A single-ring micro-step continuous defocus mirror and a design method thereof

Abstract

The application provides a single-ring micro-step continuous defocus mirror and a design method thereof. The single-ring micro-step continuous defocus mirror comprises a central micro-defocus emmetropia area, a progressive defocus area and an edge arc area. The central micro-defocus emmetropia area and the progressive defocus area are both near-vision defocus curved surfaces, and the edge arc area is a far-vision defocus curved surface. A single-ring micro-step fault is connected between the progressive defocus area and the central micro-defocus emmetropia area, and the single-ring micro-step fault has a Hermite interpolation optimized micro-step elevation at a curved surface joint of the progressive defocus area and the central micro-defocus emmetropia area. The curved surface of the progressive defocus area and the edge arc area and the joint thereof have a continuous first derivative. The single-ring micro-step fault and the adjacent curved surface joint are provided with the Hermite interpolation optimized micro-step elevation, the entrance pupil defocus amount and the smoothness of the arc segment joint are increased, the joint of the progressive defocus area and the edge arc area has a continuous first derivative, high-frequency noise caused by stray light is eliminated, the imaging quality is high, the wearing is comfortable, the myopia prevention and control effect is good, and the single-ring micro-step continuous defocus mirror can be applied to contact lenses.

Description

Technical Field

[0001] This invention belongs to the field of ophthalmic lens technology, and particularly relates to a single-ring micro-step continuous defocus lens and its design method; the single-ring micro-step continuous defocus lens and its design method are applicable to contact lenses, eyeglasses or intraocular lenses, and are especially suitable for contact lenses. Background Technology

[0002] The peripheral myopic defocus theory is a widely accepted and validated theory in the field of myopia control. It posits that the eyeball has a mechanism for following the image point as it grows. Under the premise of ensuring the central retina is in a symmetric state, if other parts of the retina exhibit hyperopic defocus, it will induce continuous elongation of the axial length, accelerating myopia progression. Conversely, if other parts of the retina exhibit myopic defocus, it can inhibit axial elongation and slow myopia progression. The imaging states of myopic and hyperopic defocus are as follows: Figure 1 As shown, the morphology of the myopia defocus signal is not a key factor; both continuous and intermittent signals can play a role. The myopia defocus signal must continuously enter the pupil to be effective. The area, volume, total amount, and duration of the defocus signal in the entrance pupil area are the core factors affecting the myopia control effect. Therefore, achieving a balance between enhancing the amount of defocus signal entering the pupil and improving visual quality is an ongoing challenge.

[0003] Traditional defocus lenses are designed with progressive defocus and concentric ring designs. Compared to progressive defocus, the concentric ring design has multiple large differences in optical power, resulting in strong glare and affecting wearing comfort. There is also a certain defocus gap between the rings, affecting the total amount of defocus. On the other hand, the progressive defocus design is more pupil-dependent. The larger the pupil, the more defocus is achieved. Conversely, it is less effective at myopia control for small pupils.

[0004] To address the aforementioned problems, it is necessary to develop a continuous defocus lens that can not only overcome the glare and discomfort caused by the progressive defocus optical power difference, but also improve entrance pupil defocus to alleviate pupil dependence and enhance myopia control. Summary of the Invention

[0005] The purpose of this invention is to solve the above-mentioned technical problems and provide a single-ring micro-step continuous defocus lens to overcome the glare discomfort caused by the progressive defocus optical power difference, and also to improve the entrance pupil defocus to alleviate pupil dependence and enhance the myopia control effect.

[0006] To achieve the above objectives, the present invention adopts the following technical solution:

[0007] A single-ring micro-step continuous defocus lens includes a central micro-defocus emergent zone, a progressive defocus zone, and an edge arc zone. The progressive defocus zone is located outside the central micro-defocus emergent zone and inside the edge arc zone. Both the central micro-defocus emergent zone and the progressive defocus zone are myopia-enhancing defocus surfaces, and the edge arc zone is a hyperopia-enhancing defocus surface. The defocus amount of the progressive defocus zone and the single-ring micro-step is greater than that of the central micro-defocus emergent zone. A single-ring micro-step is connected between the progressive defocus zone and the central micro-defocus emergent zone to increase the entrance pupil defocus amount. The junction of the single-ring micro-step with the surfaces of the progressive defocus zone and the central micro-defocus emergent zone has Hermite interpolation-optimized micro-step elevation. The surfaces containing the progressive defocus zone and the edge arc zone, and their junction, have continuous first derivatives.

[0008] This invention fills the defocus gap between rings in the concentric ring design by continuously defocusing the entire arc segment of the central micro-defocus emmetropic zone, the progressive defocus zone, and the edge arc zone. Furthermore, the single-ring micro-step defocus design alleviates the dependence on the pupil in traditional progressive defocus designs, allowing even small pupils to have sufficient myopia-correcting defocus, significantly increasing the amount of defocus entering the pupil and further enhancing the myopia control effect. This invention connects the progressive defocus zone and the central micro-defocus emmetropic zone with a single-ring micro-step section. The connection between the single-ring micro-step section and the curved surfaces of the progressive defocus zone and the central micro-defocus emmetropic zone features Hermite interpolation-optimized micro-step elevation. Additionally, the curved surfaces of the progressive defocus zone and the edge arc zone, and their connection points, have continuous first derivatives, eliminating high-frequency noise caused by stray light, optimizing the smoothness of the arc segment connection, improving the imaging quality of the retina, and reducing potential discomfort during wear.

[0009] Furthermore, the surface shape of the edge arc region has a continuous first derivative with the surface where the progressive defocus region is located.

[0010] Furthermore, the micro-level elevation refers to the difference in elevation between the curved surfaces, where the elevation is 0~30 μm and the curved surfaces exhibit an optical power of 0~6 D.

[0011] Furthermore, the central micro-defocus frontal view area, the progressive defocus area, and the edge arc area satisfy equation (Ⅰ), where the optical axis is in the z-direction. It is the sag, the z-component of the surface displacement from the vertex. It is a radial coordinate perpendicular to the optical axis, while , Representing a piecewise curve Values, aspherical surfaces are represented by curves on the YOZ plane; where 0-r1 represents the arc segment with a central slightly out-of-focus front view area; r1-r2 represents the arc segment with a progressively out-of-focus area; and r2-r3 represents the arc segment with an edge arc area.

[0012] (I)

[0013] Equation (Ⅰ) is the standard formula for the surface shape of an even-order aspherical surface. a 、 b 、 d All coefficients are even-degree terms. c For vertex curvature, k is the conicity factor; where the parameter a 1 represents the even-order aspherical polynomial of the central slightly defocused frontal view arc segment. r 4 The aspherical coefficients of the term represent the fourth-order correction for the basic conic surface; b1 represents the even-order aspherical polynomial of the arc segment in the central slightly defocused front view area. r 6 The aspherical coefficient of the term represents the sixth-order correction for the basic conic surface; c 1 represents the curvature of the apex of the arc segment in the central slightly out-of-focus viewing area; d 1 represents the even-order aspherical polynomial of the central slightly defocused frontal view arc segment. r 8 The aspherical coefficient of the term represents the eighth-order correction for the basic conic surface; a 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 4 The aspheric coefficient of the term; b 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 6 The aspheric coefficient of the term; c 2 represents the curvature at the vertex of the arc segment in the progressive defocus region; d 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 8 The aspheric coefficient of the term; a 3 represents the even-order aspherical polynomial of the arc segment in the edge arc region. r 4 The aspheric coefficient of the term; b 3 represents the aspherical polynomial of the arc segment in the edge arc region. r 6 The aspheric coefficient of the term; c 3 represents the curvature of the vertex of the arc segment in the edge arc region; d 3 represents the even-order aspherical polynomial of the arc segment in the edge arc region. r 8 The aspheric coefficient of the term; k 1 represents the conicity of the even-order aspherical surface of the arc segment in the central micro-defocus front view area; k 2 represents the conic coefficient of the arc segment in the progressive defocusing region; k 3 represents the conic coefficient of an even-order aspherical surface in the arc segment of the edge arc region;

[0014] For the two arc segments, the progressive defocus zone and the edge arc zone, assuming and Let be two points on the connecting curve of the two arc segments. At the junction of the arc segments, let be... It can be concluded that , exist The derivative in the direction satisfies the following equation (II):

[0015] , (II).

[0016] Furthermore, the arc segment at the junction of the single-ring micro-step fault is obtained by 2-point cubic Hermite interpolation.

[0017] Furthermore, the arc segment at the junction of the single-ring micro-step fault is obtained by 2-point cubic Hermite interpolation, including performing 2-point cubic Hermite interpolation on the line segment at the junction of the single-ring micro-step fault and the arc segment at the junction of the progressive defocus zone or the central micro-defocus frontal view zone curved surface. The 2-point cubic Hermite interpolation needs to satisfy:

[0018] According to equation (Ⅰ), the coordinates and first derivatives of points A and B at the junction of the arc segments can be obtained, respectively. , The coordinate system for interpolation is constructed with the center point of the front surface as the origin, using a polynomial. By performing three Hermite interpolation reconstructions on the line connecting points A and B, a unique Hermite interpolation polynomial is obtained.

[0019] (III)

[0020] in, , , , Let f(x) denote a basis function, which is a polynomial of degree 3, and satisfies:

[0021] (Ⅲ-1);

[0022] (Ⅲ-2);

[0023] (Ⅲ-3);

[0024] (Ⅲ-4).

[0025] Furthermore, the arc defocus amount of the central micro-defocus front view area is 0-1.5 D.

[0026] Preferably, the defocusing amount of the progressive defocusing zone is 0 D-7 D.

[0027] Preferably, the defocusing amount at the junction of the single-ring micro-step fault with the progressive defocusing zone and the central micro-defocusing frontal view area is 0 D-7 D.

[0028] Furthermore, the arc diameter R1 of the central micro-defocus frontal viewing area is 1~2 mm.

[0029] Furthermore, the arc diameter R2 of the progressive defocusing region is 1~4 mm.

[0030] Furthermore, the central micro-defocus front view area, the progressive defocus area, and the edge arc area are spherical.

[0031] Preferably, the defocus, power, and toric of the single-ring micro-sequential defocus lens can be randomly distributed on the surface of the central micro-defocus front view area, the progressive defocus area, and the edge arc area.

[0032] Preferably, the defocus, power, and toric distribution of the single-ring micro-sequential defocus lens are reflected on the front surface of the central micro-defocus front view area, the progressive defocus area, and the edge arc area.

[0033] Furthermore, the arc diameter R3 of the edge arc region is 1~5 mm.

[0034] Preferably, the single-ring micro-step continuous defocusing lens can be made of silicone hydrogel, hydrogel, hydrophilic or hydrophobic acrylate, resin or PC, etc.

[0035] Preferably, the single-ring micro-step continuous defocusing lens is an ophthalmic lens such as an intraocular lens, orthokeratology lens, contact lens, or eyeglasses.

[0036] Furthermore, the present invention provides a design method for a single-ring micro-order continuous defocusing mirror, comprising the following steps:

[0037] S1. Select a surface shape that satisfies the central micro-defocus front view area, the progressive defocus area, and the edge arc area, wherein the curved surface where the progressive defocus area and the edge arc area are located and their junctions have continuous first derivatives;

[0038] The central micro-defocus front view area, the progressive defocus area, and the edge arc area satisfy equation (Ⅰ), where the optical axis is in the z-direction. It is the sag, the z-component of the surface displacement from the vertex. It is a radial coordinate perpendicular to the optical axis, while , Representing a piecewise curve The value, aspherical surface is represented by a curve on the YOZ plane, where O is the optical center of the central micro-defocus front view area; where 0-r1 represents the arc segment with the central micro-defocus front view area; r1-r2 represents the arc segment of the progressive defocus area; and r2-r3 represents the arc segment of the edge arc area.

[0039] (I)

[0040] Equation (Ⅰ) is the standard formula for the surface shape of an even-order aspherical surface. a 、 b 、 d All coefficients are even-degree terms. c For vertex curvature, k is the conicity factor; where the parameter a 1 represents the even-order aspherical polynomial of the central slightly defocused frontal view arc segment. r 4 The aspherical coefficients of the term represent the fourth-order correction for the basic conic surface; b1 represents the even-order aspherical polynomial of the arc segment in the central slightly defocused front view area. r 6 The aspherical coefficient of the term represents the sixth-order correction for the basic conic surface; c 1 represents the curvature of the apex of the arc segment in the central slightly out-of-focus viewing area; d 1 represents the even-order aspherical polynomial of the central slightly defocused frontal view arc segment. r 8 The aspherical coefficient of the term represents the eighth-order correction for the basic conic surface; a 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 4 The aspheric coefficient of the term; b 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 6 The aspheric coefficient of the term; c 2 represents the curvature at the vertex of the arc segment in the progressive defocus region; d 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 8 The aspheric coefficient of the term; a 3 represents the even-order aspherical polynomial of the arc segment in the edge arc region. r 4 The aspheric coefficient of the term; b 3 represents the aspherical polynomial of the arc segment in the edge arc region. r 6 The aspheric coefficient of the term; c 3 represents the curvature of the vertex of the arc segment in the edge arc region; d 3 represents the even-order aspherical polynomial of the arc segment in the edge arc region. r 8 The aspheric coefficient of the term; k 1 represents the conicity of the even-order aspherical surface of the arc segment in the central micro-defocus front view area; k 2 represents the conic coefficient of the arc segment in the progressive defocusing region; k3 represents the conic coefficient of an even-order aspherical surface in the arc segment of the edge arc region;

[0041] For the two arc segments, the progressive defocus zone and the edge arc zone, assuming and Let be two points on the connecting curve of the two arc segments. At the junction of the arc segments, let be... It can be concluded that , exist The derivative in the direction satisfies the following equation (II):

[0042] , (II);

[0043] S2. Perform 2-point cubic Hermite interpolation optimization on the arc segment at the junction of the single-ring micro-step fault, reconstruct the surface shape, and design a single-ring micro-step continuous defocusing mirror.

[0044] The arc segment at the junction of the single-ring micro-step fault is obtained by 2-point cubic Hermite interpolation, which includes performing 2-point cubic Hermite interpolation on the line segment at the junction of the single-ring micro-step fault with the arc segment at the junction of the curved surface of the progressive defocus zone or the central micro-defocus frontal view zone. The 2-point cubic Hermite interpolation needs to satisfy the following:

[0045] According to equation (Ⅰ), the coordinates and first derivatives of points A and B at the junction of the arc segments can be obtained, respectively. , The coordinate system for interpolation is constructed with the center point of the front surface as the origin, using a polynomial. By performing three Hermite interpolation reconstructions on the line connecting points A and B, a unique Hermite interpolation polynomial is obtained.

[0046] (III)

[0047] in, , , , Let f(x) denote a basis function, which is a polynomial of degree 3, and satisfies:

[0048] (Ⅲ-1);

[0049] (Ⅲ-2);

[0050] (Ⅲ-3);

[0051] (Ⅲ-4).

[0052] The beneficial effects of this invention are as follows:

[0053] (1) This invention fills the defocus gap between rings in the concentric ring design by continuously defocusing the central micro-defocus frontal view zone, the progressive defocus zone and the edge arc zone across the entire arc. The progressive defocus design, compared to the abrupt changes in optical power of the ordinary concentric ring design, has two abrupt changes in one ring, resulting in a greater glare under the same amount of defocus. This design is more comfortable to wear than the concentric ring design. In addition, the single-ring micro-step defocus design alleviates the dependence of the pupil on the traditional progressive defocus design. Even with a small pupil, there can be sufficient myopia-reducing defocus, which greatly increases the amount of defocus entering the pupil and further enhances the myopia control effect.

[0054] (2) The present invention connects the progressive defocus zone and the central micro-defocus emmetropic zone with a single-ring micro-step section. The single-ring micro-step section has Hermite interpolation optimized micro-step elevation at the junction of the curved surfaces of the progressive defocus zone and the central micro-defocus emmetropic zone, which improves the starting point optical power of the arc segment, further enhances the amount of defocus at the entrance pupil, and improves the myopia control effect. The surface shape of the single-ring micro-step section is continuous with the curved surface of the central micro-defocus emmetropic zone or the progressive defocus zone, and has a continuous first derivative, which eliminates high-frequency noise caused by stray light, optimizes the smoothness of the arc segment junction, improves the imaging quality of the retina, and also reduces the discomfort that may be caused during wearing.

[0055] (3) This single-ring micro-step continuous defocus lens and its design method are applicable to contact lenses, eyeglasses or artificial lenses, and are especially suitable for contact lenses. Attached Figure Description

[0056] Figure 1 This is a schematic diagram of the imaging states of myopic defocus and hyperopic defocus.

[0057] Figure 2 This is a schematic diagram of the arc segment distribution of this single-ring micro-sequential defocus lens; in the figure, 1 represents the central micro-defocus frontal view area; 2 represents the progressive defocus area; 3 represents the edge arc area; R1, R2, and R3 represent the arc segment diameter widths of the central micro-defocus frontal view area, the progressive defocus area, and the edge arc area, respectively.

[0058] Figure 3 This is a schematic diagram of the surface shape of one implementation method of the single-ring micro-level continuous defocus lens; in the figure, 1 represents the central micro-defocus front view area; 2 represents the progressive defocus area; 3 represents the edge arc area; Detail A represents micro-level elevation; (a) represents the surface shape before reconstruction; (b) represents the surface shape after 2-point cubic Hermite interpolation optimization.

[0059] Figure 4 Let A and B be the coordinates of the points where the central micro-defocus front view area and the arc segment representing the gradual defocus area meet.

[0060] Figure 5A schematic diagram of the optical power distribution of a single-ring micro-level continuous defocusing lens according to an embodiment of the present invention. Detailed Implementation

[0061] 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 of the invention and are not intended to limit the invention; the specific implementation of the invention will be described in detail below with reference to specific embodiments.

[0062] The terms used in this implementation are explained as follows:

[0063] Progressive defocus refers to the gradual change in optical power as the aperture increases, and progressive defocus design has multiple focal points.

[0064] A defocus lens is a lens with two or more focal points. The defocus amount is the difference in optical power between the two points.

[0065] The central defocus zone is the area where the central focus falls on the retina and the peripheral focus falls in front of the retina.

[0066] Micro-step elevation refers to a step-like difference in elevation at the junction of arc segments on a surface.

[0067] Example 1

[0068] This embodiment provides a single-ring micro-step continuous defocus lens, including a central micro-defocus emergent viewing area 1, a progressive defocus area 2, and an edge arc area 3. The progressive defocus area 2 is located outside the central micro-defocus emergent viewing area 1 and inside the edge arc area 3. Both the central micro-defocus emergent viewing area 1 and the progressive defocus area 2 are curved surfaces for myopia-inducing defocus, and the edge arc area 3 is a curved surface for hyperopia-inducing defocus. A single-ring micro-step section is connected between the progressive defocus area 2 and the central micro-defocus emergent viewing area 1 to increase the amount of defocus at the entrance pupil. The defocus amount of the progressive defocus area 1 and the single-ring micro-step section is greater than the defocus amount of the central micro-defocus emergent viewing area 1. The junction of the single-ring micro-step section with the curved surfaces of the progressive defocus area 2 and the central micro-defocus emergent viewing area 1 has a micro-step elevation optimized by Hermite interpolation. The curved surfaces of the progressive defocus area 2 and the edge arc area 3 and their junction have continuous first derivatives.

[0069] As an optional solution, the micro-step elevation is characterized by a difference in elevation between the curved surfaces, with the elevation ranging from 0 to 30 μm, and the curved surfaces exhibiting an optical power of 0 to 6 D.

[0070] As an optional solution, the arc defocus amount of the central micro-defocus frontal viewing area is 0-1.5 D. The defocus amount of the progressive defocus area is 0 D-7 D; the elevation defocus amount at the junction of the single-ring micro-step fault with the curved surface of the progressive defocus area and the central micro-defocus frontal viewing area is 0 D-7 D; the arc diameter R1 of the central micro-defocus frontal viewing area is 1~2 mm; the arc diameter R2 of the progressive defocus area is 1~4 mm. As an optional solution, the arc diameter R3 of the edge arc area is 1~5 mm; preferably, the above parameters can be selected as 4 mm.

[0071] As an optional solution, the central micro-defocus front view area, the progressive defocus area, and the edge arc area are spherical or aspherical surfaces; the aspherical surface is an aspherical surface without higher-order terms or an aspherical surface containing higher-order terms.

[0072] As an optional solution, the defocus, power, and toric of the single-ring micro-level continuous defocus lens can be randomly distributed on the surface of the central micro-defocus front view area, the progressive defocus area, and the edge arc area; as a preferred solution, the distribution of the defocus, power, and toric of the single-ring micro-level continuous defocus lens is reflected on the front surface of the central micro-defocus front view area, the progressive defocus area, and the edge arc area.

[0073] As an optional solution, the design method of the above-mentioned single-ring micro-order continuous defocusing mirror includes the following steps:

[0074] S1. Select a surface shape that satisfies the central micro-defocus front view area, the progressive defocus area, and the edge arc area, wherein the curved surface where the progressive defocus area and the edge arc area are located and their junctions have continuous first derivatives;

[0075] As an optional scheme, the central micro-defocus frontal view area, the progressive defocus area, and the edge arc area satisfy equation (Ⅰ), where the optical axis is in the z-direction. It is the sag, the z-component of the surface displacement from the vertex. It is a radial coordinate perpendicular to the optical axis, while , Representing a piecewise curve The value, aspherical surface is represented by a curve on the YOZ plane, where the origin is set at the vertex of the central slightly defocused front view arc segment; where 0-r1 represents the arc segment with the central slightly defocused front view arc segment; r1-r2 represents the arc segment with the progressive defocus arc segment; and r2-r3 represents the arc segment with the edge arc segment.

[0076] (I)

[0077] Equation (Ⅰ) is the standard formula for the surface shape of an even-order aspherical surface. a 、 b 、 d All coefficients are even-degree terms. c For vertex curvature,k is the conicity factor; where the parameter a 1 represents the even-order aspherical polynomial of the central slightly defocused frontal view arc segment. r 4 The aspherical coefficients of the term represent the fourth-order correction for the basic conic surface; b1 represents the even-order aspherical polynomial of the arc segment in the central slightly defocused front view area. r 6 The aspherical coefficient of the term represents the sixth-order correction for the basic conic surface; c 1 represents the curvature of the apex of the arc segment in the central slightly out-of-focus viewing area; d 1 represents the even-order aspherical polynomial of the central slightly defocused frontal view arc segment. r 8 The aspherical coefficient of the term represents the eighth-order correction for the basic conic surface; a 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 4 The aspheric coefficient of the term; b 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 6 The aspheric coefficient of the term; c 2 represents the curvature at the vertex of the arc segment in the progressive defocus region; d 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 8 The aspheric coefficient of the term; a 3 represents the even-order aspherical polynomial of the arc segment in the edge arc region. r 4 The aspheric coefficient of the term; b 3 represents the aspherical polynomial of the arc segment in the edge arc region. r 6 The aspheric coefficient of the term; c 3 represents the curvature of the vertex of the arc segment in the edge arc region; d 3 represents the even-order aspherical polynomial of the arc segment in the edge arc region. r 8 The aspheric coefficient of the term; k 1 represents the conicity of the even-order aspherical surface of the arc segment in the central micro-defocus front view area; k 2 represents the conic coefficient of the arc segment in the progressive defocusing region; k 3 represents the conic coefficient of an even-order aspherical surface in the arc segment of the edge arc region;

[0078] For the two arc segments, the progressive defocus zone and the edge arc zone, assuming and Let be two points on the connecting curve of the two arc segments. At the junction of the arc segments, let be... It can be concluded that , exist The derivative in the direction satisfies the following equation (II):

[0079] , (II).

[0080] S2. Perform 2-point cubic Hermite interpolation optimization on the arc segment at the junction of the single-ring micro-step fault, reconstruct the surface shape, and design a single-ring micro-step continuous defocusing mirror.

[0081] As an optional solution, the arc segment at the junction of the single-ring micro-step fault is obtained by 2-point cubic Hermite interpolation, which includes performing 2-point cubic Hermite interpolation on the line segment at the junction of the single-ring micro-step fault and the arc segment at the junction of the progressive defocus zone or the central micro-defocus frontal view zone curved surface. The 2-point cubic Hermite interpolation needs to satisfy:

[0082] According to equation (Ⅰ), the coordinates and first derivatives of points A and B at the junction of the arc segments can be obtained, respectively. , The coordinate system for interpolation is constructed with the center point of the front surface as the origin, using a polynomial. By performing three Hermite interpolation reconstructions on the line connecting points A and B, a unique Hermite interpolation polynomial is obtained.

[0083] (III)

[0084] in, , , , Let f(x) denote a basis function, which is a polynomial of degree 3, and satisfies:

[0085] (Ⅲ-1);

[0086] (Ⅲ-2);

[0087] (Ⅲ-3);

[0088] (Ⅲ-4).

[0089] Example 2

[0090] This invention designs and develops a single-ring micro-step continuous defocus lens, employing the theory of myopia-induced peripheral defocus. Myopia-induced defocus, simply put, means that the image is focused in front of the retina, such as... Figure 1 When the image is focused on the retina, it is a normal vision state, allowing for clear vision. The reason why ordinary soft lenses can worsen myopia is that the peripheral image is focused behind the retina, resulting in hyperopia and defocus, and the eyeball grows to follow the image point.

[0091] The central micro-defocusing area, progressive defocusing area, and edge arc area of ​​this single-ring micro-sequential defocusing lens are distributed as follows: Figure 2 As shown, they are sequentially labeled as arc 1, arc 2, and arc 3. The main function of the central micro-defocus emphyseal zone is to provide a clear optical area and a small amount of entrance pupil defocus. Its diameter is 2 mm to 4 mm. The progressive defocus zone is distributed outside the central micro-defocus emphyseal zone. There is a single-ring micro-step design at the junction with the central micro-defocus emphyseal zone, which greatly improves the entrance pupil defocus. This part of the design is mainly to alleviate the pupil dependence of traditional progressive defocus, so that even small pupils can have a stable entrance pupil defocus signal.

[0092] Arc 1, the frontal view area, employs a frontal micro-defocus design. This arc segment uses an even-order aspherical surface to precisely control the defocus curve, and the defocus amount is achieved using... express, , The diameter R1 of arc segment 1 is in the range of 1~2mm; the progressive defocusing zone of arc segment 2 adopts an even-order aspherical design. Due to different design requirements, this arc segment uses a higher-order term different from that of arc segment 1, and the defocusing amount... , The diameter R2 of arc segment 2 is in the range of 1~4mm; to further increase the defocus amount at the entrance pupil, this invention designs a micro-step fault ring at the connection between arc segment 1 and arc segment 2 to enhance the defocus amount. , The edge arc adopts a hyperopic defocus design to compensate for the reduced lens thickness caused by the first two myopia defocus segments, so that the lens does not collapse and the wearing experience is improved. The arc segment's 3-diameter width R3 is in the range of 1~5 mm.

[0093] Because the front surface of this invention has a multi-region structure design with inconsistent design parameters for each arc segment, even after segmental optimization in Zemax, unevenness still exists at the junctions of the arc segments. Discontinuous surfaces lead to stray light and wavefront discontinuities, resulting in a decrease in the system's imaging quality. Therefore, the boundaries of the stitched surfaces should have continuity. Surface continuity has the following two definitions: ①C 0 Continuity means that the end point of the previous surface segment is the same as the starting point of the next surface segment; ②C 1 The derivative must be continuous to ensure that the surfaces remain smooth at the junctions and do not have sharp edges. However, C 0 The continuity of continuous surfaces is insufficient because their orientation may change abruptly; smooth surfaces require C... 1 Continuity, which requires C 0 Continuity and continuous first derivatives.

[0094] The expression for the piecewise surface in this design is:

[0095] (I)

[0096] (Ⅰ-1)

[0097] (Ⅰ-2)

[0098] Assuming the optical axis is in the z-direction, It is the sag, the z-component of the surface displacement from the vertex. It is a radial coordinate perpendicular to the optical axis, while , Representing a piecewise curve According to this definition, an aspherical surface is represented as a curve on the YOZ plane. For the central region, Let be the curvature of the surface vertex. It is a quadratic constant. , and These are the fourth, sixth, and eighth order deformation coefficients, which describe the deformation caused by... and Surface deviation of the specified axisymmetric quadratic surface It is the curve of arc segment 1 and arc segment 2. The difference in values, the coefficients with subscripts 2 and 3 correspond to the coefficients with subscript 1, representing the outermost arc segment and the outermost arc segment, respectively.

[0099] The following derivation takes the two arc segments of the progressive defocus zone and the edge arc zone as examples, assuming... and Let be two points on the connecting curve of the two arc segments. At the junction of the arc segments, let be... It is easy to obtain. We can also conclude exist The derivative in the direction is as follows:

[0100] (Ⅰ-3)

[0101] (Ⅰ-4)

[0102] To satisfy C 1 Continuity requirements must meet the following conditions:

[0103] , (II)

[0104] Thus, we obtained C. 1 The mathematical requirement of continuity exists; however, the smoothness of the surface along a non-radial curve remains to be proven. Taking a curve as an example, its projection onto the XOY plane is a straight line. The curve on the XOY plane is defined as follows:

[0105] (Ⅱ-1)

[0106] in and It is any real number.

[0107] We can also get

[0108] (Ⅱ-2)

[0109] In addition, at the intersection of the arc segments

[0110] (Ⅱ-3)

[0111] This represents the y-value of the intersection point where the two arc segments meet.

[0112] The derivatives are respectively

[0113] (Ⅱ-4)

[0114] (Ⅱ-5)

[0115] exist In the case of comparison and It is obvious

[0116] (Ⅱ-6)

[0117] Similarly, we can also conclude

[0118] (Ⅱ-7)

[0119] Therefore, it is obvious

[0120] (Ⅱ-8)

[0121] For this curve, and It is linearly correlated, but according to other deductive results, and For higher-order correlations, we can obtain the same result. After C... 1 The continuously optimized curve ensures that the generation of reasonable CNC tool trajectories has no breaks, which will greatly improve machining accuracy and efficiency.

[0122] This type of C 1Continuity optimization is more suitable for the design of arc segments 2 and 3. For the connection between arc segments 1 and 2, the z-axis plane needs to retain a slight elevation design. We can perform 2-point cubic Hermite interpolation on the line segment at the arc connection to achieve the effect of wavefront denoising. Compared with linear interpolation and Newton interpolation, Hermite interpolation has better smoothness and higher accuracy. However, the polynomial degree obtained by directly using Hermite interpolation is high, which may lead to the risk of Runge phenomenon.

[0123] This design uses a 2-point cubic Hermite interpolation polynomial, such as Figure 3 As shown, the intersection of the arc segments is optimized from (a) to (b), and the Hermite interpolation optimization is as follows: Figure 4 Let A be the coordinates of the point where arc segment 1 connects to arc segment 2. According to equation (Ⅰ), the coordinates and first derivatives of points A and B can be obtained, respectively. , The coordinate system used for interpolation has the center point of the front surface as the origin. However, since the difference in sag at the junction of arc segment 1 and arc segment 2 is on the order of micrometers, it is inconvenient to observe. Figure 4 To facilitate observation of the virtual coordinate system, a polynomial of degree ≤ 3 is directly constructed. A cubic Hermite interpolation reconstruction is performed on the line connecting points A and B. According to the theorem, the Hermite interpolation polynomial satisfying the interpolation conditions exists and is unique. The solution method is as follows: Due to the large number of undetermined coefficients, four basis functions are introduced here. , , , The four basis functions are all polynomials of degree 3. Let

[0124] (III)

[0125] in

[0126] (Ⅲ-1)

[0127] Similarly, we can obtain

[0128] (Ⅲ-2)

[0129] (Ⅲ-3)

[0130] (Ⅲ-4)

[0131] The surface shape reconstructed through 2x3 Hermite interpolation filters out some unwanted stray light, enhancing visual quality and improving wearing comfort to some extent. Furthermore, this surface reconstruction method better eliminates high-frequency noise caused by changes in ambient light, resulting in a smoother and more precise surface shape. This not only improves image quality on the retina but also reduces potential discomfort during wear, enhancing the overall user experience.

[0132] Example 3

[0133] Table 1 shows the parameters of the single-ring micro-order continuous defocusing mirror constructed by the method in Example 2 above, which correspond to Table 1 below. Figure 5 This is the optical power distribution diagram of this design. It can be seen that the diameter of the central micro-defocused front view area is 2~4 mm, and the defocus amount is D1, 0D≤D1≤1.5D. The progressive defocus area is distributed outside the central micro-defocused front view area, and there is a defocus of (D2-D1) at the junction, where 0D≤(D2-D1)≤7D. The defocus amount of the progressive defocus area is equal to (D3-D2). The defocus amount (D3-D2) of the progressive defocus area is much greater than the defocus amount D1 of the central micro-defocused front view area. The front surface of this design preferably adopts a high-order aspherical design for the entire arc segment, but an aspherical design or a spherical design can also be used.

[0134] Table 1 Front surface parameters of this design

[0135]

[0136] Note: Defocus amount = optical power of the endpoint coordinate - optical power of the starting coordinate. A positive defocus amount is myopia-induced defocus, and a negative defocus amount is hyperopia-induced defocus.

[0137] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A single-ring micro-scale continuous defocusing lens, characterized in that, It includes a central micro-defocus emergent region, a progressive defocus region, and a lateral arc region. The progressive defocus region is located outside the central micro-defocus emergent region and inside the lateral arc region. Both the central micro-defocus emergent region and the progressive defocus region are curved surfaces for myopia-induced defocusing, while the lateral arc region is a curved surface for hyperopia-induced defocusing. The defocus amount of the progressive defocus region and the single-ring micro-step is greater than that of the central micro-defocus emergent region. A single-ring micro-step is connected between the progressive defocus region and the central micro-defocus emergent region to increase the entrance pupil defocus amount. The junction of the single-ring micro-step with the curved surfaces of the progressive defocus region and the central micro-defocus emergent region has a micro-step elevation optimized by Hermite interpolation. The curved surfaces containing the progressive defocus region and the lateral arc region, and their junctions, have continuous first derivatives. The micro-step elevation is a difference in elevation between the curved surfaces.

2. The single-ring micro-level continuous defocusing lens according to claim 1, characterized in that, The sagittal height is 0~30 μm, and the surface exhibits an optical power of 0~6 D.

3. The single-ring micro-level continuous defocusing lens according to claim 1, characterized in that, The central micro-defocus front view area, the progressive defocus area, and the edge arc area satisfy equation (Ⅰ), where the optical axis is in the z-direction. It is the sag, the z-component of the surface displacement from the vertex. It is a radial coordinate perpendicular to the optical axis, while , Representing a piecewise curve The value, aspherical surface is represented by a curve on the YOZ plane, where O is the optical center of the central micro-defocus front view area; where 0-r1 represents the arc segment with the central micro-defocus front view area; r1-r2 represents the arc segment of the progressive defocus area; and r2-r3 represents the arc segment of the edge arc area. ，（Ⅰ） Equation (Ⅰ) is the standard formula for the surface shape of an even-order aspherical surface. a 、 b 、 d All coefficients are even-degree terms. c For vertex curvature, k is the conic coefficient; where the parameter a 1 represents the even-order aspherical polynomial of the central slightly defocused frontal view arc segment. r 4 The aspherical coefficients of the term represent the fourth-order correction for the basic conic surface; b1 represents the even-order aspherical polynomial of the arc segment in the central slightly defocused front view area. r 6 The aspherical coefficient of the term represents the sixth-order correction for the basic conic surface; c 1 represents the curvature of the apex of the arc segment in the central slightly out-of-focus viewing area; d 1 represents the even-order aspherical polynomial of the central slightly defocused frontal view arc segment. r 8 The aspherical coefficient of the term represents the eighth-order correction for the basic conic surface; a 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 4 The aspheric coefficient of the term; b 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 6 The aspheric coefficient of the term; c 2 represents the curvature at the vertex of the arc segment in the progressive defocus region; d 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 8 The aspheric coefficient of the term; a 3 represents the even-order aspherical polynomial of the arc segment in the edge arc region. r 4 The aspheric coefficient of the term; b 3 represents the aspherical polynomial of the arc segment in the edge arc region. r 6 The aspheric coefficient of the term; c 3 represents the curvature of the vertex of the arc segment in the edge arc region; d 3 represents the even-order aspherical polynomial of the arc segment in the edge arc region. r 8 The aspheric coefficient of the term; k 1 represents the conicity of the even-order aspherical surface of the arc segment in the central micro-defocus front view area; k 2 represents the conic coefficient of the arc segment in the progressive defocusing region; k 3 represents the conic coefficient of an even-order aspherical surface in the arc segment of the edge arc region; For the two arc segments, the progressive defocus zone and the edge arc zone, assuming and Let be two points on the connecting curve of the two arc segments. At the junction of the arc segments, let be... It can be concluded that , exist The derivative in the direction satisfies the following equation (II): ， （Ⅱ）。 4. The single-ring micro-level continuous defocusing lens according to claim 1, characterized in that, The arc segment at the junction of the single-ring micro-step fault is obtained by 2-point cubic Hermite interpolation, which includes performing 2-point cubic Hermite interpolation on the line segment at the junction of the single-ring micro-step fault with the arc segment at the junction of the curved surface of the progressive defocus zone or the central micro-defocus frontal view zone. The 2-point cubic Hermite interpolation needs to satisfy the following: According to equation (Ⅰ), the coordinates and first derivatives of points A and B at the junction of the arc segments can be obtained, respectively. , The coordinate system for interpolation is constructed with the center point of the front surface as the origin, using a polynomial. By performing three Hermite interpolation reconstructions on the line connecting points A and B, a unique Hermite interpolation polynomial is obtained. （Ⅲ） in, , , , Let f(x) denote a basis function, which is a polynomial of degree 3, satisfying: （Ⅲ-1）； （Ⅲ-2）； （Ⅲ-3）； （Ⅲ-4）。 5. The single-ring micro-level continuous defocusing lens according to claim 1, characterized in that, The surface shapes of the central micro-defocus front view area, the progressive defocus area, and the edge arc area are selected from one or a combination of spherical surfaces, aspherical surfaces without higher-order terms, or aspherical surfaces containing higher-order terms.

6. The single-ring micro-level continuous defocusing lens according to claim 1, characterized in that, The central micro-defocus front view area has an arc defocus amount of 0-1.5 D.

7. The single-ring micro-level continuous defocusing lens according to claim 1, characterized in that, The arc diameter R1 of the central micro-defocus front view area is 0~2 mm.

8. The single-ring micro-sequential defocusing lens according to claim 1, characterized in that, The arc diameter R2 of the progressive defocusing zone is 0~4 mm.

9. The single-ring micro-level continuous defocusing lens according to claim 1, characterized in that, The arc diameter R3 of the edge arc region is 1~4 mm.

10. A design method for a single-ring micro-level continuous defocusing lens according to claim 1, characterized in that, Includes the following steps: S1. Select a surface shape that satisfies the central micro-defocus front view area, the progressive defocus area, and the edge arc area, wherein the curved surface where the progressive defocus area and the edge arc area are located and their junctions have continuous first derivatives; The central micro-defocus front view area, the progressive defocus area, and the edge arc area satisfy equation (Ⅰ), where the optical axis is in the z-direction. It is the sag, the z-component of the surface displacement from the vertex. It is a radial coordinate perpendicular to the optical axis, while , Representing a piecewise curve The value, aspherical surface is represented by a curve on the YOZ plane, where O is the optical center of the central micro-defocus front view area; where 0-r1 represents the arc segment with the central micro-defocus front view area; r1-r2 represents the arc segment of the progressive defocus area; and r2-r3 represents the arc segment of the edge arc area. ，（Ⅰ） Equation (Ⅰ) is the standard formula for the surface shape of an even-order aspherical surface. a 、 b 、 d All coefficients are even-degree terms. c For vertex curvature, k is the conic coefficient; where the parameter a 1 represents the even-order aspherical polynomial of the central slightly defocused frontal view arc segment. r 4 The aspherical coefficients of the term represent the fourth-order correction for the basic conic surface; b1 represents the even-order aspherical polynomial of the arc segment in the central slightly defocused front view area. r 6 The aspherical coefficient of the term represents the sixth-order correction for the basic conic surface; c 1 represents the curvature of the apex of the arc segment in the central slightly out-of-focus viewing area; d 1 represents the even-order aspherical polynomial of the central slightly defocused frontal view arc segment. r 8 The aspherical coefficient of the term represents the eighth-order correction for the basic conic surface; a 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 4 The aspheric coefficient of the term; b 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 6 The aspheric coefficient of the term; c 2 represents the curvature at the vertex of the arc segment in the progressive defocus region; d 2 represents the even-order aspherical polynomial of the asymptotic defocusing arc segment. r 8 The aspheric coefficient of the term; a 3 represents the even-order aspherical polynomial of the arc segment in the edge arc region. r 4 The aspheric coefficient of the term; b 3 represents the aspherical polynomial of the arc segment in the edge arc region. r 6 The aspheric coefficient of the term; c 3 represents the curvature of the vertex of the arc segment in the edge arc region; d 3 represents the even-order aspherical polynomial of the arc segment in the edge arc region. r 8 The aspheric coefficient of the term; k 1 represents the conicity of the even-order aspherical surface of the arc segment in the central micro-defocus front view area; k 2 represents the conic coefficient of the arc segment in the progressive defocusing region; k 3 represents the conic coefficient of an even-order aspherical surface in the arc segment of the edge arc region; For the two arc segments, the progressive defocus zone and the edge arc zone, assuming and Let be two points on the connecting curve of the two arc segments. At the junction of the arc segments, let be... It can be concluded that , exist The derivative in the direction satisfies the following equation (II): ， （Ⅱ）； S2. Perform 2-point cubic Hermite interpolation optimization on the arc segment at the junction of the single-ring micro-step fault, reconstruct the surface shape, and design a single-ring micro-step continuous defocusing mirror. The arc segment at the junction of the single-ring micro-step fault is obtained by 2-point cubic Hermite interpolation, which includes performing 2-point cubic Hermite interpolation on the line segment at the junction of the single-ring micro-step fault with the arc segment at the junction of the curved surface of the progressive defocus zone or the central micro-defocus frontal view zone. The 2-point cubic Hermite interpolation needs to satisfy the following: According to equation (Ⅰ), the coordinates and first derivatives of points A and B at the junction of the arc segments can be obtained, respectively. , The coordinate system for interpolation is constructed with the center point of the front surface as the origin, using a polynomial. By performing three Hermite interpolation reconstructions on the line connecting points A and B, a unique Hermite interpolation polynomial is obtained. （Ⅲ） in, , , , Let f(x) denote a basis function, which is a polynomial of degree 3, satisfying: （Ⅲ-1）； （Ⅲ-2）； （Ⅲ-3）； （Ⅲ-4）。

Images