A method for manufacturing a freeform toric lens

Abstract

This invention discloses a method for fabricating a free-form torus lens. The method enhances the degree of freedom by optimizing the meridians at multiple different angles within the entire plane point-by-point. The method includes the following steps: S1, constructing a simplified lens eye model; S2, determining the optical power F2 and the radius of curvature r at the vertices. 20 This invention calculates the free torus coefficients of the vertical and horizontal meridians. Then, due to the rotational symmetry of the lens, it only considers the first quadrant of the surface, dividing the first quadrant into regions at fixed angles. For each region, a meridian is taken. The free torus coefficients of all meridians except the horizontal and vertical directions are calculated using a formula about the angle of the taken meridian. The calculated free torus coefficients are then substituted into the formula for a hypercurvature quadratic surface. Finally, the surface shape of the free torus is determined based on the sag data of each point on the taken meridian. The resulting lens is thinner, the image is clearer, and the wearing comfort is higher.

Description

Technical Field

[0001] This invention relates to the field of lens technology, specifically to a method for manufacturing a free-circular torus lens. Background Technology

[0002] The eyes are an important organ for people to obtain information. In order to obtain external information clearly and accurately, teenagers with myopia must improve their vision system by correcting refractive errors. There are usually two methods: one is to wear optical lenses, including eyeglasses and contact lenses; the other is to change a refractive element of the eye, such as by using excimer laser correction surgery.

[0003] Furthermore, with the development of the times, people's requirements for lens design are no longer limited to simply being able to see clearly; they also demand greater personalization, innovation, and comfort. Ordinary endoscopic non-refractive (EMN) and double non-refractive (BNR) lenses only optimize along two meridians, offering limited freedom and failing to better control aberrations, thus affecting the visual experience. Moreover, for individuals with complex vision correction needs, traditional lenses may not provide optimal vision correction. The visible area of ​​traditional lenses is usually relatively small, meaning that the field of vision at the periphery may be limited. Summary of the Invention

[0004] The purpose of this invention is to provide a method for manufacturing a free-circular toroidal lens to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a method for manufacturing a free-circular torus lens, which improves the degree of freedom by optimizing the meridians at multiple different angles within the entire plane point by point. This manufacturing method includes the following steps:

[0006] S1. Construct a simplified mirror eye model;

[0007] S2, Determine the optical power F2 and radius of curvature r of the vertex. 20 ;

[0008] S3. Calculate the main aberrations that affect image quality: oblique astigmatism, field curvature, and distortion;

[0009] S4. Point-by-point optimization using a recursive algorithm: Since oblique astigmatism has the greatest impact on image sharpness, it is considered the primary aberration to be corrected when designing lenses. Oblique astigmatism compensation is performed, and the above operation is repeated for points on the two meridians. Point-by-point optimization is carried out using a recursive algorithm, where:

[0010]

[0011]

[0012] Where y2 and x2 are the heights of the intersection points of the light rays with the horizontal and vertical meridians of the lens surface, that is, the height of the outgoing light rays from the optical axis, and T is the tangential optical power error in the directions of the vertical and horizontal meridians.

[0013] S5. Calculate the free toroidal surface coefficients: Due to the rotational symmetry of the lens, consider dividing the first quadrant of the surface into regions every 10°. Take one meridian for each region, for a total of 10 meridians. Calculate the free toroidal surface coefficients excluding horizontal and vertical ones, using the following formula:

[0014]

[0015] Where θ represents the rotation angle of the meridian relative to the horizontal direction;

[0016] S6. Correcting Field Curvature and Distortion: Substitute the surface coefficients of each meridian obtained above into the sagittal formula, which is based on the hypercurvature quadratic surface formula and corrected with multiple higher-order terms, to obtain discrete data points. Finally, the surface after free torus is reconstructed using the least squares method, as shown in the following formula:

[0017]

[0018] Among them, c x and c y Let c represent the curvature in the x and y directions, respectively. x =c y =1 / r 20 r represents the height of the incident ray on the surface, B, C, D, and E are higher-order coefficients of the free torus, and x and y represent the coordinates of the projection of a point on the surface along the z-axis onto the xoy plane.

[0019] As a further improvement of the present invention, step S1 specifically involves the following steps:

[0020] Establish a three-dimensional rectangular coordinate system with the vertex of the front surface of the lens as the origin, so that the center of the lens falls on the z-axis, and the vertical meridian of the lens is parallel to the y-axis, and the horizontal meridian of the lens is parallel to the x-axis.

[0021] As a further improvement of the present invention, the specific steps in step S2 are as follows:

[0022] The front and back surfaces of the lens are both set as spherical, and the radius of curvature r is determined according to the given base curvature F1. 10 The optical power F2 and radius of curvature r at the back surface vertex are determined by the center thickness d and refractive index n. 20 Since the designed lens does not have astigmatism, the optical power of the front and rear surfaces is equal in both the horizontal and vertical directions.

[0023] As a further improvement of the present invention, the r 10 =1000(n-1) / F1

[0024] r 20 =1000(1-n) / F2

[0025] Where n is the refractive index of the lens medium.

[0026] As a further improvement of the present invention, P in step S4 B and P C These are the free torus coefficients of the meridians in the vertical and horizontal directions, respectively.

[0027] As a further improvement of the present invention, the method for calculating oblique astigmatism, field curvature, and distortion in step S3 is as follows: at a 30° field of view, starting from the center of eye rotation, first, reverse tracing is performed on the vertical and horizontal meridians to calculate the intersection point y2 of the light ray with the vertical meridian of the rear surface and the intersection point x2 of the light ray with the horizontal meridian. Then, the tangential oblique vertex spherical focal length f of the lens is obtained by forward ray tracing. T And the focal length f of the spherical vertex of the axial direction S Then, the tangential optical power F is calculated. T and the directional optical power F S Subtracting F2 from T and S gives the tangential error T and the sagittal error S, which in turn allows us to calculate the main aberrations affecting image quality: oblique astigmatism (OAE), field curvature (MOE), and distortion.

[0028] As a further improvement of the present invention, in step S4, the operation is repeated to remove points other than the 30° field of view.

[0029] As a further improvement of the present invention, B, C, D, and E can be solved using Zemax software.

[0030] Compared with the prior art, the beneficial effects of the present invention are:

[0031] This invention first constructs a simplified lens-eye model, establishing a three-dimensional rectangular coordinate system with the vertex of the lens's front surface as the origin. Then, ray tracing is used to optimize the two meridians in the horizontal and vertical directions point by point, obtaining the free torus coefficients of the vertical and horizontal meridians. Due to the rotational symmetry of the lens, only the first quadrant of the surface is considered. The first quadrant is divided into regions at fixed angles, and a meridian is taken from each region. The free torus coefficients of the meridians other than the horizontal and vertical directions are obtained using the formula about the angle of the taken meridian. The obtained free torus coefficients are then substituted into a formula based on the hypercurvature quadratic surface formula and corrected with higher-order coefficients to determine the sag. Finally, the surface shape of the free torus surface is determined based on the sag data of each point on the taken meridian. The resulting lens is thinner, the image is clearer, and the wearing comfort is higher.

[0032] Figure 1 This is a schematic diagram of the lens optimization principle A of the present invention;

[0033] Figure 2 This is a schematic diagram of the lens optimization principle B of the present invention;

[0034] Figure 3 This is a comparison diagram of the distortion of the free-circular torus lens of the present invention and a spherical lens of the same specification;

[0035] Figure 4 This is a comparison diagram of the OAE (Optical Image) of the free-circular torus lens of the present invention and a spherical lens of the same specification.

[0036] Figure 5 This is a comparison diagram of the MOE (Modular Optical Equivalent) of the free-circular torus lens of the present invention and a spherical lens of the same specifications. Detailed Implementation

[0037] To make the technical problems to be solved, the technical solutions, and the beneficial effects of the present invention clearer, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.

[0038] It should be noted that when an element is referred to as "fixed," "mounted," "connected," or "set" with another element, it can be directly on or indirectly on the other element. It should be understood that the terms "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientation or positional relationships, are based on the orientation or positional relationships shown in the accompanying drawings and are only for the convenience of describing the invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention.

[0039] As a further improvement of the present invention, the terms "first," "second," "third," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature.

[0040] Example 1

[0041] Please refer to 1-5. This invention provides a technical solution: a method for manufacturing a free-circular lens, which improves the degree of freedom by optimizing the meridians at multiple different angles within the entire plane point by point. This manufacturing method includes the following steps:

[0042] S1. Establish a three-dimensional rectangular coordinate system with the vertex of the front surface of the lens as the origin, so that the center of the lens falls on the z-axis, and the vertical meridian of the lens is parallel to the y-axis, and the horizontal meridian of the lens is parallel to the x-axis.

[0043] S2. Set both the front and rear surfaces of the lens as spherical surfaces, and determine the optical power F2 at the vertex of the rear surface and the radius of curvature r20 based on the given base curve F1, radius of curvature r10, center thickness d and refractive index n. Since the designed lens does not have astigmatism, the optical power of the front and rear surfaces in the horizontal and vertical directions is equal.

[0044] S3. Calculate the main aberrations affecting image quality: oblique astigmatism, field curvature, and distortion. Then, use a geometric ray tracing algorithm, such as... Figure 2 As shown, the incident ray is obliquely incident at u' = 30°, passes through the center of rotation and intersects the vertex sphere at K, and intersects the inner and outer surfaces of the lens at points B2 and B1 respectively. The magnitudes of the incident angle i and the exit angle i' of the incident ray on each surface can be calculated using the standard equation for ray path calculation. The following equations are applicable to both the front and back surfaces.

[0045]

[0046]

[0047]

[0048]

[0049] Where n and n' are the refractive indices of the incident and exiting media, respectively; i and i' are the incident and exit angles of the light rays on the surface, respectively; u and u' are the angles between the incident and exiting rays and the optical axis, respectively; l and l' are the horizontal distances between the intersection points of the incident and exiting rays with the optical axis and the intersection points of the incident and exiting rays with the lens surface, respectively; and r0 is the radius of curvature of the lens surface.

[0050] Then, the coordinates of the intersection points of the light rays with each surface are obtained by tracing the light rays in the forward direction, and the positions of the meridional image and the sagittal image are calculated by using the Coddington equation. Then, the main aberrations that affect the image quality are calculated: oblique astigmatism (OAE), field curvature (MOE) and distortion.

[0051]

[0052]

[0053] Where s and s' are the sagittal object distance and image distance, respectively, t and t' are the meridional object distance and image distance, respectively, and r S and r T These are the radii of curvature of the sagittal plane and the meridional plane, respectively.

[0054] Specifically, tangential error occurs because light rays are incident at different points on aspherical lenses or curved optical elements, resulting in a difference between the actual position and direction of the emitted light rays and the ideal emitted light rays. For example... Figure 2 In the tangential plane shown, assuming the lens is +8.00D and its front surface power is +3.00D, the convergence / divergence of the light rays passing through the lens to point K is +7.75D. This implies a tangential power error of -0.25D. To eliminate this error, a geometric ray tracing algorithm can be used at a 30° field of view. Starting from the eye's rotation center, the algorithm first performs reverse tracing of the vertical and horizontal meridians, calculating the height y1 of the intersection point of the ray with the vertical meridian of the rear surface and the height x1 of the intersection point of the ray with the horizontal meridian. Figure 2 In the case of astigmatism, the incident light ray is affected by astigmatism after refraction, in Q T A tangential image is formed at Q. S A sagittal image is formed at a distance of KQ. T Let f be the focal length of the spherical surface at the tangential oblique vertex. T Distance from KQ S Let f be the focal length of the spherical surface at the vertex of the axial slant. S When f T and f S When using meters as the unit, the tangential optical power F T =1 / f T , directional optical power F S =1 / f S The tangential optical power F can be determined by tracing the forward rays. T and the directional optical power F S Then the tangential error T = F T -F2, Vector error S=F S -F2, and then the main aberrations affecting image quality can be calculated: oblique astigmatism (OAE), field curvature (MOE), and distortion.

[0055] S4. Point-by-point optimization using a recursive algorithm: Since oblique astigmatism has the greatest impact on image sharpness, it is considered the primary aberration to be corrected when designing lenses. Oblique astigmatism compensation is performed, and the above operation is repeated for points on the two meridians (excluding points with a 30° field of view). Point-by-point optimization is then performed using a recursive algorithm, where:

[0056]

[0057]

[0058] Where y2 and x2 are the heights of the intersection points of the light rays with the horizontal and vertical meridians of the lens surface, respectively, i.e., the heights of the outgoing light rays from the optical axis; T is the tangential optical power error along the vertical and horizontal meridians; and P... B and P C These are the free torus coefficients of the meridians in the vertical and horizontal directions, respectively;

[0059] S5. Calculate the free torus surface coefficients: Due to the rotational symmetry of the lens, consider dividing the first quadrant of the surface into regions every 10°, such as... Figure 1 θ1, θ2, and θ3, and so on, up to θ8 in the diagram, for a total of 8 θ angles. One meridian is taken for each region, resulting in a total of 10 meridians. The free torus coefficients, excluding horizontal and vertical ones, are calculated using the following formula:

[0060]

[0061] Where θ represents the rotation angle of the meridian relative to the horizontal direction;

[0062] S6. Correcting Field Curvature and Distortion: Substitute the surface coefficients of each meridian obtained above into the sagittal formula, which is based on the hypercurvature quadratic surface formula and corrected with multiple higher-order terms, to obtain discrete data points. Finally, the surface after free torus is reconstructed using the least squares method, as shown in the following formula:

[0063]

[0064] Among them, c x and c y Let c represent the curvature in the x and y directions, respectively. x =c y =1 / r 20Let r represent the height of the incident ray on the surface, x and y represent the coordinates of the projection of a point on the surface along the z-axis onto the xoy plane, and B, C, D, and E are the higher-order coefficients of the free torus (B, C, D, and E can be solved using Zemax software). First, create or import a hypercurvature quadratic surface in Zemax, then select the higher-order coefficients to be used for correction. Using the selected higher-order coefficients, build a correction model that associates the higher-order coefficients with the surface shape. Use the optimization tool in Zemax to run the correction. During the optimization process, Zemax will automatically adjust the selected higher-order coefficients to minimize OAE, MOE, and distortion, so that the simulation results match the required optical performance. The values ​​of the higher-order coefficients can then be solved. r represents the height of the incident ray on the surface, x and y represent the coordinates of the projection of a point on the surface along the z-axis onto the xoy plane, and z represents the distance between the surface along the z-axis and the xoy plane, i.e., the sagitta of the surface.

[0065] As a further improvement of the present invention, the r 10 =1000(n-1) / F1

[0066] r 20 =1000(1-n) / F2

[0067] Where n is the refractive index of the lens medium.

[0068] As a further improvement of the present invention, the method for calculating oblique astigmatism, field curvature, and distortion in step S3 is as follows: at a 30° field of view, starting from the center of eye rotation, first, reverse tracing is performed on the vertical and horizontal meridians to calculate the intersection point y2 of the light ray with the vertical meridian of the rear surface and the intersection point x2 of the light ray with the horizontal meridian. Then, the tangential oblique vertex spherical focal length f of the lens is obtained by forward ray tracing. T And the focal length f of the spherical vertex of the axial direction S Then, the tangential optical power F is calculated. T and the directional optical power F S Subtracting F2 from T and S gives the tangential error T and the sagittal error S, which in turn allows us to calculate the main aberrations affecting image quality: oblique astigmatism (OAE), field curvature (MOE), and distortion.

[0069] In this invention, spectacle lenses with a refractive index of 1.74 and a power of -8.00D are optimized using the methods described above. The comparison results between the optimized lenses and spherical lenses of the same specifications are shown in Table 1. For oblique astigmatism, the images formed in the two directions do not converge at the same point, which has the greatest impact on image sharpness. Therefore, this invention prioritizes sacrificing a portion of the field curvature to optimize oblique astigmatism, minimizing it to 0.64D compared to spherical lenses, providing excellent sharpness from the center to the periphery. Although the field curvature is slightly larger than that of spherical lenses, it is still within the acceptable range for spectacle lens wear. Distortion does not change image sharpness but affects image shape. Free-torus lenses have a distortion reduction of 1.1% compared to spherical lenses, correcting the image shape. The optimization principle is as follows: Figure 2 As shown in the comparison diagram of distortion, OAE, and MOE, see below. Figure 3 , Figure 4 and Figure 5 As shown

[0070]

[0071] Table 1

[0072] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus.

[0073] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for manufacturing a free-form torus lens, characterized by improving the degree of freedom by optimizing the meridians at multiple different angles within the entire plane point by point, wherein: This production method includes the following steps: S1. Construct a simplified mirror eye model; S2, determining the optical power F2 and the radius of curvature r of the vertex 20 ; S3. Calculate the main aberrations that affect image quality: oblique astigmatism, field curvature, and distortion; S4. Point-by-point optimization using a recursive algorithm: Since oblique astigmatism has the greatest impact on image sharpness, it is considered the primary aberration to be corrected when designing lenses. Oblique astigmatism compensation is performed, and step S3 is repeated for points on the two meridians, along with the process of using oblique astigmatism as the primary aberration to be corrected when designing lenses. Where: Among them, P B and P C y1 and x2 are the free torus coefficients of the meridians in the vertical and horizontal directions, respectively; y2 and x2 are the heights of the intersection points of the light rays with the horizontal and vertical meridians of the lens surface, i.e., the heights of the outgoing light rays from the optical axis; and T is the tangential optical power error in the vertical and horizontal meridian directions. S5. Calculate the free toroidal surface coefficients: Due to the rotational symmetry of the lens, consider dividing the first quadrant of the surface into regions every 10°. Take one meridian for each region, for a total of 10 meridians. Calculate the free toroidal surface coefficients excluding horizontal and vertical ones, using the following formula: Where P is the free torus coefficient excluding horizontal and vertical directions. This indicates the angle of rotation of the meridian relative to the horizontal direction; S6. Correcting Field Curvature and Distortion: Substitute the surface coefficients of each meridian obtained above into the sagittal formula, which is based on the hypercurvature quadratic surface formula and corrected with multiple higher-order terms, to obtain discrete data points. Finally, the surface after free torus is reconstructed using the least squares method, as shown in the following formula: Where z represents the distance between the surface along the z-axis and the xoy plane, i.e., the sag of the surface, r represents the height of the incident ray on the surface, and c x and c y Let c represent the curvature in the x and y directions, respectively. x =c y =1 / r 20 r represents the height of the incident ray on the surface, B, C, D, and E are higher-order coefficients of the free torus, and x and y represent the coordinates of the projection of a point on the surface along the z-axis onto the xoy plane.

2. The method for manufacturing a free-circular torus lens according to claim 1, characterized in that: The specific steps of step S1 are as follows: Establish a three-dimensional rectangular coordinate system with the vertex of the front surface of the lens as the origin, so that the center of the lens falls on the z-axis, and the vertical meridian of the lens is parallel to the y-axis, and the horizontal meridian of the lens is parallel to the x-axis.

3. The method for manufacturing a free-circular torus lens according to claim 1, characterized in that: The specific steps in step S2 are as follows: The front and back surfaces of the lens are both set as spherical, and the radius of curvature r is determined according to the given base curvature F1. 10 The optical power F2 and radius of curvature r at the back surface vertex are determined by the center thickness d and refractive index n. 20 Since the designed lens does not have astigmatism, the optical power of the front and rear surfaces is equal in both the horizontal and vertical directions.

4. The method for manufacturing a free-circular torus lens according to claim 3, characterized in that: The r 10 =1000(n-1) / F1 r 20 =1000(1-n) / F2 Where n is the refractive index of the lens medium.

5. The method for manufacturing a free-circular torus lens according to claim 1, characterized in that: In step S4, P B and P C These are the free torus coefficients of the meridians in the vertical and horizontal directions, respectively.

6. The method for manufacturing a free-circular torus lens according to claim 1, characterized in that: In step S3, the calculation of oblique astigmatism, field curvature, and distortion is performed as follows: starting from the eye's rotation center at a 30° field of view, first, reverse tracing is performed along the vertical and horizontal meridians to calculate the intersection point y2 of the ray with the vertical meridian of the rear surface and the intersection point x2 of the ray with the horizontal meridian. Then, the tangential oblique vertex spherical focal length f of the lens is determined by forward ray tracing. T And the focal length f of the spherical vertex of the axial direction S Then, the tangential optical power F is calculated. T and the directional optical power F S Subtracting F2 from T and S gives the tangential error T and the sagittal error S, which in turn allows us to calculate the main aberrations affecting image quality: oblique astigmatism (OAE), field curvature (MOE), and distortion.

7. The method for manufacturing a free-circular toroidal lens according to claim 1, characterized in that: In step S4, the operation is repeated to remove points outside the 30° field of view.

8. The method for manufacturing a free-circular torus lens according to claim 1, characterized in that: The B, C, D, and E values ​​were solved using the Zemax software.

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