Design method of free-form surface lens with optimized astigmatism
By designing baselines in both the horizontal and vertical directions of the lens, and by optimizing freeform lenses using translation and rotation techniques, the problem of mismatched field of vision in aspherical lenses has been solved, resulting in a lens design with a wider field of vision and greater wearing comfort.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- JIANGSU SHENGPU OPTICAL TECH CO LTD
- Filing Date
- 2026-02-10
- Publication Date
- 2026-04-17
AI Technical Summary
Existing aspherical lenses have a mismatch between the horizontal and vertical fields of vision, resulting in a decline in visual quality, and the problem of astigmatism at the lens edges has not been optimized.
By employing freeform surface technology, independent baselines are designed in the horizontal and vertical directions. The lens surface is obtained through translation and rotation. The nodes are redistributed using cubic spline interpolation to form a freeform surface lens that does not have rotational symmetry.
It improves the wearing comfort of the lens, with the central effective area reaching 1.33 times that of traditional aspherical lenses. The lens has a wider field of vision in the horizontal direction, which conforms to the actual eye use habits of the human eye and meets the needs of different scenarios.
Smart Images
Figure CN121879002A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a design method for freeform surface lenses with astigmatism optimization, belonging to the field of spectacle lens design technology. Background Technology
[0002] Currently, aspherical lenses have been accepted by the market, but existing aspherical lenses all share a common problem: decreased visual quality due to peripheral astigmatism. This invention optimizes peripheral astigmatism by employing freeform surface technology, thereby improving the peripheral visual effect of the lens.
[0003] Existing aspherical lenses, for single-vision applications, use the same aspherical parameters in both the horizontal and vertical directions, obtaining an aspherical surface by rotating the generatrix of the planar aspherical surface around the Z-axis. This method produces aspherical surfaces with rotational symmetry, meaning the cylindricality distribution is identical in all directions. However, the human eye's field of vision differs in the horizontal and vertical directions: the normal field of vision is 56 degrees upwards, 74 degrees downwards, 65 degrees nasally, and 91 degrees temporally. Simply put, the human eye has approximately 65 + 91 = 156 degrees of visual field horizontally, but only 56 + 74 = 130 degrees vertically. Therefore, the effective visual area of the human eye on glasses should correspond to this proportion for nearsightedness. However, current double-aspheric lenses have the same field of vision in all directions, which is clearly unreasonable. This invention uses freeform surface technology to directly design a larger visual area in the horizontal direction than in the vertical direction, thereby improving the wearing comfort of the lenses. See appendix. Figure 1 and Figure 2 The diagram shows a comparison between the cylindrical plot of a traditional double-non-linear surface and the cylindrical plot of a double-freeform surface with single light. Both plots use a resolution of 0.25D.
[0004] In view of the above-mentioned shortcomings, the present invention aims to create a design method for freeform surface lenses with astigmatism optimization, making them more valuable for industrial applications. Summary of the Invention
[0005] To address the aforementioned technical problems, the purpose of this invention is to provide a design method for astigmatism-optimized freeform surface lenses.
[0006] The present invention provides a design method for a freeform surface lens with astigmatism optimization, the specific design steps of which are as follows:
[0007] (1) Design a baseline in the Y direction: ; (2) Design a baseline in the X direction: ; (3) On the positive Y-axis, take an interval of dy and take m nodes at equal intervals. The coordinates corresponding to these m nodes are ; (4) For each node in the previous step, set up a path based on The curves correspond to each other, and each curve is exactly the same, only the position changes; the specific changes are as follows: First, perform a translation, the translation amount is... Then rotate it around the X-axis by a specific angle; The specific description is as follows: The curve corresponding to y=0 in the positive X-axis direction; taking intervals of dx, and selecting n nodes at equal intervals. The coordinates of these n nodes are ; when At that time, based on the above analysis, the corresponding nodes Perform translation and rotation to obtain the curve node data at the corresponding point: The translated point is: ; For ease of description and definition That is, the point after translation is ; The point after rotating around X is: ; Since it rotates around the X-axis, the x-coordinate remains unchanged, that is: ; corresponding According to the coordinate rotation formula, it can be expressed as: ; ; (5) For fixed Point set The equation of the curve is obtained by using cubic spline interpolation. The nodes in the Y direction are redistributed using this equation: Transformed into the original At this point Transform into points .
[0008] (6) Traverse according to the steps and methods described above. Obtain a new m n matrix data points Based on the obtained matrix data, the final design surface data can be obtained, and then a freeform surface lens with astigmatism optimization can be obtained.
[0009] Furthermore, in step (2), the effective diameter of the baseline in the X direction is greater than that in the Y direction, and the ratio of the effective diameter of the baseline in the X direction to the effective diameter of the baseline in the Y direction is 156:133.
[0010] Furthermore, in step (4), the rotation around the X-axis by a specific angle is along the Y-axis curve. At point The angle between the normal direction at a point and the Z-axis can be expressed as: , for The first derivative.
[0011] By means of the above-described solution, the present invention has at least the following advantages: (1) Under the same conditions, the effective area of the center is 1.33 times that of the traditional aspherical surface; (2) The lens is a true free-form surface and does not have rotational symmetry, so a positioning mark is required for assembly; (3) The lens has a wider field of vision in the horizontal direction than in the vertical direction, which is more in line with actual eye use habits; (4) Since different aspherical surfaces can be used in the horizontal and vertical directions, the design has more options to meet the needs of different scenarios.
[0012] The above description is merely an overview of the technical solution of the present invention. In order to better understand the technical means of the present invention and to implement it in accordance with the contents of the specification, the preferred embodiments of the present invention are described in detail below with reference to the accompanying drawings. Attached Figure Description
[0013] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show a certain embodiment of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.
[0014] Figure 1 It is a traditional double-non-cylindrical diagram; Figure 2 It is a cylindrical shape diagram of a traditional double freeform surface for single light; Figure 3 This is a schematic diagram illustrating the generation of the curved surface of this invention; Figure 4 This is a schematic diagram of the equivalent spherical power of the freeform surface lens with astigmatism optimization designed in Embodiment 1 of the present invention; Figure 5 This is a schematic diagram of the cylindricality of the freeform surface lens with astigmatism optimization designed in Embodiment 1 of the present invention. Detailed Implementation
[0015] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.
[0016] See Figure 1 and Figure 2 The preferred embodiment of this invention describes a method for designing a freeform surface lens for astigmatism optimization. Instead of using a rotating surface to obtain the final surface, it designs two baselines with two central effective areas in the vertical and horizontal directions of the lens, respectively. Then, one baseline is moved along the other to obtain the entire surface. During the movement, it is ensured that the plane of the moving baseline and the normal at the corresponding position of the fixed baseline are in the same plane. This is achieved through additional... Figure 3 To show; The surface designed in the above manner is a standard free surface and no longer has rotational symmetry: a positioning mark is required during assembly.
[0017] The following is a detailed design process for the curved surface: (1) Design a baseline in the Y direction according to the traditional aspherical design method: ; (2) Design a baseline in the X direction according to the traditional aspherical design method. The effective diameter of the baseline in the X direction is larger than that of the baseline in the Y direction. The ratio of the effective diameter of the baseline in the X direction to that of the baseline in the Y direction is 156:133, which is the same as the ratio of the horizontal field of view to the vertical field of view of the human eye.
[0018] The traditional aspherical design method is as follows: 1. Define an aspherical surface as the profile sag, specifically as a rotationally symmetric surface with the following equation: ; 2. Set the lens material refractive index to n, the lens forward curvature to F1, the total refractive power of the lens to F, and the distance from the rear surface of the lens to the center of rotation of the human eye to be... =27mm; 3. Calculate the following parameters:
[0019] 4. Calculate the refractive power of the lens posterior surface based on F1 and F: ; 5. Calculate X: ; 6. Calculate Y and N Y = -1, N = EX + FY; 7. Calculation , and
[0020] ; ; ; 8. Calculation results show the aspherical parameters: R, k: ; ; 9. Substitute the calculated data k and R into step (1) to determine the baseline.
[0021] (3) Since the surface is symmetrical about the X-axis and also about the Y-axis, we only need to consider the region where x≥0 and y≥0. On the positive Y-axis, we take an interval of dy and equidistant nodes m. The coordinates corresponding to these m nodes are .
[0022] (4) For each node in the previous step, there is a path based on The curve corresponding to this one is exactly the same, only the position changes, as follows: First, perform a translation, the translation amount is... Then rotate around the X-axis by a specific angle, which is along the Y-axis curve. At point The angle between the normal direction at a point and the Z-axis can be expressed as: , for The first derivative.
[0023] The specific description is as follows: Along the positive X-axis, take n nodes at equal intervals with an interval of dx. The coordinates of these n nodes are This is the curve corresponding to y=0. When At that time, based on the above analysis, the corresponding nodes are... Perform translation and rotation to obtain the curve node data at the corresponding point: The translated point is: ; For ease of description and definition That is, the point after translation is ; The point after rotating around X is: ; Because it rotates around the X-axis, the x-coordinate remains unchanged, that is: ; corresponding According to the coordinate rotation formula, it can be expressed as: ; ; (5) For fixed Point set The equation of the curve can be obtained using cubic spline interpolation. The nodes in the Y direction are redistributed using this equation: Transformed into the original At this point Transform into points .
[0024] (6) Traverse using the above method You can then obtain a new m n data points This is a standard m For n-matrix data, the final interpretation expression can be obtained using Lagrange interpolation.
[0025] The matrix data obtained in the previous step can be used to obtain the final design surface data, and then the freeform surface lens with astigmatism optimization can be obtained.
[0026] Example Example 1 The equation for the aspherical surface in this embodiment is: Where c = 1 / R; Actual lens design: refractive index n=1.597; spherical power sph=-8.00D.
[0027] 1. Design an aspherical baseline in the Y direction: R = 59.7, k = -0.4; 2. Design the aspherical baseline in the X direction: R = 74.625, k = -0.6; 3. In the Y direction, 36 nodes are selected at 1mm intervals, with a maximum Y value of 35. The coordinates corresponding to these 36 nodes and the coordinates corresponding to these m nodes are: ; 4. On the positive X-axis, take n nodes at equal intervals of 1. The coordinates of these n nodes are .
[0028] For Y=0, the above nodes are the corresponding moving curves.
[0029] For Y=1, Corresponding rotation angle Degree. For the original point set , … The set of points after translation and rotation is: , … .
[0030] ... For Y=35, Corresponding rotation angle Degree. For the original point set , … The set of points after translation and rotation is: , … .
[0031] 5. Based on each i-th column of the above dataset, construct a new dataset and reconstruct the Y-interval data using cubic spline interpolation.
[0032] 6. The final design surface data can be obtained from the matrix data obtained in the previous step, as shown in the attached figure. Figure 4 and attached Figure 5 As shown: Ultimately, a freeform surface lens with optimized astigmatism was obtained.
[0033] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method of designing an astigmatism-optimized freeform spectacle lens, characterized in that The specific design steps are as follows: (1) Design a baseline in the Y direction: ; (2) Design a baseline in the X direction: ; (3) On the positive Y-axis, take an interval of dy and take m nodes at equal intervals. The coordinates of these m nodes are ; (4) For each node in the previous step, set up a path based on The curves correspond to each other, and each curve is exactly the same, only the position changes; the specific changes are as follows: First, perform a translation, the translation amount is... Then rotate it around the X-axis by a specific angle; The specific description is as follows: The curve corresponding to y=0 in the positive X-axis direction; taking intervals of dx, and selecting n nodes at equal intervals. The coordinates of these n nodes are ; when At that time, based on the above analysis, the corresponding nodes Perform translation and rotation to obtain the curve node data at the corresponding point: The translated point is: ; For ease of description and definition That is, the point after translation is ; The point after rotating around X is: ; Since it rotates around the X-axis, the x-coordinate remains unchanged, that is: ； corresponding According to the coordinate rotation formula, it can be expressed as: ； ； (5) For fixed Point set The equation of the curve is obtained by using cubic spline interpolation. The nodes in the Y direction are redistributed using this equation: Transformed into the original At this point Transform into points ; (6) Traverse according to the steps and methods described above. Obtain a new m n matrix data points Based on the obtained matrix data, the final design surface data can be obtained, and then a freeform surface lens with astigmatism optimization can be obtained.
2. The design method for a freeform surface lens with astigmatism optimization according to claim 1, characterized in that: In step (2), the effective aperture of the baseline in the X direction is greater than that of the baseline in the Y direction, and the ratio of the effective aperture of the baseline in the X direction to that of the baseline in the Y direction is 156:
133.
3. The design method for a freeform surface lens with astigmatism optimization according to claim 1, characterized in that: The rotation around the X-axis by a specific angle mentioned in step (4) is along the Y-axis curve. At point The angle between the normal direction at a point and the Z-axis can be expressed as: , for The first derivative.