Single-ring micro-order continuous defocus lens and design method thereof

Abstract

The invention provides a single-ring micro-order continuous defocus lens and a design method thereof, the single-ring micro-order continuous defocus lens comprises a central micro-defocus front view area, a progressive defocus area and an edge arc area, the central micro-defocus front view area and the progressive defocus area are both myopic defocus curved surfaces, and the edge arc area is a hyperopic defocus curved surface; a single-ring micro-order fault is connected between the progressive defocus area and the central micro-defocus front view area, and the joint of the single-ring micro-order fault and the curved surfaces of the progressive defocus area and the central micro-defocus front view area is provided with a micro-order elevation optimized by Hermite interpolation; and a continuous first-order derivative is arranged on the curved surfaces of the progressive defocus region and the side arc region and the joint thereof. According to the method, the Hermite interpolation optimized micro-order elevation is arranged at the joint of the single-ring micro-order fault and the adjacent curved surface, so that the entrance pupil defocusing amount and the smoothness of the arc segment joint are increased; meanwhile, a continuous first-order derivative is arranged at the joint of the progressive defocus region and the side arc region, so that high-frequency noise caused by stray light is eliminated; the lens is high in imaging quality, comfortable to wear, good in myopia prevention and control effect and applicable to contact lenses.

Description

Technical Field

[0001] The present invention belongs to the technical field of ophthalmic lenses, and in particular relates to a single-ring micro-step continuous defocusing lens and a design method thereof; the single-ring micro-step continuous defocusing lens and the design method thereof are suitable for contact lenses, frame glasses or artificial lenses, and are particularly suitable for contact lenses in contact lenses. Background Art

[0002] The peripheral myopia defocus theory is a widely recognized and proven effective theory in the field of myopia prevention and control. It believes that the eyeball has a mechanism to grow in pursuit of the image point. Under the premise of ensuring that the central part is in the emmetropia state, if there is a hyperopic defocus state in other parts of the retina, it will induce the eye axis to continue to lengthen and deepen the progression of myopia; conversely, if there is a myopic defocus state in other parts of the retina, it can inhibit the elongation of the eye axis and delay the progression of myopia. The imaging states of myopic defocus and hyperopic defocus are as follows: Figure 1 As shown in the figure, the form of myopic defocus signal is not a key factor, and continuous or intermittent signals can work. Myopic defocus signal must continuously enter the pupil to work. The area, volume, total amount and duration of the defocus signal in the pupil area are the core factors affecting the myopia control effect. Therefore, it is an eternal issue to strike a balance between enhancing the defocus signal in the pupil and improving the visual quality.

[0003] Traditional defocus glasses are designed with progressive defocus and concentric ring designs. Compared with progressive defocus, the concentric ring design has multiple larger optical power differences, a strong sense of glare, and affects the wearing comfort. There is a certain defocus gap between the rings, which affects the total defocus amount. The progressive defocus design is more dependent on the pupil. The larger the pupil, the greater the entrance defocus amount. On the contrary, the myopia prevention and control effect will be at a disadvantage for people with small pupils.

[0004] In order to solve the above-mentioned problems, it is necessary to develop a continuous defocus lens, which can not only overcome the glare discomfort caused by the gradual defocus light focal difference, but also increase the entrance pupil defocus to alleviate pupil dependence and enhance the myopia prevention and control effect. Summary of the invention

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

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A single-ring micro-step continuous defocus lens comprises a central micro-defocus emmetropia zone, a progressive defocus zone and an edge arc zone, wherein the progressive defocus zone is arranged on the outer side of the central micro-defocus emmetropia zone and the inner side of the edge arc zone, the central micro-defocus emmetropia zone and the progressive defocus zone are both myopic defocusing surfaces, and the edge arc zone is a hyperopic defocusing surface; the defocusing amount of the progressive defocus zone and the single-ring micro-step fault is greater than the defocusing amount of the central micro-defocus emmetropia zone; a single-ring micro-step fault for increasing the entrance pupil defocusing amount is connected between the progressive defocus zone and the central micro-defocus emmetropia zone, and the connection between the single-ring micro-step fault and the progressive defocus zone and the central micro-defocus emmetropia zone has a micro-step elevation optimized by Hermite interpolation; the surfaces where the progressive defocus zone and the edge arc zone are located and their connection have continuous first-order derivatives.

[0008] The present invention fills the defocus gap between the rings in the concentric ring design by continuous defocusing of the entire arc segment of the central micro-defocus emmetropia zone, the progressive defocus zone and the side arc zone. In addition, the single-ring micro-step defocus design alleviates the dependence of the traditional progressive defocus design on the pupil, and a small pupil can also have sufficient myopic defocus, which greatly increases the entrance pupil defocus amount and further enhances the myopia prevention and control effect. The present invention has a single-ring micro-step fault connected between the progressive defocus zone and the central micro-defocus emmetropia zone, and the connection between the single-ring micro-step fault and the progressive defocus zone and the central micro-defocus emmetropia zone has a micro-step elevation optimized by Hermite interpolation; and the surface where the progressive defocus zone and the side arc zone are located and their connection have a continuous first-order derivative, which eliminates high-frequency noise caused by stray light, optimizes the smoothness of the arc segment connection, improves the imaging quality of the retina, and reduces the discomfort that may be caused during wearing.

[0009] Furthermore, the surface shape of the edge arc area and the curved surface where the progressive defocus area is located have a continuous first-order derivative.

[0010] Furthermore, the micro-step elevation is a difference in sagittal height between the curved surfaces, the sagittal height is 0 to 30 μm, and the optical focal length of the curved surface is 0 to 6D.

[0011] Furthermore, the central micro-defocused emmetropia zone, the progressive defocused zone and the edge arc zone satisfy formula (I), wherein the optical axis is in the z direction, z(r) is the sag, the z component of the surface displacement from the vertex, r is the radial coordinate perpendicular to the optical axis, and r 2 =(x 2 +y 2 ), r1, r2 represent the r value of the segmented curve, and the aspheric surface is represented by a curve on the YOZ plane; 0-r1 represents the arc segment of the central slightly defocused emmetropia zone; r1-r2 represents the arc segment of the progressive defocus zone; r2-r3 represents the arc segment of the edge arc zone;

[0012]

[0013] Taking the two arc segments of the progressive defocus zone and the edge arc zone as examples, assuming that z=z1 and z=z2 are two points on the connecting curve of the two arc segments, respectively, at the connecting point of the arc segments, set x=0, it can be obtained that y=r2, and the derivative of z in the y direction satisfies the following formula (II):

[0014]

[0015] Furthermore, the arc segment at the junction of the single-ring micro-step fault is obtained by 2-point cubic Hermite interpolation.

[0016] Further, 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 arc segment at the junction of the single-ring micro-step fault and the progressive defocus area or the central micro-defocus emmetropia area curved surface, and the 2-point cubic Hermite interpolation needs to meet the following requirements:

[0017] According to formula (I), the coordinates and first-order derivatives of points A and B at the connection point of the arc segment can be obtained, which are: The coordinate system during interpolation takes the center point of the previous surface as the origin and constructs a polynomial z(y)=ay 3 +by 2 +cy+d, perform cubic Hermite interpolation reconstruction on the line between points A and B to obtain the unique Hermite interpolation polynomial;

[0018] z(y)=z0α0(y)+z1α1(y)+z′0β0(y)+z1′β1(y)(Ш)

[0019] Among them, α0(y), α1(y), β0(y), β1(y) represent basis functions, which are polynomials of degree 3 and satisfy:

[0020]

[0021]

[0022]

[0023]

[0024] Furthermore, the arc segment defocus amount of the central micro-defocused normal vision area is 0-1.5D.

[0025] Preferably, the defocus amount of the progressive defocus zone is 0D-7D.

[0026] Preferably, the raised defocus amount at the junction of the single-ring micro-step fault with the progressive defocus zone and the central micro-defocus normal vision zone is 0D-7D.

[0027] Furthermore, the arc segment width R1 of the central slightly defocused normal viewing area is 1 to 2 mm.

[0028] Furthermore, the arc width R2 of the progressive defocusing zone is 1 to 4 mm.

[0029] Furthermore, the central micro-defocus emmetropia area, the progressive defocus area and the edge arc area are spherical surfaces.

[0030] Preferably, the defocus, degree and Toric of the single-ring micro-step continuous defocus lens can be randomly distributed on the surfaces of the central micro-defocus emmetropia area, the progressive defocus area and the edge arc area.

[0031] Preferably, the defocus, degree and Toric distribution of the single-ring micro-step continuous defocus lens are reflected on the front surfaces of the central micro-defocus emmetropia area, the progressive defocus area and the edge arc area.

[0032] Furthermore, the arc segment width R3 of the side arc area is 1 to 5 mm.

[0033] Preferably, the material of the single-ring micro-step continuous defocusing mirror can be silicone hydrogel, hydrogel, hydrophilic or hydrophobic acrylate, resin or PC, etc.

[0034] Preferably, the single-ring micro-step continuous defocusing lens is an ophthalmic lens such as an artificial lens, a corneal reshaping lens, a contact lens or a frame glasses.

[0035] Furthermore, the present invention provides a design method for a single-ring micro-order continuous defocusing mirror, comprising the following steps:

[0036] S1. Selecting a face shape that satisfies the central micro-defocused emmetropia area, the progressive defocused area and the side arc area, wherein the surface where the progressive defocused area and the side arc area are located and their junctions have continuous first-order derivatives;

[0037] The central micro-defocused emmetropia zone, the progressive defocused zone and the edge arc zone satisfy formula (I), wherein the optical axis is in the z direction, z(r) is the sag, the z component of the surface displacement from the vertex, r is the radial coordinate perpendicular to the optical axis, and r 2 =(x 2 +y 2 ), r1, r2 represent the r value of the segmented curve, and the aspheric surface is represented by a curve on the YOZ plane, where O is the optical center of the central slightly defocused emmetropia zone; 0-r1 represents the arc segment with the central slightly defocused emmetropia zone; r1-r2 represents the arc segment of the progressive defocus zone; r2-r3 represents the arc segment of the edge arc zone;

[0038]

[0039] Taking the two arc segments of the progressive defocus zone and the edge arc zone as examples, assuming that z=z1 and z=z2 are two points on the connecting curve of the two arc segments, respectively, at the connecting point of the arc segments, set x=0, it can be obtained that y=r2, and the derivative of z in the y direction satisfies the following formula (II):

[0040]

[0041] S2. Perform 2-point cubic Hermite interpolation optimization on the arc segment where the single-ring micro-step fault connects, reconstruct the surface shape, and design a single-ring micro-step continuous defocus mirror;

[0042] 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 arc segment at the junction of the single-ring micro-step fault and the progressive defocus area or the central micro-defocus emmetropia area curved surface, and the 2-point cubic Hermite interpolation needs to meet the following requirements:

[0043] According to formula (I), the coordinates and first-order derivatives of points A and B at the connection point of the arc segment can be obtained, which are: The coordinate system during interpolation takes the center point of the previous surface as the origin and constructs a polynomial z(y)=ay 3 +by 2 +cy+d, perform cubic Hermite interpolation reconstruction on the line between points A and B to obtain the unique Hermite interpolation polynomial;

[0044] z(y)=z0α0(y)+z1α1(y)+z′0β0(y)+z1′β1(y)(Ш)

[0045] Among them, α0(y), α1(y), β0(y), β1(y) represent basis functions, which are polynomials of degree 3 and satisfy:

[0046]

[0047]

[0048]

[0049]

[0050] The beneficial effects of the present invention are as follows:

[0051] (1) The present invention fills the defocus gap between the rings in the concentric ring design by continuous defocusing of the entire arc segment of the central micro-defocus emmetropia zone, the progressive defocus zone and the edge arc zone; and the defocus is designed in a progressive manner. Compared with the sudden focal length of the ordinary concentric ring design, one ring has two sudden changes, and the glare sensation is heavier under the same amount of defocus. Compared with the concentric ring design, the present design is more comfortable to wear. In addition, the single-ring micro-step defocus design alleviates the dependence of the traditional progressive defocus design on the pupil. Small pupils can also have sufficient myopic defocus, which greatly increases the entrance pupil defocus and further enhances the myopia prevention and control effect.

[0052] (2) The present invention connects a single-ring micro-step fault between the progressive defocus zone and the central micro-defocus emmetropia zone. The micro-step elevation optimized by Hermite interpolation is provided at the connection between the single-ring micro-step fault and the progressive defocus zone and the central micro-defocus emmetropia zone, thereby increasing the focal length of the arc starting point, further enhancing the entrance pupil defocus amount, and improving the myopia prevention and control effect. The single-ring micro-step fault has a surface shape that is continuous with the surface where the central micro-defocus emmetropia zone or the progressive defocus zone is located, and has a continuous first-order derivative, thereby eliminating high-frequency noise caused by stray light, optimizing the smoothness of the arc connection, improving the imaging quality of the retina, and reducing the discomfort that may be caused during wearing.

[0053] (3) The single-ring micro-step continuous defocusing lens and the design method thereof are suitable for contact lenses, frame glasses or intraocular lenses, and are particularly suitable for contact lenses in contact lenses. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Schematic diagram of the imaging state of myopic defocus and hyperopic defocus.

[0055] Figure 2 Schematic diagram of arc segment distribution of the single-ring micro-step continuous defocusing lens; in the figure, 1 represents the central micro-defocusing normal vision area; 2 represents the progressive defocusing area; 3 represents the side arc area; R1, R2, and R3 represent the arc segment widths of the central micro-defocusing normal vision area, the progressive defocusing area, and the side arc area, respectively.

[0056] Figure 3 This is a schematic diagram of the surface shape of one implementation method of the single-ring micro-step continuous defocusing mirror; Detail A in the figure represents the micro-step lifting; (a) represents the surface shape before reconstruction; (b) represents the surface shape after 2-point cubic Hermite interpolation optimization.

[0057] Figure 4 The coordinates A and B are the points where the central micro-defocused normal vision area and the arc segment representing the progressive defocused area meet.

[0058] Figure 5 Schematic diagram of the optical power distribution of a single-ring micro-step continuous defocusing mirror according to an embodiment of the present invention. DETAILED DESCRIPTION

[0059] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention; the specific implementation of the present invention is described in detail below in conjunction with the specific embodiments.

[0060] The terms involved in this implementation are explained as follows:

[0061] Progressive defocus means that the optical power gradually changes as the aperture increases, and the progressive defocus design has multiple focal points.

[0062] A defocused lens is a lens with two or more focal points, and the defocus amount is the difference in optical power between the two points.

[0063] The central slightly defocused emmetropia zone is where the central focus falls on the retina and the peripheral focus falls in front of the retina.

[0064] Micro-step elevation refers to a step-like height difference at the connection of arc segments on the surface.

[0065] Example 1

[0066] The present embodiment provides a single-ring micro-step continuous defocus lens, comprising a central micro-defocus emmetropia zone 1, a progressive defocus zone 2 and an edge arc zone 3, wherein the progressive defocus zone 2 is arranged on the outer side of the central micro-defocus emmetropia zone 1 and the inner side of the edge arc zone 3, the central micro-defocus emmetropia zone 1 and the progressive defocus zone 2 are both myopic defocus surfaces, and the edge arc zone 3 is a hyperopic defocus surface; a single-ring micro-step fault for increasing the entrance pupil defocus amount is connected between the progressive defocus zone 2 and the central micro-defocus emmetropia zone 1, the defocus amount of the progressive defocus zone 1 and the single-ring micro-step fault is greater than the defocus amount of the central micro-defocus emmetropia zone 1; the connection between the single-ring micro-step fault and the progressive defocus zone 2 and the central micro-defocus emmetropia zone 1 has a micro-step elevation optimized by Hermite interpolation; the surface where the progressive defocus zone 2 and the edge arc zone 3 are located and their connection have a continuous first-order derivative.

[0067] As an optional solution, the micro-step elevation is a difference in sagittal height between the curved surfaces, the sagittal height is 0 to 30 μm, and the optical focal length of the curved surface is 0 to 6D;

[0068] As an optional solution, the arc segment defocus amount of the central micro-defocus embrasure zone is 0-1.5D. The defocus amount of the progressive defocus zone is 0D-7D; the elevation defocus amount at the connection between the single-ring micro-step fault and the progressive defocus zone and the central micro-defocus embrasure zone is 0D-7D; the arc segment diameter width R1 of the central micro-defocus embrasure zone is 1-2mm; the arc segment diameter width R2 of the progressive defocus zone is 1-4mm. As an optional solution, the arc segment diameter width R3 of the side arc zone is 1-5mm. Preferably, the above parameters can be selected as 4mm.

[0069] As an optional solution, the central micro-defocus emmetropia area, the progressive defocus area and the edge arc area are spherical surfaces or aspherical surfaces; the aspherical surface is an aspherical surface without high-order terms or an aspherical surface containing high-order terms.

[0070] As an optional solution, the defocus, degree and Toric of the single-ring micro-step continuous defocus mirror can be randomly distributed on the surfaces of the central micro-defocus emphases area, the progressive defocus area and the edge arc area; preferably, the defocus, degree and Toric distribution of the single-ring micro-step continuous defocus mirror are reflected on the front surfaces of the central micro-defocus emphases area, the progressive defocus area and the edge arc area.

[0071] As an optional solution, the design method of the single-ring micro-order continuous defocusing mirror comprises the following steps:

[0072] S1. Selecting a face shape that satisfies the central micro-defocused emmetropia area, the progressive defocused area and the side arc area, wherein the surface where the progressive defocused area and the side arc area are located and their junctions have continuous first-order derivatives;

[0073] As an optional solution, the central micro-defocus emmetropia zone, the progressive defocus zone and the edge arc zone satisfy formula (I), wherein the optical axis is in the z direction, z(r) is the sagittal height, the z component of the surface displacement from the vertex, r is the radial coordinate perpendicular to the optical axis, and r 2 =(x 2 +y 2 ), r1, r2 represent the r value of the segmented curve, and the aspheric surface is represented as a curve on the YOZ plane, wherein the origin is set at the vertex of the central slightly defocused emmetropia arc segment; wherein 0-r1 represents the arc segment with the central slightly defocused emmetropia arc segment; r1-r2 represents the arc segment of the progressive defocusing area; and r2-r3 represents the arc segment of the edge arc segment;

[0074]

[0075] Taking the two arc segments of the progressive defocus zone and the edge arc zone as examples, assuming that z=z1 and z=z2 are two points on the connecting curve of the two arc segments, respectively, at the connecting point of the arc segments, set x=0, it can be obtained that y=r2, and the derivative of z in the y direction satisfies the following formula (II):

[0076]

[0077] S2. Perform 2-point cubic Hermite interpolation optimization on the arc segment where the single-ring micro-step fault connects, reconstruct the surface shape, and design a single-ring micro-step continuous defocus mirror;

[0078] 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, including performing 2-point cubic Hermite interpolation on the line segment at the junction of the arc segment at the junction of the single-ring micro-step fault and the progressive defocus area or the central micro-defocus emmetropia area curved surface, and the 2-point cubic Hermite interpolation needs to meet the following requirements:

[0079] According to formula (I), the coordinates and first-order derivatives of points A and B at the connection point of the arc segment can be obtained, which are: The coordinate system during interpolation takes the center point of the previous surface as the origin and constructs a polynomial z(y)=ay 3 +by 2 +cy+d, perform cubic Hermite interpolation reconstruction on the line between points A and B to obtain the unique Hermite interpolation polynomial;

[0080] z(y)=z0α0(y)+z1α1(y)+z′0β0(y)+z1′β1(y)(Ш)

[0081] Among them, α0(y), α1(y), β0(y), β1(y) represent basis functions, which are polynomials of degree 3 and satisfy:

[0082]

[0083]

[0084]

[0085]

[0086] Example 2

[0087] The present invention designs and develops a single-ring micro-step continuous defocusing lens, which adopts the theory of myopic peripheral defocusing. The so-called myopic defocusing is simply to image in front of the retina. Figure 1 , the image is formed on the retina, which is the emmetropia state, and objects can be seen clearly. The reason why ordinary soft lenses deepen myopia is that the peripheral image is formed behind the retina, forming hyperopia defocus, and the eyeball grows along with the imaging point.

[0088] The central micro-defocusing positron area, the progressive defocusing area and the edge arc area of ​​the single-ring micro-step continuous defocusing lens are distributed as follows: Figure 2As shown, they are recorded as arc segment 1, arc segment 2, and arc segment 3 respectively. The main function of the central micro-defocus emmetropia area is to provide an optical area for clear vision and a slight amount of entrance pupil defocus. The diameter is 2mm to 4mm. The progressive defocus area is distributed outside the central micro-defocus emmetropia area, and there is a single-ring micro-step fault design at the connection with the central micro-defocus emmetropia area, which greatly increases the entrance pupil defocus. The design of this part is mainly to alleviate the pupil dependence of traditional progressive defocus, so that people with small pupils can also have a stable entrance pupil defocus signal.

[0089] The micro-defocused emphases area of ​​arc segment 1 adopts an emphases micro-defocus design. This arc segment uses an even-order aspheric surface to accurately control the defocus curve. The defocus amount is expressed by ΔF1, ΔF1=D1, 0<ΔF1<1.5D, and the diameter width R1 of arc segment 1 is in the range of 1 to 2mm; the progressive defocus area of ​​arc segment 2 adopts an even-order aspheric design. Due to different design requirements, this arc segment uses a higher-order term different from arc segment 1. The defocus amount ΔF3=D3-D2, ΔF3> >ΔF1, the diameter width R2 of arc segment 2 is in the range of 1 to 4mm; in order to further increase the entrance pupil defocus, the present invention designs a micro-step fault ring at the connection between arc segment 1 and arc segment 2 to raise the defocus amount ΔF2=D2-D1, ΔF2>>ΔF1; the edge arc adopts a hyperopic defocus design to compensate for the lens thickness weakened by the myopic defocus of the first two sections, so that the lens does not collapse and the wearing experience is improved, and the diameter width R3 of arc segment 3 is in the range of 1 to 5mm.

[0090] Since the front surface of the present invention is designed with a multi-region structure, the design parameters of each arc segment are inconsistent. Even if the curve is segmentally optimized in Zemax, there will still be unevenness at the connection of the arc segments. The discontinuous surface will cause stray light and wavefront discontinuity, resulting in a decrease in the imaging quality of the system. Therefore, the boundary of the spliced ​​surface should be continuous. There are two definitions of surface continuity: ①C 0 Continuous, that is, the end point of the previous surface is the same as the starting point of the next surface; ②C 1 The derivative is continuous, so that the surfaces remain smooth and without edges at the junction. However, C 0 Continuity of continuous surfaces is not sufficient, since their directions may change suddenly; smooth surfaces require C 1 Continuity, which requires C 0 Continuity and continuous first derivatives.

[0091] The expression of the segmented surface in this design is:

[0092]

[0093]

[0094]

[0095] Assuming the optical axis is in the z direction, z(r) is the sag, the z component of the surface displacement from the vertex, r is the radial coordinate perpendicular to the optical axis, and r 2 =(x 2 +y 2 ), r1, r2 represent the r value of the segmented curve. According to this definition, the aspheric surface is a curve on the YOZ plane. For the central area, c1 is the vertex curvature of the surface, k1 is a quadratic constant, a1, b1 and d1 are the fourth-order, sixth-order and eighth-order deformation coefficients, respectively, which describe the surface deviation of the axisymmetric quadratic surface specified by r and k, Δz1 is the difference in z value between the curves of arc segment 1 and arc segment 2, and the coefficients with subscripts 2 and 3 correspond to the coefficients with subscript 1, representing the outer arc segment and the outermost arc segment, respectively.

[0096] The following derivation takes the two arc segments of the progressive defocus area and the edge arc area as examples. Assume that z=z1 and z=z2 are two points on the connecting curve of the two arc segments. At the connecting point of the arc segments, set x=0, and it is easy to get y=r2. We can also get the derivative of z in the y direction, as follows:

[0097]

[0098]

[0099] In order to satisfy C 1 Continuity requirements must meet the following conditions:

[0100]

[0101] So far, we have obtained C 1 The mathematical requirement of continuity, however, is that the surface is smooth along non-radial curves. Take a curve as an example, whose projection on the XOY plane is a straight line. The definition of the curve on the XOY plane is as follows:

[0102] x=my+n(Ⅱ-1)

[0103] Where m and n are arbitrary real numbers.

[0104] We can also get

[0105] r 2 =x 2 +y 2 =(m 2 +1)y 2 +2mny+n 2 (Ⅱ-2)

[0106] In addition, at the intersection of the arc segments

[0107]

[0108] y0 represents the y value of the intersection point where two arc segments meet.

[0109] The derivatives are

[0110]

[0111]

[0112] exist In the case of and It's obvious

[0113]

[0114] Similarly, we can also derive

[0115]

[0116] Therefore, it is clear that

[0117]

[0118] For this curve, x and y are linearly related, and according to other deductive results, we can get the same result when x and y are highly correlated. 1 The curve after continuity optimization can ensure the generation of reasonable CNC tool trajectory without breakpoints, which will greatly improve the processing accuracy and efficiency.

[0119] This kind of C 1 Continuity optimization is more suitable for the design of 2 and 3 arc segments. The z-axis surface at the junction of 1 and 2 arc segments needs to retain the micro-order elevation design. We can perform 2-point cubic Hermite interpolation on the line segment at the junction of the arc segments 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 obtained by directly using Hermite interpolation has a higher degree and there is a risk of Runge phenomenon.

[0120] This design uses a 2-point cubic Hermite interpolation polynomial, such as Figure 3 As shown in the figure, the intersection of arc segments is optimized from (a) to (b), and the Hermite interpolation optimization is as follows: Figure 4 is the coordinate of the point where arc segment 1 and arc segment 2 meet. According to formula (I), the coordinates and first-order derivatives of points A and B can be obtained, which are The coordinate system during interpolation takes the center point of the previous surface as the origin. However, since the difference in sagittal height at the junction of arc segment 1 and arc segment 2 is at the micron level, it is not convenient to observe. Figure 4 It is just a virtual coordinate system established for the convenience of observation. A polynomial z(y)=ay with a degree ≤ 3 is directly constructed.3 +by 2 +cy+d, perform cubic Hermite interpolation reconstruction on the line between points A and B. From the theorem, we know that the Hermite interpolation polynomial that satisfies the interpolation conditions exists and is unique. The solution is as follows: Due to the large number of undetermined coefficients, four basis functions need to be introduced here, α0(y), α1(y), β0(y), β1(y). The four basis functions are all polynomials of degree 3. Let

[0121] z(y)=z0α0(y)+z1α1(y)+z′0β0(y)+z1′β1(y)(Ш)

[0122] in

[0123]

[0124] The same can be said

[0125]

[0126]

[0127]

[0128] The surface shape reconstructed by 2-point cubic Hermite interpolation filters out some excess stray light, enhances visual quality, and improves wearing comfort to a certain extent. In addition, by reconstructing the surface through this processing method, high-frequency noise caused by changes in ambient light can be better eliminated, thereby obtaining a smoother and more precise surface shape. This not only improves the imaging quality on the retina, but also reduces the discomfort that may be caused during wearing, improving the overall user experience.

[0129] Example 3

[0130] Table 1 shows the parameters of the single-ring micro-step continuous defocusing mirror constructed by the method of the above-mentioned embodiment 2, which corresponds to the following Table 1: Figure 5 : is the optical power distribution diagram of the present design. It can be seen that the diameter of the central micro-defocus emmetropia zone is 2-4mm, the defocus amount is D1, 0D≤D1≤1,5D, the progressive defocus zone is distributed outside the central micro-defocus emmetropia zone, and there is a defocus of (D2-D1) at the junction, wherein 0D≤(D2-D1)≤7D, the defocus amount of the progressive defocus zone is equal to (D3-D2), and the defocus amount (D3-D2) of the progressive defocus zone is much larger than the defocus amount D1 of the central micro-defocus emmetropia zone. The front surface of the present design preferably adopts a high-order aspherical design for the entire arc segment, and may also adopt an aspherical design or a spherical design.

[0131] Table 1 Front surface parameters of this design

[0132]

[0133] Note: Defocus amount = end point coordinate focal length - start point coordinate focal length. Positive defocus amount is myopic defocus, and negative defocus amount is hyperopic defocus.

[0134] 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 in the protection scope of the present invention.

Claims

1. A single-ring micro-step continuous defocusing mirror, characterized in that: It includes a central micro-defocus emmetropia zone, a progressive defocus zone and an edge arc zone, the progressive defocus zone is arranged on the outer side of the central micro-defocus emmetropia zone and the inner side of the edge arc zone, the central micro-defocus emmetropia zone and the progressive defocus zone are both myopic defocus surfaces, and the edge arc zone is a hyperopic defocus surface; the defocus amount of the progressive defocus zone and the single-ring micro-step fault is greater than the defocus amount of the central micro-defocus emmetropia zone; a single-ring micro-step fault for increasing the entrance pupil defocus amount is connected between the progressive defocus zone and the central micro-defocus emmetropia zone, and the single-ring micro-step fault has a Hermite interpolation optimized micro-step elevation at the connection between the progressive defocus zone and the central micro-defocus emmetropia zone; the surfaces where the progressive defocus zone and the edge arc zone are located and their connection have continuous first-order derivatives.

2. The single-ring micro-step continuous defocusing mirror according to claim 1, characterized in that: The micro-step elevation is a difference in sagittal height between the curved surfaces, the sagittal height is 0 to 30 μm, and the optical focal length of the curved surface is 0 to 6D.

3. The single-ring micro-step continuous defocusing mirror according to claim 1, characterized in that: The central micro-defocused emmetropia zone, the progressive defocused zone and the edge arc zone satisfy formula (I), wherein the optical axis is in the z direction, z(r) is the sag, the z component of the surface displacement from the vertex, r is the radial coordinate perpendicular to the optical axis, and r 2 =(x 2 +y 2 ), r1, r2 represent the r value of the segmented curve, and the aspheric surface is represented by a curve on the YOZ plane, where O is the optical center of the central slightly defocused emmetropia zone; 0-r1 represents the arc segment with the central slightly defocused emmetropia zone; r1-r2 represents the arc segment of the progressive defocus zone; r2-r3 represents the arc segment of the edge arc zone; Taking the two arc segments of the progressive defocus zone and the edge arc zone as examples, assuming that z=z1 and z=z2 are two points on the connecting curve of the two arc segments, respectively, at the connecting point of the arc segments, set x=0, it can be obtained that y=r2, and the derivative of z in the y direction satisfies the following formula (II):

4. The single-ring micro-step continuous defocusing mirror 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, including performing 2-point cubic Hermite interpolation on the line segment at the junction of the arc segment at the junction of the single-ring micro-step fault and the progressive defocus area or the central micro-defocus emmetropia area curved surface, and the 2-point cubic Hermite interpolation needs to meet the following requirements: According to formula (I), the coordinates and first-order derivatives of points A and B at the connection point of the arc segment can be obtained, which are A(y0,z0,d z0 / d y0 )、B(y1,z1,d z1 / d y1 ), the coordinate system for interpolation takes the center point of the previous surface as the origin, and constructs a polynomial z(y)=ay 3 +by 2 +cy+d, perform cubic Hermite interpolation reconstruction on the line between points A and B to obtain the unique Hermite interpolation polynomial; z(y)=z0α0(y)+z1α1(y)+z′0β0(y)+z1′β1(y)(Ш) Among them, α0(y), α1(y), β0(y), β1(y) represent basis functions, which are polynomials of degree 3 and satisfy:

5. The single-ring micro-step continuous defocusing mirror according to claim 1, characterized in that: The surface types of the central micro-defocus emmetropia zone, the progressive defocus zone and the edge arc zone are selected from one or a combination of a spherical surface, an aspherical surface without high-order terms or an aspherical surface with high-order terms.

6. The single-ring micro-step continuous defocusing mirror according to claim 1, characterized in that: The arc segment defocus amount of the central micro-defocused emmetropia area is 0-1.5D.

7. The single-ring micro-step continuous defocusing mirror according to claim 1, characterized in that: The arc segment width R1 of the central micro-defocused normal viewing area is 0 to 2 mm.

8. The single-ring micro-step continuous defocusing mirror according to claim 1, characterized in that: The arc width R2 of the progressive defocusing zone is 0-4 mm.

9. The single-ring micro-step continuous defocusing mirror according to claim 1, characterized in that: The arc segment width R3 of the side arc area is 1 to 4 mm.

10. The design method of the single-ring micro-order continuous defocusing mirror according to claim 1, characterized in that: The steps include: S1. Selecting a face shape that satisfies the central micro-defocused emmetropia area, the progressive defocused area and the side arc area, wherein the surface where the progressive defocused area and the side arc area are located and their junctions have continuous first-order derivatives; The central micro-defocused emmetropia zone, the progressive defocused zone and the edge arc zone satisfy formula (I), wherein the optical axis is in the z direction, z(r) is the sag, the z component of the surface displacement from the vertex, r is the radial coordinate perpendicular to the optical axis, and r 2 =(x 2 +y 2 ), r1, r2 represent the r value of the segmented curve, and the aspheric surface is represented by a curve on the YOZ plane, where O is the optical center of the central slightly defocused emmetropia zone; 0-r1 represents the arc segment with the central slightly defocused emmetropia zone; r1-r2 represents the arc segment of the progressive defocus zone; r2-r3 represents the arc segment of the edge arc zone; Taking the two arc segments of the progressive defocus zone and the edge arc zone as examples, assuming that z=z1 and z=z2 are two points on the connecting curve of the two arc segments, respectively, at the connecting point of the arc segments, set x=0, it can be obtained that y=r2, and the derivative of z in the y direction satisfies the following formula (II): S2. Perform 2-point cubic Hermite interpolation optimization on the arc segment where the single-ring micro-step fault connects, reconstruct the surface shape, and design a single-ring micro-step continuous defocus mirror; 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 arc segment at the junction of the single-ring micro-step fault and the progressive defocus area or the central micro-defocus emmetropia area curved surface, and the 2-point cubic Hermite interpolation needs to meet the following requirements: According to formula (I), the coordinates and first-order derivatives of points A and B at the connection point of the arc segment can be obtained, which are A(y0,z0,d z0 / d y0 )、B(y1,z1,d z1 / d y1 ), the coordinate system for interpolation takes the center point of the previous surface as the origin, and constructs a polynomial z(y)=ay 3 +by 2 +cy+d, perform cubic Hermite interpolation reconstruction on the line between points A and B to obtain the unique Hermite interpolation polynomial; z(y)=z0α0(y)+z1α1(y)+z′0β0(y)+z1′β1(y)(Ш) Among them, α0(y), α1(y), β0(y), β1(y) represent basis functions, which are polynomials of degree 3 and satisfy:

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