Method for Calculation of the Magnification and/or Distortion and Method for Production of a Spectacle Lens with Low Magnification and/or Distortion

• US 20100198515A1
• Filed: 11/24/2006
• Published: 08/05/2010
• Est. Priority Date: 12/01/2005
• Status: Active Grant

• Current Assignee: Rodenstock GmbH (Bridgepoint Advisers Group Limited)
• Original Assignee: Rodenstock GmbH (Bridgepoint Advisers Group Limited)
• Inventors: Altheimer, Helmut, Becken, Wolfgang, Esser, Gregor, Uttenweiler, Dietmar
• Granted Patent: US 8,805,612 B2
• Time in Patent Office: Days
• US Class Current: 702/1
• CPC Class Codes: G02C 7/024 Methods of designing ophthalmic lenses
• CPC Class Codes: G02C 7/027 considering wearer's parameters
• CPC Class Codes: G02C 7/028 Special mathematical design techniques
• CPC Class Codes: G02C 7/061 Spectacle lenses with progressively varying focal power
• CPC Class Codes: G02C 7/063 Shape of the progressive surface

Abstract

The invention relates to a method for calculation of the local magnification and/or the local distortion of a spectacle lens in at least one predetermined or predeterminable viewing direction, with the spectacle lens being designed to correct a refraction deficit of an eye, and having at least one object-side surface and one second eye-side surface, comprising the following steps: Calculation for the predetermined or predeterminable viewing direction of the profile of a main beam which originates from a predetermined or predeterminable infinitesimally small object and, after refraction by the spectacle lens, passes through the rotation point of the eye, through the entrance pupil of the eye or through the principal plane of the eye; determination of the main curvatures and directions of a local wavefront associated with the main beam on refraction by the spectacle lens; calculation of the local magnification and/or the local distortion of the spectacle lens from the determined main curvatures and directions of the local wavefront, the data relating to the profile of the main beam, and the data relating to the spectacle lens.

Claims

1-22. -22. (canceled)

23. A method of calculating local magnification and/or local distortion of a spectacle lens in at least one predetermined or predeterminable viewing direction, the spectacle lens being configured for correcting a refractive deficit of an eye and having at least a first object-side surface and a second eye-side surface, comprising:

calculating a course of a main beam for the predetermined or predeterminable viewing direction, which main beam originates from a predetermined or predeterminable infinitesimally small object and, after refraction by the spectacle lens, passes through a rotation point of the eye, through eye entrance pupils or through an eye principal plane;

determining main curvatures and directions of a local wave front associated with the main beam on refraction by the spectacle lens; and

calculating a local magnification and/or a local distortion of the spectacle lens from the determined main curvatures and local wave front directions, with main beam course data and spectacle lens data.

24. The method of claim 23, wherein calculating the local magnification and/or the local distortion takes into account a finite distance of the object from the spectacle lens.

25. The method of claim 23, wherein at least one of the first and second surfaces is a rotationally asymmetrical surface, and the spectacle lens data comprise data with respect to rise heights and/or local curvatures of the at least one rotationally asymmetrical surface.

26. The method of claim 25, wherein the at least one rotationally asymmetrical surface is one of a progressive surface with a continuously changing refractive power between a far and a near reference point and an aspherical or atoric surface.

27. The method of claim 23, wherein the calculation of the local magnification and/or of the local distortion takes place by paraxial approximation.

28. The method of claim 23, wherein calculating the local magnification and/or the local distortion takes into account a non-paraxial course of the main beam.

29. The method of claim 23, wherein calculating the local magnification and/or the local distortion further comprises calculating a local magnification matrix from characteristics of the local wave front, and calculating magnification of the spectacle lens as an average value of Eigenvalues of the magnification matrix and the distortion is calculated as the difference between the Eigenvalues of the magnification matrix.

30. The method of claim 29, wherein the local magnification matrix is calculated according to following formulas set forth herein, wherein individual local factors or quantities are always evaluated at intersection points of the main beam with the respective surface of the spectacle lens,

$N_g^{-1}=\sigma$

·

N e - 1 

N s - 1 $N_e^{-1}=1-\frac{d}{n}<br><br>S_1^{\mathrm{\prime <br><br>}}$ $N_s^{-1}=1-e<br><br><br><br>S_2^{\mathrm{\prime <br><br>}}$ $S_2^{\mathrm{\prime <br><br>}}=S_2+D_2$ $S_2=N_e<br><br>S_1^{\mathrm{\prime <br><br>}}$ $S_1^{\mathrm{\prime <br><br>}}=S_1+D_1$ $S_1=\frac{1}{s_1}<br><br>1$

wherein;

σ

a indicates a scaling factor for taking into account a finite focal length s₁ calculated according to the formula

$\mathrm{\sigma <br><br>}=\frac{<br><br>s_1<br><br>}{<br><br>s_1+d+e<br><br>};<br><br>$

s₁ indicates a vector of a length s₁ in the light direction of the object-side main beam between an object viewed in a predetermined viewing direction and the intersection point (D1) of the main beam with the first surface,

d indicates a vector of the length d in the light direction of the main beam between the intersection point (D1) of the main beam with the first surface and the intersection point (D2) of the main beam with the second surface,

e indicates a vector of a length e in the light direction of the image-side main beam between the intersection point (D2) of the main beam with the second surface and the eye entrance pupil, eye the rotation point (Z′

) or the eye principal plane of the eye,

n indicates the refractive index of the spectacle lens,

N_e<sup>−

1</sup> indicates the local inverse matrix of the inherent magnification,

N_s<sup>−

1</sup> indicates the local inverse matrix of the system magnification,

S_i, i=1,2 indicates the local curvature matrix of the incident spherical wave front on the i-th surface of the spectacle lens,

S′

_i, i=1,2 indicates the local curvature matrix of the wave front after the refraction on the i-th surface of the spectacle lens,

D_i, i=1,2 indicates the local surface power matrix of the i-th surface of the spectacle lens which is calculated according to the formulas

$D_i=\left(\begin{array}{cc}{\mathrm{Sph}}_i-\frac{{\mathrm{Zyl}}_i}{2}<br><br>\cos <br><br><br><br>2<br><br>\mathrm{\psi <br><br>}<br><br><br><br>i& -\frac{{\mathrm{Zyl}}_i}{2}<br><br>\sin <br><br><br><br>2<br><br>\mathrm{\psi <br><br>}<br><br><br><br>i\\ \frac{{\mathrm{Zyl}}_i}{2}<br><br>\sin <br><br><br><br>2<br><br>\mathrm{\psi <br><br>}<br><br><br><br>i& {\mathrm{Sph}}_i+\frac{{\mathrm{Zyl}}_i}{2}<br><br>\cos <br><br><br><br>2<br><br>\mathrm{\psi <br><br>}<br><br><br><br>i\end{array}\right)$ ${\mathrm{Sph}}_i=\frac{\left(n-1\right)}{2}<br><br>\left(\frac{1}{r_i^a}-\frac{1}{r_i^b}\right)$ ${\mathrm{Zyl}}_i=\frac{\left(n-1\right)}{2}<br><br>\left(\frac{1}{r_i^a}-\frac{1}{r_i^b}\right),<br><br>i=1,2;<br><br>$

wherein

r_i^a,b, i=1,2 indicate the local main curvature radii of the i-th surface in the respective main beam intersection point (D1, D2) beam with the i-th surface of the spectacle lens, and

Ψ

_i indicates the angle between the normal vector p_i of the refraction plane at the i-th surface and the direction (q_i) in which the more curved main section extends.

31. The method of claim 30, wherein the local magnification matrix, the local inverse matrix of the inherent magnification, the local inverse matrix of the system magnification, the local curvature or vergency matrix of the incident spherical wave front on the first surface of the spectacle lens, the local curvature or vergency matrix of the wave front after the refraction at the i-th surface of the spectacle lens S′

_i, i=1,2 and the local curvature or vergency matrix S₂ of the wave front incident on the second surface of the spectacle lens are proportional to the unit matrix.

32. The method of claim 29, wherein the magnification matrix is calculated according to the following formulas, wherein the individual local factors or quantities are always evaluated at the main beam intersection points (D1, D2) with the respective surface of the spectacle lens,

$N_g^{-1}=\sigma$

·

R 1 - 1 

T 1 - 1 

N e - 1 

R 12 

T 2 - 1 

N s - 1 

R 2 $N_e^{-1}=1-\frac{d}{n}<br><br>S_1^{\mathrm{\prime <br><br>}}$ $N_s^{-1}=1-{\mathrm{eS}}_2^{\mathrm{\prime <br><br>}},$

wherein;

σ

a indicates a scaling factor for taking into account a finite focal length s₁ calculated according to the formula

$\mathrm{\sigma <br><br>}=\frac{<br><br>s_1<br><br>}{<br><br>s_1+d+e<br><br>};<br><br>$

s₁ indicates a vector of a length s₁ in the light direction of the object-side main beam between the object viewed in a predetermined viewing direction and the main beam intersection point (D1) with the first surface,

d indicates a vector of the length d₁ in the light direction of the main beam between the main beam intersection point (D1) with the first surface and the main beam intersection point (D2) with the second surface,

e indicates a vector of a length e in the light direction of the image-side main beam between the main beam intersection point (D2) with the second surface and the eye entrance pupil, the eye rotation point (Z′

) or the eye principal plane,

n indicates the refractive index of the spectacle lens,

N_e<sup>−

1</sup> indicates the local inverse matrix of the inherent magnification,

N_s<sup>−

1</sup> indicates the local inverse matrix of the system magnification,

and wherein

$R_1=R<br><br>\left({\mathrm{\phi <br><br>}}_1\right)=\left(\begin{array}{cc}\cos <br><br><br><br>{\mathrm{\phi <br><br>}}_1& -\sin <br><br><br><br>{\mathrm{\phi <br><br>}}_1\\ \sin <br><br><br><br>{\mathrm{\phi <br><br>}}_1& \cos <br><br><br><br>{\mathrm{\phi <br><br>}}_1\end{array}\right)$ indicates the 2 ×

2 rotation matrix within the plane perpendicular to the object- side main beam s₁ from the system of the first surface, defined by the normal vector p₁ perpendicular to the plane of refraction at the first surface, onto a suitable reference direction defined by the reference direction vector p₀ φ

₁ indicates the angle between the normal vector p₁ and the reference direction vector p₀ $R_2=R<br><br>\left({\mathrm{\phi <br><br>}}_2\right)=\left(\begin{array}{cc}\cos <br><br><br><br>{\mathrm{\phi <br><br>}}_2& -\sin <br><br><br><br>{\mathrm{\phi <br><br>}}_2\\ \sin <br><br><br><br>{\mathrm{\phi <br><br>}}_2& \cos <br><br><br><br>{\mathrm{\phi <br><br>}}_2\end{array}\right)$ indicates the 2 ×

2 rotation matrix within the plane perpendicular to the object- side main beam e from the system of the second surface, defined by the normal vector p₂ perpendicular to the plane of refraction at the second surface, onto a suitable reference direction p₀ φ

₂ indicates the angle between the normal vector p₂ and the reference direction vector p₀ $R_{12}=R<br><br>\left({\mathrm{\phi <br><br>}}_{12}\right)=\left(\begin{array}{cc}\cos <br><br><br><br>{\mathrm{\phi <br><br>}}_{12}& -\sin <br><br><br><br>{\mathrm{\phi <br><br>}}_{12}\\ \sin <br><br><br><br>{\mathrm{\phi <br><br>}}_{12}& \cos <br><br><br><br>{\mathrm{\phi <br><br>}}_{12}\end{array}\right)$ indicates the 2 ×

2 rotation matrix within the plane perpendicular to the main beam d between the surfaces of the spectacle lens, which transforms the normal vector p₁ into the normal vector p₂ φ

₁₂ indicates the angle between the normal vectors p₁ and p₂;

$\begin{array}{c}{T}_i=<br><br>C_i<br><br>{C^{\mathrm{\prime <br><br>}}}_i^{-1},i=1,2\\ C_i=<br><br>\left(\begin{array}{cc}\cos <br><br><br><br>{\mathrm{\alpha <br><br>}}_i& 0\\ 0& 1\end{array}\right),i=1,2\\ {C^{\mathrm{\prime <br><br>}}}_i=<br><br>\left(\begin{array}{cc}\cos <br><br><br><br>{{\mathrm{\alpha <br><br>}}^{\mathrm{\prime <br><br>}}}_i& 0\\ 0& 1\end{array}\right),i=1,2\end{array}\hspace{1em}<br><br>$ indicate the 2 ×

2 slope matrices for taking into account the influence that a oblique incidence of the main beam at the i-th surface of the spectacle lens has on the magnification;

α

_i indicates the incidence angle at the i-th surface of the spectacle lens, defined as the angle between the vector along main beam emerging from the i-th surface and the normal vector n_i, i = 1, 2 perpendicular to the i-th surface of the spectacle lens α

_i^′

indicates the angle of reflection at the i-th surface of the spectacle lens, defined as the angle between the vector along the main beam emerging from the i-th surface and the spectacle lens and the normal vector n_i, i = 1, 2 perpendicular to the i-th surface of the spectacle lens $S_1=\frac{1}{s_1}<br><br>1$ indicates the curvature or vergency matrix of the spherical wave front incident on the first surface S_i^′

= T_iS_iT_i + {tilde over (D)}_i indicates the local curvature or vergency matrices of the wave fronts after the refraction at the i-th surface of the spectacle lens, calculated according to the law of refraction while taking into account a main beam oblique angle of incidence S₂ = R₁₂<sup>−

1</sup>N_eS′

₁R₁₂ indicates the local curvature or vergency matrix of the wave front incident on the second surface which is calculated after the transfer from the first surface {tilde over (D)}_i = v_iC′

_i<sup>−

1</sup>D_iC′

_i<sup>−

1</sup> indicates the corrected local surface power matrix of the i-th surface of the spectacle lens, which takes into account a non-paraxial incidence of the wave front $D_i=\left(\begin{array}{cc}{\mathrm{Sph}}_i-\frac{{\mathrm{Zyl}}_i}{2}<br><br>\cos <br><br><br><br>2<br><br>{\mathrm{\psi <br><br>}}_i& -\frac{{\mathrm{Zyl}}_i}{2}<br><br>\sin <br><br><br><br>2<br><br>{\mathrm{\psi <br><br>}}_i\\ -\frac{{\mathrm{Zyl}}_i}{2}<br><br>\sin <br><br><br><br>2<br><br>{\mathrm{\psi <br><br>}}_i& {\mathrm{Sph}}_i+\frac{{\mathrm{Zyl}}_i}{2}<br><br>\cos <br><br><br><br>2<br><br>{\mathrm{\psi <br><br>}}_i\end{array}\right)$ indicates the local surface power matrix of the i-th surface of the spectacle lens ψ

_i indicates the angle between the normal vector p_i of the refraction plane at the i-th surface of the spectacle lens and the direction q_i into which the more curved main section extends ${\mathrm{Sph}}_i=\frac{\left(n-1\right)}{2}<br><br>\left(\frac{1}{r_i^a}+\frac{1}{r_i^b}\right),i=1,2$ indicates the spherical equivalent of the i-th surface of the spectacle lens ${\mathrm{Zyl}}_i=\frac{\left(n-1\right)}{2}<br><br>\left(\frac{1}{r_i^a}-\frac{1}{r_i^b}\right),i=1,2$ indicates the cylinder of the i-th surface of the spectacle lens r_i^a,b, i = 1, 2 indicates the main curvature radii of the i-th surface of the spectacle lens $v_1=\frac{n<br><br><br><br>\cos <br><br><br><br>{{\mathrm{\alpha <br><br>}}_1}^{\mathrm{\prime <br><br>}}-\cos <br><br><br><br>{\mathrm{\alpha <br><br>}}_1}{n-1}$ indicates the correction factor for taking into account the main beam oblique angle of incidence at the first surface (20). $v_2=\frac{\cos <br><br><br><br>{{\mathrm{\alpha <br><br>}}_2}^{\mathrm{\prime <br><br>}}-n<br><br><br><br>\cos <br><br><br><br>{\mathrm{\alpha <br><br>}}_2}{1-n}$ indicates the correction factor for taking into account the main beam oblique angle of incidence at the second surface.

33. The method of claim 23, wherein the local magnification and/or distortion of the spectacle lens is determined for a plurality of predetermined or predeterminable viewing directions.

34. The method of claim 23, further comprising:

collecting data relating to the spectacle lens, particularly data concerning a thickness, rising heights of a front face and a back face of the spectacle lens and/or a local curvatures of the front face and back face of the spectacle lens.

35. A computer program product that is designed, when loaded and executed on a computer, for implementing the method of calculating local magnification and/or local distortion of a spectacle lens in at least one predetermined or predeterminable viewing direction, the spectacle lens being configured for correcting a refractive deficit of an eye and having at least a first object-side surface and a second eye-side surface, comprising:

calculating a course of a main beam for the predetermined or predeterminable viewing direction, which main beam originates from a predetermined or predeterminable infinitesimally small object and, after refraction by the spectacle lens, passes through a rotation point of the eye, through eye entrance pupils or through an eye principal plane;

determining main curvatures and directions of a local wave front associated with the main beam on refraction by the spectacle lens; and

calculating a local magnification and/or a local distortion of the spectacle lens from the determined main curvatures and local wave front directions, with main beam course data and spectacle lens data.

36. A data carrier having a computer program stored thereon, wherein the computer program is designed, when loaded and executed on a computer, to carry out the method of calculating local magnification and/or local distortion of a spectacle lens in at least one predetermined or predeterminable viewing direction, the spectacle lens being configured for correcting a refractive deficit of an eye and having at least a first object-side surface and a second eye-side surface, comprising:

calculating a course of a main beam for the predetermined or predeterminable viewing direction, which main beam originates from a predetermined or predeterminable infinitesimally small object and, after refraction by the spectacle lens, passes through a rotation point of the eye, through eye entrance pupils or through an eye principal plane;

determining main curvatures and directions of a local wave front associated with the main beam on refraction by the spectacle lens; and

calculating a local magnification and/or a local distortion of the spectacle lens from the determined main curvatures and local wave front directions, with main beam course data and spectacle lens data.

37. A system for calculating a local magnification and/or a local distortion of a spectacle lens in at least one predetermined or predeterminable viewing direction, the spectacle lens being designed for correcting a refraction deficit of an eye and having at least a first object-side surface and a second eye-side surface, comprising:

collecting devices for the collection of data relative to the spectacle lens;

calculating devices for calculating by means of the data relative to the spectacle lens the course of a main beam for the predetermined or predeterminable viewing direction, the main beam originating from a predetermined or predeterminable infinitesimally small object and, after the refraction by the spectacle lens, extending through the rotation point of the eye, through the entrance pupil of the eye or through the principal plane of the eye;

calculating devices for calculating the main curvatures and directions of a local wave front pertaining to the main beam during the refraction by the spectacle lens; and

calculating devices for calculating the local magnification and/or the local distortion of the spectacle lens from the determined main curvatures and directions of the local wave front, the data of the course of the main beam and the data relative to the spectacle lens.

38. A method of producing a spectacle lens while taking into account a magnification and/or a distortion of the spectacle lens, the spectacle lens being designed for a correction of a refraction deficit of an eye and at least having a first object-side surface and a second eye-side surface, the method comprising a calculation or optimization step, the calculating or optimization step taking place such that a performance function F is minimized,

wherein

$\min $



F = min 

( ∑

i 

G V , i 

( N Ist 

( i ) - N Soll 

( i ) ) 2 + ( G Z , i 

( Z Ist 

( i ) - Z Soll 

( i ) ) 2 ) ) ,

and wherein

N_actual(i) indicates the actual magnification of the spectacle lens at the i-th evaluation point

N_des(i) indicates the desired magnification of the spectacle lens at the i-th evaluation point

G_v,j indicates the weighting of the magnification of the spectacle lens at the i-th evaluation point

Z_actual(i) indicates the actual distortion of the spectacle lens at the i-th evaluation point

Z_des(i) indicates the desired distortion at the i-th evaluation point, and

G_z,j indicates the weighting of the distortion at the i-th evaluation point.

39. The method of claim 38, wherein the weighting G_v,j of the magnification in the performance function F or the weighting Z_actual(i) in the performance function F is equal to zero.

41. The method of claim 38, wherein the calculation or optimization step takes place such that additionally the refraction errors and/or the astigmatic error of the spectacle lens are minimized.

40. A method of calculating local magnification and/or local distortion of a spectacle lens in at least one predetermined or predeterminable viewing direction, the spectacle lens being configured for correcting a refractive deficit of an eye and having at least a first object-side surface and a second eye-side surface, comprising:

calculating a course of a main beam for the predetermined or predeterminable viewing direction, which main beam originates from a predetermined or predeterminable infinitesimally small object and, after refraction by the spectacle lens, passes through a rotation point of the eye, through eye entrance pupils or through an eye principal plane,

determining main curvatures and directions of a local wave front associated with the main beam on refraction by the spectacle lens;

calculating a local magnification and/or a local distortion of the spectacle lens from the determined main curvatures and local wave front directions, with main beam course data and spectacle lens data; and

minimizing a performance function F, wherein

$\min <br><br><br><br>F=\min <br><br>\left(\begin{array}{c}\underset{i}{\sum <br><br>}<br><br>{G_{V,i}<br><br>\left(N_{\mathrm{Ist}}<br><br>\left(i\right)-N_{\mathrm{Soll}}<br><br>\left(i\right)\right)}^2+\\ \left(G_{Z,i}<br><br>{\left(Z_{\mathrm{Ist}}<br><br>\left(i\right)-Z_{\mathrm{Soll}}<br><br>\left(i\right)\right)}^2\right)\end{array}\right),$

and wherein

N_actual(i) indicates the actual magnification of the spectacle lens at the i-th evaluation point

N_des(i) indicates the desired magnification of the spectacle lens at the i-th evaluation point

G_v,j indicates the weighting of the magnification of the spectacle lens at the i-th evaluation point

Z_actual(i) indicates the actual distortion of the spectacle lens at the i-th evaluation point

Z_des(i) indicates the desired distortion at the i-th evaluation point, and

G_z,j indicates the weighting of the distortion at the i-th evaluation point.

42. A computer program product that is designed, when loaded and executed on a computer, for implementing a method of optimizing a spectacle lens while taking into account a magnification and/or a distortion of the spectacle lens, the method for the optimization of the spectacle lens comprising a calculation or optimization step which takes place such that the performance function F is minimized,

$\min $



F = min 

( ∑

i 

G V , i 

( N Ist 

( i ) - N Soll 

( i ) ) 2 + ( G Z , i 

( Z Ist 

( i ) - Z Soll 

( i ) ) 2 ) ) ,

wherein

N_actual(i) indicates the actual magnification of the spectacle lens at the i-th evaluation point,

N_des(i) indicates the desired magnification of the spectacle lens at the i-th evaluation point,

G_v,j indicates the weighting of the magnification of the spectacle lens at the i-th evaluation point,

Z_actual(i) indicates the actual distortion of the spectacle lens at the i-th evaluation point,

Z_des(i) indicates the desired distortion at the i-th evaluation point,

G_z,j indicates the weighting of the distortion at the i-th evaluation point.

43. A data carrier having a computer program stored thereon, wherein the computer program is designed, when loaded and executed on a computer, for implementing a method of optimizing a spectacle lens while taking into account the magnification and/or the distortion of the spectacle lens, the method of optimizing the spectacle lens comprising a calculating or optimizing step, the calculating or optimization step taking place such that a performance function F is minimized,

wherein

$\min $



F = min 

( ∑

i 

G V , i 

( N Ist 

( i ) - N Soll 

( i ) ) 2 + ( G Z , i 

( Z Ist 

( i ) - Z Soll 

( i ) ) 2 ) ) ,

and wherein

N_actual(i) indicates the actual magnification of the spectacle lens at the i-th evaluation point,

N_des(i) indicates the desired magnification of the spectacle lens at the i-th evaluation point,

G_v,j indicates the weighting of the magnification of the spectacle lens at the i-th evaluation point,

Z_actual(i) indicates the actual distortion of the spectacle lens at the i-th evaluation point,

Z_des(i) indicates the desired distortion at the i-th evaluation point,

G_z,j indicates the weighting of the distortion at the i-th evaluation point.

44. A system for producing a spectacle lens while taking into account a magnification and/or a distortion of the spectacle lens, which is designed for correcting a refraction deficit of an eye and has at least a first object-side and a second eye-side surface, wherein the system comprises:

collecting devices for collecting target data of a spectacle lens; and

calculating and optimizing devices for calculating and optimizing at least one surface of the spectacle lens, the calculation and optimization respectively taking place such that a performance function F is minimized,

wherein

$\min <br><br><br><br>F=\min <br><br>\left(\begin{array}{c}\underset{i}{\sum <br><br>}<br><br>{G_{V,i}<br><br>\left(N_{\mathrm{Ist}}<br><br>\left(i\right)-N_{\mathrm{Soll}}<br><br>\left(i\right)\right)}^2+\\ \left(G_{Z,i}<br><br>{\left(Z_{\mathrm{Ist}}<br><br>\left(i\right)-Z_{\mathrm{Soll}}<br><br>\left(i\right)\right)}^2\right)\end{array}\right),$

and wherein

N_actual(i) indicates the actual magnification of the spectacle lens at the i-th evaluation point,

N_des(i) indicates the desired magnification of the spectacle lens at the i-th evaluation point,

G_v,j indicates the weighting of the magnification of the spectacle lens at the i-th evaluation point,

Z_actual(i) indicates the actual distortion of the spectacle lens at the i-th evaluation point,

Z_des(i) indicates the desired distortion at the i-th evaluation point,

G_z,j indicates the weighting of the distortion at the i-th evaluation point.