Multi-axis progressive addition lens and design method

Abstract

The present invention discloses a multi-axis progressive cyclofocal lens and a design method. A minimization model that satisfies the sag of the lens surface is constructed with the angles of multiple visual axes. By solving the minimization model, the sag value of the surface of the multi-axis progressive cyclofocal lens is obtained, and the surface shape of the lens is constructed. The multi-axis progressive cyclofocal lens provided by the design scheme of the present invention addresses the problem that traditional progressive multifocal lenses only have a single visual axis from the far vision zone to the near vision zone along the meridian direction, and cannot meet the problem that the visual axis rotates during the dynamic vision process of switching between far and near. The multi-axis progressive cyclofocal lens provides the human eye with the required optical power for dynamic vision along 360° multi-axis directions; and by making the optical power smoothly transition from the central fixed focus area to the peripheral defocus area and slowly increase, the peripheral astigmatism of the lens is mainly concentrated at the edge of the lens, reducing the degree of influence on the clear vision of the human eye.

Description

Technical Field

[0001] The invention relates to a multi-axis progressive cyclofocal lens and a design method thereof, belonging to the technical field of optical design. Background Art

[0002] Currently, adolescents with refractive errors primarily use two methods to correct their vision: wearing optical lenses such as glasses or contact lenses; or using methods such as excimer laser correction surgery to modify a specific refractive element of the eye. Single-vision lenses require proper adjustment for close-up vision. Long-term wear can lead to eye fatigue, worsening myopia, and eye deformation. Bifocal lenses cannot overcome the shift in focal power, resulting in image jumps. Progressive addition lenses continuously decrease in power from the distance zone through the transition zone to the near zone, minimizing eye fatigue and effectively alleviating near-distance vision. However, progressive addition lenses have blind spots on either side of the transition zone, which can affect clear distance vision. Furthermore, progressive addition lenses have a single visual axis, running along the meridian from the distance to the near zone, and are unable to accommodate the dynamic visual axis rotation experienced during distance and near-distance vision.

[0003] Before the present invention was made, the document “Design of Progressive Anchor-Focus Free-Form Surface Lenses” (Optical Technology, 2018, 44(04): 404-408.) proposed a design method for progressive anchor-focus free-form surface lenses, which constructs a multifocal lens from the perspective of peripheral defocus control and gradual change of optical power. A circular central fixed focus area is formed in the center of the lens, and multiple annular peripheral fixed focus areas are formed on the periphery. The optical power of the lens gradually changes from the inside to the outside along the lens meridian and the horizontal axis of the lens according to a set optical power high-order polynomial; based on the principle that the tangent planes of the edge points of adjacent fixed focus areas coincide, the sagittal heights of all points on the back surface of each fixed focus area are calculated in sequence from the inside to the outside, and then the back surface of the lens is generated based on the sagittal height data of all points on the back surface of all fixed focus areas. Although this design method can make the optical power and astigmatism of the lens meet the theoretical design requirements, it only has the visual axis along the horizontal and meridian directions of the lens, which cannot fully meet the needs of the human eye for dynamic vision. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the present invention provides a multi-axis progressive addition lens and a design method thereof, which can push peripheral astigmatism to the outer edge of the lens at a 360° multi-axis angle.

[0005] The technical solution to achieve the purpose of the present invention is to provide a design method for a multi-axis progressive annular lens, wherein the lens includes a central fixed focus area and a peripheral defocus area, and comprises the following steps:

[0006] (1) Construct a minimization model M(z(x,y)) that satisfies the lens surface sag z(x,y):

[0007]

[0008] Where z(x,y) is the sag value of each point on the lens surface; Ω is the integration domain of the surface; A(x,y) is the weight distribution function related to astigmatism, and B(x,y) is the weight distribution function related to optical power; k1(x,y) and k2(x,y) are the maximum and minimum principal curvatures corresponding to each point on the lens surface, respectively; C(x,y) is the preset average curvature of the lens surface.

[0009] (2) Determine the preset average curvature C(x,y) of the lens surface:

[0010] C(x,y)=P(x,y) / (n-1)

[0011] Where P(x,y) is the surface power of the lens; n is the refractive index of the lens;

[0012] (3) Determine the optical power distribution P(x,y) on the lens surface:

[0013] P(x,y)=P c (x,y)+(P o (x,y)-P c (x,y))*sin(π(pa) / 2(ba))

[0014] Among them, P c (x, y) is the preset optical power of the central fixed focus area; P o (x, y) is the maximum preset optical power of the peripheral defocus area; p is the distance from the center point of the lens to any point in the radial direction; a is the width adjustment factor of the central fixed focus area; b is the progressive optical power adjustment factor;

[0015] (4) Through the average curvature H(x,y) and Gaussian curvature K(x,y) of the lens surface, the relationship between the maximum principal curvature k1(x,y), the minimum principal curvature k2(x,y) and the surface sag z(x,y) is constructed:

[0016] H(x,y)=(k1(x,y)+k2(x,y)) / 2,

[0017]

[0018] K(x,y)=k1(x,y)*k2(x,y)),

[0019]

[0020] Among them, z(x,y) x, z(x, y) y are the first-order partial derivatives of the surface sag z(x, y) at any point on the lens surface in the x and y directions respectively; z(x, y) xx , z(x, y) yy are the second-order partial derivatives of the surface sag z(x, y) at any point on the lens surface in the x and y directions respectively; z(x, y) xy is the second-order partial derivative of the surface sag z(x, y) at any point on the lens surface first in the x direction and then in the y direction;

[0021] (5) Calculate the surface sag value z(x, y) of the multi-visual-axis progressive annular focus lens surface by using the minimized model M(z(x, y)) constructed in step (1).

[0022] In the present invention, a design method of a multi-visual-axis progressive annular focus lens is provided. In the central fixed-focus area of the lens with a radial distance of 0 < p ≤ 18, a low weight value is assigned to the weight distribution function related to astigmatism: 0 < A(x, y) < 1; in the peripheral defocus area of the lens with a radial distance of 18 < p ≤ 30, a high weight value is assigned to the weight distribution function related to astigmatism: 0 < A(x, y) < 40.

[0023] In the central fixed-focus area of the lens with a radial distance of 0 < p < 18, a high weight value is assigned to the weight distribution function related to the optical power: 295 < B(x, y) < 305; in the peripheral defocus area of the lens with a radial distance of 18 < p ≤ 26, a low weight value is assigned to the weight distribution function related to the optical power: 25 < B(x, y) < 35; in the peripheral defocus area of the lens with a radial distance of 26 < p ≤ 30, a high weight value is assigned to the weight distribution function related to the optical power: 295 < B(x, y) < 305. <​​​​​​​​​​​​This invention proposes a design method for a multi-axis progressive toric lens, based on multiple visual axes. This method provides the required optical power for dynamic vision along a 360-degree multi-axis direction. This addresses the problem of traditional progressive multifocal lenses, which only have a single visual axis along the meridian from the far to the near vision zone and cannot meet the requirements of the visual axis rotation during dynamic vision switching between far and near. Furthermore, by smoothly transitioning the optical power from the central fixed focus zone to the peripheral defocus zone, with a gradual increase in power, the peripheral astigmatism of the lens is primarily concentrated at the lens edge, reducing the impact on clear vision. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 Schematic diagram of the regional distribution of a multi-axis progressive addition cyclofocal lens provided by an embodiment of the present invention.

[0030] Figure 2 This is a surface curvature distribution diagram of a multi-axis progressive addition cyclofocal lens provided by an embodiment of the present invention.

[0031] Figure 3 4 is a weight distribution diagram of a function A(x, y) related to astigmatism of a multi-axis progressive addition cyclofocal lens provided by an embodiment of the present invention.

[0032] Figure 4 4 is a weight distribution diagram of a function B(x, y) related to the optical power of a multi-axis progressive addition cyclofocal lens provided by an embodiment of the present invention.

[0033] Figure 5 This is a sagittal diagram of a multi-axis progressive addition cyclofocal lens provided by an embodiment of the present invention.

[0034] Figure 6 This is a spherical power distribution diagram of a multi-axis progressive addition cyclofocal lens provided by an embodiment of the present invention.

[0035] Figure 7 This is a cylinder power distribution diagram of a multi-axis progressive addition cyclofocal lens provided by an embodiment of the present invention.

[0036] Figure 1 Center: 1. Center focused area; 2. Peripheral out-of-focus area. DETAILED DESCRIPTION

[0037] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0038] Example 1

[0039] This embodiment provides a multi-axis progressive addition lens and a design method.

[0040] See attached Figure 1, which is a regional distribution diagram of a multi-axis progressive toric lens provided in this embodiment. The multi-axis progressive toric lens includes a central fixed focus area 1 and a peripheral defocus area 2. The central fixed focus area is used to correct myopic defocus in the macular area, achieving clear vision; the peripheral defocus area introduces continuously varying optical power at different radial distances from the lens, forming myopic defocus in the peripheral area of ​​the retina, which has the effect of preventing and controlling myopia.

[0041] In this embodiment, based on the wearer's eye examination results and glasses fitting needs, the lens parameters are set as follows:

[0042] Preset optical power of the central fixed focus area -4.0D Maximum preset optical power in the peripheral out-of-focus area -3.0D Lens refractive index 1.53 Width adjustment factor a of the central focus area 18mm Progressive power adjustment factor b 24mm

[0043] In this embodiment, the lens radius is 30 mm, the lens surface is divided into a 61×61 matrix, and the distance between each point is 1.0 mm.

[0044] In this embodiment, the coordinate system is a Cartesian space rectangular coordinate system constructed with the center point of the lens surface as the origin O, the positive direction of the x-axis is horizontally to the right along the sagittal direction of the lens surface, the positive direction of the y-axis is vertically upward along the meridian direction of the lens surface, the z-axis is perpendicular to the xoy plane, and satisfies the right-hand rule with the x-axis and the y-axis.

[0045] The specific implementation steps of lens design are as follows:

[0046] (1) Construct the minimization model M(z(x,y)) that the lens surface sagittal height z(x,y) satisfies. That is, the minimization model M(z(x,y)) of the difference between the principal curvature and the average curvature of the lens surface and the preset principal curvature and the average curvature is shown in formula (1):

[0047]

[0048] Where z(x,y) is the sag value of each point on the lens surface; Ω is the integration domain of the surface; A(x,y) is the weight distribution function related to astigmatism, and B(x,y) is the weight distribution function related to optical power; k1(x,y) and k2(x,y) are the maximum and minimum principal curvatures corresponding to each point on the lens surface, respectively; C(x,y) is the preset average curvature of the lens surface.

[0049] (2) Determine the preset average curvature C(x,y) of the lens surface as shown in formula (2):

[0050] C(x,y)=P(x,y) / (n-1)(2)

[0051] Where P(x,y) is the surface power of the lens; n is the refractive index of the lens.

[0052] (3) Determine the optical power distribution P(x,y) on the lens surface as shown in formula (3):

[0053] P(x,y) = P c (x,y) + (P o (x,y) - P c (x,y)) * sin(π(p - a) / 2(b - a))(3)

[0054] Where, P c (x,y) is the preset optical power of the central focusing area; P o (x,y) is the maximum preset optical power of the peripheral defocus area; p is the distance from the center point of the lens to any point on the radial direction; a is the width adjustment factor of the central focusing area; b is the progressive optical power adjustment factor.

[0055] See Attachment Figure 2 , which is the surface curvature distribution diagram of a multi - visual - axis progressive annular - focus lens provided in this embodiment.

[0056] (4) Reasonably allocate the weight distribution function on the lens surface:

[0057] In the central focusing area of the lens, that is, within the radial distance 0 < p ≤ 18, assign a low weight value to the weight distribution function related to astigmatism: A(x,y) = 0.5; in the peripheral defocus area of the lens, that is, within the radial distance 18 < p ≤ 30, assign a high weight value to the weight distribution function related to astigmatism: A(x,y) = 30. See Attachment Figure 3 , which is the weight distribution diagram of the function A(x,y) related to astigmatism of a multi - visual - axis progressive annular - focus lens provided in this embodiment.

[0058] In the central focusing area of the lens, that is, within the radial distance 0 < p ≤ 18, assign a high weight value to the weight distribution function related to optical power: B(x,y) = 300; in the peripheral defocus area of the lens, within the radial distance 18 < p ≤ 26, assign a low weight value to the weight distribution function related to optical power: B(x,y) = 30; in the peripheral defocus area of the lens, within the radial distance 26 < p ≤ 30, assign a high weight value to the weight distribution function related to optical power: B(x,y) = 300. See Attachment Figure 4 , which is the weight distribution diagram of the function B(x,y) related to optical power of a multi - visual - axis progressive annular - focus lens provided in this embodiment.

[0059] (5) After reasonably allocating the weight function on the lens surface, establish a simultaneous relationship between the maximum and minimum principal curvatures, that is, k1(x,y) and k2(x,y), and the surface sag z(x,y) through the mean curvature H(x,y) and the Gaussian curvature K(x,y).

[0060] The relationships between the mean curvature H(x,y) and the Gaussian curvature K(x,y) and the maximum principal curvature k1(x,y) and the minimum principal curvature k2(x,y) are shown in equations (4) and (5) respectively:

[0061] H(x,y)=(k1(x,y)+k2(x,y)) / 2(4)

[0062] K(x,y)=k1(x,y)*k2(x,y))(5)

[0063] The relationship between the mean curvature H(x,y) and Gaussian curvature K(x,y) and the surface sag z(x,y) is shown in equations (6) and (7), respectively:

[0064]

[0065] Among them, z(x,y) x and z(x,y) y is the first-order partial derivative of the surface sagitta z(x,y) of any point on the lens surface in the x and y directions respectively; z(x,y) xx and z(x,y) yy is the second-order partial derivative of the surface sag z(x,y) of any point on the lens surface in the x and y directions respectively; z(x,y) xy It is the second-order partial derivative of the surface sag z(x,y) of any point on the lens surface, first in the x direction and then in the y direction.

[0066] (6) By solving the minimization model, the vector height value z(x,y) of the multi-axis progressive cyclofocal lens is obtained.

[0067] See attached Figure 5 , is a surface sagittal height distribution diagram of a multi-axis progressive addition cyclofocal lens provided in this embodiment. It can be seen that the surface distribution of the lens is smooth and has no sudden changes.

[0068] See attached Figure 6 , is a spherical power distribution diagram for a multi-axis progressive addition lens provided in this embodiment. At the center of the lens is a circular area with a focal power of -3.96D. The national standard tolerance for eyeglass lenses is ±0.12D. From the central fixed-focus area to the peripheral defocus area, the focal power distribution on the lens shows a progressive trend along the radial direction. There are no sudden changes in focal power across the entire lens, indicating that the focal power on the lens surface meets design requirements and provides the required focal power for clear vision along all 360° of the multi-axis directions.

[0069] See attached Figure 7 , is a cylindrical power distribution diagram of a multi-axis progressive addition cyclofocal lens provided in this embodiment; the astigmatism is mainly concentrated at the edge of the lens, and the astigmatism within the center range of the lens is small and approximately zero.

[0070] Results demonstrate that the multi-axis progressive addition lens and design method provided by the present invention provide the required optical power for dynamic vision along multiple visual axes over a 360-degree range. This addresses the problem that conventional progressive addition lenses only have a single visual axis along the meridian, running from the far to near vision zone, and are unable to meet the requirements of the visual axis's rotation during dynamic vision switching between near and far vision. Furthermore, by smoothly transitioning the optical power from the central fixed focus zone to the peripheral defocus zone, with a gradual increase in power, the lens's peripheral astigmatism is primarily concentrated at the lens edge, minimizing the impact on clear vision.

Claims

1. A method for designing a multi-axis progressive annular lens, wherein the lens comprises a central fixed focus area (1) and a peripheral defocus area (2), characterized in that It includes the following steps: (1) Construct a minimization model M(z(x, y)) satisfied by the sagittal height z(x, y) of the lens surface: where z(x, y) is the sagittal height value of each point on the lens surface; Ω is the integral domain of the surface; A(x, y) is the weight distribution function related to astigmatism, B(x, y) is the weight distribution function related to the optical power; k1(x, y) and k2(x, y) are the maximum and minimum principal curvatures corresponding to each point on the lens surface respectively; C(x, y) is the preset average curvature of the lens surface; (2) Determine the preset average curvature C(x, y) of the lens surface: C(x, y) = P(x, y) / (n - 1) where P(x, y) is the optical power of the lens surface; n is the refractive index of the lens; (3) Determine the optical power distribution P(x, y) of the lens surface: P(x,y)=P c (x,y)+(P o (x,y)-P c (x,y))*sin(π(pa) / 2(ba)) Among them, P c (x, y) is the preset optical power of the central focusing area; P o (x, y) is the maximum preset optical power of the peripheral defocus area; p is the distance from the center point of the lens to any point on the radial direction; a is the width adjustment factor of the central focusing area; b is the progressive optical power adjustment factor; the value range of the width adjustment factor a of the central focusing area is: 15 mm < a < 20 mm, and the value range of the progressive optical power adjustment factor b is: 20 mm < b < 25 mm; (4) Construct the correlation between the maximum principal curvature k1(x, y), the minimum principal curvature k2(x, y) and the surface sagittal height z(x, y) through the average curvature H(x, y) and the Gaussian curvature K(x, y) of the lens surface: H(x, y) = (k1(x, y) + k2(x, y)) / 2, K(x, y) = k1(x, y) * k2(x, y)), Among them, z(x,y) x 、z(x,y) y is the first-order partial derivative of the surface sagitta z(x,y) of any point on the lens surface in the x and y directions respectively; z(x,y) xx 、z(x,y) yy is the second-order partial derivative of the surface sag z(x,y) of any point on the lens surface in the x and y directions respectively; z(x,y) xy is the second-order partial derivative of the surface sag z(x,y) of any point on the lens surface, first in the x direction and then in the y direction; (5) According to the minimization model M(z(x, y)) constructed in step (1), calculate the sagittal height value z(x, y) of the multi - visual - axis progressive annular - focus lens surface.

2. The method for designing a multi-axis progressive addition lens according to claim 1, wherein: In the central focusing area of the lens with a radial distance of 0 < p ≤ 18, assign a low weight value to the weight distribution function related to astigmatism: 0 < A(x, y) < 1; in the peripheral defocus area of the lens with a radial distance of 18 < p ≤ 30, assign a high weight value to the weight distribution function related to astigmatism: 30 ≤ A(x, y) < 40.

3. The method for designing a multi-axis progressive addition lens according to claim 1, wherein: In the central focusing area of the lens with a radial distance of 0 < p < 18, assign a high weight value to the weight distribution function related to the optical power: 295 < B(x, y) < 305; in the peripheral defocus area of the lens with a radial distance of 18 < p ≤ 26, assign a low weight value to the weight distribution function related to the optical power: 25 < B(x, y) < 35; in the peripheral defocus area of the lens with a radial distance of 26 < p ≤ 30, assign a high weight value to the weight distribution function related to the optical power: 295 < B(x, y) < 305.

4. A multi - visual - axis progressive annular - focus lens obtained by the design method according to claim 1.

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