frames"), any difference in thickness distribution in the two lenses that make up a pair can become very obvious and is considered undesirable by wearers who want to see their glasses more symmetrical. A known solution to this problem is to use spherical or toric shaped carrier surfaces that have a step change in slope and curvature on the boundary between the central prescription area and the peripheral temporal area. This approach requires a two-pass surface processing process and is incompatible with the free-form soft pad polishing tools currently used in the lens surface processing industry.

[0005] Based on the disclosure of document WO 97 / 35224, early attempts to introduce hybrid carriers were not accepted by wearers and were abandoned. No provision was made to reduce the difference in edge thickness between a pair of lenses for both eyes, and the approach was not flexible enough to suit this application. Unlike WO 97 / 35224, the carrier surface needed to be applied to both the single vision lens surface and the progressive lens surface.

[0006] With further reference to the United States patent application US 2015 / 0338680 A1 of the same applicant published on November 26, 2015, a computer-implemented method for providing an uncut lens blank with a modified lens shape is shown.

[0007] Other documents related to lens design are WO 03 / 050596 A1, WO 04 / 029694 A1; US ​​2007 / 008488 A; US 2005 / 206840 A; US 2005 / 225719 A; US 2006 / 274258 A; US 2008 / 024719 A; US 2008 / 284978 A; WO 08 / 135178 A1; US ​​2012 / 008089 A; US 2010 / 296048 A; US 2011 / 134388 A; US 7,070,274 B2; US 7,445,333 B2; US 7,527,376 B2; US 8,002,404 B2; US8,118,425 B2; US 8,449,111; US ​​4,561,736 A and US 2013 / 107205 A. Summary of the invention

[0008] Based on this, an object of the present invention is to overcome the above problems.

[0009] According to a first aspect of the present invention, there is provided a computer-implemented method for providing a lens shape for an ophthalmic lens, the method comprising the following steps:

[0010] a) providing an ophthalmic lens, in particular an uncut finished spectacle lens, having a front surface and a back surface, with a predetermined lens shape, wherein the predetermined lens shape comprises a predetermined shape of the front surface and comprises a predetermined shape of the back surface within a prescription area of ​​the back surface bounded by a first boundary line, such that the ophthalmic lens satisfies predetermined optical properties within the prescription area;

[0011] b) determining a carrier point on the rear surface within the prescription area, and a plurality of carrier lines, each carrier line extending from the carrier point towards a respective direction, in particular straight towards a respective radial direction;

[0012] c) determining a transition zone of the back surface, wherein the transition zone extends radially outward from the first boundary line toward the outer edge of the ophthalmic lens and terminates at a second boundary line radially outwardly adjoining the transition zone;

[0013] d) for each carrier line, setting a desired constant curvature gradient in the transition region, in particular wherein the desired constant curvature gradient is different from zero;

[0014] e) determining, for each carrier line, a curvature profile of the back surface along the carrier line between the first boundary line and the outer edge of the ophthalmic lens, and wherein the curvature profile in the transition zone is determined based on a respectively desired constant curvature gradient.

[0015] In particular, the predetermined lens shape may comprise a predetermined shape of the entire front surface. In particular, the plurality of carrier lines may comprise 4 carrier lines, more preferably 8 carrier lines, and even more preferably 18 carrier lines. In particular, the constant curvature gradient in the transition zone is in the direction of the respective carrier line. Further, in particular, the curvature distribution of the back surface along the carrier line between the first boundary line and the outer edge of the ophthalmic lens is in the direction of the carrier line. In particular, the curvature along the carrier line between the second boundary line and the outer edge is substantially constant, in particular constant, and equal to the curvature along the carrier line in the transition zone at the second boundary line.

[0016] The desired constant curvature gradient may be the same for each carrier line. However, step d does not need to be performed for all carrier lines before starting step e) for one carrier line. Steps d) and e) may be completed for one carrier line and subsequently performed for another carrier line. The desired constant curvature gradient may be different for different carrier lines. The desired constant curvature gradient may be set individually or independently for each carrier line. However, steps d) and e) may also be performed simultaneously for different carrier lines. Typically, steps d) and e) may also be defined as a single step. This single step may comprise: for each carrier line, setting the desired constant curvature gradient in the transition zone, in particular wherein the desired constant curvature gradient is different from zero; and determining the curvature distribution of the rear surface along the carrier line between the first boundary line and the outer edge of the ophthalmic lens, and wherein the curvature distribution in the transition zone is determined based on the corresponding desired constant curvature gradient.

[0017] Further, according to a second aspect of the present invention, there is provided a method for providing a smooth extended surface from a plurality of carrier lines extending radially outwardly from a prescription area, the method comprising the steps of:

[0018] I) providing a plurality of carrier lines each extending from a carrier point in the prescription area towards a respective direction, wherein a curvature profile of the surface along each carrier line radially outwards from the prescription area is provided by a cubic spline, in particular a respective cubic spline;

[0019] II) forming a set of truncated Fourier series of explicit order (specifically, at least second, third or fourth order) that approximate the corresponding spline coefficients for all carrier line directions.

[0020] Further, according to a third aspect of the present invention, there is provided a method for providing a surface defined by a carrier line extending radially outwards from a prescription area bounded by a first boundary line, the method comprising the steps of:

[0021] i) providing a plurality of carrier lines each extending from a carrier point in the prescription area in a respective direction, wherein the curvature distribution of the surface in a direction along each carrier line radially outwards from the prescription area has at least one section, wherein the curvature distribution of the corresponding section of each carrier line is provided by a respective or corresponding polynomial, in particular wherein the coefficients of the polynomial are different for each carrier line,

[0022] ii) forming a series of coefficient values ​​of corresponding coefficients of a polynomial for each carrier line, in particular wherein the series of coefficient values ​​of corresponding coefficients of these polynomials are formed by corresponding coefficients in angular directions,

[0023] iii) determining, for each corresponding coefficient, a first Fourier series approximating to a first order the series of values ​​of these coefficients, so as to obtain a first set of Fourier series, each Fourier series depending on an angle around the carrier point.

[0024] In particular, the first set of Fourier series can be obtained such that it describes any carrier line or carrier line profile in a radial direction at a given angle. The angle around the carrier point can also be defined as an angle in a tangent direction. The carrier line extends in a radial direction. In particular, in any aspect of the present invention and in any improvement, the Fourier series can be at least second order, third order or fourth order. In particular, the first order of the first Fourier series and / or the second order of the second Fourier series can be at least 2nd order or 3rd order or 4th order.

[0025] Further, according to a fourth aspect of the present invention, a method for manufacturing an ophthalmic lens is provided, the method comprising the following steps: providing an ophthalmic lens with a lens shape according to the first aspect of the present invention or one of its improvements or according to the third aspect of the present invention or one of its improvements; and manufacturing the ophthalmic lens according to the lens shape.

[0026] Further, according to a fifth aspect of the present invention, an ophthalmic lens is provided, the ophthalmic lens comprising a front surface and a back surface, wherein the front surface is a rotationally symmetrical convex surface, and wherein the back surface comprises an asymmetric prescription area, a rim portion, and a transition zone between the prescription area and the rim portion, and wherein the curvature gradient of the back surface along a straight line emanating from a certain point on the back surface is constant within the transition zone. Specifically, along any straight line emanating from the point, the transition zone may have the same length. Specifically, the length is measured parallel to a plane tangent to a point or a carrier point of the back surface. Instead of the prescription area being "asymmetric", the prescription area may also be defined as not having point symmetry or line symmetry. Specifically, in the straight line direction along the straight line, the curvature of the rim portion is substantially constant, particularly constant. Further, the substantially constant curvature, particularly the constant curvature, may be equal to the curvature of the rim portion or the boundary of the rim portion in the transition zone along the carrier line in the direction of the straight line.

[0027] In particular, according to all aspects and in each refinement of the invention, the ophthalmic lens may be a finished lens or a finished spectacle lens, in particular for the manufacture of spectacle lenses. A "finished lens" or a "finished spectacle lens" is a lens which has its final optical surface on both sides and may be edged or uncut. In particular, the ophthalmic lens may be an uncut finished spectacle lens for the manufacture of spectacle lenses.

[0028] Further, according to a sixth aspect of the present invention, there is provided a method for minimizing the thickness difference between two ophthalmic lenses of the same spectacles, the method comprising the following steps:

[0029] A) for each ophthalmic lens, providing an original lens shape satisfying predetermined optical properties over the entire back surface and a modified lens shape having a front surface and a back surface, wherein the modified lens shape comprises the predetermined shape of the front surface and comprises the predetermined shape of the back surface within a prescription area of ​​the back surface bounded by a first boundary line, so that the ophthalmic lens satisfies the predetermined optical properties within the prescription area, and the modified lens shape comprises an extension of the back surface radially outward from the prescription area by a carrier line;

[0030] B) adapting a modified lens shape of the ophthalmic lens having a smaller maximum thickness by replacing the back surface with a combination of the original lens shape and the modified lens shape according to the following formula:

[0031]

[0032] Wherein CS is the sag of the combined back surface, OS is the sag of the back surface of the original lens shape, MS is the sag of the back surface of the modified lens shape, and A is a value from and including 0 to and including 1, and

[0033] C) Optimize A so that the thickness difference between the two ophthalmic lenses is minimized.

[0034] In particular, the sag CS, the sag OS and the sag MS are respectively determined in the same reference system. In particular, the thickness may be the maximum edge thickness, in particular along the frame line. In particular, the two ophthalmic lenses may be negative lenses or negative power lenses.

[0035] According to a seventh aspect, a particularly non-transitory computer program product is provided comprising a program code, which is used to execute the steps of the method according to the first aspect of the invention or one of its improvements or the third aspect of the invention or one of its improvements or the sixth aspect of the invention or one of its improvements, particularly when the computer program product is run on a data processing device.

[0036] According to an eighth aspect, a particularly non-transitory computer-readable storage medium storing a computer program is provided, the computer program comprising program code, the program code being used to execute the steps of the method according to the first aspect of the invention or one of its improvements or the third aspect of the invention or one of its improvements or the sixth aspect of the invention or one of its improvements, particularly when the computer program or the program code is run on a data processing device.

[0037] Further, according to a ninth aspect of the present invention, there is provided a method for constructing a surface defined by carrier lines extending radially outward from a prescription region bounded by a first boundary line, the surface closely matching the prescription region at the first boundary and having a high angle smoothness at a second boundary line, the method comprising the following steps:

[0038] aa) providing a plurality of carrier lines each extending from a design reference point or a carrier point in the prescription region toward a corresponding direction, wherein a curvature distribution of the surface along each carrier line radially outward from the prescription region (particularly, between a first boundary line and a second boundary line) is provided by a cubic spline;

[0039] bb) forming a first set of well-defined high-order truncated Fourier series, each truncated Fourier series approximating the corresponding coefficient of the first spline for all carrier line directions,

[0040] cc) forming a second set of well-defined low-order truncated Fourier series, each truncated Fourier series approximating the corresponding coefficient of the second spline for all carrier line directions,

[0041] dd) determining a third spline sufficient to determine the surface height at any radial position within the range of the carrier lines for any given carrier line direction by a weighted average of the first and second splines for that direction, wherein the weighting function is a specified polynomial function of the radial distance from the first boundary.

[0042] In other words, the present invention proposes to introduce a hybrid decorative carrier in the peripheral area of ​​the lens which is rarely used for foveal vision, while maintaining an optimized optical design in the central area or prescription zone of the lens. The carrier surface may blend smoothly into the prescription zone and may be selected to have an approximately constant maximum radial power gradient of moderate size, which has been found to be acceptable to most wearers. In a pair of lenses, the selected radial power gradient of the carrier surface may be different for the two eyes in order to minimize the maximum temporal edge thickness difference between the pairs of lenses. To this end, a portion of the optically optimized free-form lens surface is replaced by a decorative extension having a constant or nearly constant tangential rate of change of curvature (ROC) in the radial direction, for example at a radius R 内 and R as the second boundary line 外 On the ring formed by o , y o ) and is centered on the 外 The coordinate (x o , y o ) specifies specifically a carrier point on the rear surface. The extension is at a radius R with respect to the central portion or prescription area 内 The circle is smoothly blended to ensure that R 内 Continuity of surface height, slope and curvature at the boundaries. The center of the ring defining the carrier or carrier point is preferably off-centered in the nasal direction relative to the prism reference point (PRP) to limit the presence of the carrier extension to the temporal side of the edged and fitted lens. The extent of the ring and the curvature ROC in the carrier zone or transition zone may depend on the amount of lens thickness reduction required to achieve a cosmetically acceptable maximum edge thickness of the lens in a frame for a minus lens or to achieve a center thickness for a plus lens or plus-power lens, which is typically determined by the prescription or predetermined optical characteristics. For example, the width of the transition zone may range from 10 mm to 20 mm and the curvature gradient may vary from 0.05 to 1.0 diopters / mm (D / mm), preferably from 0.05 to 0.5 D / mm, more preferably from 0.05 to 0.25 D / mm. Typically, the sign of the radial gradient is negative for minus-power lenses and positive for plus-power lenses to reduce their center thickness.

[0043] Specifically, the carrier extension can be calculated as follows:

[0044] • For a predetermined number, for example 8, 16, 32, 64, 128, 180, 256, 360 or 512 equally spaced radial directions, initial radial extensions or carrier lines are calculated, each intended to provide a desired curvature profile.

[0045] ● In each of these directions, the 内 ) to the outer radius (R 外 ) is divided into equal steps, specifically, each step is no more than 1 mm, preferably no more than 0.5 mm. Generally, steps of unequal lengths can also be selected.

[0046] ● The height Z and the slope dZ / dR are determined and can be temporarily stored, for each step endpoint, as follows:

[0047] - Calculate the height and 1st and 2nd derivatives of the prescription area at R along the corresponding carrier line.

[0048] - For example, by iterative calculation, determine the cubic polynomial P(R) so that P, dP / dR and d 2 P / dR 2 , P and its first and second derivatives in R 内 The desired amount is the change in curvature at the end of the corresponding step length with a constant curvature gradient. This provides the values ​​of Z and dZ / dR at the end of the step length and P, dP / dR and dP / dR at the beginning of the next step length. 2 P / dR 2 .

[0049] - Repeat this process for each step size.

[0050] - It may happen that the desired curvature change is achieved within a single step where the change in curvature along the step becomes very nonlinear. This condition can be detected by checking the curvature of P(R) at the midpoint of the step. If this condition is detected, then from that point onwards, until R is reached 外 , P(R) from the previous step can continue unchanged for that particular direction.

[0051] - When the process reaches R 外 , the coefficients of the continuous fourth expansion of the loop are calculated and can be temporarily stored.

[0052] - Optionally, a basic procedure for evaluating the extension could be to use the values ​​of Z and dZ / dR at the end of the step in R 内 With R 外 or by performing cubic interpolation within the step size between R 外Also evaluates quartic polynomials.

[0053] - Optionally, to provide angular smoothing, the coefficients determined for each radial direction may not be used directly. Instead, for each coefficient, a Fourier series may be constructed. The corresponding coefficient for the overall direction is then determined by evaluating its Fourier series. At this point, a pair of Fourier series may be constructed for each coefficient, one of which is high order, such as 16th order, and the other is low order, such as 4th order. The high order is needed to obtain the best fit in R 内 A good match is achieved between the inner surface below and the start of the extension. The low order is needed to provide the corner smoothing that is often required for complex gradient surfaces. The final extended surface can then be defined by a mixture of high-order and low-order forms of the extension:

[0054] ■ For R 内 <=R< R 内 +delta; where Z1 is a low-order Fourier series at an angle A and a radial distance R from the carrier point, where Z2 is a high-order Fourier series at an angle A and a radial distance R from the carrier point, and

[0055] ■ For R 外 >= R >= R 内 + delta, Z = Z1;

[0056] Where W(R) is a fifth-order polynomial ,in , where RD is R 内 And delta is the width of the mixing zone.

[0057] This provides the 内 or a higher order form of the extension of the first boundary line to the R 内 +delta. The width delta of this blending zone can be R 内 This has been found to work well in practice. Additional improvements can be made by comparing the initial surface at (x o , y o ) is constructed in a coordinate system aligned with the tangent plane at .

[0058] Therefore, in a method for providing a lens shape for an ophthalmic lens according to the first aspect, a transition zone is predetermined between a first boundary line or inner radius and a second boundary line or outer radius. In one embodiment, the transition zone can be predetermined to have a constant width. Within the transition zone, a constant curvature gradient is formed by the method. This provides advantageous effectiveness in terms of achieving the goals, visual comfort and simplicity of implementation. Further, the carrier extension can be found in a forward-only manner via a predetermined length and a constant curvature gradient in the transition zone. Specifically, via a step-by-step development starting from the first boundary line toward the second boundary line, a function describing each carrier extension can be found in a reliable manner. This can also provide a stable method for producing a viable solution, but once the optical properties of the prescription zone have been predetermined, the need for further optimization routines can also be avoided.

[0059] By the method for angular smoothing of the surface determined by the carrier line radially outward from the prescription zone according to the third aspect, a general description of the carrier line at a certain angle and a certain radial distance from the carrier point can be found. Therefore, a general function that provides the carrier extension in any given angular direction will be found. This is done by describing the carrier line in a specific direction via a corresponding polynomial. Preferably, these polynomials have the same order and are polynomials of the same type. Thus, there are corresponding coefficients in each polynomial. The corresponding coefficients can now be placed in a series in the angular direction, and the series can be described by a Fourier series. By using the appropriate order of the Fourier series, a flattening or smoothing of the polynomial can be found. Therefore, for each coefficient of the polynomial describing the carrier extension in the transition zone, a Fourier series can be found according to the angle. This can be done for a transition zone described by a single polynomial (e.g., only a cubic polynomial), which means that the transition zone has only one section. However, in the case of the improved stepwise method according to the first aspect of the invention, the transition zone can also include more than one section, each section being described by a corresponding polynomial and a corresponding coefficient for each carrier line in each direction. Thus, this may also apply to more than one zone, in case the corresponding zone is described by a corresponding polynomial in each angular direction.Furthermore, the polynomial or profile function outside the prescription zone should be twice continuously differentiable in the radial direction.

[0060] This results therefore in a manufacturing method according to the fourth aspect of the invention and an uncut finished spectacle lens according to the fifth aspect of the invention embodying corresponding advantages.

[0061] The method for minimizing the thickness difference between two ophthalmic lenses of the same spectacles according to the sixth embodiment provides a stable and simple optimization to adapt the lens shape of the lens so as to minimize the measured value of the thickness difference between the two ophthalmic lenses of the same spectacles. In particular, this is not achieved by replacing the back surface outside the prescription area with a carrier extension, but by starting from a complete description of the back surface that meets the predetermined optical properties, only a small part of the difference between the modified lens shapes is applied, which can be achieved, for example, by the method according to the first aspect of the invention or one of its improvements or the second aspect of the invention or the third aspect of the invention or one of its improvements. This can be used to provide two ophthalmic lenses with corresponding aesthetic appearances.

[0062] Therefore, the computer program product according to the seventh aspect of the machine-readable storage medium according to the eighth aspect embodies the same advantages as the methods according to the first, second and fifth aspects of the present invention.

[0063] The term "uncut finished spectacle lens" according to the present application is intended to mean a lens blank having two surfaces, namely a front surface and a back surface, which surfaces both have their final shape before edging. This corresponds to section 8.4.7 of the standard DIN EN ISO 13666: 1998-11 of DIN Deutschenlnstitut für Normung eV. And the term "uncut lens" according to section 8.4.7 of the standard DIN EN ISO 13666: 1998-11 of DIN Deutschen lnstitut für Normung eV may be used. The coating may not be applied to the surface or to one or both of the surfaces. The lens may have a circular or oval shape. In the case of a circular lens blank, the diameter may be at least 60 mm, in particular from 60 mm to and including 90 mm. In the case of an oval lens blank, the minimum diameter may be at least 60 mm, in particular from 60 mm to and including 90 mm.

[0064] According to Section 5.7.1 of DIN EN ISO 13666, “meridian” is intended to mean any plane containing the centre of curvature of such a surface.

[0065] In the context of the present application, "eye point" is in this case intended to mean the point on the back surface of the spectacle lens at which the line of sight intersects the back surface of the spectacle lens when the eye assumes a relaxed position. According to section 5.31 of standard DIN EN ISO 13666, this is also referred to as the "primary position", i.e. the position of the eye relative to the body with the eye looking straight ahead in the direction of gaze at an object located at the horizon. The position of the fitting point can be placed and read as a marking in the uncut finished spectacle lens.

[0066] According to section 5.23 of the standard DIN EN ISO 13666 for spectacle lenses, in the case of decentration, a center point is required which differs from the frame center in the form of an edged spectacle lens, compare section 5.23 "decentering" and section 5.24 "center point" of the standard DIN EN ISO 13666. In particular, the cross-sectional plane may then include a "fitting point" according to section 5.24 of the standard DIN EN ISO 13666, i.e. a point on the front surface of the spectacle lens or the uncut finished spectacle lens which, according to the manufacturer's specifications, is to be used as a reference point for positioning the lens in front of the eye. The position of the fitting point is usually placed and read as a marking in the uncut finished spectacle lens.

[0067] The terms "front surface" and "back surface" in the context of the present application correspond to the front surface and back surface of the standard DIN EN ISO 13666: 1998-11 of DIN Deutschen lnstitutfür Normung eV. According to section 5.8 of the standard DIN EN ISO 13666, the term "front surface" is intended to mean the surface of a spectacle lens in a pair of spectacles that is intended to face away from the eye. According to section 5.9 of the standard DIN EN ISO 13666, the term "back surface" is intended to mean the surface of a spectacle lens in a pair of spectacles that is intended to face toward the eye. However, the terms "front surface" and "back surface" can also be interchanged with "first surface" and "second surface", respectively.

[0068] A "prescription" is generally referred to as the optical values ​​that an optical design is to achieve to correct the aberrations of the wearer's eye. Specifically, a prescription may provide spherical, cylindrical and axial values ​​or equivalent parameters. Further, a prescription addition may be prescribed, i.e., the difference between the near and distance vision zones of the lens, as well as certain prismatic powers along the relevant axes.

[0069] A "carrier point" on the back surface is a point from which a carrier line, in particular a straight carrier line, originates. The carrier point may be any point on the back surface of the lens. Preferably, however, it is a point within the surface area, i.e. the prescription area, which is located within the first boundary line. In an example, the carrier point may be the viewpoint and / or the geometric center of the uncut finished spectacle lens. In particular, the carrier point may be 10 mm eccentric to the nose from the prism reference point. In particular, the eccentricity may be determined to be within the design reference plane or to be determined to extend into a plane parallel to or identical to the tangent plane of the geometric center of the back surface of the corresponding lens. The prism reference point may be a point on the front surface specified by the manufacturer for determining the prismatic effect of the finished lens.

[0070] The "first borderline" determines the outer border of the rear surface area to be retained or the prescription area. The borderline is not a straight line. The borderline can be a part of a circle, but does not necessarily need to be a part of a circle. It is a curve that encloses the prescription area, i.e. the rear surface area to be retained. It can be a closed line. However, it can also start and end on the outer edge of the uncut finished spectacle lens, i.e. so that the enclosed surface area is "opened" radially outwards. In particular, it can cover only one side of the lens area, for example the temporal side. The line can be a circle or have a different shape, for example corresponding to the shape of the frame in which the ophthalmic lens is to be inserted.

[0071] Thus, the "prescription zone" is to be understood as the surface area of ​​the rear surface that is retained and meets the desired optical properties (e.g., prescription). The carrier wire then extends radially outward from that prescription zone. As an alternative to the "prescription zone", the term "optical zone" may be used.

[0072] “Curvature distribution” means the distribution or development of the curvature of a surface in a specific direction. Specifically, it may be the curvature distribution of the rear surface along the carrier line (ie, in the direction of the carrier line).

[0073] As previously explained, a "carrier line" may be a carrier line extending at a specific angle and emanating from a carrier point. Specifically, it may be a straight carrier line extending into a suitably oriented plane (e.g., a plane tangent to the geometric center of the rear surface of the lens). The geometric center may be defined as the intersection of a horizontal center line and a vertical center line of the shape of a lens (specifically, an ophthalmic lens or an uncut finished lens blank). For example, in the case where the carrier point is the geometric center of an uncut finished eyeglass lens, the angle will develop around the geometric center line of the lens. In the case where the carrier point is not the geometric center, a corresponding line parallel to the geometric center line may be defined as passing through the carrier point.

[0074] A "thickness requirement" for an ophthalmic lens is a condition or boundary condition. For example, the thickness requirement may be a value set for the minimum thickness of the outer edge of the lens along the perimeter of an uncut finished spectacle lens. This applies specifically to plus lenses or plus-power lenses. As another example, the thickness requirement may be the minimum thickness of the outer edge of the uncut finished spectacle lens along its perimeter. Thus, the value of the minimum thickness of the outer edge of the uncut finished spectacle lens along its perimeter must be equal to or greater than the minimum thickness. Furthermore, it may be a maximum thickness along the frame line, i.e. the outer edge of the edged lens. This applies specifically to minus lenses.

[0075] Therefore, the above numbers are fully realized.

[0076] In a refinement of the method according to the first aspect of the invention, the curvature along the carrier line between the second boundary line and the outer edge is substantially constant, in particular constant. The curvature between the second boundary line and the outer edge may be equal to the curvature along the carrier line at the second boundary line in the transition zone.

[0077] The curvature along the carrier line is the curvature in the direction of the respective carrier line. A constant curvature can be achieved, for example, by continuing the carrier line as a circular arc or a circular arc segment beyond the second boundary line toward the outer edge. In the case where the curvature should be zero, it is theoretically also possible to continue the carrier line as a straight line. The substantially constant curvature between the second boundary line and the outer edge can also be constructed via a fourth-order expansion or a fourth-order polynomial of the circular extension.

[0078] In an improvement of the method according to the first aspect of the invention, a desired constant curvature gradient is set based on boundary conditions of the curvature of the prescription zone at the first boundary line and the curvature in the transition zone. Specifically, the curvature gradient can be set based on a desired thickness reduction or a desired thickness requirement of the ophthalmic lens along the carrier line.

[0079] Thus, a constant curvature gradient that meets the desired needs can be found. Typically, the constant curvature gradient may be the same for each carrier line. Alternatively, the constant curvature gradient may be different for different carrier lines. For each carrier line, the constant curvature gradient may be set individually. In other words, the constant curvature gradient may vary with angle. The boundary conditions for the curvature within the transition zone may be zero and / or the curvature of the front surface in the same reference system. Of course, other curvatures may be set. Further, the curvature gradient may be set so as to achieve a desired thickness reduction or a desired thickness at a specific point along the carrier line (e.g., a second boundary line or at the outer edge of the ophthalmic lens). Specifically, in the case of a negative lens, the boundary condition may be that the curvature and / or slope of the rear surface should not become smaller than the curvature and / or slope of the front surface in the same reference system. This means that according to that boundary condition, the lens cannot become too thin radially outward. Further, by setting the boundary condition to zero, changes in the curvature will be avoided.

[0080] According to another improvement of the method of the first aspect, a desired constant curvature gradient can be set based on the curvature of the prescription area at the first boundary line and the curvature target to be reached at the second boundary line, and wherein the curvature target is zero and / or the curvature of the front surface. Specifically, the curvature of the front surface is determined in the same coordinate system or reference system as the curvature of the rear surface. Further, specifically, the front surface is a spherical surface.

[0081] Thus, if the curvature of the prescription zone at the first boundary line and the curvature at the second boundary line target zero or the curvature of the front surface in the same reference frame, the start and end points of the curvature along the carrier line through the transition zone are set. Given the width or length of the transition zone (specifically, the constant length), the constant curvature gradient or the desired constant curvature gradient can be determined in a straightforward manner.

[0082] In a further development of the method according to the first aspect, the curvature gradient is set to negative in case the ophthalmic lens is a minus lens or a minus power lens, and the curvature gradient is set to positive in case the ophthalmic lens is a plus lens or a plus power lens.

[0083] Of course, this may depend on the chosen reference system. In case the plane tangent to the vertex of the front surface (specifically the spherical front surface) or the plane tangent to the back surface at the geometric center of the back surface of the lens is chosen as the zero plane, the curvature of the front surface may be chosen to be positive. Subsequently, the curvature gradient, set to be negative in the case of a negative lens, will cause the curvature of the back surface to decrease and the back surface to bend "back" towards the zero plane, for example until the zero curvature is met, i.e. the back surface is no longer curved but extends straight radially outwards from a certain point.

[0084] In a further improvement of the method according to the first aspect of the invention, the curvature distribution is determined by determining a cubic spline from the first boundary line to the second boundary line, wherein the cubic spline consists of a plurality of segments each described by a cubic polynomial, and wherein the cubic polynomial is determined segment by segment from the inner boundary line to the outer boundary line. This can be done so that the sag, slope and curvature of the back surface along the carrier line are continuous and the curvature along the carrier line changes on each segment, thereby producing an approximate and constant curvature gradient on the transition zone. Specifically, by setting a constant length for the segment, the curvature along the carrier line can change by the same amount on each segment.

[0085] In this way, the desired constant curvature gradient can be realized on the transition zone by using a cubic spline composed of a plurality of sections each described by a cubic polynomial. Expand in steps from the first boundary line to the second boundary line. The cubic spline is a third-order polynomial, meaning that four parameters can be used to construct the corresponding polynomial. The vector height, first-order derivative or slope and second-order derivative or slope in the radial direction at the beginning of the carrier line and the first boundary line have determined three of these parameters. Therefore, the fourth parameter is kept for designing the curvature gradient on the transition zone. By knowing the target curvature at the second boundary line or the outer boundary line, the curvature that should be achieved at the end of each step can be predicted in advance to find the approximate constant curvature gradient on the entire transition zone. Therefore, the target curvature at the end of each step length is also known and used to set the fourth parameter of the cubic polynomial of each step length. This again produces the initial conditions of the next step length, etc. Thus, using cubic splines and step-by-step expansion, an approximate constant curvature gradient starting from the first boundary line toward the second boundary line can be formed.

[0086] In a further improvement of the method according to the first aspect of the invention, the curvature distribution is determined by determining a cubic spline from a first boundary line to a second boundary line, wherein the cubic spline consists of a plurality of segments each described by a cubic polynomial, and wherein the cubic polynomial is determined segment by segment from the inner boundary line to the outer boundary line so that the vector height, slope and curvature of the rear surface along the carrier line are continuous, and the curvature gradient is reset to a constant curvature gradient desired by each polynomial at the radially inward end of each segment.

[0087] In this way, instead of using a curvature target at the end of each step length for defining a cubic polynomial for each step length, the curvature gradient can be reset to the desired constant curvature gradient at the beginning of each segment. In particular, in case of a relatively small step length selection, this can also be used to find an approximate constant curvature gradient over the transition zone via a cubic spline composed of a cubic polynomial. The smaller the step length selected, the closer the constant curvature gradient can be.

[0088] In a further development, the length of the transition zone along each carrier line is constant, resulting in the second boundary line adjoining the transition zone radially outwardly and being radially offset from the first boundary line by this length.

[0089] In this refinement, a constant length is set for the transition zone along each zone. However, this is only one possible embodiment. The length of the transition zone can also be determined independently for each carrier line. The length of the transition zone can be different for each carrier line.

[0090] In a further development of the method of the first aspect of the invention, the length of the transition zone is in the range of at least 10 mm up to and including 20 mm. In particular, it may be 10 mm, 15 mm or 17.5 mm.

[0091] In a further refinement of any aspect of the invention, the constant curvature gradient may have a magnitude in the range from and including 0.05 diopters / mm to and including 1.5 diopters / mm, in particular it may be 1.2 diopters / mm. In particular, the constant curvature gradient may have a magnitude different from zero. In particular, the constant curvature gradient has a magnitude in the range from and including 0.05 diopters / mm to and including 1.0 diopters / mm, wherein the length of the transition zone is greater than 12 mm. The constant curvature gradient has a magnitude in the range from and including 1.0 diopters / mm to and including 1.5 diopters / mm, wherein the length of the transition zone is less than or equal to 12 mm. For even smaller lengths of the transition zone, the constant curvature gradient may be greater than 1.5 diopters / mm, for example 4 diopters / mm or even 5 diopters / mm.

[0092] These parameters have been found to provide a very aesthetic ophthalmic lens with good peripheral vision and dynamic vision performance over the common prescription range.

[0093] In a further refinement of the method of the first aspect of the invention, the length of each segment is in the range of at least and including 0.5 mm up to and including 2 mm. In particular, the length of each segment may be 1 mm.

[0094] It has been found that this is a sufficiently short interval to provide an approximately constant curvature gradient. Typically, the length of each segment may be constant, i.e. each segment along the respective carrier line may have the same length. Further, the length may be constant for all carrier lines. Alternatively, however, the length may be set independently or differently for each carrier line. In this way, for example, the number of segments may remain constant between different carrier lines even if the length of the transition zone varies.

[0095] In a further development of the method according to the first aspect of the invention, the method further comprises the following steps: for each carrier line, checking whether the thickness of the spectacle lens at the outer edge and / or at the intended frame line along which the ophthalmic lens is to be edged is above a predefined threshold or meets a predetermined thickness requirement, and if not, changing, in particular reducing or increasing, the size of the desired constant curvature gradient. Thus, if for any reason the lens thickness according to the obtained lens design is too small, the size of the desired constant curvature gradient can be reduced in the case of a minus lens or a minus power lens, and can be increased in the case of a plus lens or a plus power lens. Subsequently, the method can be performed again to provide an appropriate lens design. By performing such a check for each carrier line, unfeasible solutions or results providing too small a thickness can be avoided.

[0096] According to a further development of the method of the first aspect of the invention, the ophthalmic lens is an uncut finished spectacle lens.

[0097] Such an uncut finished spectacle lens is larger than the final edged ophthalmic lens of the spectacle and may be round or oval in shape.The intended frame line along which the ophthalmic lens should be edged may be known in advance and the carrier points may therefore be placed accordingly.

[0098] According to a further development of the method of the first aspect of the invention, the curvature distribution of the predetermined lens shape of the back surface is preserved within the first boundary line.

[0099] Thereby, predetermined optical properties are maintained within the prescription area.

[0100] According to a further improvement of the method of the first aspect of the present invention, at least the sagittal height of the prescription area of ​​the back surface transitions continuously into each carrier line at the first boundary line. Preferably, further, in the direction along the carrier line, the slope of the prescription area of ​​the back surface transitions continuously into each carrier line at the first boundary line. Even more preferably, further, in the direction along the carrier line, the curvature of the prescription area of ​​the back surface transitions continuously into each carrier line at the first boundary line.

[0101] For each carrier line, the back surface may be continuous at the first boundary line. Preferably, for each carrier line, the back surface is continuously differentiable in the radial direction, in the direction of the carrier line, at the first boundary line. Even more preferably, for each carrier line, the back surface is quadratically or twice continuously differentiable in the radial direction, i.e. in the direction of the carrier line, at the first boundary line. The vector height and the first-order derivative of the back surface in the radial direction along the carrier line may be continuous at the first boundary line. The second-order derivative of the back surface in the radial direction along the carrier line may also be continuous. No jumps or kinks may be provided in the back surface. The curvature may be continuous. However, jumps, in particular slight jumps, may be allowed at the first boundary line.

[0102] According to a further improvement of the method of the first aspect of the invention, the length is measured in a plane parallel to the tangent plane at the carrier point of the back surface. The length can also be measured in a plane parallel to or the same plane as the plane tangent to the geometric center of the back surface of the lens or in a tangent plane of the back surface at the geometric center of the back surface of the lens.

[0103] As a result, a length or a width of the transition region of the rear surface between the first boundary line and the second boundary line can be provided in the radial direction, in particular a constant length or a constant width.

[0104] According to a further development of the method of the first aspect of the invention, the carrier point is offset from a prism reference point of the ophthalmic lens towards the nose.

[0105] In that way, the nose of the lens in the frame comprises a prescription zone with good optical properties. Outwards towards the temporal side of the ophthalmic lens, the prescription zone blends smoothly into the border zone.

[0106] According to a further refinement of the method of the first aspect of the invention, the first boundary line is circular and the second boundary line is circular.

[0107] It has been found that such a circular boundary line simplifies the determination step. In this refinement, the first boundary line and the second boundary line have the same center point, which is the carrier point. In particular, the circle can have a sufficiently large radius so that the boundary line extends on the temporal side of the carrier point on the ophthalmic lens and does not exist on the nasal side of the design reference. However, other contours of the boundary line can be selected, for example, corresponding to the expected frame line.

[0108] In a further development of the method according to the first aspect of the invention, the curvature distribution along each carrier line radially outwards from the second boundary line is determined via or as a circle arc or a circle arc segment.

[0109] In this way, the carrier line can be continued with a constant curvature. A single fourth-order polynomial can also be determined to provide a substantially constant curvature and a substantially circular extension of the carrier line. In particular, the curvature, slope and sag in the transition zone at the second boundary line can be continuously extended outwards through the edging area. A fourth-order polynomial is determined accordingly. In the case where the curvature outside the second boundary line does not need to be constant, a quadratic polynomial can be used. A quadratic polynomial has been determined by requiring the carrier line to have the same sag and continuous first and second derivatives at the second boundary line.

[0110] In a further development of the method according to the first aspect of the invention, a method comprises the further step of angularly smoothing the rear surface from the first boundary line radially outwards.

[0111] Thereby, a complete description of the rear surface radially outwards from the first boundary line can be found.Furthermore, the differences between the sags of adjacent carrier lines can be flattened to provide a smoother curvature profile radially outwards from the first boundary line.

[0112] In a further improvement of the method according to the first aspect of the invention, a further step of angular smoothing of the rear surface radially outward from the first boundary line is carried out in the following manner: via approximation, specifically by means of a polynomial or spline function or Fourier series, the curvature distribution of the prescription area along the first boundary line (the curvature is in the direction of the carrier line) is flattened to obtain a flat curvature distribution, and wherein the flat curvature distribution is used as the starting curvature value for each carrier line.

[0113] By using this flat curvature distribution as the radially inward starting curvature value for each carrier line, discontinuities may exist at the first boundary line in the transition from the prescription area to the carrier line. However, when this lens design is transferred to manufacturing, these discontinuities can be overcome when determining the final manufacturing parameters for the processing tool. Typically, during manufacturing, bicubic splines are used to provide processing parameters for the manufacturing tool. These bicubic splines are set in a rectangular grid of x and y coordinates. At the intersection of this grid, which is usually spaced at 1 mm intervals, the sag is submitted via a determined lens design. Further, the first-order derivative in the x and / or y direction can be provided along the outer perimeter of the grid. The space between the intersections of the grid is then interpolated via bicubic splines. However, that bicubic spline can then compensate for discontinuities that may occur due to the forced flattening of the curvature distribution along the first boundary line.

[0114] However, this very robust method of flattening the curvature profile along the first boundary line may already provide adequate results, since the method already flattens the surface of the transition zone and the trim portion at the "root" of the curvature profile at the first boundary line. However, it must generally be noted that a complete surface description of the lens design in the trim portion and the transition zone is not necessarily required radially outward from the prescription zone. As described above, for manufacturing, only the sagitta at the intersections of the manufacturing grid and the first derivatives along the outer perimeter are required. In the case of carrier lines being determined in a relatively narrow pattern or in a pattern that ensures that the carrier lines extend so that they will intersect the intersections of the manufacturing grid, the sagitta necessary for input into the manufacturing tool is already known.

[0115] In a further improvement of the method according to the first aspect of the invention, the method further comprises the following steps for angularly smoothing the rear surface radially outwards from the first boundary line:

[0116] i) forming a series of coefficient values ​​of corresponding coefficients of a respective function describing each carrier line in the transition region, in particular a cubic polynomial for each carrier line,

[0117] ii) determining, for each corresponding coefficient, a first Fourier series approximating to a first order the series of values ​​of these coefficients to obtain a first set of Fourier series, each Fourier series depending on an angle around the carrier point, the first set of Fourier series describing any carrier line in a radial direction at a given angle.

[0118] Thus, a general description of the carrier line at any angle is provided. Further, the description is smoothed in the angular direction via an explicit Fourier series of a predetermined order. In this refinement, the Fourier series can have any order that is considered satisfactory. In particular, the smoothing depends on the order of the Fourier series. The higher the order of the Fourier series, the more accurate the approximation provided.

[0119] In a further improvement of the method according to the first aspect of the invention, the method comprises the further steps of:

[0120] iii) determining, for each coefficient, a second Fourier series approximating the second order of the series of values ​​of the coefficients so as to obtain a second set of Fourier series, each Fourier series depending on an angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction at 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,

[0121] iv) radially outwards over a mixing zone, mixing the second set of Fourier series into the first set of Fourier series, in particular such that outside the mixing zone only the first set of Fourier series is applied.

[0122] Thus, the smoothing can be further blended from the first boundary line (i.e. at the prescription zone) towards the second boundary line (i.e. at the end of the transition zone) and towards the fringing zone. At the first boundary line, a high-order Fourier series is used, which does not provide much smoothing but rather describes a series of coefficient values ​​of the polynomial series that are close to their previously determined original values. A lower-order Fourier series provides greater smoothing. Over the transition zone, the Fourier series are then blended from the higher-order Fourier series towards the lower-order Fourier series.

[0123] In a further improvement of the method of the first aspect of the invention, the mixing step is performed via the following formula:

[0124]

[0125] Wherein, Z is the obtained sag, A is the angle around the carrier point, R is the radial distance from the carrier point, Z1(A, R) is the sag at the angle A and the radial distance R based on the first Fourier series set, and Z2(A, R) is the sag at the angle and the radial distance based on the second Fourier series set, and wherein, W(R) is a fifth-order mixing polynomial, in particular wherein,

[0126]

[0127] in , 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 mixing 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.

[0128] In this way, it is found that a satisfactory mixing from a clear high-order Fourier series toward a clear low-order Fourier series can be provided. A five-order mixing polynomial is selected because it provides a smooth transition from a clear high-order Fourier series toward a clear low-order Fourier series. Specifically, that polynomial provides a t value of zero when R is equal to RD, i.e., at the first boundary line. Therefore, W(0) = 0, W'(0) = 0 and W''(0) = 0. Further, for R = R + delta, t is 1 and W is also 1. However, W'(t=1)=0 and W''(t=1)=0. This provides a smooth transition between a high-order Fourier series and a low-order Fourier series.

[0129] In a further improvement of the method according to the third aspect of the invention, the method comprises the further steps of:

[0130] iv) determining, for each coefficient, a second Fourier series approximating the second order of the series of values ​​of the coefficients so as to obtain a second set of Fourier series, each Fourier series depending on an angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction at 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,

[0131] v) radially outwards over a mixing zone, mixing the second set of Fourier series into the first set of Fourier series, in particular such that outside the mixing zone only the first set of Fourier series is applied.

[0132] Therefore, similar advantages can be achieved in the method according to the third aspect of the present invention.

[0133] In a further improvement of the method of the third aspect of the invention, the mixing step is performed via the following formula:

[0134]

[0135] Wherein, Z is the obtained sag, A is the angle around the carrier point, R is the radial distance from the carrier point, Z1(A, R) is the sag at angle A and radial distance R based on the first Fourier series set, and Z2(A, R) is the sag at angle A and radial distance R based on the second Fourier series set, and wherein, W(R) is a fifth-order mixing polynomial, in particular wherein,

[0136]

[0137] in , 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 mixing 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.

[0138] Likewise, a smooth blending from the first Fourier series towards the second Fourier series can thereby be provided.

[0139] In particular, the above methods and teachings can be applied to negative lenses or negative power lenses, in particular in the case of sports eyewear. In particular, the teachings can be applied to lenses having a front surface curvature of 6 to 9 diopters at a refractive index of 1.53.

[0140] Likewise, in an improvement of an ophthalmic lens, in particular an uncut finished spectacle lens, according to the fifth aspect of the present invention, the transition zone has the same length along any straight line emanating from the point, in particular, the length is measured parallel to a plane tangent to the point of the back surface or tangent to the back surface at the point of the back surface.

[0141] In a further development of the ophthalmic lens, in particular the uncut finished spectacle lens, according to the fifth aspect of the invention, the length of the transition zone is in the range of at least 10 mm up to and including 20 mm, in particular 10 mm, 15 mm or 17.5 mm.

[0142] It goes without saying that the features mentioned above and the features still to be explained below can be used not only in the respectively cited combination but also in other combinations or alone, without departing from the scope of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0143] Exemplary embodiments of the invention are illustrated in the drawings and are explained in more detail in the following description.

[0144] Figure 1 An embodiment of a method for providing a lens shape for an ophthalmic lens is shown,

[0145] Figure 2 Shows and displays Figure 1 A simplified diagram of an embodiment of the different steps of the method,

[0146] Figure 3 A further overall simplified diagram showing and illustrating the different steps of the method for positive and negative lenses is shown,

[0147] Figure 4 An embodiment of an ophthalmic lens, in particular an uncut finished spectacle lens, is shown.

[0148] Figure 5 Shown along the section line XX Figure 4 of uncut finished eyeglass lenses,

[0149] Figure 6 Another embodiment of an ophthalmic lens, in particular an uncut finished spectacle lens, is shown.

[0150] Figure 7 Shows Figure 6 Different areas of embodiment and design,

[0151] Figure 8 Shows Figure 6 and Figure 7 An example of the development of curvature in the radial direction at a specific angle of embodiment,

[0152] Figure 9a Another embodiment of an ophthalmic lens, in particular an uncut finished spectacle lens, is shown.

[0153] Figure 9b Shows Figure 9a An example of the development of the curvature in the radial direction of the 180 degree meridian,

[0154] Fig.9c Shows Figure 9a An example of the thickness development in the radial direction of the 180 degree meridian of an embodiment,

[0155] Fig.10a shows the surface and optical astigmatism in an exemplary minus lens provided according to the method of angular smoothing of a surface defined by a carrier line,

[0156] Fig.10b shows surfaces and optical astigmatism in an exemplary plus lens provided according to a method of angular smoothing of a surface defined by a carrier line, Fig.11 An embodiment of a method for angular smoothing of a surface defined by a carrier line is shown,

[0157] Fig.12 An embodiment of a method for minimizing the thickness difference between two ophthalmic lenses of the same eyeglass is shown, and

[0158] Fig.13 A block diagram of an embodiment of a manufacturing method is shown. DETAILED DESCRIPTION

[0159] Figure 1 An embodiment of a method according to a first aspect of the invention is shown. The method is generally indicated by reference numeral 100 .

[0160] References below Figure 1 and Figure 2 The execution of the method is explained.

[0161] First, perform step 102: provide an ophthalmic lens having a front surface and a back surface, in particular, a predetermined lens shape 10 of an uncut finished eyeglass lens, wherein the predetermined lens shape includes a predetermined shape of the front surface and includes a predetermined shape of the back surface within a prescription area of ​​the back surface bounded by a first boundary line, so that the ophthalmic lens meets predetermined optical properties within the prescription area.

[0162] exist Figure 2, an uncut finished spectacle lens 10 is schematically shown, with a view of the rear surface at the top left. The method 100 then follows the arrow to the bottom line. The uncut finished spectacle lens has a periphery or outer edge 16 of an ophthalmic lens, which can be an uncut finished spectacle lens. For example, a minimum rotation angle 12 of the eye about which the optical properties of the rear surface should be preserved can be provided, however, this is not required. Further, a carrier point or design reference point is determined on the rear surface. As an example only, the carrier point can be the geometric center of the ophthalmic lens. The carrier point can also be located at or behind the fitting cross of the ophthalmic lens. The carrier point can also be shifted towards the nose. As an example only, when viewed in a direction corresponding to the direction of a standard framing system, the carrier point can be shifted from the prism reference point towards the nose, specifically by 10 mm. The plane for measuring the nasal displacement can alternatively be defined as a plane tangential to the geometric center of the rear surface of the lens. The periphery of the uncut finished spectacle lens can have a circular or elliptical form.

[0163] Subsequently, in step 104, a first boundary line 18 is determined. Specifically, the curvature distribution of the original shape of the rear surface is retained within the first boundary line 18. Further specifically, the carrier point 14 is arranged on the rear surface, in the given example at the geometric center, and the first boundary line 18 on the rear surface is determined, especially in the case where the curvature distribution of the original shape of the rear surface is to be retained within the first boundary line 18. Therefore, if Figure 2As shown in the upper right of the figure, the first boundary line 18 is usually drawn to enclose the expected minimum rotation angle of the eye 12. The first boundary line 18 encloses the domain of transition points of the light for observing the eye at the back surface. More precisely, the points of this domain refer to all light rays up to 12 degrees of eye viewing angle. The shape of the boundary line can be selected to be the same as the shape of the frame into which the final lens is to be inserted. However, as shown in a further example, it can also be a circle. Within the first boundary line 18, the curvature distribution of the original lens shape 10 is to be retained. It can be considered to cut off the rest of the original lens shape of the back surface. Therefore, only the original periphery is shown with a dotted line 26. The lens shape will now be determined by adding a carrier line or carrier curve extending radially outward from the prescription area 20. In the transition portion or transition zone 24, a desired constant curvature gradient is set for each carrier line in a subsequent step 108, so that the curvature will transition from the curvature of the lens shape retained within the boundary line 18 toward the constant curvature in the edging portion 28. Therefore, the second boundary line 22 can be considered as the outer boundary of the transition zone 24, wherein the boundary line 18 is the inner boundary line of the transition zone 24. Therefore, in step 106, a carrier point on the back surface and a plurality of carrier lines are determined within the prescription zone, each carrier line extending straight from the carrier point toward a corresponding radial direction. Each straight carrier line 30 to 37 extends at a different angle φ. As in the example given, the periphery of the uncut finished spectacle lens 10 has the form of a circle, and each carrier line extends in a plane that cuts through the major diameter of the circle. As in the example given, the front surface has a spherical shape, and the carrier point 14 is at the geometric center, and each carrier line 30 to 37 extends on the meridian of the front surface. In the example provided, eight carrier lines are used so that the separation angle φ between them is 45 degrees. However, any different number of carrier lines can be used, for example, 128, 180 or 360.

[0164] However, the transition region 24, the border portion 28 and the outer boundary line 22 are fixedly determined by the constant width of the transition region 24 or the length of the transition region along each carrier line. Each carrier line extends straightly radially outwards from a carrier point.

[0165] In a next step 108, for each carrier line, a desired constant curvature gradient in the transition region is set. This constant curvature gradient is in the direction of the respective carrier line.

[0166] In step 110, for each carrier line, a curvature profile of the back surface along the carrier line between a first boundary line and an outer edge of the lens blank is determined, wherein the curvature along the carrier line between a second boundary line and the outer edge is constant and equal to the curvature along the carrier line at the second boundary line in a transition zone, and wherein the curvature gradient in the transition zone is determined based on a corresponding desired constant curvature gradient. Figure 2 In the picture on the middle right, only the final exemplary surface is shown.

[0167] On the first boundary line 18, the curvature of the new curvature profile in the plane of the straight carrier line (i.e., in the given example, the tangential or radial curvature) is equal to the curvature of the optically preserved surface area of ​​the original lens shape 10 within the boundary line 18. This means that the curvatures inside and outside the boundary line are equal to each other close to the boundary line 18. Therefore, the curvature along the first boundary line 18 is preferably determined to be continuous. This means that preferably no kink is provided at the boundary line 18.

[0168] The curvature profile of the predetermined shape within the boundary line 18 is fixed with the new curvature profile outside the boundary line 18 attached to it. In an intuitive view of the back surface, the determined and fixed back surface profile therefore looks like a "spider" at this stage, with the optically preserved curvature profile within the boundary line 18 being the main body and each new curvature profile along the carrier line forming a leg. This description of the back surface may already be sufficient for manufacturing an ophthalmic lens.

[0169] However, in an optional further step, a complete description of the back surface may be provided for subsequent manufacturing and for providing angular smoothing. Therefore, the method may further comprise the step of providing angular smoothing of the back surface radially outwards from the first boundary line. First, a series of coefficient values ​​describing corresponding coefficients of a corresponding function for each carrier line in the transition region (in particular, a cubic polynomial for each carrier line) may be formed. Subsequently, for each corresponding coefficient, a first Fourier series approximating the first order of these series of coefficient values ​​may be determined to obtain a first set of Fourier series, each Fourier series depending on the angle around the carrier point, the first set of Fourier series describing any carrier line in a radial direction at a given angle. Even further, for each coefficient, a second Fourier series approximating the second order of the series of values ​​of these coefficients may be determined so as to obtain a second set of Fourier series, each Fourier series depending on the angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction at 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. Subsequently, radially outwards over the mixing zone, the second set of Fourier series may be mixed into the first set of Fourier series, in particular such that only the first set of Fourier series is applied outside the mixing zone. Specifically, it may be possible via the following formula Mixing is performed, where Z is the resulting sag, A is the angle around the carrier point, R is the radial distance from the carrier point, Z1(A, R) is the sag at the angle A and radial distance R based on the first Fourier series set, and Z2(A, R) is the sag at the angle and radial distance based on the second Fourier series set, and where W(R) is a fifth-order mixing polynomial, in particular, where, ,in , and wherein RD is the radial distance between the first boundary line and the carrier point at angle A, and wherein delta is the width of the mixing zone, in particular wherein delta is 0.6 times the radial distance between the first boundary line and the carrier point at angle A.

[0170] For a negative lens, the method could have ended here. However, in the case of a positive lens, it may be necessary to further readjust the sagittal of the fixed curvature profile within the borderline. In the case that the reduced lens thickness should be considered important, so that the optical properties within the borderline 18 may deteriorate due to the reduced thickness and the condition of the real lens, an optimization step can be performed, which starts with the original lens shape of the rear surface and readjusts it to restore the optical properties of the original lens shape.

[0171] Figure 3 A further simplified diagram is shown to generally illustrate the development of the lens shape through the method. Figure 3 Generally independent of Figure 2 In the left column, the development of the shape of the positive lens is shown. In the right column, the development of the shape of the negative lens is shown.

[0172] Regarding 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 includes the predetermined shape of the front surface 70 of the uncut finished spectacle lens 60 and the predetermined shape of the back surface 72, so that the uncut finished spectacle lens 60 meets the predetermined optical properties. Subsequently, 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 retained within the first boundary line 18. Subsequently, a carrier extension 38 of the back surface 72 between the first boundary line 18 and the outer edge 16 of the uncut finished spectacle lens 60 is determined, wherein the curvature of the carrier extension 38 at the first boundary line 18 may be equal to the boundary curvature. In the case of a plus lens, the predetermined lens shape 10 provides a plus power. Therefore, a lens shape 40 of the uncut finished spectacle lens 60 is determined, wherein the modified lens shape 40 includes the predetermined shape of the front surface 70 and the modified shape of the back surface 72. This results in determining a new curvature profile for the rear surface, which can then be moved towards the front surface until the thickness requirement is met.

[0173] Regarding a negative 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 includes a predetermined shape of the front surface 70 of the uncut finished spectacle lens 60 and a predetermined shape of the back surface 72, such that the uncut finished spectacle lens 60 meets predetermined optical properties within a prescription area. Subsequently, a first boundary line 18 on the back surface 72 is determined, wherein a curvature distribution of the predetermined shape of the back surface 72 is to be retained within the first boundary line 18. Subsequently, a new curvature distribution 38 of the back surface 72 between the first boundary line 18 and the outer edge 16 of the uncut finished spectacle lens 60 is determined, wherein a curvature of the new curvature distribution 38 at the first boundary line 18 may be equal to the boundary curvature. In the case of a negative lens, the predetermined lens shape 10 provides a negative focal power. The sagittal of the fixed curvature distribution of the predetermined lens shape 10 of the back surface 72 within the first boundary line 18 is maintained or retained. Thus, the thickness of the modified shape is reduced. Thus, a modified lens shape 40 of the uncut finished spectacle lens 60 is determined, wherein the modified lens shape 40 comprises a predetermined shape of the front surface 70 and a modified shape of the back surface 72 with the carrier extension. This results in a new curvature profile of the back surface being determined.

[0174] Figure 4 An uncut finished spectacle lens or ophthalmic lens 60 is shown. It has a perimeter or outer edge 16 which may be circular or oval. Figure 4 In the example of , it is circular. Then, as described above, the carrier point can be the geometric center 14. Figure 4 On the rear surface shown, the first boundary line 18 covers a reserved area 62, which is a surface area of ​​the rear surface within the first boundary line 18, which has a free-form surface, that is, a surface curvature distribution that does not have symmetry. It is neither a point nor a plane, nor rotationally symmetrical. Between the trim portion 66 and the prescription area 20, there is a transition zone 64 with 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 of the carrier point 14.

[0175] Figure 5 Shown along Figure 4The front surface of the uncut finished spectacle lens is spherical. Therefore, it is rotationally symmetric about the geometric center and has a single curvature. The back surface is denoted by reference numeral 72. The first boundary line 18 is selected so that the minimum eye rotation angle 12 is within the boundary line 18. In other words, the first boundary line 18 is selected so that for all light rays passing through the eye with an eye viewing angle less than or equal to 12 degrees, the corresponding intersection point of the light rays passing through the back surface is within the boundary line 18. Based on the standard eye used for calculation, the rotation center of the eye 74 can be determined. 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 an asymmetric prescription zone, a border portion, and a transition zone between the prescription zone and the border portion, and wherein the curvature gradient of the back surface is constant within the transition zone along a straight line emanating from a point on the back surface, 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 tangent to the vertex of the front surface or a plane tangent to the back surface at the geometric center of the back surface of the lens.

[0176] refer to Figures 6 to 8 , further principles for determining the carrier line within the transition region are described.

[0177] Typically, it can start from the rear surface of the eyeglass lens, the frame outline 19 and the position of the fitting cross 15. First, the radius and the center of the inner boundary line 18 can be determined. It can be provided that the first boundary line 18 does not intersect the frame line 19 on the nose side, such as Figure 6 The distance 13 from the fitting cross 15 to the first boundary line 18 can be measured along the 180 meridian. The center and radius of the circle describing the inner boundary line 18 can be determined to meet the distance requirement from the fitting cross to the inner boundary, and should not intersect the frame line 19 on the nose side.

[0178] Once the first boundary line 18 is defined, the change in the surface in the transition zone 64 must be determined and applied. The radial curvature should then remain constant from the second boundary line 22 of the transition zone 64 to at least the edge of the frame. This circular extension may continue to the edge of the uncut finished spectacle lens. Figure 7 Relevant regions and boundaries are shown.

[0179] The general approach for providing the desired constant curvature gradient is to construct piecewise cubic polynomials for the transition region, rather than a single monolithic cubic polynomial. This eliminates the difficulty of achieving the desired gradient and can be determined directly. The one-dimensional curvature is given by:

[0180]

[0181] in and are the first and second derivatives of the surface height in the direction of the corresponding carrier line. Then the gradient It is just the derivative of

[0182] .

[0183] For the initial condition, the slope can be used , curvature and gradient , and will is set to zero. The corresponding value of the optical zone at the first boundary line can be used as a substitute value. Then for the first interval, it is

[0184]

[0185] in

[0186]

[0187] Furthermore, in the first interval

[0188] .

[0189] therefore The equation becomes

[0190]

[0191] or

[0192] .

[0193] Now, the carrier line function can be developed in small steps. So if in general it is written for the ith interval

[0194]

[0195] in ,So

[0196]

[0197]

[0198]

[0199] .

[0200] This can be solved by numerical integration. The idea is that the output series will be represented by a standard cubic spline. Past the end of the transition zone and radially outward, the curvature gradient can be set to zero, resulting in a constant curvature function through the second boundary line. Optionally, if the slope of the function exceeds the boundary value, the function can be extended with a quadratic polynomial through that point to prevent the curve from becoming too steep.

[0201] Figure 8 The one-dimensional curvature of a carrier line starting at 13 diopters is shown with a gradient of -4 diopters / mm over a length of 5 mm. The function is a cubic spline consisting of 1 mm steps of numerically integrated functions. The final curvature after the transition zone is about -6.97 diopters.

[0202] Figures 9a to 9c A simple example of an ophthalmic lens 60 which may be an uncut finished spectacle lens is shown. This example is intended to be a simple single vision example of a carrier extension. The lens prescription is -5 diopters, the front surface is a 3.5 diopters spherical surface with a refractive index of 1.530, the material index is 1.586, and the back surface is 8.02 diopters with a refractive index of 1.530 at the geometric center. Generally, throughout this application, curvatures are given in diopters with a refractive index of 1.53 as a reference value and are independent of the refractive index of the material actually used. Therefore, where the curvature is given in diopters, the corresponding curvature of the radius can be obtained by r = This will provide a radius in meters. This recalculation is well known to those skilled in the art, with the refractive index being known throughout this application to be 1.53. The major diameter of the blank shown is 80 mm. The first boundary line 18 is an extension of the inner radius R of 25 mm. 内 , and the second boundary line 22 has an outer radius R of 35 mm 外 The center of the circular extension boundary is displaced 10 mm nasally from the geometric center of the lens blank. 内 With R 外 The gradient of tangential curvature in the annulus between is -0.8 diopters / mm. This gradient takes the tangential curvature from just over eight diopters 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 will be about 8 mm without the extension; with the carrier extension reduced to less than 5.0 mm.

[0203] Fig.10a The example in shows the implementation of a carrier extension on a single progressive lens design with a distance prescription of -3.00 diopters and a lower add of +2.50 diopters. The carrier extension ring (x o , y o) is centered at (10, 0) and eccentric 10 mm from the prism reference point to the nose. 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 or curvature gradient in the ring is fixed to -0.25 D / mm. Fig.10a The power diagram in shows the surface astigmatism and residual optical astigmatism added to the frame outline. The frame size is 64×36 mm, the bridge width is 18 mm, the anteversion angle is 5°, the frame wrap angle is 15°, the wearer's monocular pupil distance is 32 mm, and the fitting height is 21 mm. The thick ring shows the location of the first boundary line.

[0204] Fig.10b The example in shows the implementation of a carrier extension on a single progressive lens design with a +3.00 diopter distance prescription and +2.50 diopter lower add. o , y o ) is centered at (10, 0) and 10 mm off-center from the prism reference point toward the nose. 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 or curvature gradient in the ring is fixed at -0.507 D / mm. Fig.10b The optical power diagram in the figure shows the surface astigmatism and residual optical astigmatism added to the frame outline. The frame size is 64×36 mm, the bridge width is 18 mm, the anteversion angle is 5°, the frame wrap angle is 15°, the wearer's monocular pupil distance is 32 mm, and the fitting height is 21 mm. The thick ring shows the location of the first boundary line. The center thickness of this lens is 4.21 mm, and Fig.10b The edge thickness around the perimeter of the frame shown in varies from 1.0 mm to 3.5 mm. For comparison, the same lens is shown without the carrier curve. This lens has a 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 has the effect of reducing the center thickness by 3 mm and reducing the maximum edge thickness by the same amount, resulting in a much more uniform edge thickness profile.

[0205] exist Fig.11 In the method 150, a surface defined by a carrier line extending radially outward from a prescription area bounded by a first boundary line is angularly smoothed.

[0206] In step 152, a plurality of carrier lines can be provided, each extending in a particularly straight direction from a carrier point in the prescription area in a corresponding radial direction, wherein the curvature distribution of the surface in the direction along each carrier line radially outward from the prescription area has at least one segment, wherein the curvature distribution of the corresponding segment of each carrier line is provided by a corresponding polynomial.

[0207] In step 154, a series of coefficient values ​​for corresponding coefficients of the polynomial for each carrier line may be formed.

[0208] In step 156, for each corresponding coefficient, a first Fourier series approximating the first order of the series of coefficient values ​​may be determined to obtain a first set of Fourier series, each Fourier series depending on an angle around the carrier point, the first set of Fourier series describing any carrier line in a radial direction at a given angle.

[0209] In a further development, for each coefficient, a second Fourier series approximating the second order of the series of values ​​of these coefficients can be determined so as to obtain a second set of Fourier series, each Fourier series depending on the angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction at 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. Subsequently, radially outwards over the mixing zone, the second set of Fourier series can be mixed into the first set of Fourier series, in particular so that only the first set of Fourier series is applied outside the mixing zone.

[0210] Specifically, the mixing can be performed via the following formula:

[0211]

[0212] Wherein, Z is the obtained sag, A is the angle around the carrier point, R is the radial distance from the carrier point, Z1(A, R) is the sag at angle A and radial distance R based on the first Fourier series set, and Z2(A, R) is the sag at angle A and radial distance R based on the second Fourier series set, and wherein, W(R) is a fifth-order mixing polynomial, in particular wherein,

[0213]

[0214] in , 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 mixing 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.

[0215] exist Fig.12, a method 200 for minimizing the thickness difference between two ophthalmic lenses of the same eyeglass is shown. The method comprises: for each ophthalmic lens, providing 202 an original lens shape satisfying predetermined optical properties over the entire back surface and a modified lens shape having a front surface and a back surface, wherein the modified lens shape comprises the predetermined shape of the front surface and comprises the predetermined shape of the back surface within a prescription zone of the back surface bounded by a first boundary line, so that the ophthalmic lens satisfies the predetermined optical properties within the prescription zone, and the modified lens shape comprises an extension of the back surface radially outward from the prescription zone by a carrier line.

[0216] Subsequently, in step 204, a modified lens shape of the ophthalmic lens having a smaller maximum thickness is adapted by replacing the back surface with a combination of the original lens shape and the modified lens shape according to the following formula:

[0217]

[0218] Wherein, CS is the sag of the combined back surface, OS is the sag of the back surface of the original lens shape, MS is the sag of the back surface of the modified lens shape, and A is a value from and including 0 to and including 1.

[0219] Subsequently, in step 206 , parameter A may be optimized such that the thickness difference between the two ophthalmic lenses is minimized.

[0220] In practice, if for either lens the edge thickness exceeds, for example, 5 mm at any point outside the first boundary line or the frame line or frame boundary, then a carrier extension may be applied to both lenses of the spectacle frame. When a carrier line has been determined for the minus lens, then a maximum edge thickness may be determined for both lenses. If the difference is greater than a specified threshold (e.g., 1 mm), then in order to balance the edge thickness of the lenses for the right and left eye, the extension of the thinner lens is modified, as described above.

[0221] This determination can produce a lens edge thickness map for a pair of lenses with very different prescriptions for 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 of light added, the maximum temporal edge thickness balance may result in both lenses having a maximum temporal edge thickness of 7.55 mm.

[0222] at last, Fig.13A manufacturing method is shown which is generally indicated by reference numeral 300. After starting, the method 100 according to the first aspect and / or the method 150 according to the third aspect is carried out in step 302. Afterwards, based on the modified lens shape, a manufacturing step 304 of manufacturing an uncut finished spectacle lens 60 will be carried out. Subsequently, the uncut finished spectacle lens 60 may be further processed, in particular in an edging process, which cuts the lens from the uncut finished spectacle lens towards its final shape, in particular the lens may then be transported to an ophthalmic dispenser. The method may then end.

[0223] Further, the present invention includes embodiments according to the following clauses:

[0224] Clause 1. A computer-implemented method for providing a lens shape for an ophthalmic lens, the method comprising the steps of:

[0225] a) providing a predetermined lens shape of an ophthalmic lens having a front surface and a back surface, wherein the predetermined lens shape includes a predetermined shape of the front surface and includes a predetermined shape of the back surface within a prescription area of ​​the back surface bounded by a first boundary line, such that the ophthalmic lens satisfies predetermined optical properties within the prescription area;

[0226] b) determining a carrier point on the rear surface within the prescription area, and a plurality of carrier lines, each carrier line extending from the carrier point toward a corresponding direction;

[0227] c) determining a transition zone of the back surface, wherein the transition zone extends radially outward from the first boundary line toward the outer edge of the ophthalmic lens and terminates at a second boundary line radially outwardly adjoining the transition zone;

[0228] d) for each carrier line, setting a desired constant curvature gradient in the transition region;

[0229] e) determining, for each carrier line, a curvature profile of the back surface along the carrier line between the first boundary line and the outer edge of the ophthalmic lens, and wherein the curvature profile in the transition zone is determined based on a respectively desired constant curvature gradient.

[0230] Clause 2. The method according to clause 1, wherein the curvature along the carrier line between the second boundary line and the outer edge is substantially constant, in particular constant and equal to the curvature along the carrier line in the transition region at the second boundary line.

[0231] Clause 3. The method of clause 1, wherein the desired constant curvature gradient is set based on boundary conditions of a curvature of the prescription zone at the first boundary line and a curvature within the transition zone.

[0232] Clause 4. The method of Clause 3, wherein the curvature gradient is further set based on a desired thickness reduction of the ophthalmic lens along the carrier line.

[0233] Clause 5. The method of clause 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 achieved at the second boundary line, and wherein the curvature target is zero and / or the curvature of the front surface.

[0234] Clause 6. The method of Clause 5, wherein the curvature of the front surface is determined in the same coordinate system as the curvature of the back surface.

[0235] Clause 7. The method of clause 5, wherein the front surface is a spherical surface.

[0236] Clause 8. The method of Clause 1, wherein the curvature gradient is set to be negative if the ophthalmic lens is a minus lens and the curvature gradient is set to be positive if the ophthalmic lens is a plus lens.

[0237] Clause 9. A method according to clause 1, wherein the curvature distribution is determined by determining a cubic spline from the first boundary line to the second boundary line, wherein the cubic spline consists of a plurality of segments each described by a cubic polynomial, and wherein the cubic polynomial is determined segment by segment from the first boundary line to the second boundary line.

[0238] Item 10. A method according to Item 9, wherein a cubic polynomial is determined segment by segment from the first boundary line to the second boundary line so that the vector height, slope and curvature of the rear surface along the carrier line are continuous, and the curvature along the carrier line changes in each segment, thereby producing an approximately constant curvature gradient in the transition zone.

[0239] Clause 11. A method according to clause 1, wherein the curvature distribution is determined by determining a cubic spline from the first boundary line to the second boundary line, wherein the cubic spline consists of a plurality of segments each described by a cubic polynomial, and wherein these cubic polynomials are determined segment by segment from the first boundary line to the second boundary line so that the vector height, slope and curvature of the rear surface along the carrier line are continuous, and the curvature gradient is reset to the constant curvature gradient desired by each polynomial at the radially inward end of each segment.

[0240] Clause 12. The method of clause 1, wherein the length of the transition zone along each carrier line is constant, thereby causing the second boundary line to adjoin the transition zone radially outwardly and the second boundary line to be radially offset from the first boundary line by the length.

[0241] Clause 13. The method of clause 8, wherein the length of the transition zone is in the range of at least 10 mm up to and including 20 mm.

[0242] Clause 14. The method of Clause 1, wherein the constant curvature gradient has a magnitude in a range from and including 0.05 Diopters / mm to and including 1.5 Diopters / mm.

[0243] Clause 15. The method of clause 9, wherein the length of each segment is in the range of at least 0.5 mm up to and including 2 mm.

[0244] Clause 16. A method according to clause 1, wherein the method comprises a further step of checking, for each carrier line, whether the thickness of the ophthalmic lens at the outer edge and / or at the expected frame line along which the ophthalmic lens is to be edged is above a predefined threshold and, if not, reducing or increasing the size of the desired constant curvature gradient.

[0245] Clause 17. The method of Clause 1, wherein the ophthalmic lens is an uncut finished spectacle lens.

[0246] Clause 18. The method of Clause 1, wherein a curvature distribution of the predetermined lens shape of the back surface is preserved within the first boundary line.

[0247] Clause 19. The method of Clause 1, wherein at least the sagittal height of the prescription area of ​​the rear surface transitions continuously into each carrier line at the first boundary line.

[0248] Clause 20. The method according to Clause 19, wherein, further, a slope of the prescription area of ​​the rear surface in a direction along the carrier lines continuously transitions into each carrier line at the first boundary line.

[0249] Clause 21. The method according to Clause 20, wherein, further, the curvature of the prescription area of ​​the rear surface in a direction along the carrier lines continuously transitions into each carrier line at the first boundary line.

[0250] Clause 22. The method of clause 12, wherein the length is measured in a plane parallel to a tangent plane at a carrier point of the rear surface.

[0251] Clause 23. The method of clause 1, wherein the carrier point is offset nasally from a prism reference point of the ophthalmic lens.

[0252] Clause 24. The method of Clause 1, wherein the first boundary line is circular and the second boundary line is circular.

[0253] Clause 25. The method of clause 1, wherein the curvature distribution along each carrier line radially outward from the second boundary line is determined via a circular arc.

[0254] Clause 26. The method of clause 1, wherein the method comprises the further step of angularly smoothing the rear surface radially outward from the first boundary line.

[0255] Item 27. A method according to Item 1, wherein a further step of angularly smoothing the rear surface radially outward from the first boundary line is performed by flattening the curvature distribution of the prescription area in the direction of these carrier lines along the first boundary line via approximation by a polynomial or a spline function or a Fourier series to obtain a flat curvature distribution, and wherein the flat curvature distribution is used as the starting curvature value radially inward for each carrier line.

[0256] Clause 28. The method of clause 1, wherein the method further comprises the following steps for providing angular smoothing to the rear surface radially outward from the first boundary line:

[0257] i) forming a series of coefficient values ​​for corresponding coefficients of a respective function describing each carrier line in the transition region,

[0258] ii) determining, for each corresponding coefficient, a first Fourier series approximating to a first order the series of values ​​of these coefficients to obtain a first set of Fourier series, each Fourier series depending on an angle around the carrier point, the first set of Fourier series describing any carrier line in a radial direction at a given angle.

[0259] Clause 29. The method according to clause 28, wherein the method comprises the following additional steps:

[0260] iii) determining, for each coefficient, a second Fourier series approximating the second order of the series of values ​​of the coefficients so as to obtain a second set of Fourier series, each Fourier series depending on an angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction at 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,

[0261] iv) mixing the second set of Fourier series into the first set of Fourier series radially outwardly over the mixing region.

[0262] Clause 30. The method according to clause 29, wherein the mixing step is performed via the following formula:

[0263]

[0264] Wherein, Z is the obtained vector height, A is the angle around the carrier point, R is the radial distance from the carrier point, Z1(A, R) is the vector height at the angle A and the radial distance R based on the first Fourier series set, and Z2(A, R) is the vector height at the angle and the radial distance based on the second Fourier series set, and wherein, W(R) is a fifth-order mixing polynomial.

[0265] Clause 31. The method according to clause 30, wherein

[0266]

[0267] in , 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 mixing zone.

[0268] Clause 32. The method of clause 31, wherein delta is 0.6 times the radial distance between the first boundary line and the carrier point at the angle A.

[0269] Clause 33. A method for providing a smooth extended surface from a plurality of carrier threads extending radially outward from a prescription area, the method comprising the steps of:

[0270] I) providing a plurality of carrier lines each extending from a carrier point in the prescription region in a respective direction, wherein a curvature profile of the surface along each carrier line radially outward from the prescription region is provided by a cubic spline;

[0271] II) Forming a set of truncated Fourier series of explicit order, each of which approximates the corresponding spline coefficients for all carrier line directions.

[0272] Clause 34. A method for constructing a surface defined by carrier lines extending radially outward from a prescription region, the method comprising the steps of:

[0273] aa) providing a plurality of carrier lines each extending from a carrier point in the prescription region in a respective direction, wherein a curvature profile of the surface along each carrier line radially outward from the prescription region is provided by a cubic spline;

[0274] bb) forming a first set of well-defined high-order truncated Fourier series, each truncated Fourier series approximating the corresponding coefficient of the first spline for all carrier line directions,

[0275] cc) forming a second set of well-defined low-order truncated Fourier series, each truncated Fourier series approximating the corresponding coefficient of the second spline for all carrier line directions,

[0276] dd) determining a third spline sufficient to determine the surface height at any radial position within the range of the carrier lines for any given carrier line direction by a weighted average of the first and second splines for that direction, wherein the weighting function is a specified polynomial function of the radial distance from the first boundary.

[0277] Clause 35. A method for providing a surface defined by a carrier line extending radially outward from a prescription area bounded by a first boundary line, the method comprising the steps of:

[0278] i) providing a plurality of carrier lines each extending from a carrier point in the prescription area towards a respective direction, wherein the curvature distribution of the surface in a direction along each carrier line radially outward from the prescription area has at least one segment, wherein the curvature distribution of a corresponding segment of each carrier line is provided by a respective polynomial,

[0279] ii) the series of coefficient values ​​forming the corresponding coefficients of the polynomial for each carrier line,

[0280] iii) determining, for each corresponding coefficient, a first Fourier series approximating to a first order the series of values ​​of these coefficients, so as to obtain a first set of Fourier series, each Fourier series depending on an angle around the carrier point.

[0281] Clause 36. The method according to clause 35, wherein the method comprises the following additional steps:

[0282] iv) determining, for each coefficient, a second Fourier series approximating the second order of the series of values ​​of the coefficients so as to obtain a second set of Fourier series, each Fourier series depending on an angle around the carrier point, the second set of Fourier series describing any carrier line in a radial direction at 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,

[0283] v) mixing the second set of Fourier series into the first set of Fourier series radially outwardly over the mixing zone.

[0284] Clause 37. The method according to clause 36, wherein the mixing step is performed via the following formula:

[0285]

[0286] Wherein, Z is the obtained vector height, A is the angle around the carrier point, R is the radial distance from the carrier point, Z1(A, R) is the vector height at the angle A and the radial distance R based on the first Fourier series set, and Z2(A, R) is the vector height at the angle A and the radial distance R based on the second Fourier series set, and wherein, W(R) is a fifth-order mixing polynomial.

[0287] Clause 38. The method according to clause 37, wherein

[0288]

[0289] in , 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 mixing zone.

[0290] Clause 39 The method of Clause 38, wherein delta is 0.6 times the radial distance between the first boundary line and the carrier point at the angle A.

[0291] Clause 40. A method for manufacturing an ophthalmic lens, the method comprising the step of providing a lens shape for the ophthalmic lens according to a method comprising the following steps: providing a predetermined lens shape of an ophthalmic lens having a front surface and a back surface, wherein the predetermined lens shape includes a predetermined shape of the front surface and includes a predetermined shape of the back surface within a prescription area of ​​the back surface bounded by a first boundary line, so that the ophthalmic lens satisfies predetermined optical properties within the prescription area; determining a carrier point on the back surface within the prescription area, and a plurality of carrier lines, each carrier line extending from the carrier point in a corresponding direction; determining the back surface The invention relates to a method of manufacturing the ophthalmic lens according to the present invention. The method comprises the steps of: providing a transition zone of a rear surface of the ophthalmic lens, wherein the transition zone extends radially outward from the first boundary line toward the outer edge of the ophthalmic lens and terminates at a second boundary line radially outwardly adjacent to the transition zone; for each carrier line, setting a desired constant curvature gradient in the transition zone; for each carrier line, determining a curvature distribution of the rear surface along the carrier line between the first boundary line and the outer edge of the ophthalmic lens, and wherein the curvature distribution in the transition zone is determined based on the corresponding desired constant curvature gradient; and the manufacturing method further comprises the step of manufacturing the ophthalmic lens according to the lens shape.

[0292] Item 41. A method for manufacturing an ophthalmic lens, the method comprising the step of providing a lens shape for the ophthalmic lens according to a method for providing a smooth extended surface from a plurality of carrier lines extending radially outward from a prescription area, the method for providing comprising the steps of: providing a plurality of carrier lines each extending in a corresponding direction from a carrier point in the prescription area, wherein the curvature distribution of the surface along each carrier line radially outward from the prescription area is provided by a cubic spline; forming a set of truncated Fourier series of a definite order, each truncated Fourier series approximating a corresponding spline coefficient for all carrier line directions; and the manufacturing method further comprising the step of manufacturing the ophthalmic lens according to the lens shape.

[0293] Clause 42. A method for manufacturing an ophthalmic lens, the method comprising the step of providing an ophthalmic lens with a lens shape according to a method for constructing a surface defined by carrier lines extending radially outward from a prescription zone, the construction method comprising the steps of: providing a plurality of carrier lines each extending from a carrier point in the prescription zone toward a respective direction, wherein the curvature profile of the surface along each carrier line extending radially outward from the prescription zone is provided by a cubic spline; forming a first set of well-defined high-order truncated Fourier series, each truncated Fourier series approximating corresponding coefficients of a first spline for all carrier line directions; forming a second set of well-defined low-order truncated Fourier series, each truncated Fourier series approximating corresponding coefficients of a second spline for all carrier line directions; determining a third spline sufficient to determine the surface height at any radial position within the range of the carrier lines for any given carrier line direction by a weighted average of the first spline and the second spline for that direction, wherein the weighting function is a specified polynomial function of the radial distance from the first boundary; and the manufacturing method further comprising the step of manufacturing the ophthalmic lens according to the lens shape.

[0294] Clause 43. A method for manufacturing an ophthalmic lens, the method comprising the step of providing an ophthalmic lens with a lens shape according to a method for providing a surface defined by carrier lines extending radially outward from a prescription area bounded by a first boundary line, the providing method comprising the steps of: providing a plurality of carrier lines each extending in a corresponding direction from a carrier point in the prescription area, wherein the curvature distribution of the surface in the direction along each carrier line extending radially outward from the prescription area has at least one segment, wherein the curvature distribution of the corresponding segment of each carrier line is provided by a corresponding polynomial; forming a coefficient value series of corresponding coefficients of the polynomial for each carrier line; for each corresponding coefficient, determining a first Fourier series approximating the first order of these coefficient value series so as to obtain a first set of Fourier series, each Fourier series depending on the angle around the carrier point; and the manufacturing method further comprising the step of manufacturing the ophthalmic lens according to the lens shape.

[0295] Item 44. An ophthalmic lens comprising a front surface and a back surface, wherein the front surface is a rotationally symmetric convex surface, and wherein the back surface comprises an asymmetric prescription zone, a border portion, and a transition zone between the prescription zone and the border 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.

[0296] Clause 45. The ophthalmic lens of Clause 44, wherein the transition zone has the same length along any straight line emanating from the point.

[0297] Clause 46. The ophthalmic lens of Clause 45, wherein the length of the transition zone is in the range of at least 10 mm up to and including 20 mm.

[0298] Clause 47. A method for minimizing the thickness difference between two ophthalmic lenses of the same eyeglass, comprising the steps of:

[0299] A) for each ophthalmic lens, providing an original lens shape satisfying predetermined optical properties over the entire back surface and a modified lens shape having a front surface and a back surface, wherein the modified lens shape comprises the predetermined shape of the front surface and comprises the predetermined shape of the back surface within a prescription area of ​​the back surface bounded by a first boundary line, so that the ophthalmic lens satisfies the predetermined optical properties within the prescription area, and the modified lens shape comprises an extension of the back surface radially outward from the prescription area by a carrier line;

[0300] B) adapting a modified lens shape of the ophthalmic lens having a smaller maximum thickness by replacing the back surface with a combination of the original lens shape and the modified lens shape according to the following formula:

[0301]

[0302] Wherein CS is the sag of the combined back surface, OS is the sag of the back surface of the original lens shape, MS is the sag of the back surface of the modified lens shape, and A is a value from and including 0 to and including 1, and

[0303] C) Optimize A so that the thickness difference between the two ophthalmic lenses is minimized.

[0304] Clause 48. A computer program product, comprising a program code, the program code being used to execute 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 providing method comprising the following steps: providing a predetermined lens shape of an ophthalmic lens having a front surface and a back surface, wherein the predetermined lens shape includes a predetermined shape of the front surface and includes a predetermined shape of the back surface within a prescription area of ​​the back surface bounded by a first boundary line, so that the ophthalmic lens satisfies predetermined optical properties within the prescription area; determining a carrier point on the back surface within the prescription area , and a plurality of carrier lines, each carrier line extending from the carrier point in a corresponding direction; determining a transition zone of the back surface, wherein the transition zone extends radially outward from the first boundary line toward the outer edge of the ophthalmic lens and terminates at a second boundary line radially outwardly adjacent to the transition zone; for each carrier line, setting a desired constant curvature gradient in the transition zone; for each carrier line, determining a curvature distribution of the back surface along the carrier line between the first boundary line and the outer edge of the ophthalmic lens, and wherein the curvature distribution in the transition zone is determined based on the corresponding desired constant curvature gradient.

[0305] Clause 49. A computer program product comprising program code for executing the steps of a method for providing a smooth extended surface from a plurality of carrier lines extending radially outward from a prescription area when the computer program product is run on a data processing device, the providing method comprising the following steps: providing a plurality of carrier lines each extending in a corresponding direction from a carrier point in the prescription area, wherein the curvature distribution of the surface along each carrier line radially outward from the prescription area is provided by a cubic spline; forming a set of truncated Fourier series of a definite order, each truncated Fourier series approximating a corresponding spline coefficient for all carrier line directions; and the manufacturing method further comprising the step of manufacturing the ophthalmic lens according to the lens shape.

[0306] Clause 50. A computer program product comprising program code for executing the steps of a method for constructing a surface defined by carrier lines extending radially outward from a prescription region when the computer program product is run on a data processing device, the construction method comprising the steps of: providing a plurality of carrier lines each extending from a carrier point in the prescription region in a respective direction, wherein the curvature distribution of the surface along each carrier line extending radially outward from the prescription region is provided by a cubic spline; forming a first set of well-defined high-order truncated Fourier series, each truncated Fourier series approximating a first set of well-defined high-order truncated Fourier series for all carrier line directions; forming a second set of well-defined low-order truncated Fourier series, each truncated Fourier series approximating the corresponding coefficients of the second spline for all carrier line directions; determining a third spline sufficient to determine the surface height at any radial position within the range of these carrier lines for that direction by a weighted average of the first spline and the second spline for any given carrier line direction, wherein the weighting function is a specified polynomial function of the radial distance from the first boundary; and the manufacturing method also includes the step of manufacturing the ophthalmic lens according to the lens shape.

[0307] Clause 51. A computer program product comprising program code for executing, when the computer program product is run on a data processing device, the steps of a method for providing a surface defined by carrier lines extending radially outward from a prescription area bounded by a first boundary line, the providing method comprising the following steps: providing a plurality of carrier lines each extending in a corresponding direction from a carrier point in the prescription area, wherein the curvature distribution of the surface in the direction along each carrier line extending radially outward from the prescription area has at least one segment, wherein the curvature distribution of the corresponding segment of each carrier line is provided by a corresponding polynomial; forming a coefficient value series of corresponding coefficients of the polynomial for each carrier line; for each corresponding coefficient, determining a first Fourier series approximating the first order of these coefficient value series so as to obtain a first set of Fourier series, each Fourier series depending on the angle around the carrier point; and the manufacturing method further comprising the step of manufacturing the ophthalmic lens according to the lens shape.

[0308] Clause 52. A computer program product comprising program code for executing the steps of a method for minimizing the thickness difference between two ophthalmic lenses of the same eyeglasses when the computer program product is run on a data processing device, the minimization method comprising the following steps: for each ophthalmic lens, providing an original lens shape that meets predetermined optical properties over the entire back surface and a modified lens shape having a front surface and a back surface, wherein the modified lens shape includes the predetermined shape of the front surface and includes the predetermined shape of the back surface within a prescription area of ​​the back surface bounded by a first boundary line, so that the ophthalmic lens meets these predetermined optical properties within the prescription area, and the modified lens shape includes an extension of the back surface radially outward from the prescription area at a carrier line; adapting the modified lens shape of the ophthalmic lens having a smaller maximum thickness by replacing the back surface with a combination of the original lens shape and the modified lens shape according to the following formula:

[0309]

[0310] Wherein, CS is the sagitta of the combined back surface, OS is the sagitta of the back surface of the original lens shape, MS is the sagitta of the back surface of the modified lens shape, and A is a value from and including 0 to and including 1; and A is optimized so that the thickness difference between the two ophthalmic lenses is minimized.

Claims

1. A method (200) for minimizing the thickness difference between two ophthalmic lenses (60) of the same eyeglass, comprising the following steps: A) for each ophthalmic lens (60), providing (202) an original lens shape satisfying predetermined optical properties over the entire back surface and a modified lens shape having a front surface and a back surface, wherein the modified lens shape includes the predetermined shape of the front surface and includes the predetermined shape of the back surface within a prescription area (20) of the back surface bounded by a first boundary line (18), so that the ophthalmic lens (60) satisfies these predetermined optical properties within the prescription area (20), and the modified lens shape includes a portion of the back surface extending radially outward from the prescription area (20) along carrier lines (30-37), wherein each carrier line extends in a corresponding direction from a carrier point on the back surface within the prescription area and for each carrier line, a desired constant curvature gradient is provided in a transition area of ​​the back surface, the transition area extending radially outward from the first boundary line toward the outer edge of the ophthalmic lens and terminating at a second boundary line radially outwardly adjacent to the transition area; B) adapting (204) a modified lens shape of the ophthalmic lens (60) having a smaller maximum thickness by replacing the back surface with a combination of the original lens shape and the modified lens shape according to the following formula: CS=OS+A·(MS-OS) Wherein CS is the sag of the combined back surface, OS is the sag of the back surface of the original lens shape, MS is the sag 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 thickness difference between the two ophthalmic lenses (60) is minimized.

2. A machine-readable storage medium having a computer program stored thereon, the computer program comprising program code for executing the steps of the method according to claim 1 when the computer program or the program code is run on a data processing device.

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