A first-order differential without break concentric ring alternating outer ring defocus method and myopia lens

Abstract

The application relates to the technical field of myopic lenses, and discloses a concentric ring alternating type outer ring defocusing method with first-order differential without discontinuity and a myopic lens. The method comprises the following steps: taking a lens center as an origin to establish a radial coordinate system, and dividing a lens surface into a central vision area and an outer ring defocusing area; M concentric ring circles of the outer ring defocusing area are divided into odd ring circles and even ring circles to form a ring belt structure with alternating wide and narrow rings; at a boundary position r m , constraint conditions of an mth ring circle and an m+1th ring circle in the ring belt structure are established, and a surface function of the m+1th ring circle is solved to form a ring defocusing surface with first-order differential without discontinuity. The application solves the optical aberration problem caused by first-order differential discontinuity at the junction of the ring belt in the prior art, adopts the design of first-order differential without discontinuity, and improves the optical performance and wearing comfort of the lens.

Description

Technical Field

[0001] This invention relates to the field of myopia lens technology, and in particular to a first-order differential non-discontinuous concentric ring alternating outer ring defocusing method and a myopia lens. Background Technology

[0002] Existing outer-ring defocus lenses achieve defocusing effects by designing multiple concentric rings around the lens periphery. However, a common problem arises at the junctions of adjacent rings: the continuity of the surface. Traditional design methods only ensure depth continuity at the ring junctions, neglecting the continuity control of the first-order derivative of the surface. This leads to abrupt changes in the tangent slope at the junctions, resulting in significant spherical aberration and coma. Wearers experience visual jumps when their gaze moves between different rings, and glare and chromatic aberration occur under certain lighting conditions. Prolonged wear can also cause eye strain. Therefore, achieving a smooth transition at the ring junctions while maintaining the difference in focal power between the rings has become a pressing technical problem. Summary of the Invention

[0003] The main objective of this invention is to provide a first-order differential non-discontinuity concentric ring alternating outer ring defocusing method and a myopia lens. This invention solves the optical aberration problem caused by the first-order differential discontinuity at the junction of the rings in the prior art. By adopting a first-order differential non-discontinuity design, the optical performance and wearing comfort of the lens are improved.

[0004] To achieve the above objectives, this invention provides a first-order differential non-discontinuous concentric ring alternating outer ring defocusing method, comprising the following steps:

[0005] A radial coordinate system is established with the center of the lens as the origin, and the lens surface is divided into the central visual area and the outer ring defocus area;

[0006] The M concentric rings of the outer ring defocused area are divided into odd-numbered rings and even-numbered rings to form a ring structure with alternating wide and narrow rings;

[0007] At boundary position r m At the point, establish the constraint conditions between the m-th ring and the (m+1)-th ring in the ring structure, and solve the surface function of the (m+1)-th ring to form a first-order differential ring-shaped defocused surface without discontinuity.

[0008] Optionally, in a first implementation of the first aspect of the present invention, a radial coordinate system is established with the lens center as the origin, and the lens surface is divided into a central visual area and an outer ring defocus area, including:

[0009] Define the horizontal distance from any point on the lens surface to the origin as the radial coordinate r and the vertical depth of the arbitrary point as z, and establish a depth function to express the surface profile of the lens.

[0010] Based on the depth function, the radial range of the central visual area is set to 0 to r0, and the radial range of the outer defocus area is set to r0 to r. M The outer ring defocused area is divided radially into M concentric rings.

[0011] Optionally, in a second implementation of the first aspect of the present invention, it further includes:

[0012] Based on the difference between the outer radius r0 of the central visual area and the preset radius, calculate the outer radius r1 of the first ring, and then calculate the outer radius r of the m-th ring sequentially. m Equal to the outer radius r of the (m-1)th ring m-1 Adding the difference in radius between adjacent rings forms a sequence of increasing outer radii of the rings;

[0013] Based on the refractive index of the lens material and the target curvature of each ring, a corresponding focal length D is assigned to the m-th ring. m This forms a ring-shaped focal length sequence.

[0014] Optionally, in a third implementation of the first aspect of the present invention, the M concentric rings of the outer ring defocused area are divided into odd-numbered rings and even-numbered rings to form an alternating wide and narrow ring structure, including:

[0015] Based on the parity of the ring number m, the M concentric rings of the outer ring defocus area are divided into odd-numbered rings and even-numbered rings. The radial width values ​​of the odd-numbered rings and the even-numbered rings are calculated based on the increasing sequence of the outer edge radii of the rings and set to different values.

[0016] Based on the ring focal length sequence, different radial width values ​​are set for the odd-numbered rings and the even-numbered rings;

[0017] The odd-numbered rings are configured with a first focal length, and the even-numbered rings are configured with a second focal length. The difference between the first focal length and the second focal length is a preset focal length difference, forming a ring structure with alternating wide and narrow rings.

[0018] Optionally, in a fourth implementation of the first aspect of the present invention, at the boundary position rm, constraints are established between the m-th ring and the (m+1)-th ring in the annular structure, and the surface function of the (m+1)-th ring is solved to form a first-order differential annular defocused surface without discontinuity, including:

[0019] Establish a depth value equality constraint so that the m-th loop is at the boundary position r m The vertical depth value of the contour at point m is equal to the value of the (m+1)th loop at the boundary position r. m Vertical depth value of the contour at the location;

[0020] Establish a first-order differential value equality constraint such that the m-th loop is at the boundary position r mThe slope of the tangent at point r is equal to the slope of the (m+1)th loop at the boundary. m The slope of the tangent at that point;

[0021] Establish a constraint that the second-order differential values ​​are unequal, such that the m-th loop is at the boundary position r. m The rate of change of curvature at point r is not equal to that at point r of the (m+1)th ring on the boundary. m The rate of change of curvature at that point;

[0022] Based on the constraints of equal depth values, equal first-order differential values, and unequal second-order differential values, the surface function of the (m+1)th loop is solved to form a ring-shaped defocused surface with no first-order differential.

[0023] Optionally, in the fifth implementation of the first aspect of the invention, a constraint of unequal second-order differential values ​​is established, such that the m-th loop is at the boundary position r. m The rate of change of curvature at point r is not equal to that at point r of the (m+1)th ring on the boundary. m The rate of change of curvature at a given point includes:

[0024] Based on the focal length D of the m-th ring m Given the refractive index of the lens material, calculate the position r of the m-th ring at the boundary. m The rate of change of curvature at that point;

[0025] Based on the focal length D of the (m+1)th ring m+1 Given the refractive index of the lens material, calculate the position r of the (m+1)th ring at the boundary. m The rate of curvature change at point r causes the (m+1)th loop to be at the boundary position r m The rate of change of curvature at point r is not equal to that of the m-th loop at the boundary position r. m The rate of change of curvature at a given point yields the constraint of unequal second-order differential values.

[0026] Optionally, in a sixth implementation of the first aspect of the present invention, the surface function of the (m+1)th loop is solved according to the equal depth value constraint, the equal first-order differential value constraint, and the unequal second-order differential value constraint to form a ring-shaped defocused surface with no first-order differential, including:

[0027] F1: Based on the equality constraints of depth values ​​and the equality constraints of first-order derivative values, the m-th ring is positioned at the boundary position r. m The vertical depth value and tangent slope at the point are set as the initial boundary conditions for the (m+1)th loop;

[0028] F2: Based on the inequality constraint of the second-order differential value combined with the focal length D of the (m+1)th ring. m+1 By performing two integration calculations and using the initial boundary conditions to determine the integration constant, the surface function of the (m+1)th loop is obtained;

[0029] F3: Repeat the solution process of steps F1-F2 for all M rings, combine the surface functions of each ring to form a first-order differential ring-shaped defocused surface without discontinuity.

[0030] Optionally, in a seventh implementation of the first aspect of the present invention, step F2 includes:

[0031] Based on the focal length D of the (m+1)th ring m+1 A second-order differential equation is established with respect to the refractive index of the lens material. The first integration of the second-order differential equation yields a first-order differential function.

[0032] Using the m-th ring at the boundary position r m The slope of the tangent at a certain point is used as a boundary condition to determine the first integration constant of the first-order differential function;

[0033] The first-order differential function is integrated a second time, utilizing the m-th loop at the boundary position r. m The vertical depth value of the contour at a certain point is used as a boundary condition to determine the second integration constant, thus obtaining the surface function of the (m+1)th loop.

[0034] Optionally, in an eighth implementation of the first aspect of the present invention, it further includes:

[0035] The annular defocused curved surface is machined, and at the boundary position r of each ring... m Increase toolpath density in the surrounding area;

[0036] At the boundary position r of each ring m At this point, dense sampling is performed along the radial direction to obtain multiple sampling points, and the first-order differential value of adjacent sampling points is calculated.

[0037] Calculate the boundary position r m The deviation between the first-order derivative values ​​on both sides is calculated, and the deviation is verified to be less than a preset threshold.

[0038] The present invention also provides a myopia lens for implementing the steps of the above-mentioned first-order differential non-discontinuous concentric ring alternating outer ring defocusing method.

[0039] In summary, this invention establishes a three-level constraint system—equal depth values, equal first-order differential values, and unequal second-order differential values—to achieve continuous vertical depth and tangent slope at the boundary of adjacent rings. Simultaneously, it maintains the abrupt change in curvature rate to create rings of different focal lengths, thus solving the optical aberration problem caused by first-order differential discontinuity at the ring boundary in existing technologies. The vertical depth and tangent slope of the previous ring at its boundary are used as the initial boundary conditions for the next ring. Combined with the focal length parameter, the integration constant is determined through two integral calculations, automatically satisfying the first-order differential continuity of the surface function at the boundary, eliminating the abrupt change in light refraction angle caused by abrupt changes in tangent direction. The alternating wide and narrow ring structure, combined with the focal length difference configuration of odd and even rings, optimizes the periodicity and uniformity of the defocus distribution while ensuring myopia control effectiveness. Numerical differentiation methods verify that the first-order differential deviation at the boundary is less than a preset threshold, ensuring that the processing accuracy meets the first-order derivative continuity requirement. This invention employs a first-order differential design with no discontinuity, which improves the optical performance and wearing comfort of the lens. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the steps of the first-order differential non-discontinuous concentric ring alternating outer ring defocusing method in one embodiment of the present invention;

[0041] Figure 2 This is a depth distribution diagram of the annular defocus surface contour in one embodiment of the present invention;

[0042] Figure 3 This is a continuous distribution diagram of the first-order differential of the surface profile in one embodiment of the present invention;

[0043] Figure 4 This is a distribution diagram of the second-order differential steps of the surface profile in one embodiment of the present invention;

[0044] Figure 5 This is a diagram showing the alternating distribution of focal length in a ring according to one embodiment of the present invention;

[0045] Figure 6 This is a cross-sectional schematic diagram of the optical working principle of a first-order differential non-discontinuous outer ring defocusing lens in one embodiment of the present invention.

[0046] The realization of the objective, functional features and advantages of the present invention will be further explained in conjunction with the embodiments and with reference to the accompanying drawings. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the 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 and not intended to limit the invention.

[0048] Reference Figure 1This embodiment provides a first-order differential non-discontinuous concentric ring alternating outer ring defocusing method, including the following steps:

[0049] S1, establish a radial coordinate system with the center of the lens as the origin, and divide the lens surface into the central visual area and the outer ring defocus area;

[0050] S2, divide the M concentric rings of the outer ring defocus area into odd-numbered rings and even-numbered rings to form a ring structure with alternating wide and thin rings;

[0051] S3, at boundary position r m At the point, establish the constraint conditions between the m-th ring and the (m+1)-th ring in the ring structure, and solve the surface function of the (m+1)-th ring to form a first-order differential ring-shaped defocused surface without discontinuity.

[0052] In one example, a radial coordinate system is established with the lens center as the origin, dividing the lens surface into a central visual zone and an outer ring defocus zone, including:

[0053] Define the horizontal distance from any point on the lens surface to the origin as the radial coordinate r and the vertical depth of the arbitrary point as z, and establish a depth function to express the surface profile of the lens.

[0054] Based on the depth function, the radial range of the central visual area is set to 0 to r0, and the radial range of the outer defocus area is set to r0 to r. M The outer ring defocused area is divided radially into M concentric rings.

[0055] In this example, the lens geometry is constructed using rotationally symmetric surface modeling. A polar coordinate system is established with the lens axis as the origin. In the polar coordinate system, any point on the lens surface can be represented by its horizontal distance from the origin. Characterizing its radial position, while the depth value of that point in the vertical direction is represented by a function. The expression, or function, defines the three-dimensional contour characteristics of the lens surface extending outward from the center. Based on optical design requirements, the lens is divided into two different functional zones: the central visual zone is used to provide correction for the wearer's normal vision, therefore its corresponding radial range is set as... Within this region, the depth function This is achieved by using spherical or aspherical functions with continuous curvature to achieve good imaging performance in the central video field. And from... Extend outward to the maximum working radius of the lens The region is defined as the outer ring defocus zone, which is used to construct a multifocal intervention structure. This structure achieves positive defocus modulation of the peripheral retina by superimposing multiple rings of different focal lengths. To refine the structure of the outer ring defocus zone, [further details are needed]. Divide into inner radial direction A series of concentric rings are used, allowing individual control over the focal length characteristics of each ring. A monotonically increasing sequence of radii is defined. ,in , The outermost radius is used, and for each interval... Define a corresponding depth subfunction Used to control the first The vertical depth distribution of the rings results in the overall lens profile being represented by the following segments and forms:

[0056]

[0057] The piecewise function structure achieves the specified optical power within each loop, and through the connection point... A continuity constraint is applied to maintain a smooth visual transition across the entire lens surface. To eliminate the visual abruptness introduced by the multi-loop structure, a first-order derivative continuity constraint is introduced at the intersection of each function segment:

[0058]

[0059] Ensure the continuity of vertical depth and tangent slope.

[0060] In one example, it also includes:

[0061] Based on the difference between the outer radius r0 of the central visual area and the preset radius, calculate the outer radius r1 of the first ring, and then calculate the outer radius r of the m-th ring sequentially. m Equal to the outer radius r of the (m-1)th ring m-1 Adding the difference in radius between adjacent rings forms a sequence of increasing outer radii of the rings;

[0062] Based on the refractive index of the lens material and the target curvature of each ring, a corresponding focal length D is assigned to the m-th ring. m This forms a ring-shaped focal length sequence.

[0063] In this example, the radial boundary of the known central visual area is used. As the starting radius of the outer ring defocusing area, combined with the preset radius difference parameter Calculate the outer edge radius of the first outer ring defocusing ring. ,in The value is taken within the range of 0.2mm to 0.8mm, depending on factors such as actual fitting requirements, pupil size, and visual field requirements. The outer radius of subsequent rings is calculated using an arithmetic progression, expressed by the formula: The complete sequence of outer radii is obtained by iterative summation. This sequence is strictly increasing, forming a concentric circle structure radiating outwards. Based on the completed construction of the outer radius sequence, to ensure each ring possesses different focal power characteristics, thereby generating a peripheral retinal defocus effect, the optical refractive index of the lens material is considered. and the radius of curvature to be set for each ring region Calculate the focal length corresponding to this region. According to the formula for the power of a single-sided lens in geometric optics, the power value is approximately expressed as: ,in For the first The diopter corresponding to each ring The refractive index of the material (e.g., 1.60, 1.67, etc.). For the lens at the The local radius of curvature at each ring. The formula reflects the inverse relationship between focal length and curvature; therefore, while keeping the refractive index constant, the greater the curvature (i.e., the greater the local radius of curvature at each ring), the greater the local radius of curvature. The smaller the focal length, the higher the focal length. The higher the value, the better. By setting different target curvature values ​​for each ring, different focal lengths are obtained, thus constructing a focal length jump structure. To control the degree of defocusing, an alternating assignment method is used to create a difference in focal length between odd-numbered and even-numbered rings. For example, odd-numbered rings are configured as the basic correction focal length. Even-numbered rings are configured as follows ,in The range is from 3.0D to 7.0D, from which a focal length series is generated. .

[0064] In one example, the M concentric rings of the outer ring defocused region are divided into odd-numbered rings and even-numbered rings, forming an alternating wide and narrow ring structure, including:

[0065] Based on the parity of the ring number m, the M concentric rings of the outer ring defocus area are divided into odd-numbered rings and even-numbered rings. The radial width values ​​of the odd-numbered rings and the even-numbered rings are calculated based on the increasing sequence of the outer edge radii of the rings and set to different values.

[0066] Based on the ring focal length sequence, different radial width values ​​are set for the odd-numbered rings and the even-numbered rings;

[0067] The odd-numbered rings are configured with a first focal length, and the even-numbered rings are configured with a second focal length. The difference between the first focal length and the second focal length is a preset focal length difference, forming a ring structure with alternating wide and narrow rings.

[0068] In this example, a design logic based on the coordinated control of structural parity allocation and optical parameters is adopted, within a given number of rings. Outer radius sequence and the focal series Based on this, the structure and function are differentiated according to the ring number. All rings are configured according to their sequence number. Classify by parity, satisfying A cycle with mod 2 = 1 is defined as an odd-numbered cycle. A ring with mod 2 = 0 is defined as an even-numbered ring, thus constructing an alternating grouping of rings. Based on the increasing sequence of the outer radii of the rings, the radial width of each ring is calculated; that is, for any given ring... Its radial width can be determined by It means that among them and These are the inner and outer diameters of the ring, respectively. By setting the radius difference between odd-numbered and even-numbered rings to be taken from two different intervals, for example, the odd-numbered rings... mm, even-numbered rings [0.5, 0.8] mm, so that odd-numbered rings form thin rings and even-numbered rings form wide rings, or vice versa, forming an alternating structure of "wide-thin-wide", thereby constructing a visually significant rhythmic distribution of wide and thin rings throughout the outer ring out-of-focus area. Simultaneously, based on the established focal length series... Different focal length values ​​are assigned to odd and even rings respectively. Let the odd-numbered rings be uniformly assigned the first focal length. Even-numbered rings are uniformly configured as the second focal length. And requires that the two meet a preset focal length difference. The difference is set between 3.0D and 7.0D to provide effective peripheral positive defocus stimulation. The first focal value is selected as the baseline corrected refractive power of the central visual area, so that it can provide clear imaging function as a vision correction ring, while the second focal value deviates from the corrected refractive power value to form an anterior retinal focusing effect, which is used as a defocus ring for myopia control.

[0069] In one example, at boundary position r m At the specified location, establish the constraint conditions between the m-th ring and the (m+1)-th ring in the ring structure, and solve the surface function of the (m+1)-th ring to form a first-order differential ring-shaped defocused surface without discontinuity, including:

[0070] Establish a depth value equality constraint so that the m-th loop is at the boundary position r m The vertical depth value of the contour at point m is equal to the value of the (m+1)th loop at the boundary position r. m Vertical depth value of the contour at the location;

[0071] Establish a first-order differential value equality constraint such that the m-th loop is at the boundary position r m The slope of the tangent at point r is equal to the slope of the (m+1)th loop at the boundary. m The slope of the tangent at that point;

[0072] Establish a constraint that the second-order differential values ​​are unequal, such that the m-th loop is at the boundary position r. m The rate of change of curvature at point r is not equal to that at point r of the (m+1)th ring on the boundary. m The rate of change of curvature at that point;

[0073] Based on the constraints of equal depth values, equal first-order differential values, and unequal second-order differential values, the surface function of the (m+1)th loop is solved to form a ring-shaped defocused surface with no first-order differential.

[0074] In this example, within a given radial coordinate system and piecewise ring modeling framework, the lens surface profile is constructed ring by ring using a constraint-driven piecewise surface inverse method. Within the outer ring defocus zone, the surface function of the m-th ring is assumed to be... It has been determined, and its defined range is: ,in Let be the outer radius of the ring, and let be the overall depth function of the lens surface, expressed in a piecewise form. or They are valid within their respective intervals. The m-th ring and the... The common boundary location of a ring At this point, the first constraint, namely the equal depth constraint, is introduced. By requiring that the vertical depths of the two adjacent inner and outer rings be completely identical at this radial position, a mathematical expression is established. This ensures that the lens surface does not exhibit any abrupt changes in geometric height, avoiding the formation of "discontinuity" structures that are actually perceptible during processing. Based on depth continuity, a constraint of equal first-order differential values ​​is introduced. Because the first-order differential... Geometrically, this corresponds to the slope of the tangent on the lens surface in the radial direction; therefore, the following condition must be met at the boundary of the ring: Ensure that the m-th ring is directed towards the m-th ring. When transitioning between the rings, the tangent direction of the curved surface remains consistent, preventing significant abrupt changes in refraction direction as light crosses the rings. This visually eliminates abrupt changes in brightness, astigmatism, or the "ring effect" perceived by the wearer. After satisfying these two continuity conditions, to achieve focal length differences between the different rings in terms of optical function, an unequal second-order derivative value constraint is introduced at the same boundary position. Because the second-order derivative... It is directly related to the curvature of the surface and its rate of change, and determines the optical power of the region; therefore, it is set at the boundary position. This causes a jump in the rate of curvature change at the loop, thus creating a stepped distribution of optical focal length while maintaining geometric continuity and a smooth first-order transition. Based on the above three types of constraints, in the specific solution of the... When using a loop surface function, pre-select... The function can be in the form of a quadratic or cubic polynomial, spline function, or other differentiable function, with its undetermined coefficients as unknowns. This is achieved by substituting the conditions for equality of depth values ​​and the conditions for equality of first-order differential values ​​into the function. The expression at the m-th position forms a system of equations about the unknown coefficients. Simultaneously, considering the expected curvature level of the loops, a different objective value is introduced into the second derivative of the function than that of the m-th loop, thus naturally satisfying the design requirement of unequal second-order differentials during the solution process. Through a joint solution method of "continuity constraint + curvature jump constraint," the m-th loop is mathematically uniquely or stably determined. Surface functions of a loop And ensure that the function is Place and The function is strictly continuous at the level of function values ​​and first derivatives, but exhibits controlled differences at the level of second derivatives. This process is recursively applied loop by loop along the radial direction until the outermost loop is reached. A first-order differential non-discontinuous annular defocused surface is constructed, which has continuous depth and tangent in the overall contour, but whose curvature changes in a step-like manner.

[0075] Figure 2 This is a depth distribution diagram of the annular defocus surface contour. The horizontal axis represents the radial distance r, ranging from 0 to 17.5 mm, consistent with actual lens dimensions; the vertical axis represents the contour depth z(r), ranging from 0 to 1.6 mm, consistent with the depth variation of the lens surface curvature. The curve rises smoothly and continuously. r1 to r7 are marked as the outer radii of the ring, and the depth continuity points at the boundaries are marked to reflect z. m (r m )=z m+1 (r m The depth without discontinuity is the first level of the three-level continuity constraint of this invention.

[0076] In one example, a constraint of inequality of second-order differential values ​​is established such that the m-th loop is at the boundary position r. m The rate of change of curvature at point r is not equal to that at point r of the (m+1)th ring on the boundary. m The rate of change of curvature at a given point includes:

[0077] Based on the focal length D of the m-th ring m Given the refractive index of the lens material, calculate the position r of the m-th ring at the boundary. m The rate of change of curvature at that point;

[0078] Based on the focal length D of the (m+1)th ring m+1 Given the refractive index of the lens material, calculate the position r of the (m+1)th ring at the boundary. m The rate of curvature change at point r causes the (m+1)th loop to be at the boundary position r m The rate of change of curvature at point r is not equal to that of the m-th loop at the boundary position r. mThe rate of change of curvature at a given point yields the constraint of unequal second-order differential values.

[0079] In this example, based on the thin lens approximation theory, in a one-sided optical system, a unit focal power (expressed as diopter D) is obtained through the material's refractive index. With surface curvature radius The relationship is represented as , Indicates local optical diopter. The refractive index of the lens material, and Let be the radius of curvature of the corresponding annular region on the vertical cross section. If we consider the lens profile function as... Then its radius of curvature This can be deduced from the second derivative of the surface at that point (i.e., the rate of change of curvature). Curvature In the radial coordinate system, it can be given by the following expression:

[0080]

[0081] When the first derivative exist When the curvature is continuous and small, the rate of change of curvature is approximately considered to be... Corresponding to the main source of focal length. Connecting focal length with... Establish a correspondence, represented as follows:

[0082]

[0083] in To match the refractive index of the material The relevant constant scaling factor. Based on this relationship, for the ... A ring, given its focal length is... And the refractive index of the lens material is Under the premise of calculating its boundary The second derivative value at This allows us to determine the rate of change of curvature at that location. Similarly, for the ... Each ring, configured with different focal length values Under the same conditions, the rate of change of curvature at its boundary is calculated in the same way. In order to construct ring structures with different focal lengths while maintaining continuity in vertical depth and tangent slope, the following conditions must be met: This is the second-order differential inequality constraint, its physical meaning being a "focal abrupt change," where the curvature of different rings undergoes a sudden change at the transition boundary, leading to a significant alteration in the local imaging light-gathering ability, thus creating controlled myopic defocus in front of the retina. Because the first derivative in... The curve is continuous at this point, so there is no geometric discontinuity, and CNC machining can proceed along the continuous tangential direction. However, the discontinuity of the second derivative at this point means that the machining tool needs to achieve a jump in feed curvature before and after this point, thereby forming the desired defocus step at the optical level. By deriving the curvature based on focal length and refractive index for two adjacent rings respectively, and then applying these two to the intersection point... Perform a second-order differential difference comparison at the point to obtain the desired result. The mathematical and optical constraints.

[0084] In one example, based on the equal depth value constraint, the equal first-order differential value constraint, and the unequal second-order differential value constraint, the surface function of the (m+1)th loop is solved to form a first-order differential non-discontinuous annular defocused surface, including:

[0085] F1: Based on the equality constraints of depth values ​​and the equality constraints of first-order derivative values, the m-th ring is positioned at the boundary position r. m The vertical depth value and tangent slope at the point are set as the initial boundary conditions for the (m+1)th loop;

[0086] F2: Based on the inequality constraint of the second-order differential value combined with the focal length D of the (m+1)th ring. m+1 By performing two integration calculations and using the initial boundary conditions to determine the integration constant, the surface function of the (m+1)th loop is obtained;

[0087] F3: Repeat the solution process of steps F1-F2 for all M rings, combine the surface functions of each ring to form a first-order differential ring-shaped defocused surface without discontinuity.

[0088] In this example, when the first Contour function of each loop When known, directly at the boundary position Calculate its vertical depth value. and its first derivative The former represents the surface height, and the latter represents the tangent slope. Based on the equality constraints of depth values ​​and first-order derivative values, these two values ​​constitute the first... Cyclic functions The initial boundary conditions. That is, the new function in Point satisfies:

[0089]

[0090] In order to make the first Each ring possesses independent optical power characteristics, which are then incorporated into its target power. This is then converted into an equivalent second derivative form using optical formulas. Combined with the refractive index... The basic relationship with focal length:

[0091]

[0092] Convert the desired focal length to a fixed second derivative value. Inside the loop, it is considered a constant or a gradually changing function. Solve for the... The surface function of a loop is thus transformed into a problem of integrating twice with respect to the second derivative. Let:

[0093]

[0094] The first integral yields the first derivative:

[0095]

[0096] Integrating this equation a second time yields the complete surface function:

[0097]

[0098] Where the integration constant and Based on the boundary conditions known in step F1 and Uniquely determined. This process ensures that the surface functions of each new loop are not only geometrically continuous but also mathematically maintain the uninterrupted nature of the first derivative, while simultaneously achieving the optical focal length step structure through the jump of the second derivative. The solution logic of F1-F2 is incorporated into... to Repeat the process within the specified range, ensuring that each subsequent loop constructs the surface function based on the boundary inputs provided by the preceding loop. (This process is repeated for all loops.) By combining piecewise functions, a complete lens profile function is formed:

[0099]

[0100] The function satisfies the condition of connecting the boundaries in each loop. It possesses the properties of continuous depth values ​​and continuous first derivatives, while maintaining jumps on the second derivative, thus achieving a first-order differential non-discontinuous annular defocus surface with visual continuity, tangential continuity, but focal length step changes.

[0101] In one example, step F2 includes:

[0102] Based on the focal length D of the (m+1)th ring m+1 A second-order differential equation is established with respect to the refractive index of the lens material. The first integration of the second-order differential equation yields a first-order differential function.

[0103] Using the m-th ring at the boundary position r mThe slope of the tangent at a certain point is used as a boundary condition to determine the first integration constant of the first-order differential function;

[0104] The first-order differential function is integrated a second time, utilizing the m-th loop at the boundary position r. m The vertical depth value of the contour at a certain point is used as a boundary condition to determine the second integration constant, thus obtaining the surface function of the (m+1)th loop.

[0105] In this example, based on the target focal length value With the refractive index of the material Establish the equivalent geometric curvature expression for this ring based on optical formulas. Determine the radius of curvature of the region The curvature itself can be approximated as a second derivative in rotationally symmetric coordinates. Therefore, it is approximately assumed that this focal length corresponds to a specified set of rates of curvature change. If the focal length is considered constant within this ring, then the second derivative can be set as a constant:

[0106]

[0107] in To match the refractive index of the material The scaling factor related to unit transformation. The first integration of the second-order differential equation, i.e., from... Integrating yields the first derivative. :

[0108]

[0109] Let be the integration constant, representing the offset of the initial slope in the radial direction. To determine the integration constant, boundary positions are introduced. The known first derivative value at a given point is used as a constraint condition, and this value is determined by the first derivative value at the given point. A loop function at its outer edge tangent slope at Provided. Substitute it into the above formula:

[0110]

[0111] Thus, the first integral constant is uniquely determined. And construct the first derivative function. Then, a second integration is performed to obtain the surface function expression:

[0112]

[0113] in This is the second integration constant, corresponding to the initial depth value in the vertical direction. This constant is also provided by the boundary conditions, i.e., the... Each ring in Depth value at Substitute and solve:

[0114]

[0115] Through the known Calculated and Determine the first Each ring is within its defined domain. Surface functions on:

[0116]

[0117] This function is at the boundary position. The depth and first derivative are continuous with the previous ring, and because Unlike the curvature constant of the previous ring, there is a clear jump at the second derivative level, satisfying the power abrupt change requirement for constructing the defocus function. By repeating this process for all subsequent rings, the outer ring defocus surface of the entire lens is gradually constructed, ensuring that it maintains first-order differential continuity at all boundaries and exhibits a step-like jump in power distribution, forming an optically controllable and visually smooth first-order differential seamless ring defocus structure.

[0118] Figure 3 This is a continuous distribution diagram of the first-order differential of the surface profile. The horizontal axis represents the radial distance r in mm, and the vertical axis represents the slope of the tangent line of the surface, which is dimensionless or in mm / mm. The curve remains continuous at all ring boundaries r1 to r7. Existing technologies only guarantee depth continuity, and the first-order differential breaks at the boundaries. This invention achieves continuity through z' m (r m )=z m+1 (r m This achieves continuous tangent slope and eliminates optical abrupt changes.

[0119] Figure 4 This is a distribution diagram of the second-order differential steps of the surface profile. The horizontal axis represents the radial distance r in mm, and the vertical axis represents the second-order differential z''(r) = d. 2 z / dr 2 Unit mm -1 This is directly related to curvature K and focal length φ. The curve presents a stepped rectangular wave, with vertical jumps at the boundaries of the loops, indicated by dashed lines representing discontinuities. Odd-numbered loops with thinner rings and lower second-order derivatives correspond to corrected focal length, while even-numbered loops with wider rings and higher second-order derivatives correspond to defocused focal length, reflecting z'' m (r m )≠z'' m+1 (r m The second-order differential discontinuity characteristics of ).

[0120] In one example, it also includes:

[0121] The annular defocused curved surface is machined, and at the boundary position r of each ring... m Increase toolpath density in the surrounding area;

[0122] At the boundary position r of each ring m At this point, dense sampling is performed along the radial direction to obtain multiple sampling points, and the first-order differential value of adjacent sampling points is calculated.

[0123] Calculate the boundary position r m The deviation between the first-order derivative values ​​on both sides is calculated, and the deviation is verified to be less than a preset threshold.

[0124] In this example, it is based on the piecewise function model constructed in the CAD system. This transforms the annular defocused surface into trajectory commands suitable for five-axis CNC machining tools. The boundary of each annular loop is taken into account. The region at this point is the connecting region between adjacent surface segments. Theoretically, mathematical modeling has ensured the continuity of its first derivative, i.e. However, in actual machining, due to factors such as machine tool response characteristics, tool tip trajectory interpolation errors, and material micro-deformation, errors occur at this location. Therefore, enhanced control is needed in the boundary region. Near each Within a tiny interval, that is Increasing the toolpath density within the range allows the CNC system to generate small tool steps with stable tangential direction and controlled curvature fluctuations in this area at a higher interpolation frequency, thereby reducing the step effect caused by trajectory discretization. After machining, the process enters the inspection stage, where a high-precision coordinate measuring machine (CMM) performs a full-area scan of the lens surface, especially at all boundary positions. A dense sampling path was laid out radially nearby, and the coordinates of a series of sampling points were obtained. In each set of local data, the approximate value of the first derivative is calculated using the finite difference method between adjacent points, i.e., by using:

[0125]

[0126] The local tangent slope at each sampling point is obtained in the form of [formula missing]. Then, the left side of the boundary [text missing]. The first derivative value in the interval is denoted as right side The first derivative value in the interval is denoted as Calculate the numerical deviation between the two:

[0127]

[0128] This deviation represents the degree of tangent discontinuity at the boundary of the actual machined surface. Based on the optical design requirements for a smooth visual transition, this value is controlled within a preset threshold range, for example, less than 0.002. If all measured values... If all values ​​are less than the threshold, it proves that the first derivative remains continuous at all connections, satisfying the design standard of no discontinuity in the first derivative. Otherwise, analyze the error distribution between the tool path data and the measurement results, and backtrack to optimize the machine tool control parameters until the error tolerance is met.

[0129] Figure 5 This is a diagram showing the alternating distribution of focal power in the rings. The horizontal axis represents the radial distance *r* (in mm), and the vertical axis represents the focal power *D(r)* (in diopters). The curve exhibits a stepped rectangular wave pattern. Odd-numbered, thinner rings represent the correction ring (focal power -3.0D) with a wider width (approximately 0.35-0.8 mm), while even-numbered, wider rings represent the defocus ring (focal power +2.0D) with a narrower width (approximately 0.2-0.5 mm), forming an alternating structure of wide and thin rings. The focal power difference ΔD = 5.0D is marked, and the red markings show the size comparison between the wide and thin rings. This demonstrates that the invention combines the width difference of odd and even rings with the focal power difference to form a periodic correction-defocus optical rhythm, achieving myopia control.

[0130] Reference Figure 6 , Figure 6 This is a cross-sectional schematic diagram illustrating the optical working principle of the first-order differential non-discontinuous outer ring defocus lens of this invention. The lens structure includes two functional areas: a central plano lens area (central visual area) and an outer ring defocus area. The central plano lens area provides basic corrective refractive power to ensure clear imaging of the central visual field. The outer ring defocus area consists of M concentric rings arranged in alternating wide and thin rings, with odd and even rings providing corrective and defocus powers, respectively. When parallel light rays enter from the left and pass through the lens, the light rays in the central area are refracted by the central plano lens area and accurately focused on the fovea centralis of the retina to achieve normal visual correction. However, the peripheral light rays passing through the outer ring defocus area, due to the positive defocus provided by the defocus rings, have their focal point shifted forward to in front of the retina, creating a myopic defocus effect, labeled as "peripheral area imaging focal advance." This peripheral defocus blurs the imaging of the retina around the macula, forming an optical barrier that inhibits the eyeball from growing in the direction of hyperopic defocus, thereby inhibiting excessive axial elongation and achieving a myopia control effect of "real-time promotion of axial shortening." This invention utilizes a first-order differential, uninterrupted curved surface connection technology to ensure continuous tangent slopes at the boundaries of adjacent rings, eliminating optical aberrations and visual jumps at the junctions of rings in traditional defocus lenses, thus improving wearing comfort. The peripheral defocus zone corresponds to the alternating wide and narrow ring outer ring defocus structure of this invention. Through a configuration pattern where odd-numbered rings (narrow rings) provide corrective power consistent with the central zone, and even-numbered rings (wide rings) provide positive defocus, it achieves periodic clear-defocus visual stimulation, effectively controlling myopia. This embodiment provides a myopia lens for implementing the steps of the aforementioned first-order differential, uninterrupted concentric ring alternating outer ring defocus method.

[0131] In this embodiment, the specific implementation of each unit in the above device embodiment is described in the above method embodiment, and will not be repeated here.

[0132] It should be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, apparatus, article, or method that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, apparatus, article, or method. Unless otherwise specified, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, apparatus, article, or method that includes that element.

[0133] The above description is only a preferred embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent structural or procedural transformations made based on the content of the present invention specification and drawings, or direct or indirect applications in other related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A first-order differential non-discontinuous concentric ring alternating outer ring defocusing method, characterized in that, include: A radial coordinate system is established with the center of the lens as the origin, and the lens surface is divided into the central visual area and the outer ring defocus area; The M concentric rings of the outer ring defocused area are divided into odd-numbered rings and even-numbered rings to form a ring structure with alternating wide and narrow rings; At boundary position r m At the specified location, constraints are established between the m-th ring and the (m+1)-th ring in the ring structure, and the surface function of the (m+1)-th ring is solved to form a first-order differential ring-shaped defocused surface without discontinuity; wherein, a constraint of equal depth value is established, such that the m-th ring is at the boundary position r m The vertical depth value of the contour at point m is equal to the value of the (m+1)th loop at the boundary position r. m The vertical depth value of the contour at the location; establish a first-order differential value equality constraint, so that the m-th loop is at the boundary position r m The slope of the tangent at point r is equal to the slope of the (m+1)th loop at the boundary. m The slope of the tangent at point r; establish a constraint that the second-order differential values ​​are unequal, so that the m-th loop is at the boundary position r m The rate of change of curvature at point r is not equal to that at point r of the (m+1)th ring on the boundary. m The rate of change of curvature at a given point; specifically including: based on the focal length D of the m-th ring. m Given the refractive index of the lens material, calculate the position r of the m-th ring at the boundary. m The rate of change of curvature at point; based on the focal length D of the (m+1)th ring. m+1 Given the refractive index of the lens material, calculate the position r of the (m+1)th ring at the boundary. m The rate of curvature change at point r causes the (m+1)th loop to be at the boundary position r m The rate of change of curvature at point r is not equal to that of the m-th loop at the boundary position r. m The rate of change of curvature at the point is used to obtain the second-order differential value inequality constraint; based on the depth value equality constraint, the first-order differential value equality constraint, and the second-order differential value inequality constraint, the surface function of the (m+1)th ring is solved to form a first-order differential non-discontinuous ring-shaped defocused surface; specifically including: F1: based on the depth value equality constraint and the first-order differential value equality constraint, the mth ring at the boundary position r m The vertical depth value and tangent slope at the point are set as the initial boundary conditions for the (m+1)th loop; F2: Based on the unequal second-order differential value constraint combined with the focal length D of the (m+1)th loop. m+1 By performing two integral calculations and using the initial boundary conditions to determine the integration constant, the surface function of the (m+1)th ring is obtained; F3: Repeat the solution process of steps F1-F2 for all M rings, and combine the surface functions of each ring to form a first-order differential ring-shaped defocused surface without discontinuity.

2. The first-order differential non-discontinuous concentric ring alternating outer ring defocusing method according to claim 1, characterized in that, A radial coordinate system is established with the center of the lens as the origin, dividing the lens surface into a central visual zone and an outer defocus zone, including: Define the horizontal distance from any point on the lens surface to the origin as the radial coordinate r and the vertical depth of the arbitrary point as z, and establish a depth function to express the surface profile of the lens. Based on the depth function, the radial range of the central visual area is set to 0 to r0, and the radial range of the outer defocus area is set to r0 to r. M The outer ring defocused area is divided radially into M concentric rings.

3. The first-order differential non-discontinuous concentric ring alternating outer ring defocusing method according to claim 1, characterized in that, Also includes: Based on the difference between the outer radius r0 of the central visual area and the preset radius, calculate the outer radius r1 of the first ring, and then calculate the outer radius r of the m-th ring sequentially. m Equal to the outer radius r of the (m-1)th ring m-1 Adding the difference in radius between adjacent rings forms a sequence of increasing outer radii of the rings; Based on the refractive index of the lens material and the target curvature of each ring, a corresponding focal length D is assigned to the m-th ring. m This forms a ring-shaped focal length sequence.

4. The first-order differential non-discontinuous concentric ring alternating outer ring defocusing method according to claim 3, characterized in that, The M concentric rings of the outer ring defocused area are divided into odd-numbered rings and even-numbered rings, forming an alternating wide and narrow ring structure, including: Based on the parity of the ring number m, the M concentric rings of the outer ring defocus area are divided into odd-numbered rings and even-numbered rings. The radial width values ​​of the odd-numbered rings and the even-numbered rings are calculated based on the increasing sequence of the outer edge radii of the rings and set to different values. Based on the ring focal length sequence, different radial width values ​​are set for the odd-numbered rings and the even-numbered rings; The odd-numbered rings are configured with a first focal length, and the even-numbered rings are configured with a second focal length. The difference between the first focal length and the second focal length is a preset focal length difference, forming a ring structure with alternating wide and narrow rings.

5. The first-order differential non-discontinuous concentric ring alternating outer ring defocusing method according to claim 1, characterized in that, Step F2 includes: Based on the focal length D of the (m+1)th ring m+1 A second-order differential equation is established with respect to the refractive index of the lens material. The first integration of the second-order differential equation yields a first-order differential function. Using the m-th ring at the boundary position r m The slope of the tangent at a certain point is used as a boundary condition to determine the first integration constant of the first-order differential function; The first-order differential function is integrated a second time, utilizing the m-th loop at the boundary position r. m The vertical depth value of the contour at a certain point is used as a boundary condition to determine the second integration constant, thus obtaining the surface function of the (m+1)th loop.

6. The first-order differential non-discontinuous concentric ring alternating outer ring defocusing method according to claim 1, characterized in that, Also includes: The annular defocused curved surface is machined, and at the boundary position r of each ring... m Increase toolpath density in the surrounding area; At the boundary position r of each ring m At this point, dense sampling is performed along the radial direction to obtain multiple sampling points, and the first-order differential value of adjacent sampling points is calculated. Calculate the boundary position r m The deviation between the first-order derivative values ​​on both sides is calculated, and the deviation is verified to be less than a preset threshold.

7. A myopia lens, characterized in that, The steps are for implementing the first-order differential non-discontinuous concentric ring alternating outer ring defocusing method according to any one of claims 1 to 6.

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