Progressive multi-focus ophthalmic lens contour line numerical design method

Abstract

The invention discloses a progressive multi-focus ophthalmic lens contour line numerical design method, and relates to the field of progressive multi-focus ophthalmic lens design. According to the method, a contour line is designed based on a Laplacian equation numerical solution, the boundary of a selected equation is a rectangular boundary, the meridian is a long side of a rectangle, and the other three sides are tangent to a circular lens; segmenting the other long side of the rectangle by adopting a node method; constructing the function form of the boundary condition into a smooth gradually-changing function form; and solving a numerical solution of the Laplacian equation by adopting a nine-point difference format method. The progressive multi-focus ophthalmic lens provided by the invention has a far-vision area and a near-vision area with wide visual fields and an extremely short progressive channel, so that the effective vision range of the ophthalmic lens is greatly improved; according to the invention, rectangular boundary conditions are controlled by adopting a node method, so that the progressive multi-focus ophthalmic lens can meet different visual requirements of presbyopia wearers.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of progressive multifocal ophthalmic lens design, in particular to a numerical design method of a progressive multifocal ophthalmic lens profile line. BACKGROUND

[0002] The progressive multifocal lens gradually becomes the mainstream choice for presbyopia correction and has broad application prospects because it can correct distance, intermediate and near vision at the same time and has an attractive appearance.

[0003] In order to improve the visual experience of the wearer, the effective vision range of the distance vision zone, the near vision zone and the progressive channel zone should be as large as possible when designing the progressive multifocal ophthalmic lens, and the range of the astigmatic zone should be as small as possible. However, the performance of the progressive multifocal ophthalmic lens is affected by the meridian power design, the profile line design and the progressive surface sag equation design, etc. Therefore, the design is complex. In the prior art, part of the isochromatic lines of the power will form a closed curve on the lens surface. The area enclosed by the closed curve is the applicable range of the corresponding power. Since the curve is closed, the enclosed area is small. Therefore, the progressive multifocal ophthalmic lens has the problems of small vision range for part of the power and insufficient field of view. The area enclosed by the isochromatic line of 0.5 diopter astigmatism is less than half of the lens surface area, which means that the effective vision range of the lens is small and the utilization efficiency of the lens is low. In addition, the length of the progressive channel is not short enough, which affects the visual comfort experience of the wearer during the zooming process. SUMMARY

[0004] The present application aims to provide a numerical design method of a progressive multifocal ophthalmic lens profile line.

[0005] Technical scheme: The numerical design method of the progressive multifocal ophthalmic lens profile line comprises the following steps:

[0006] Constructing a Laplace equation, selecting a rectangular boundary as the boundary of the Laplace equation, and setting one long side of the rectangular boundary on the meridian line and the other three sides tangent to the ophthalmic lens;

[0007] Two position-adjustable nodes are arranged on the other long side of the rectangular boundary, and the boundary condition function is set as a segmented function by using the nodes; the boundary condition adopts a function form of smooth transition;

[0008] The Laplace equation is solved by using a nine-point difference format method to obtain a numerical solution of the profile line.

[0009] Further, the profile line function u(x, y) satisfies the Laplace equation:

[0010] The function form of the boundary condition of the Laplace equation is:

[0011]

[0012] For the long side of the rectangular boundary on the meridian, i is the order of the first high-order non-zero derivative of u with respect to x at point A, j is the order of the first high-order non-zero derivative of u with respect to x at point B, c m is a polynomial coefficient, A is a far vision zone reference point of the ophthalmic lens, B is a near vision zone reference point of the ophthalmic lens, AB is a meridian, l is a distance of the A point relative to the center O of the lens, and h is a distance between the A point and the B point;

[0013] A Cartesian coordinate system is established with the center point O of the ophthalmic lens as the origin, and the x-axis is arranged along the meridian, and the y-axis is perpendicular to the x-axis;

[0014] The nodes arranged on the other long side of the rectangular boundary are denoted as C and D, the distance of the C point to the y-axis is l0, the distance between the C point and the D point is h0, and l≤l0≤R and h≤h0≤2R, wherein R is the radius of the ophthalmic lens.

[0015] Further, the boundary conditions of the Laplace equation are constructed, and the boundary condition of the long side of the rectangular boundary on the meridian is expressed as:

[0016]

[0017] The boundary condition of the other long side of the rectangular boundary is expressed as:

[0018]

[0019] The boundary conditions of the two short sides of the rectangular boundary are straight line equations, and are expressed as:

[0020]

[0021] Further, the process of solving the Laplace equation by using the nine-point difference format method includes:

[0022] M-2 equidistant points are taken on one short side of the rectangular boundary, and N-2 equidistant points are taken on one long side of the rectangular boundary, excluding the vertices of the rectangle, and two clusters of parallel lines parallel to the coordinate axes are drawn through these points, thereby dividing the rectangle into (M-1)×(N-1) grids of equal size, and the parallel lines are referred to as grid lines, and the points where the grid lines intersect are referred to as grid points;

[0023] Suppose that the grid is a square with a side length of 1, and according to the nine-point difference format method, the contour line function value u i,j of the central grid point is expressed as:

[0024]

[0025] Wherein, i, j respectively represent the row and column number of the grid line, represent the coordinate position of the grid point, 2≤i≤M-1, 2≤j≤N-1;

[0026] The profile function value of the grid point on the rectangular boundary satisfies the boundary condition, and the initial value of other grid points is 0;

[0027] The profile function value u i,j The expression is calculated by loop calculation for i and j, and after the profile function value of each grid point tends to converge, the final profile numerical solution is obtained.

[0028] Advantages: compared with the prior art, the present application has the following advantages:

[0029] 1. In the present application, the meridian of the ophthalmic lens is used as the boundary, so that the smooth transition degree of the profile can be directly controlled;

[0030] 2. In the present application, the function form of the boundary condition is a smooth transition function form, so that the designed profile is more smooth and transition, and the effective vision range of the progressive multifocal ophthalmic lens can be greatly improved;

[0031] 3. In the present application, the node method is used to set the boundary condition function as a segmented function, so that the progressive multifocal ophthalmic lens which can meet the different visual needs of the wearer can be more conveniently designed. BRIEF DESCRIPTION OF DRAWINGS

[0032] Figure 1 is the schematic diagram of the progressive multifocal ophthalmic lens circular plane and Laplace equation rectangular boundary of the present application;

[0033] Figure 2 is the schematic diagram of the grid division of the Laplace equation rectangular boundary of the present application;

[0034] Figure 3 is the boundary condition curve diagram provided by embodiment 1 of the present application;

[0035] Figure 4 is the profile contour line diagram provided by embodiment 1 of the present application;

[0036] Figure 5 is the power diagram provided by embodiment 1 of the present application;

[0037] Figure 6 is the astigmatism diagram provided by embodiment 1 of the present application;

[0038] Figure 7 is the boundary condition curve diagram provided by embodiment 2 of the present application;

[0039] Figure 8 is the profile contour line diagram provided by embodiment 2 of the present application;

[0040] Figure 9 is the power map provided by the embodiment 2 of the present application;

[0041] Figure 10 is the astigmatism map provided by the embodiment 2 of the present application;

[0042] Figure 11 is the boundary condition curve map provided by the embodiment 3 of the present application;

[0043] Figure 12 is the contour line contour map provided by the embodiment 3 of the present application;

[0044] Figure 13 is the power map provided by the embodiment 3 of the present application;

[0045] Figure 14 is the astigmatism map provided by the embodiment 3 of the present application. DETAILED DESCRIPTION

[0046] The embodiments of the present application will be further described below in conjunction with the drawings and embodiments. It can be understood that the specific embodiments described herein are only used to explain the embodiments of the present application, but not to limit the embodiments of the present application. In addition, it should be noted that, in order to facilitate the description, only the parts related to the embodiments of the present application are shown in the drawings, but not all the structures.

[0047] In the following description, specific details are set forth such as target system architecture, techniques in order to provide a thorough understanding of the embodiments of the present application. However, it should be apparent to those skilled in the art that the embodiments of the present application can be practiced without these specific details. In other instances, well-known systems, structures, circuits, and techniques have been omitted in order not to obscure the description of the embodiments of the present application with unnecessary detail.

[0048] It should be understood that the term "comprising" as used in the specification and the appended claims indicates the presence of the recited features, integers, steps, operations, elements, and / or components, but does not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0049] It should also be understood that the term "and / or" as used in the specification and the appended claims indicates any combination of one or more of the associated listed items and all possible combinations of the items.

[0050] In addition, in the description of the specification and the appended claims, the terms "first", "second", and the like are only used to distinguish descriptions, and cannot be understood as indicating or implying relative importance.

[0051] Reference to "one embodiment" or "some embodiments" or "one implementation" or "some implementations" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. The appearances of the phrase "in one embodiment" or "in some embodiments" in various places in the specification are not necessarily all referring to the same embodiment, although it can. Furthermore, the particular features, structures, or characteristics can be combined in any suitable manner in one or more embodiments.

[0052] The profile numerical design method of the progressive multi-focal ophthalmic lens according to the embodiment comprises the following steps:

[0053] Step 1, constructing Laplace equation, selecting rectangular boundary as the boundary of Laplace equation, one long side of the rectangular boundary is on the meridian line, and the other three sides are tangent to the ophthalmic lens.

[0054] In one example, as shown in Figure 1 , the circle in the figure represents the circular plane of the ophthalmic lens, point A is the reference point of the far vision area of the ophthalmic lens, point B is the reference point of the near vision area of the ophthalmic lens, the line AB is the meridian line, and the Cartesian coordinate system is established with the center point O of the ophthalmic lens as the origin, the x-axis is arranged along the meridian line, and the y-axis is perpendicular to the x-axis. Select the rectangular boundary as the boundary of Laplace equation, one long side of the rectangular boundary is on the meridian line, i.e. the long side on the left is on the meridian line and also on the x-axis, and the other three sides are tangent to the ophthalmic lens. Figure 1 In the figure, l is the distance of point A from the center O of the lens, and h is the distance between points A and B.

[0055] Step 2, two position-adjustable nodes are arranged on the other long side of the rectangular boundary, and the boundary condition function is set as a piecewise function by using the nodes; the boundary condition adopts a function form of smooth transition.

[0056] Further, the profile function u(x, y) satisfies the Laplace equation:

[0057] The function form of the boundary condition of the Laplace equation is:

[0058]

[0059] The above equation has good smooth transition characteristics, and the smooth transition equation group can be obtained as follows:

[0060]

[0061] According to the above equation, the polynomial coefficients c m are solved.

[0062] Where, for the longer side of the rectangular boundary along the meridian, i is the order of the first higher-order non-zero derivative of u with respect to x at point A, j is the order of the first higher-order non-zero derivative of u with respect to x at point B, and c m For the polynomial coefficients, point A is the reference point for the farsighted zone of the eye lens, point B is the reference point for the nearsighted zone of the eye lens, the line connecting AB is the meridian, l is the distance of point A relative to the center point O of the lens, and h is the distance between A and B; the other three sides on the boundary of the rectangle are deduced in the same way.

[0063] Establish a Cartesian coordinate system with the center point O of the ophthalmic lens as the origin. The x-axis is set along the meridian, and the y-axis is perpendicular to the x-axis. The positive direction of the x-axis is downward, and the positive direction of the y-axis is to the right.

[0064] On the other long side of the rectangle boundary ( Figure 1 The nodes set on the right long side are denoted as C and D. The boundary condition function is set as a piecewise function using C and D. The distance from C to the y-axis is l0, the distance between C and D is h0, and l≤l0≤R, h≤h0≤2R, where R is the radius of the eye lens.

[0065] Furthermore, the boundary conditions for the Laplace equation are constructed. The boundary conditions for the longer side of the rectangular boundary along the meridian are expressed as follows:

[0066]

[0067] The boundary condition for the other longer side of the rectangle is expressed as:

[0068]

[0069] The boundary conditions for the two shorter sides of the rectangle are linear equations, expressed as follows:

[0070]

[0071] The equation of the first straight line is Figure 1 The boundary conditions for the upper shorter side of the rectangle are given first, and the boundary conditions for the lower shorter side of the rectangle are given for the second straight line. The equations of the shorter straight lines are obtained based on the continuity and monotonicity of the contour line function, because the function values ​​at the four vertices of the rectangle must remain continuous, while the function values ​​between two adjacent vertices must remain monotonic.

[0072] Step 3: Solve the Laplace equation using the nine-point difference scheme to obtain the numerical solution of the contour line.

[0073] Furthermore, the process of solving the Laplace equation using the nine-point difference scheme includes:

[0074] M-2 points are taken on one short side of the rectangular boundary at equal intervals, N-2 points are taken on one long side at equal intervals, excluding the vertices of the rectangle, two clusters of parallel lines parallel to the coordinate axes are drawn through these points, the rectangle is divided into (M-1)×(N-1) grids of equal size, the parallel lines are referred to as grid lines, and the points where the grid lines intersect are referred to as grid points, Figure 2 As shown in the figure, four adjacent grids are formed by nine grid points.

[0075] Suppose the grid is a square with a side length of 1, according to the nine-point difference format method, the contour line function value u i,j is expressed as:

[0076]

[0077] where i and j represent the row and column numbers of the grid lines respectively, representing the coordinate position of the grid point, 2≤i≤M-1, 2≤j≤N-1;

[0078] The contour line function value of the grid point on the rectangular boundary satisfies the boundary condition, and the initial value of the other grid points is 0;

[0079] The contour line function value u i,j is calculated by looping i and j, and then iteratively calculating, and after the contour line function value of each grid point converges, the final contour line numerical solution is obtained.

[0080] Example 1

[0081] In this example, the relevant parameters take the values: the radius of the lens R=30mm, l=4mm, h=14mm, the optical power of point A is 6 diopters, the additional optical power is 2 diopters, the refractive index of the ophthalmic lens material is n=1.56, l0=5mm, h0=15mm.

[0082] Substituting the relevant parameters into the boundary condition expression of the rectangular boundary, the boundary condition curve diagram of the two long sides (i.e. the left side and the right side) is obtained as shown in Figure 3 , where C and D are nodes, and A and B are reference points for the distance vision zone and the near vision zone respectively. The Laplace equation is solved by using the nine-point difference format method, and the contour line contour map is obtained as shown in Figure 4 .

[0083] The contour line numerical distribution function is obtained by processing according to the technical solutions disclosed in Chinese invention patent CN101661167B and American patent US64861153, and the optical power map is obtained as shown in Figure 5 , and the astigmatism map is obtained as shown in Figure 6 . From Figure 5 and Figure 6It can be seen that the optical power of each contour line in the lens range does not form a closed curve, which shows that the progressive multi-focal ophthalmic lens provided by the application has an open visual field range; the area surrounded by the 0.5 diopter astigmatism contour line is about half of the lens area, which shows that the progressive multi-focal ophthalmic lens provided by the application has a very large effective visual range; the length of the progressive channel is about 5 mm calculated from the inflection point of the 0.5 diopter astigmatism contour line, which shows that the progressive multi-focal ophthalmic lens provided by the application has an extremely short progressive channel, and the human eye has a very good comfort feeling in the process of zooming. Such optical performance cannot be simultaneously possessed by other progressive multi-focal ophthalmic lenses.

[0084] Example 2

[0085] Except that the positions of nodes C and D are different from those in Example 1, the design process is the same as that in Example 1.

[0086] Adjusting the position of the node, relative to Example 1, the position of node C is unchanged, and node D is moved to the bottom edge position, i.e. l0=5mm, h0=35mm, the boundary condition curve diagram is shown in Figure 7 Figure 3 It can be seen that, as node D moves towards the bottom edge, the smooth transition degree of the curve after the position of the previous D point decreases, and the smooth transition degree of the curve in the front section increases.

[0087] The contour line contour map, optical power map and astigmatism map are shown in Figure 8 , Figure 9 and Figure 10 It can be seen from Figure 9 and Figure 10 that when the position of node C is unchanged and node D moves towards the bottom edge, the progressive multi-focal ophthalmic lens provided in this example also has an open distance vision zone, near vision zone and extremely short progressive channel.

[0088] Comparing the optical power and astigmatism maps in Example 1, it can be seen that the progressive multi-focal ophthalmic lens in this example has a more open distance vision zone, but the effective vision range of the near vision zone is smaller accordingly. Therefore, improving the effective vision range of the distance vision zone is at the expense of the effective vision range of the near vision zone. By comparing the change in the size of the effective vision range with the smooth transition degree of the long side boundary condition analyzed before, it can be found that the higher the smooth transition degree, the larger the effective vision range. Therefore, by adjusting the position of the node to change the smooth transition degree of the long side boundary condition, the effective vision range of the distance vision zone and the near vision zone can be changed.

[0089] Example 3

[0090] Except that the positions of nodes C and D are different from those in Example 1 and Example 2, the design process is the same as that in Example 1. ​

[0091] Adjusting the node position, compared with Example 1, in this example the position of node D is unchanged, and node C is moved to the top edge position in the direction of the top edge, i.e. taking l0=30mm, h0=40mm. Compared with Example 2, the moving direction of the nodes in this example is opposite. The boundary condition curve diagram in this example is shown in Figure 11 Figure 3 It can be seen that, as node C is moved in the direction of the top edge, the smooth transition degree of the front section curve of the C point position before moving is reduced, and the smooth transition degree of the rear section curve is enhanced.

[0092] The contour line contour map, the power map and the astigmatism map are shown in Figure 12 , Figure 13 and Figure 14 It can be seen from Figure 13 and Figure 14 that, when the position of node D is unchanged and node C is moved in the direction of the top edge, the progressive multi-focal ophthalmic lens provided in this example also has an open distance vision zone, a near vision zone and an extremely short progressive channel.

[0093] Compared with the power and astigmatism maps of Example 1, it can be seen that the ophthalmic lens in this example has a more open near vision zone, but the effective vision range of the distance vision zone is correspondingly smaller. Therefore, improving the effective vision range of the near vision zone is at the expense of the effective vision range of the distance vision zone.

[0094] This example confirms the conclusion of Example 2: the change in the size of the effective vision range of the distance vision zone and the near vision zone is consistent with the smooth transition degree of the long side boundary condition, and the higher the smooth transition degree, the larger the effective vision range. Therefore, the method of adjusting the node position to change the smooth transition degree of the long side boundary condition to change the effective vision range of the distance vision zone and the near vision zone is indeed feasible.

[0095] The above examples provided by the present application prove that, compared with existing progressive multi-focal ophthalmic lenses, the progressive multi-focal ophthalmic lens designed by using the contour line numerical design method has a more open distance vision zone, near vision zone and shorter progressive channel.

[0096] The above examples provided by the present application also prove that, by using the node method to set the boundary condition, the effective vision range of the distance vision zone and the near vision zone can be changed by adjusting the position of the node. For example, if you want to have an open distance vision zone and near vision zone at the same time, the vertical coordinate positions of the two nodes C and D can be adjusted to be the same as the reference point A of the distance vision zone and the reference point B of the near vision zone, respectively, as shown in Figure 3 ​To obtain a wider far vision zone, the node C is kept unchanged and the node D is moved towards the bottom edge, but this will relatively reduce the effective near vision zone; to obtain a wider near vision zone, the node D is kept unchanged and the node C is moved towards the top edge, which will also relatively reduce the effective far vision zone. Therefore, the progressive multifocal ophthalmic lens can meet different visual requirements of presbyopic wearers.

Claims

1. A method of numerical design of a profile of a progressive addition spectacle lens, characterized in that, The application relates to a method for calculating the contour line function of an ophthalmic lens. The Laplace equation is constructed, a rectangular boundary is selected as the boundary of the Laplace equation, one long side of the rectangular boundary is on a meridian line, and the other three sides are tangent to the ophthalmic lens; Two position-adjustable nodes are arranged on the other long side of the rectangular boundary, and a boundary condition function is set as a segmented function by the nodes; the boundary condition adopts a smooth and gradual function form; A nine-point difference format method is adopted to solve the Laplace equation, and a numerical solution of the contour line is obtained.

2. The method of claim 1, wherein the step of determining the contour of the lens comprises the step of: The contour line function u(x, y) satisfies the Laplace equation: The function form of the boundary condition of the Laplace equation is: For the long side of the rectangular boundary on the meridian, i is the order of the first high-order non-zero derivative of u with respect to x at point A, j is the order of the first high-order non-zero derivative of u with respect to x at point B, c m are polynomial coefficients, A is a far vision zone reference point of the ophthalmic lens, B is a near vision zone reference point of the ophthalmic lens, AB is a meridian, l is the distance of point A relative to the center O of the ophthalmic lens, and h is the distance between points A and B. A Cartesian coordinate system is established with the center point O of the ophthalmic lens as the origin, the x-axis is arranged along the meridian line, and the y-axis is perpendicular to the x-axis; The nodes arranged on the other long side of the rectangular boundary are denoted as C point and D point, the distance from the C point to the y-axis is l0, the distance between the C point and the D point is h0, and l<=l0<=R and h<=h0<=2R, wherein R is the radius of the ophthalmic lens.

3. The method of claim 2, wherein the step of determining the contour line of the progressive addition spectacle lens is performed by using a computer program. The boundary condition of the Laplace equation is constructed, and the boundary condition of the long side of the rectangular boundary on the meridian line is expressed as: The boundary condition of the other long side of the rectangular boundary is expressed as: The boundary conditions of the two short sides of the rectangular boundary are straight line equations, and are expressed as:

4. The method for numerically designing the contour of a progressive multifocal ophthalmic lens according to claim 3, characterized in that, The process of solving the Laplace equation by adopting the nine-point difference format method comprises the following steps: M-2 equidistant points are taken on one short side of the rectangular boundary, and N-2 equidistant points are taken on one long side of the rectangular boundary, the points do not include the vertices of the rectangle, two clusters of parallel lines parallel to the coordinate axes are drawn through the points, the rectangular boundary is divided into (M-1) * (N-1) grids of equal size, the parallel lines are referred to as grid lines, and the points where the grid lines intersect are referred to as grid points; The grid is a square with a side length of 1. According to the nine-point difference format method, the contour line function value u of the center grid point is i,j is represented as: Wherein, i and j respectively represent the row and column numbers of the grid lines, represent the coordinate positions of the grid points, 2<=i<=M-1 and 2<=j<=N-1; The contour line function values of the grid points on the rectangular boundary satisfy the boundary condition, and the initial values of the other grid points are 0; The contour function value u i,j The expression is calculated in a loop for i, j, and then iteratively until the contour function value at each grid point converges to the final contour numerical solution.

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