Hybrid boundary contour line design method for progressive multi-focus ophthalmic lens

Abstract

The invention discloses a method for designing a mixed type boundary contour line of a progressive multi-focus ophthalmic lens, and belongs to the field of design of progressive multi-focus ophthalmic lenses. The method comprises the following steps: constructing a Laplacian equation, and selecting a mixed rectangular boundary as a boundary of the Laplacian equation; two nodes with adjustable positions are arranged on the right side edge of the second rectangular boundary; solving a Laplacian equation for the second rectangle by adopting a finite element method, and carrying out interpolation to obtain a contour line numerical matrix solution of the second rectangle; and combining the contour line numerical solutions of the first rectangle, the second rectangle and the third rectangle to obtain a contour line function numerical matrix solution of the hybrid rectangular region. According to the invention, the contour line mixed type boundary design method is utilized to greatly improve the use range of the far vision area and the near vision area of the ophthalmic lens again, reduce the astigmatism area and improve the optical performance of the lens; the contour line mixed type boundary design method provided by the invention can also be applied to the personalized design aspect of progressive multi-focus spectacle lenses.

Description

TECHNICAL FIELD

[0001] The present application relates to the progressive multi-focal ophthalmic lens design technology, in particular to a hybrid type boundary profile design method of the progressive multi-focal ophthalmic lens. BACKGROUND

[0002] The progressive multi-focal ophthalmic lens is an optical lens with continuous refractive power, which has the ability to correct the distance, intermediate and near vision at the same time, and is particularly suitable for the middle-aged and elderly population with weakened accommodation ability, so the market of the progressive multi-focal ophthalmic lens has broad application prospects.

[0003] The profile design is an important link in the design of the progressive multi-focal ophthalmic lens, after the meridian is determined, the refractive power on the meridian is extended to the whole lens through the profile equation, that is, the refractive power of the intersection point of the profile and the meridian is equal. The smoother the profile design is, the smoother the refractive power change of the progressive multi-focal ophthalmic lens is, that is, the larger the use range of the distance vision area and the near vision area is, and the smaller the peripheral astigmatism area is. Since the profile equation needs to satisfy the Laplace equation, according to the complexity of the selected boundary condition, the design method of the profile can be divided into analytical solution and numerical solution. For relatively simple boundary conditions, numerical solutions can be obtained, and a more representative design result is the conic equation. For relatively complex boundary conditions, only numerical solutions can be obtained, but due to the flexibility of the boundary condition setting, the numerical solution method is more conducive to the personalized design of the progressive multi-focal ophthalmic lens. At present, the more representative numerical design method is to set the boundary as a square boundary, and the boundary condition can be a polynomial function, a triangular polynomial function, an exponential polynomial function, etc., which is very flexible, but the shortcomings are that there are many rigid provisions for the boundary condition equation, the physical meaning is not clear, and the flexibility needs to be improved.

[0004] The progressive multi-focal ophthalmic lens can be divided into four functional areas, namely the distance vision area, the near vision area, the transition zone and the peripheral astigmatism area, wherein the peripheral astigmatism area belongs to the area that cannot be used due to the imaging distortion and blur or unclearness. Due to the limitation of the optical design principle, not only the peripheral astigmatism area is inevitable, but also the lens has inherent limitations such as the contradiction between the field of view range and the clarity, and the small use area of the distance vision area and the near vision area.

[0005] So far, although the design of the progressive multi-focal ophthalmic lens has made great progress, there is still much room for improvement in increasing the use range of the distance vision area and the near vision area and reducing the peripheral astigmatism area. SUMMARY

[0006] The purpose of the present application is to provide a hybrid type boundary profile design method of the progressive multi-focal ophthalmic lens.

[0007] Technical solution: The application discloses a hybrid boundary profile line design method of a progressive multifocal ophthalmic lens.

[0008] The Laplace equation is constructed, and a hybrid rectangular boundary is selected as the boundary of the Laplace equation, wherein the left side of the hybrid rectangular boundary is on the meridian line, and the other three sides are tangent to the ophthalmic lens.

[0009] Two position-adjustable nodes are arranged on the right side of the second rectangular boundary, and the boundary conditions of the two sides are a segmented function in a smooth transition function form.

[0010] The Laplace equation is solved by using the finite element method for the second rectangular boundary, and the profile line numerical matrix solution of the second rectangular boundary is obtained by interpolation.

[0011] The profile lines of the first rectangular boundary and the third rectangular boundary are determined according to the profile line of the second rectangular boundary.

[0012] The profile line function numerical matrix solution of the hybrid rectangular region is obtained according to the profile line numerical solutions of the first rectangular boundary, the second rectangular boundary and the third rectangular boundary.

[0013] Further, 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.

[0014] ,

[0015] Wherein, The profile line function is represented by a function form as follows:

[0016] ,

[0017] Wherein, for the left side of the second rectangular boundary, i is the order of the first high-order non-zero derivative of u with respect to x at the reference point A of the far vision area of the ophthalmic lens, j is the order of the first high-order non-zero derivative of u with respect to x at the reference point B of the near vision area of the ophthalmic lens, c m is a polynomial coefficient, l is the distance of the point A from the center point O of the ophthalmic lens, and h is the distance between the points A and B.

[0018] Further, the steps of solving the Laplace equation by using the finite element method for the second rectangular boundary and interpolating the profile line numerical matrix solution of the second rectangular boundary include:

[0019] The nodes arranged on the right side of the second rectangular boundary are denoted as the C point and the D point, the distance of the C point from the y-axis is l0, the distance between the C point and the D point is h0, and there is , ;

[0020] The boundary condition of the Laplace equation is constructed, and the boundary condition of the left side of the second rectangular boundary is expressed as:

[0021] ,

[0022] The boundary condition of the right side is expressed as:

[0023] ,

[0024] The boundary conditions of the top and bottom sides are straight line equations, and are expressed as:

[0025] .

[0026] Further, for the first rectangular region and the third rectangular region, the profile line distribution functions are constants, and are expressed as:

[0027] ,

[0028] Wherein, is the profile line of the first rectangle, is the profile line of the third rectangle.

[0029] Advantages: compared with the prior art, the present application has the following advantages:

[0030] 1. In the present application, the rectangular boundary of the profile line is divided into a mixed boundary composed of three sub-rectangular regions, different optical characteristic functions are given to different sub-regions, the second rectangular region in the middle is mainly responsible for the overall distribution of average optical power and divergence, the first rectangular region in the upper is mainly responsible for adjusting the use range of the distance vision zone, and the third rectangular region in the lower is mainly responsible for adjusting the use range of the near vision zone; since different optical characteristic functions are given to each sub-region, the use range of the distance vision zone and the near vision zone of the ophthalmic lens can be greatly improved, and the range of the astigmatic zone is reduced;

[0031] 2. In the present application, the meridian line is set as one of the rectangular boundaries, which is beneficial to control the smoothness of the profile line;

[0032] 3. In the present application, the function form of the boundary condition is set as a smooth and gradual function form, which has clear physical meaning and strong operability;

[0033] 4. In the present application, the node method is used to set the boundary condition function as a piecewise function, and the setting of the boundary condition is more flexible. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is a schematic diagram of the circular plane and the mixed rectangular boundary of the progressive multifocal ophthalmic lens of the present application.

[0035] Figure 2 is a boundary condition graph provided by an embodiment of the present application;

[0036] Figure 3 is a contour line isoline graph provided by an embodiment of the present application;

[0037] Figure 4 is a mixed rectangular boundary mean refractive power distribution graph provided by an embodiment of the present application;

[0038] Figure 5 is a mixed rectangular boundary divergence distribution graph provided by an embodiment of the present application;

[0039] Figure 6 is a non-partition single rectangular boundary mean refractive power distribution graph provided by an embodiment of the present application;

[0040] Figure 7 is a non-partition single rectangular boundary divergence distribution graph provided by an embodiment of the present application. DETAILED DESCRIPTION

[0041] 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, for the convenience of description, only the parts related to the embodiments of the present application are shown in the drawings, but not all the structures.

[0042] In the following description, specific details are set forth such as target system architectures, techniques in order to provide a thorough understanding of the embodiments of the present application. However, it will be apparent to one skilled in the art that the embodiments of the present application can be practiced without these specific details. In other instances, well-known structures, devices, circuits, and methods have been described in detail in order to avoid obscuring the description of the present application.

[0043] 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.

[0044] 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.

[0045] Furthermore, in the description of this application and the appended claims, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0046] References to "one embodiment" or "some embodiments" in this specification mean that one or more embodiments of this application include the target features, structures, or characteristics described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized.

[0047] The numerical design method for the contour line of a progressive multifocal ophthalmic lens described in this embodiment includes the following steps:

[0048] Step 1: Construct the Laplace equation by selecting a mixed rectangular boundary as the boundary of the Laplace equation.

[0049] The hybrid rectangle consists of a first rectangle, a second rectangle, and a third rectangle arranged from top to bottom. The top and bottom sides of each rectangle are equal to R, and the sum of the left side lengths of all rectangles is equal to 2R, where R is the lens radius. The first rectangle is mainly responsible for adjusting the range of vision in the distance vision zone, the second rectangle is mainly responsible for the overall distribution of average optical power and aberration, and the third rectangle is mainly responsible for adjusting the range of vision in the near vision zone. The area of ​​each sub-rectangle is adjustable, meaning that the top and bottom side lengths are fixed, while the left and right side lengths are adjusted.

[0050] like Figure 1 As shown in the diagram, the circle represents the circular plane of the ophthalmic lens. Point A is the reference point for the farsightedness zone of the lens, and point B is the reference point for the nearsightedness zone. The line connecting AB is the meridian. A Cartesian coordinate system is established with the center point O of the lens as the origin. The x-axis is set along the meridian, and the y-axis is perpendicular to the x-axis, with the positive direction of the x-axis downwards and the positive direction of the y-axis to the right. A rectangular boundary is selected as the boundary of the Laplace equation. The left side of the boundary lies on the meridian and also on the x-axis, while the other three sides are tangent to the lens. The mixed rectangular region is divided into three sub-rectangular regions: Ω1, Ω2, and Ω3, representing the first, second, and third rectangles, respectively. Side EF is the shared boundary of Ω1 and Ω2, and side GH is the shared boundary of Ω2 and Ω3. l is the distance from point A to the center point O of the lens, and h is the distance between point A and point B. The distance from side EF to the y-axis is r1, and the distance from side GH to the y-axis is r2. r1 and r2 are adjustable.

[0051] Step 2, two adjustable nodes are set on the right side of the rectangular boundary of the Ω2 region, and the boundary condition function is set as a piecewise function by using the nodes; the boundary condition adopts a smooth transition function form.

[0052] Further, the profile function satisfies the Laplace equation: ;

[0053] The function form of the boundary condition of the Laplace equation is:

[0054] ,

[0055] The above formula has good smooth transition characteristics, and a smooth transition equation group can be obtained:

[0056] ,

[0057] According to the above formula, the polynomial coefficients c m are solved.

[0058] wherein, for the left side of the rectangular boundary of the Ω2 region, 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 reference point of the distance vision zone of the ophthalmic lens, B is a reference point of the near vision zone of the ophthalmic lens, the line AB is a meridian, l is the distance of the point A from the center O of the lens, and h is the distance between A and B; the other three edges of the rectangular boundary of Ω2 are sequentially similar;

[0059] The nodes set on the right side of the rectangular boundary of Ω2 are denoted as points C and D, and the boundary condition function is set as a piecewise function by using the points C and D; wherein the distance of the point C from the y-axis is l0, the distance between the points C and D is h0, and , wherein R is the radius of the ophthalmic lens.

[0060] Further, the boundary condition of the Laplace equation is constructed, and the boundary condition on the left side of the meridian of the rectangular boundary of Ω2 is expressed as:

[0061] ,

[0062] The boundary condition on the right side of the rectangular boundary of Ω2 is expressed as:

[0063] ,

[0064] The boundary conditions on the top and bottom edges of the rectangular boundary of Ω2 are straight line equations, and are respectively expressed as:

[0065] ,

[0066] The first linear equation in equation is Figure 1 The second linear equation is the boundary condition of the bottom side of the rectangle. The linear equation is obtained according to the continuity and monotonicity of the profile function, because the function values at the four vertices of the rectangle must remain continuous, and the function values between adjacent two vertices must remain monotonic.

[0067] Step 3, the Laplace equation of the rectangle region Ω2 is solved by using the finite element method, and the numerical matrix solution of the profile of the rectangle region Ω2 is obtained after interpolation.

[0068] In this step, the finite element method is used to solve the Laplace equation of the rectangle region Ω2 by using the toolbox in the Mathematica software, and the execution time of the program is less than 1 minute. Since the obtained solution is in the form of a function, interpolation processing is also needed to obtain the numerical matrix solution of the profile of the region Ω2.

[0069] Step 4, for the regions Ω1 and Ω3, according to the continuity of the profile function, the profile distribution function is constant, which is respectively:

[0070] ,

[0071] The first equation is the profile function of the region Ω1 in equation Figure 1 , and the second equation is the profile function of the region Ω3 in equation Figure 1 .

[0072] Figure 1 In equation , the bottom side of Ω1 is EF, and the top side of Ω3 is GH, the distances of EF and GH to the y-axis are respectively r1 and r2, and r1 and r2 can be adjusted, and the adjustment range satisfies .

[0073] Further, according to the numerical solution of the profile of the regions Ω1, Ω2 and Ω3, the profile function of the mixed rectangular region is obtained .

[0074] The following examples further illustrate the superiority of the numerical design method of the profile of the progressive multifocal ophthalmic lens of the present application.

[0075] In one example, the related parameters of the progressive multifocal ophthalmic lens are as follows: the radius of the lens is , , , the optical power of point A is 6 diopters, the additional optical power is 2 diopters, and the refractive index of the ophthalmic lens material is , , , , .

[0076] Substituting the relevant parameters into the boundary condition expression for the Ω2 rectangle boundary, we obtain the following: Figure 2 The diagram shows the boundary condition curves for the left and right sides of the Ω2 rectangular region. C and D are nodes, and A and B are reference points for the far and near viewing areas, respectively. The Laplace equation for the Ω2 rectangular region is solved using the finite element method, and the numerical matrix solution of the Ω2 rectangular region's contour line is obtained after interpolation. The contour line functions of the Ω1 and Ω3 regions are interpolated to obtain numerical matrices. By merging the numerical matrices of the contour lines of the Ω1, Ω2, and Ω3 regions and utilizing the symmetry about the x-axis, the following is obtained: Figure 3 The contour map of the entire mirror surface shown is shown.

[0077] The solution from the contour line numerical matrix, processed according to the technical solutions disclosed in Chinese Invention Patent CN101661167A and US Patent US64861153, yields the following result: Figure 4 The average optical power distribution diagram shown and Figure 5 The astigmatism distribution diagram shown.

[0078] To visually demonstrate the improvement in the usable range of the far and near viewing zones, and the reduction in the astigmatic zone, this example provides an average optical power map and astigmatism map of a single rectangular boundary without partitioning for comparison. The example will use... and Change the value to , This involves extending the Ω2 region to the entire mixed rectangular region, or setting the areas of the Ω1 and Ω2 regions to zero and repeating the same calculation process as for the boundary of the mixed rectangle, resulting in the following... Figure 6 and Figure 7 The average optical power map and astigmatism map of the undivided single rectangular boundary are shown.

[0079] Compare Figure 4 and Figure 6 It can be seen that, relatively Figure 6 The coordinates of the intersection point of the contour line with an average optical power of 6 diopters and the y-axis are from... It dropped to The coordinates of the intersection point with the frame are approximately It dropped to approximately Therefore, for the usable range of the distance vision zone (here referring to the area enclosed by the isopleths of an average optical power of 6 diopter and the upper frame), the hybrid rectangular boundary contour design method of this invention increases the area by at least two times compared to the non-partitioned single rectangular boundary contour design method, which can also be clearly seen from the figure. Similarly, using the same comparison method, from... Figure 4 and Figure 6It can be seen that the use range of the near vision zone (here, the area surrounded by the 8 diopter contour and the lower frame) is at least increased by 2 times. It can also be seen from the figure that the use ranges of the far vision zone and the near vision zone are both increased to about 1 / 6 of the lens area. The above.

[0080] Comparison Figure 5 And Figure 7 With the 0.5 diopter contour as a reference, it can be seen that the relative Figure 7 The position of the highest point on the x-axis direction is lowered from -14 mm to about -9.5 mm, and the position of the lowest point is raised from 18.4 mm to about 14 mm. Therefore, the clear vision range is increased by more than 20%, reaching about 2 / 3 of the lens area, which can be directly observed from the figure.

[0081] In addition, the boundary conditions of the Ω2 region are set by the node method, and the use ranges of the far vision zone and the near vision zone can also be changed by adjusting the node positions. The use ranges of the far vision zone and the near vision zone can also be changed by changing the areas of the Ω1, Ω2 and Ω3 regions. Therefore, the mixed boundary profile line design method provided by the application can also be applied to the personalized design of progressive multifocal ophthalmic lenses.

[0082] In summary, in the mixed boundary profile line design method of the progressive multifocal ophthalmic lens, the rectangular boundary of the profile line is divided into a mixed boundary composed of three sub-regions, different optical property functions are assigned to different sub-regions, the central Ω2 region is mainly responsible for the overall distribution of the average optical power and the divergence, the upper Ω1 region is mainly responsible for adjusting the use range of the far vision zone, and the lower Ω3 region is mainly responsible for adjusting the use range of the near vision zone. Compared with the profile line design method without zoning and single rectangular boundary, the use ranges of the far vision zone and the near vision zone of the progressive multifocal ophthalmic lens provided by the application are both increased by more than 2 times, reaching more than 1 / 6 of the lens area; the clear vision range is increased by more than 20%, reaching about 2 / 3 of the lens area. Therefore, the mixed boundary profile line design method of the application greatly improves the use ranges of the far vision zone and the near vision zone of the ophthalmic lens, reduces the astigmatic zone, and improves the optical performance of the lens. The mixed boundary profile line design method provided by the application can also be applied to the personalized design of progressive multifocal ophthalmic lenses.

Claims

1. A method for designing a hybrid boundary profile for progressive multifocal ophthalmic lenses, characterized in that, include: Construct the Laplace equation by selecting the boundary of the hybrid rectangle as the boundary of the Laplace equation. The left side of the hybrid rectangle boundary is on the meridian, and the other three sides are tangent to the ophthalmic lens. The hybrid rectangle includes a first rectangle, a second rectangle, and a third rectangle distributed from top to bottom. The top and bottom side lengths of each rectangle are equal to R, and the sum of the left side lengths of each rectangle is equal to 2R, where R is the radius of the lens. The second rectangle has two adjustable nodes on its right side. The boundary conditions on both sides are piecewise functions with a smooth gradient. The Laplace equation is solved using the finite element method for the second rectangle, and the numerical matrix solution of the contour line of the second rectangle is obtained by interpolation. Based on the outline of the second rectangle, determine the outlines of the first and third rectangles; Based on the numerical solutions of the contour lines of the first, second, and third rectangles, the numerical matrix solution of the contour line function of the mixed rectangular region is obtained.

2. The method for designing a hybrid boundary contour of a progressive multifocal ophthalmic lens according to claim 1, characterized in that, Establish a Cartesian coordinate system with the center point O of the ophthalmic lens as the origin. Set the x-axis along the meridian and the y-axis perpendicular to the x-axis. The expression for the Laplace equation is: ， in, The contour line function has the following form: ， Where, for the left side of the second rectangular boundary, i is the order of the first higher-order non-zero derivative of u with respect to x at reference point A in the farsighted region of the eyeglass lens, j is the order of the first higher-order non-zero derivative of u with respect to x at reference point B in the nearsighted region of the eyeglass lens, and c m Here are the polynomial coefficients, l is the distance between point A and the center point O of the eyepiece, and h is the distance between points A and B.

3. The method for designing a hybrid boundary contour of a progressive multifocal ophthalmic lens according to claim 2, characterized in that, The steps for solving the Laplace equation using the finite element method for the second rectangle and interpolating to obtain the numerical matrix solution of the second rectangle's contour line include: The nodes set on the right side of the second rectangular boundary are denoted as points C and D. The distance from point C to the y-axis is l0, and the distance between points C and D is h0. And there exists... , ; The boundary conditions for the Laplace equation are constructed as follows: The boundary conditions on the left side of the second rectangular boundary are expressed as follows: ， The boundary conditions on the right side are expressed as follows: ， The boundary conditions for the top and bottom edges are linear equations, expressed as: 。 4. The hybrid boundary contour design method for a progressive multifocal ophthalmic lens according to claim 3, characterized in that, For both the first and third rectangular regions, the contour distribution function is a constant, expressed as: ， in, The outline of the first rectangle. This is the outline of the third rectangle.

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