Progressive addition lens based on a minimization model and design method

Abstract

The present application relates to a kind of based on the design method of minimizing model progressive multifocal lens.The front surface of the lens is progressive surface, and the back surface is standard spherical surface;According to the demand of the lens wearer, the preset optical power distribution and average curvature of the front surface of the lens are determined, the minimizing model that the sag of the front surface of the lens satisfies is constructed, and reasonable weight value is allocated to each area of the lens;By the average curvature and Gaussian curvature of the front surface of the lens, the correlation of maximum principal curvature, minimum principal curvature and surface sag is constructed, the minimizing model is solved, and the sag value of the front surface of the progressive multifocal lens is obtained.The progressive multifocal lens provided in the design scheme of the present application more effectively reduces the peripheral astigmatism under the condition that the optical power on the lens surface approximates the preset optical power, can control the maximum peripheral astigmatism within 75% add power, and improves the comfort of the lens wearer.

Description

Technical Field

[0001] This invention relates to a progressive multifocal lens based on a minimization model and its design method, belonging to the field of optical design technology. Background Technology

[0002] Progressive multifocal lenses are lenses whose surface power changes continuously due to the continuous change in surface curvature. The design steps of progressive multifocal lenses are as follows: (1) Determine the coordinates and power of the far and near points of vision, and determine the coefficients of the meridional beam curve polynomial according to the selected parameters to complete the design of the meridional line; (2) Solve the Laplace equation under the constraints of boundary conditions to obtain the contour line function; (3) Diffusion of the power on the meridional line to the entire lens surface through the contour line; (4) Determine the coordinates of the curvature center corresponding to each point of the lens, and then calculate the sag corresponding to each point through the spherical equation.

[0003] Prior to this invention, Chinese invention patent CN113253482A disclosed a two-segment meridional design method for progressive multifocal lenses. Although it can flexibly obtain meridional power variation curves of different shapes and design progressive multifocal lenses that meet user requirements, this design method may cause peripheral astigmatism to exceed one power, affecting the visual imaging effect. The literature "Design of Multi-Axis Progressive Zoom Glasses" (Optical Technology, 2015, 41(04):355-359) proposes a design method for multi-axis progressive multifocal lenses. It selects the actual pupil used by the human eye as the design element corresponding to the small pupil within the light-transmitting aperture of the glasses. On the meridional plane, the power between the far-vision point and the near-vision point of the lens needs to be determined by an 8th-order polynomial. On the pupil plane, the power of the pupils containing the far-vision zone and the adjacent near-vision zone are distributed in hyperbolic and parabolic types, respectively. Although this design method can make the surface optical power of the lens close to the preset optical power, the peripheral astigmatism of the lens is large. When the added power is 0.75D, the maximum peripheral astigmatism of the lens is close to 3.50D, which exceeds the limit that the human eye can tolerate. Summary of the Invention

[0004] This invention addresses the shortcomings of existing technologies by providing a progressive multifocal lens and its design method based on a minimization model that can more effectively reduce peripheral astigmatism while ensuring that the lens power is close to the preset power, and control the astigmatism within 75% of the added power.

[0005] The technical solution to achieve the objective of this invention is to provide a design method for a progressive multifocal lens based on a minimization model. The lens includes an effective visual area composed of a distance vision zone, a near vision zone, and a progressive channel; a peripheral astigmatism zone; and a weighted transition zone disposed between the effective visual area and the peripheral astigmatism zone. The rear surface of the lens is spherical, and the front surface is a progressive surface. The method is characterized by the following steps: (1) Construct a minimization model J(z(x,y)) that satisfies the front surface sagitta z(x,y): Where Ω is the integral domain of the surface; α(x,y) is the weighted distribution function related to astigmatism, β(x,y) is the weighted 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 front surface of the lens, respectively; P0(x,y) is the preset average curvature of the front surface of the lens. (2) Determine the preset average curvature P0(x,y) and optical power distribution P of the front surface of the lens. f (x,y): P0(x,y)=P f (x,y) / (n-1) P f (x,y)=P d (x,y)+(P n (x,y)-P d (x,y)) / (1+e (-k(A(x,y)-m) )) Where n is the refractive index of the lens; P d (x,y) represents the preset optical power for the distance viewing area; P n (x,y) is the preset optical power of the near vision zone; k is the curvature adjustment factor; A(x,y) is the distance from any point on the front surface of the lens to the center point of the front surface of the lens; m is the translation factor; (3) Using the average curvature H(x,y) and Gaussian curvature K(x,y) of the front surface of the lens, construct the relationship between the maximum principal curvature k1(x,y), the minimum principal curvature k2(x,y), and the surface sagitta z(x,y): H(x,y)=(k1(x,y)+k2(x,y)) / 2, K(x,y)=k1(x,y)*k2(x,y)), Where z(x,y) x z(x,y) y Let z(x,y) be the first-order partial derivative of the surface vector z(x,y) at any point on the front surface of the lens in the x and y directions, respectively; xx z(x,y) yy Let z(x,y) be the second-order partial derivative of the surface vector z(x,y) at any point on the front surface of the lens in the x and y directions, respectively; z(x,y) xy Let z(x,y) be the second partial derivative of the surface vector z(x,y) at any point on the front surface of the lens, first in the x direction and then in the y direction. (4) Calculating the sag value z(x,y) of the anterior surface of the progressive addition lens based on the minimization model J(z(x,y)) constructed in step (1).

[0006] In the design method of a progressive addition lens based on a minimization model according to the present invention, in the effective visual area of the lens, a high weight value is assigned to the weight distribution function related to astigmatism: 15<α(x,y)<25; in the peripheral astigmatism area of the lens, a low weight value is assigned to the weight distribution function related to astigmatism: 0<α(x,y)<1; in the weight transition area of the lens, convolution smoothing processing is adopted to make the weight distribution function related to astigmatism smoothly transition from a high weight value to a low weight value: 0.5<α(x,y)<20.

[0007] In the design method of a progressive addition lens based on a minimization model according to the present invention, in the effective visual area of the lens, a high weight value is assigned to the weight distribution function related to dioptric power: 15<β(x,y)<25; in the peripheral astigmatism area of the lens, a low weight value is assigned to the weight distribution function related to dioptric power: 0<β(x,y)<1; in the weight transition area of the lens, convolution smoothing processing is adopted to make the weight distribution function related to dioptric power smoothly transition from a high weight value to a low weight value: 0.5<β(x,y)<20.

[0008] In the design method of a progressive addition lens based on a minimization model according to the present invention, the value range of the curvature adjustment factor k is: 1<k<2; the value range of the translation factor m is: -3<m<0.

[0009] The technical solution of the present invention further comprises a progressive addition lens based on a minimization model obtained by the above design method.

[0010] In the technical solution of the present invention, the coordinate system is a Cartesian spatial rectangular coordinate system constructed with the center point of the anterior surface of the lens as the origin O, wherein the positive direction of the x-axis is horizontally right along the sagittal direction of the anterior surface of the lens, the positive direction of the y-axis is vertically upward along the meridional direction of the anterior surface of the lens, and the z-axis is perpendicular to the xoy plane and satisfies the right-hand rule with the x-axis and the y-axis.

[0011] Compared with the prior art, the beneficial effects of the present invention are: The progressive addition lens provided by the present invention constructs a minimization model of the main curvature difference and the mean curvature relative to the preset main curvature difference and mean curvature, and obtains the surface sag of the progressive addition lens through the correlation operation between the maximum main curvature, the minimum main curvature and the surface sag based on the mean curvature and Gaussian curvature of the anterior surface of the lens, which can more effectively reduce the peripheral astigmatism and control the maximum peripheral astigmatism within 75% of the add power while ensuring that the dioptric power of the lens approaches the preset dioptric power. Description of Drawings

[0012] Figure 1 This is a schematic diagram showing the regional distribution of progressive multifocal lenses; Figure 2 This is a front surface curvature distribution diagram of a progressive multifocal lens based on a minimization model provided in an embodiment of the present invention; Figure 3 This is a weight distribution diagram of the astigmatism-related function α(x,y) of a progressive multifocal lens based on a minimization model provided in an embodiment of the present invention. Figure 4 This is a weighted distribution diagram of the power-related function β(x,y) of a progressive multifocal lens based on a minimization model provided in an embodiment of the present invention. Figure 5 This is a sag diagram of a progressive multifocal lens based on a minimization model provided in an embodiment of the present invention; Figure 6 This is a sphericity distribution diagram of a progressive multifocal lens based on a minimization model provided in an embodiment of the present invention; Figure 7 This is a cylindrical power distribution diagram of a progressive multifocal lens based on a minimization model provided in an embodiment of the present invention.

[0013] Figure 1 In the middle: 1. Distant vision zone; 2. Near vision zone; 3. Progressive channel; 4. Peripheral astigmatism zone; 5. Weighted transition zone. Detailed Implementation

[0014] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0015] Example 1 This embodiment provides a progressive multifocal lens and its design method based on a minimization model.

[0016] See appendix Figure 1 This embodiment provides a region distribution map of a progressive multifocal lens based on a minimization model. The progressive multifocal lens includes a distance vision zone 1, a near vision zone 2, a progressive channel 3, a peripheral astigmatism zone 4, and a weighted transition zone 5. The distance vision zone 1, near vision zone 2, and progressive channel 3 together constitute the effective visual area. The distance vision zone is located in the upper region of the lens and is used for viewing distant objects; the near vision zone is located in the lower region of the lens and is used for viewing near objects; the progressive channel is located between the distance vision zone and the near vision zone and is used for viewing intermediate-distance objects; the peripheral astigmatism zone is mainly located on both sides of the progressive channel and the near vision zone and can affect the clarity of vision. The weighted transition zone is located between the effective visual area and the peripheral astigmatism zone. The weight distribution function of the weighted transition zone smoothly transitions from high weight values ​​to low weight values, which is beneficial for further reducing peripheral astigmatism.

[0017] In this embodiment, the rear surface of the lens is spherical, and the front surface is progressive. Based on the wearer's refraction results and lens fitting needs, the lens parameters are set as follows: Presbyopia prescription (plus diopter) 2D lens refractive index 1.53 <![CDATA[The predetermined power P of the distance vision area on the front surface d (x,y)]]> 2D <![CDATA[The predetermined power P in the near vision region of the front surface n (x,y)]]> 4D Optical power of the rear surface of the lens 4D Curvature adjustment factor k 1.8 Translation factor m -2

[0018] In this embodiment, the lens radius is 30mm, and the front surface of the lens is divided into a 61×61 matrix, with a distance of 1.0mm between each point.

[0019] In this embodiment, the coordinate system is a Cartesian rectangular coordinate system constructed with the center point of the front surface of the lens as the origin O. The positive x-axis is horizontal to the right along the arc direction of the front surface of the lens, the positive y-axis is vertically upward along the meridian direction of the front surface of the lens, and the z-axis is perpendicular to the xoy plane and satisfies the right-hand rule with the x-axis and y-axis.

[0020] The specific implementation steps for lens design are as follows: (1) Construct a minimization model J(z(x,y)) that satisfies the sagitta z(x,y) of the front surface of the lens, that is, the minimization model J(z(x,y)) of the principal curvature difference and mean curvature of the front surface of the lens with the preset principal curvature difference and mean curvature is: Where z(x,y) is the surface sagitta of the lens; Ω is the integral domain of the surface; α(x,y) is the weighted distribution function related to astigmatism, β(x,y) is the weighted 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 front surface of the lens; P0(x,y) is the preset average curvature of the front surface of the lens.

[0021] (2) Determine the preset average curvature P0(x,y) and optical power distribution P of the front surface of the lens. f (x,y): The average curvature P0(x,y) of the front surface of the lens is determined by the following formula: P0(x,y)=P f (x,y) / (n-1) Among them, P f (x,y) represents the preset optical power of the front surface of the lens, and n represents the refractive index of the lens.

[0022] Preset power distribution P on the front surface of the lens f (x,y) is determined by the following formula: P f (x,y)=P d (x,y)+(P n (x,y)-P d (x,y)) / (1+e (-k(A(x,y)-m) )) Among them, P d(x,y) represents the preset optical power for the distance viewing area; P n (x,y) is the preset optical power of the near vision zone; k is the curvature adjustment factor; A(x,y) is the distance from any point on the front surface to the center point of the front surface of the lens; m is the translation factor.

[0023] See appendix Figure 2 This embodiment provides a front surface curvature distribution map of a progressive multifocal lens based on a minimization model.

[0024] (3) Reasonably allocate the weight distribution function of the lens surface: Within the effective visual area of ​​the lens, a high weight value is assigned to the weight distribution function related to astigmatism: α(x,y) = 20; within the peripheral astigmatism region of the lens, a low weight value is assigned to the weight distribution function related to astigmatism: α(x,y) = 0.5; within the weight transition region of the lens, convolution smoothing is used to smoothly transition the weight distribution function related to astigmatism from high to low weight values: 0.5 < α(x,y) < 20. (See appendix) Figure 3 This is a weighted distribution diagram of the astigmatism-related function α(x,y) of a progressive multifocal lens based on a minimization model provided in this embodiment.

[0025] Within the effective visual area of ​​the lens, a high weight value is assigned to the weight distribution function related to optical power: β(x,y) = 20; within the peripheral astigmatic region of the lens, a low weight value is assigned to the weight distribution function related to optical power: β(x,y) = 0.5; within the weight transition region of the lens, convolution smoothing is used to smoothly transition the weight distribution function related to optical power from high to low weight values: 0.5 < β(x,y) < 20. See Appendix. Figure 4 This embodiment provides a weighted distribution diagram of the power-related function β(x,y) of a progressive multifocal lens based on a minimization model.

[0026] (4) After reasonably allocating the weight function of the lens surface, the maximum and minimum principal curvatures, namely k1(x,y) and k2(x,y), are connected with the surface sag z(x,y) through the average curvature H(x,y) and Gaussian curvature K(x,y). The relationships between the mean curvature H(x,y) and Gaussian curvature K(x,y) and the maximum principal curvature k1(x,y) and minimum principal curvature k2(x,y) are as follows: H(x,y)=(k1(x,y)+k2(x,y)) / 2 K(x,y)=k1(x,y)*k2(x,y)) The relationships between the mean curvature H(x,y) and Gaussian curvature K(x,y) and the surface sagitta z(x,y) are as follows: Where z(x,y) x and z(x,y) y Let z(x,y) be the first-order partial derivative of the surface vector z(x,y) at any point on the front surface of the lens in the x and y directions, respectively; xx and z(x,y) yy Let z(x,y) be the second-order partial derivative of the surface vector z(x,y) at any point on the front surface of the lens in the x and y directions, respectively; z(x,y) xy Let z(x,y) be the second-order partial derivative of the surface vector z(x,y) at any point on the front surface of the lens, first in the x-direction and then in the y-direction.

[0027] (5) By solving the minimization model, the sag value z(x,y) of the progressive multifocal lens is obtained.

[0028] See appendix Figure 5 This is a front surface sagittal distribution diagram of the progressive multifocal lens provided in this embodiment. It can be seen that the lens surface distribution is smooth and without abrupt changes.

[0029] See appendix Figure 6 This is a spherical power distribution diagram of the progressive multifocal lens provided in this embodiment. From the distance vision zone to the near vision zone, the optical power distribution on the lens surface shows a gradual trend without abrupt changes, and it meets the power requirements for the wearer to see clearly.

[0030] See appendix Figure 7 The cylindrical power distribution diagram of the progressive multifocal lens provided in this embodiment shows that the peripheral astigmatism area is concentrated on both sides of the progressive channel and the near vision zone, the astigmatism in the effective visual area is small, and the maximum astigmatism on the entire lens is controlled within 75% of the added power.

[0031] The results demonstrate that the progressive multifocal lens and design method based on the minimization model provided by this invention can more effectively reduce peripheral astigmatism and control the maximum peripheral astigmatism within 75% of the added power while ensuring that the lens power is close to the preset power.

Claims

1. A design method for a progressive multifocal lens based on a minimization model, wherein the lens comprises an effective visual area consisting of a distance vision zone (1), a near vision zone (2), and a progressive channel (3), a peripheral astigmatism zone (4), and a weighted transition zone (5) disposed between the effective visual area and the peripheral astigmatism zone; the rear surface of the lens is spherical, and the front surface of the lens is a progressive surface, characterized in that... Includes the following steps: (1) Construct the sagitta of the anterior surface of the lens Satisfactory Minimum Model : J z x y = ∫ Ω α x y k 1 x y - k 2 x y 2 - 0 2 + β x y k 1 x y + k 2 x y 2 - P 0 x y 2 d x d y in, For the integration domain of the surface; The weighted distribution function is related to astigmatism. The weighted distribution function is related to optical power; , These represent the maximum and minimum principal curvatures at various points on the front surface of the lens; The preset average curvature of the front surface of the lens; (2) Determine the preset average curvature of the front surface of the lens. and optical power distribution : in, The refractive index of the lens; The preset optical power for the distance viewing area; The preset optical power for the near field of view; Curvature adjustment factor; The distance from any point on the front surface of the lens to the center point of the front surface of the lens; The translation factor; (3) Average curvature of the front surface of the lens and Gaussian curvature Construct the maximum principal curvature Minimum principal curvature With surface sagitta Relationship: ， ； ， ； in, , The surface sagitta at any point on the front surface of the lens In respectively direction and First-order partial derivative in the direction; , The surface sagitta at any point on the front surface of the lens In respectively direction and Second-order partial derivative in the direction; The surface sagitta at any point on the front surface of the lens First After in the direction Second-order partial derivative in the direction; (4) Minimum model constructed according to step (1) The sag value of the front surface of the progressive multifocal lens was calculated. .

2. The design method for a progressive multifocal lens based on a minimization model according to claim 1, characterized in that: Within the effective visual area of ​​the lens, a high weight value is assigned to the weight distribution function related to astigmatism: 15< <25; Within the peripheral astigmatic region of the lens, assign low weight values ​​to the weight distribution function related to astigmatism: 0< <1; Within the lens weight transition region, convolution smoothing is used to smoothly transition the weight distribution function related to astigmatism from high weight values ​​to low weight values: 0.5< <20.

3. The design method for a progressive multifocal lens based on a minimization model according to claim 1, characterized in that: Within the effective visual area of ​​the lens, a high weight value is assigned to the weight distribution function related to optical power: 15< <25; Within the peripheral astigmatism region of the lens, assign low weight values ​​to the weighted distribution function related to optical power: 0< <1; Within the lens weight transition region, convolution smoothing is used to smoothly transition the weight distribution function related to optical power from high weight values ​​to low weight values: 0.5< <20.

4. The design method for a progressive multifocal lens based on a minimization model according to claim 1, characterized in that: Curvature adjustment factor The range of values ​​for is: 1 < <2.

5. The design method for a progressive multifocal lens based on a minimization model according to claim 1, characterized in that: Translation factor The range of values ​​for is: -3< <0.

6. A progressive multifocal lens based on a minimization model, obtained by the design method of claim 1.

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