Single aspherical lens design method, single aspherical lens

Abstract

The present application provides a method for designing a single aspherical lens and a single aspherical lens. The light incident surface of the single aspherical lens is an aspherical surface, and the light exit surface is a spherical surface. The method includes: obtaining the preset distance between the vertex of the light incident surface and the object point, the focal length of the single aspherical lens, the distance between the vertex of the light exit surface and the image point, and the central thickness of the single aspherical lens; determining the value of the radius of curvature at the vertex of the light incident surface and the value of the radius of curvature at the vertex of the light exit surface; establishing a system of parametric equations that enables the single aspherical lens to satisfy the equal optical path condition; calculating the discrete points of the surface profile of the light incident surface; fitting the discrete points of the surface profile of the light incident surface to obtain the value of the conic coefficient and the aspherical coefficient; determining the standard equation of the light incident surface; determining the height change amount; obtaining the function distribution contour diagram based on the height change amount; and determining the various parameters of the single aspherical lens based on the function distribution contour diagram. The present application can effectively improve the calibration accuracy of the aberration of the single aspherical lens.

Description

Technical Field

[0001] This application belongs to the field of optical technology. More specifically, it relates to a design method for a single aspherical lens and a single aspherical lens. Background Art

[0002] Due to the inherent aberration problem of optical spherical lenses, in practical applications, it is often necessary to use a combination of multiple lenses to form a high-performance optical system. Compared with a single optical lens, the optical path of a combination of multiple lenses has more optical surfaces, resulting in lower optical efficiency and more difficult suppression of stray light. Moreover, it requires a larger volume of space and higher-precision structural processing and assembly processes, which is not conducive to the miniaturization and mass production of the system.

[0003] In order to use a single lens to replace the combination of multiple lenses and meet the corresponding optical index requirements, aspherical lens technology needs to be adopted. In the design of aspherical lenses, the aberration of the optical system can be effectively corrected by optimizing multiple parameters. Since most of the optimization algorithms of existing commercial software are a kind of local optimization algorithm, it is necessary to gradually increase or change variables and change the weight factors of each optimization operand to perform optimization through repeated iteration. This method requires a long time and has high requirements for the experience of designers. At the same time, it is easy to cause inaccurate correction of the aberration of the aspherical lens due to neglecting some parameters. Summary of the Invention

[0004] The purpose of this application is to provide a design method for a single aspherical lens and a single aspherical lens to solve the problem of inaccurate correction of the aberration of a single aspherical lens in the prior art.

[0005] In the first aspect of the embodiments of this application, a design method for a single aspherical lens is provided. The light incident surface of the single aspherical lens is an aspherical surface, and the light exit surface is a spherical surface. The design method includes:

[0006] Obtain the pre-set distance from the vertex of the light incident surface to the object point, the focal length of the single aspherical lens, the distance from the vertex of the light exit surface to the image point, and the central thickness of the single aspherical lens;

[0007] Based on the distance from the vertex of the light incident surface to the object point, the focal length of the single aspherical lens, the distance from the vertex of the light exit surface to the image point, and the central thickness of the single aspherical lens, determine the value of the radius of curvature at the vertex of the light incident surface and the value of the radius of curvature at the vertex of the light exit surface;

[0008] According to the distance from the vertex of the light incident surface to the object point, the central thickness of the single aspherical lens, the distance from the vertex of the light exit surface to the image point, and the value of the radius of curvature at the vertex of the light exit surface, establish a system of parametric relationship equations that enables the single aspherical lens to satisfy the equal optical path condition;

[0009] Calculate the discrete points of the surface shape of the light incident surface according to the system of parametric relationship equations; fit the discrete points of the surface shape of the light incident surface to obtain the values of the conic coefficients and the aspheric coefficients, and determine the standard equation of the light incident surface based on the value of the radius of curvature at the vertex of the light incident surface, the value of the conic coefficient, and the aspheric coefficient;

[0010] After determining the standard equation of the light incident surface, determine the height change amount of the intersection points of the marginal ray and the chief ray with the image plane according to the ray tracing method;

[0011] Obtain the function distribution contour map of the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspheric lens according to the height change amount; based on the function distribution contour map, determine the parameters of the single aspheric lens.

[0012] In the second aspect of the embodiments of the present application, a single aspheric lens is provided. The light incident surface of the single aspheric lens is an aspheric surface, the light exit surface is a spherical surface, and the parameters of the single aspheric lens are obtained according to any one of the single aspheric lens design methods provided in the first aspect of the embodiments of the present application.

[0013] The beneficial effects of the single aspheric lens design method and the single aspheric lens provided by the embodiments of the present application are as follows:

[0014] In the embodiments of the present application, a single aspheric lens composed of a combination of a spherical surface and an aspheric surface is designed, which solves the problems of cumbersome design process and high design cost in the prior art for aspheric lenses and simplifies the lens design process. When designing a single aspheric lens, according to the distance from the vertex of the light incident surface to the object point, the central thickness of the single aspheric lens, the distance from the vertex of the light exit surface to the image point, and the value of the radius of curvature at the vertex of the light exit surface, a system of parametric relationship equations that enables the single aspheric lens to satisfy the equal optical path condition is established. Further, the discrete points of the surface shape of the light incident surface are calculated through the system of parametric relationship equations, and the discrete points of the surface shape are fitted, which solves the problem of initial value sensitivity based on the non-linear multivariable fitting method, and obtains the standard equation of the light incident surface with better optical performance of the single aspheric lens, improving the correction accuracy of the spherical aberration on the axis of the aspheric lens. In the present application, the function distribution contour map is drawn according to the ray tracing method. The function distribution contour map can more comprehensively and vividly depict the off-axis coma aberration change characteristics. Based on the off-axis coma aberration change characteristics, the parameters of the single aspheric lens are determined, and it is not easy to ignore the potential effective parameters of the single aspheric lens, improving the correction accuracy of the off-axis coma aberration of the aspheric lens. The present application can effectively improve the correction accuracy of the spherical aberration on the axis and the off-axis coma aberration of the single aspheric lens. Description of the Drawings

[0015] To more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the accompanying drawings required for the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0016] Figure 1 Schematic flow chart of the single aspherical lens design method provided by the embodiments of the present application;

[0017] Figure 2 Schematic diagram of the light ray transmission of the single aspherical lens provided by the embodiments of the present application;

[0018] Figure 3 Regarding d and l provided by the embodiments of the present application b of Function distribution contour diagram;

[0019] Figure 4 Regarding d and l of the secondary calculation provided by the embodiments of the present application b of |y b1 -y b | function distribution contour diagram;

[0020] Figure 5 Regarding d and l of the secondary calculation provided by the embodiments of the present application b of |y b2 -y b | function distribution contour diagram;

[0021] Figure 6 Regarding d and l of the secondary calculation provided by the embodiments of the present application b of function distribution contour diagram;

[0022] Figure 7 Spot diagram, aberration curve and lens contour diagram of the single aspherical lens designed by the present application provided by the embodiments of the present application;

[0023] Figure 8 Spot diagram, aberration curve and lens contour diagram of the single aspherical lens with zero primary coma provided by the embodiments of the present application;

[0024] Figure 9 Single aspherical coefficient fitting sag error diagram provided by the embodiments of the present application;

[0025] Figure 10 Spot diagram of the imaging characteristics of different angular fields with balanced image plane defocus provided by the embodiments of the present application;

[0026] Figure 11Schematic diagram of the lens surface shape for ideal imaging of an on-axis point and an off-axis point provided by an embodiment of the present application;

[0027] Figure 12 Scatter diagram of the lens surface shape for ideal imaging of an on-axis point and an off-axis point calculated by the equal optical path principle provided by an embodiment of the present application;

[0028] Figure 13 Spot diagram for comprehensively balancing the field of view of the surface shape provided by an embodiment of the present application. Detailed implementation manners

[0029] In the following description, specific details such as specific system structures and technologies are presented for the purpose of illustration rather than limitation, so as to thoroughly understand the embodiments of the present application. However, those skilled in the art should clearly understand that the present application can also be implemented in other embodiments without these specific details. In other cases, detailed descriptions of well-known systems, devices, circuits, and methods are omitted to avoid unnecessary details from interfering with the description of the present application.

[0030] To make the objectives, technical solutions, and advantages of the present application clearer, the following will be described through specific embodiments with reference to the accompanying drawings.

[0031] The light incident surface of a single aspherical lens is an aspherical surface, and the light exit surface is a spherical surface.

[0032] In this embodiment, due to the inherent aberration problem of spherical lenses, in practical applications, multiple lenses are often combined to form a high-performance optical system. Compared with a single lens, the optical path of multiple lens combinations has more optical surfaces, lower optical efficiency, more difficult stray light suppression, requires a larger volume of space, and higher-precision structural processing and assembly processes, which is not conducive to system miniaturization and mass production. In order to replace multiple lens combinations with a single lens and meet the corresponding performance index requirements, aspherical lens technology needs to be adopted. Aspherical lenses can effectively correct optical aberrations while reducing the system volume and lowering the system assembly difficulty. However, lenses with both the light incident surface and the light exit surface being aspherical surfaces have high requirements for actual processing technology and it is difficult to guarantee the precision. Therefore, the present application proposes to design a single aspherical lens combined with a spherical surface and an aspherical surface to solve the problems of cumbersome design process and high design cost in the prior art for aspherical lenses, and simplifies the lens design process.

[0033] Please refer to Figure 1 , Figure 1 Schematic flow diagram of the single aspherical lens design method provided by an embodiment of the present application. The method includes:

[0034] S101: Obtain the distance from the vertex of the light incident surface to the object point, the focal length of the single aspherical lens, the distance from the vertex of the light exit surface to the image point, and the central thickness of the single aspherical lens that are preset in advance.

[0035] In this embodiment, according to the actual processing and production situation of the single aspherical lens, the distance between the vertex of the light incident surface and the object point, the focal length, the distance between the vertex of the light exit surface and the image point, the central thickness, the refractive index, and the height of the object point corresponding to the field of view range of the single aspherical lens are selected. It should be noted that, in order to further improve the correction accuracy of the aspherical lens aberration, in this embodiment, before the processing and production of the single aspherical lens, the central thickness of the single aspherical lens can be calculated according to the coefficient constraint condition for eliminating the primary coma of the lens, or the central thickness of the single aspherical lens can be calculated according to the coefficient constraint conditions for eliminating the primary astigmatism, eliminating the primary field curvature, or eliminating the primary distortion. The central thickness calculated according to the constraint conditions can be used as the central thickness selected in this embodiment, and this embodiment does not limit this.

[0036] S102: Determine the value of the curvature radius at the vertex of the light incident surface and the value of the curvature radius at the vertex of the light exit surface based on the distance between the vertex of the light incident surface and the object point, the focal length of the single aspherical lens, the distance between the vertex of the light exit surface and the image point, and the central thickness of the single aspherical lens.

[0037] In this embodiment, according to the paraxial object-image position relationship of the single lens, the relationship between the curvature radii at the vertices of the light incident surface and the light exit surface and the distance between the vertex of the light exit surface and the image point, the central thickness of the lens, the distance between the vertex of the light incident surface and the object point, and the focal length is determined.

[0038] S103: Establish a system of parametric relationship equations that enables the single aspherical lens to satisfy the equal optical path condition according to the distance between the vertex of the light incident surface and the object point, the central thickness of the single aspherical lens, the distance between the vertex of the light exit surface and the image point, and the value of the curvature radius at the vertex of the light exit surface.

[0039] In this embodiment, according to Fermat's principle and the law of optical refraction, when the path of the object point on the optical axis of the single aspherical lens passing through the light incident surface and the light exit surface of the single aspherical lens to the image point satisfies the equal optical path condition, the axial spherical aberration can be eliminated. Therefore, by constructing a system of parametric relationship equations that satisfies the equal optical path condition, the axial spherical aberration can be corrected.

[0040] S104: Calculate the discrete points of the surface shape of the light incident surface according to the system of parametric relationship equations, fit the discrete points of the surface shape of the light incident surface to obtain the value of the conic coefficient and the aspherical coefficient, and determine the standard equation of the light incident surface based on the value of the curvature radius at the vertex of the light incident surface, the value of the conic coefficient, and the aspherical coefficient.

[0041] In this embodiment, it is solved according to the parameter relation equations that the function relation of the distance from the intersection point of the light ray incident from the object point and the light incident surface to the intersection point of the light exit surface with respect to the angle between the line connecting the intersection point of the incident light ray and the light exit surface and the center of the light exit surface and the optical axis, the distance from the vertex of the light incident surface to the object point, the distance from the vertex of the light exit surface to the image point, the refractive index, and the central thickness. The discrete points of the surface shape of the light incident surface are calculated according to the function relation solved from the parameter relation equations. The discrete points of the surface shape of the light incident surface are converted into a data set for linear fitting to obtain the value of the conic coefficient. According to the least square method, the discrete points of the surface shape of the light incident surface are fitted with an even polynomial to obtain the aspheric coefficient. The standard equation of the light incident surface obtained by fitting can make the optical performance of the single aspheric lens better and improve the correction accuracy of the axial spherical aberration of the aspheric lens.

[0042] In practical applications, when the field angle and relative aperture are small, the off-axis coma can be corrected by correcting the primary coma or optimizing the primary coma coefficient. However, when the field angle and aperture height of the off-axis point gradually increase and deviate from the paraxial condition, the influence ratio of the higher-order coma on the off-axis coma gradually becomes larger, and its optimization problem becomes complicated. Correcting the primary coma or optimizing the primary coma coefficient does not necessarily correspond to the optimal parameters of the single aspheric lens. Therefore, the following method is proposed in this application for the above problems.

[0043] S105: After determining the standard equation of the light incident surface, determine the height change amounts of the marginal ray and the chief ray at the intersection point with the image plane according to the ray tracing method.

[0044] In this embodiment, the marginal ray can be the upper ray or the lower ray. According to the ray tracing method, the image height corresponding to the intersection point of the chief ray and the image plane, the image height corresponding to the intersection point of the upper ray and the image plane, and the image height corresponding to the intersection point of the lower ray and the image plane are determined, and the average value of the absolute difference between the upper ray image height and the chief ray image height plus the absolute difference between the lower ray image height and the chief ray image height is calculated, and the average value is the height change amount.

[0045] S106: Obtain the function distribution contour map of the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspheric lens according to the height change amount; based on the function distribution contour map, determine the parameters of the single aspheric lens.

[0046] In this embodiment, the parameters of the single aspherical lens may include: the radius of curvature at the vertex of the light incident surface, the radius of curvature at the vertex of the light exit surface, the refractive index of the single aspherical lens, the central thickness of the single aspherical lens, the focal length of the single aspherical lens, the distance from the vertex of the light incident surface to the object point, the distance from the vertex of the light exit surface to the object point, and the aspherical coefficient of the light incident surface, etc. In this embodiment, the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens are changed, and steps S102 to S105 are repeated to draw a function distribution contour diagram of the average absolute difference between the upper ray and the lower ray and the image height of the principal ray with respect to the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens. According to the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens corresponding to the minimum value of the function distribution contour diagram, the parameters of the single aspherical mirror are determined. Changing the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens can be achieved by taking multiple discrete values at uniform intervals for the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens respectively, or by taking multiple discrete values in a non-uniform interval manner such as dense in the middle and sparse on both sides, or sparse in the middle and dense on both sides. The above function distribution contour diagram can be displayed as an isometric / elevation distribution diagram, a three-dimensional height diagram or a spatial surface diagram, which is not limited in this application.

[0047] In this embodiment, based on Fermat's principle and the law of optical refraction, the parameters for eliminating axial spherical aberration are obtained. Then, according to the selection range of the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens, a function distribution contour diagram of the change amount of the image plane intersection height of the off-axis image point in the meridional plane is obtained by the ray tracing method. The parameters of the single aspherical lens are determined according to the optimal value within this selection range. Usually, coma is the difference between the average value of the intersection heights of the pair of rays passing through the upper and lower edges of the lens with the image plane and the intersection height of the principal ray (the ray emitted from the off-axis object point passing through the vertex of the light incident surface). However, in this application, the average of the absolute value of the difference between the average value of the intersection height of the upper edge ray with the image plane and the intersection height of the principal ray plus the absolute value of the difference between the average value of the intersection height of the lower edge ray with the image plane and the intersection height of the principal ray is used to measure the imaging characteristics of the off-axis object point in the meridional plane, avoiding the influence of the results caused by the fact that the image point positions of the upper and lower edge rays are respectively distributed on both sides of the principal ray image point, and improving the correction accuracy of the off-axis coma of the single aspherical lens.

[0048] In the embodiments of the present application, a single aspherical lens combining a spherical surface and an aspherical surface is designed, which solves the problems of cumbersome design process and high design cost in the prior art, and simplifies the lens design process. When designing the single aspherical lens, according to the distance between the vertex of the light incident surface and the object point, the central thickness of the single aspherical lens, the distance between the vertex of the light exit surface and the image point, and the value of the curvature radius at the vertex of the light exit surface, a parameter relationship equation set that makes the single aspherical lens satisfy the equal optical path condition is established. Further, the discrete points of the surface shape of the light incident surface are calculated through the parameter relationship equation set, and the discrete points of the surface shape are fitted, which solves the problem of initial value sensitivity based on the non-linear multivariable fitting method, and obtains the standard equation of the light incident surface that makes the optical performance of the single aspherical lens better, improving the correction accuracy of the axial spherical aberration of the aspherical lens. The present application draws a function distribution contour diagram according to the ray tracing method. The function distribution contour diagram can more comprehensively and vividly depict the off-axis coma aberration change characteristics. Based on the off-axis coma aberration change characteristics, the parameters of the single aspherical lens are determined, and it is not easy to ignore the parameters of the potentially effective single aspherical lens, improving the correction accuracy of the off-axis coma aberration of the single aspherical lens. The present application can effectively improve the correction accuracy of the axial spherical aberration and off-axis coma aberration of the single aspherical lens.

[0049] In a possible implementation manner, the method for determining the value of the curvature radius at the vertex of the light incident surface is as follows:

[0050]

[0051] The method for determining the value of the curvature radius at the vertex of the light exit surface is as follows:

[0052]

[0053] Wherein, r' is the value of the curvature radius at the vertex of the light incident surface, r is the value of the curvature radius at the vertex of the light exit surface, n is the refractive index of the single aspherical lens, d is the central thickness of the single aspherical lens, f is the focal length of the single aspherical lens, l a is the distance between the vertex of the light incident surface and the object point, l b is the distance between the vertex of the light exit surface and the object point.

[0054] In this embodiment, according to the paraxial object-image position relationship of the single aspherical lens, the relationship between the curvature radius at the vertex of the light incident surface, the curvature radius at the vertex of the light exit surface, the distance between the vertex of the light exit surface and the object point, the distance between the vertex of the light incident surface and the object point, the central thickness, the focal length, and the refractive index is determined.

[0055] In a possible implementation manner, the parameter relationship equation set is as follows:

[0056]

[0057] Among them, r is the value of the curvature radius at the vertex of the light-emitting surface, n is the refractive index of the single aspherical lens, d is the central thickness of the single aspherical lens, l a is the distance from the vertex of the light-incident surface to the object point, l b is the distance from the vertex of the light-emitting surface to the image point, L0 is the distance from the intersection point B of the incident light ray and the light-emitting surface to the image point P′, L1 is the distance from the intersection point A of the light ray incident from the object point P and the light-incident surface to the intersection point B of the light-emitting surface, L2 is the distance from the object point P to the intersection point A of the light-incident surface, h p is the distance from the intersection point A of the incident light ray and the light-incident surface to the optical axis, θ is the angle between the line connecting the intersection point B of the incident light ray and the light-emitting surface and the center o′ of the light-emitting surface and the optical axis, α is the angle between the direction of the light beam after the light ray incident from the object point P passes through the light-incident surface and the optical axis, u is the angle between the direction of the light beam after the light ray incident from the object point P passes through the single aspherical lens and is refracted and the optical axis, z2 is the projection distance along the optical axis from the intersection point A of the incident light ray and the light-incident surface to the image point, and z1 is the projection distance along the optical axis from the intersection point B of the incident light ray and the light-emitting surface to the image point.

[0058] In this embodiment, the parameter relationship equations are established when the path of the object point on the optical axis of the single aspherical lens passing through the light-incident surface and the light-emitting surface of the single aspherical lens to the image point satisfies the equal optical path condition, and the axial spherical aberration can be eliminated.

[0059] In a possible implementation manner, calculating the discrete points of the surface shape of the light-incident surface according to the parameter relationship equations includes:

[0060] Denote the center of the light-emitting surface as o′, the intersection point of the incident light ray and the light-emitting surface as B, and the angle between the line segment o′B and the optical axis of the single aspherical lens as θ.

[0061] Perform discrete processing on θ, and according to the parameter relationship equations, calculate the distance h p from the intersection point A of the incident light ray and the light-incident surface to the optical axis and the projection distance z2 along the optical axis from the intersection point A of the incident light ray and the light-incident surface to the image point when θ takes different discrete values.

[0062] According to z p =l b +d - Z2, calculate the sagitta z p of the light-incident surface when θ takes different discrete values, and obtain the discrete points (z p , h p ) of the surface shape of the light-incident surface when θ takes different discrete values.

[0063] In this embodiment, according to the above parameter relationship equations, the functional relationship of L1 with respect to θ, l a , l b , n, and d is solved, that is, L1 = f(θ, l a , l b, n, d). Take N discrete values of θ as θ i (i = 1…N), calculate N L1 values L 1i (i = 1…N), and then successively obtain L from the above equations 0i , z 1i , z 2i , h pi (i = 1…N), so as to obtain the sag z of the light incident surface pi = l b + d - z 2i (i = 1…N) relationship table, that is, (z pi , h pi )(i = 1…N).

[0064] In a possible implementation, the method for determining the standard equation of the light incident surface is as follows:

[0065]

[0066] where k is the value of the conic coefficient, r' is the value of the radius of curvature at the vertex of the light incident surface, h p is the distance from the intersection point A of the incident light ray and the light incident surface to the optical axis, and a4, a6, a8, a 10 , a 12 , a 14 are all coefficients of the standard equation.

[0067] In this embodiment, the fitting method of the present application includes but is not limited to the least squares method, partial least squares method, weighted least squares method, etc. Introducing the radius of curvature r' at the vertex of the light incident surface to convert the aspheric discrete points (z pi , h pi )(i = 1…N) into data groups and Regarding x pi (i = 1…N) as the independent variable and y pi (i = 1…N) as the dependent variable for linear fitting to determine the value of the conic coefficient k. The above discrete points (z pi , h pi )(i = 1…N) can be fitted by the least squares method. Compared with the single aspheric lens design method in the prior art, the fitting method by the least squares method is not easily affected by the initial parameters of the lens and can better fit the standard equation of the light incident surface.

[0068] In this embodiment, the standard equation of the light incident surface is determined by combining the values of the aspheric coefficient and the conic coefficient.

[0069] To solve the coefficients of the standard equation, it is necessary to make Obtain the minimum value and transform it into solving for M using the linear least squares method N×6 a 6×1 -zp N×1 The minimum value of the weighted average sum is obtained to yield the coefficient matrix

[0070] Among them, the linear matrix is

[0071]

[0072] The coefficient matrix is

[0073] a 6×1 =[a4 a6 a8 a 10 a 12 a 14 T

[0074] Column vector

[0075] zp N×1 =[z p1 z p2 … z pN T

[0076] It can be obtained that

[0077] a 6×1 =(M N×6 T M N×6 ) -1 M N×6 T zp N×1

[0078] In addition, it should be noted that T represents the transpose of the matrix. When setting the standard equation of the light incident surface, the highest order of the standard equation can be lower than 14, such as 12, 10, 8, 6, 4, etc., and the highest order of the standard equation can also be higher than 14, such as 16, 18, 20, 22, 24, etc. Those skilled in the art can set it according to their own needs

[0079] In a possible implementation manner, the method for determining the height variation is

[0080]

[0081] Among them, y b is the height of the intersection point Q' of the light ray emitted from the off-axis object point Q passing through the vertex of the light incident surface and transmitted through the single aspherical lens and the image plane, and y b1 is the height of the intersection point Q1' of the light ray emitted from the off-axis object point Q refracted into the single aspherical lens from the upper edge A point of the light incident surface of the single aspherical lens and refracted out from the light exit surface and the image plane​​b2 It is the height of the intersection point Q2' of the light ray emitted from the off-axis object point Q passing through the lower edge of the light incident surface and transmitted through the single aspherical lens and the image plane.

[0082] In this embodiment, y b is the image height corresponding to the principal ray, y b1 is the image height corresponding to the upper ray, y b2 is the image height corresponding to the lower ray.

[0083] In a possible implementation manner, a function distribution contour map of the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens is obtained according to the height change amount, including:

[0084] Re-obtain the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens, re-determine the value of the curvature radius at the vertex of the light incident surface, the value of the curvature radius at the vertex of the light exit surface, the parameter relation equation set, the value of the conic coefficient, the aspherical coefficient, and the standard equation of the light incident surface, obtain the height change amount, and draw a function distribution contour map of the height change amount with respect to the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens.

[0085] In this embodiment, according to the distance l from the vertex of the light exit surface to the image point b and the optional range of the central thickness d of the lens (l bmin ~l bmax , d min ~d max ), N1 and N2 values are respectively taken, that is

[0086] Repeat the above S102, S103, S104, and S105, and draw a function distribution contour map of d and l b according to the ray tracing method. of the function distribution contour map.

[0087] In a possible implementation manner, based on the function distribution contour map, various parameters of the single aspherical lens are determined, including:

[0088] According to the minimum value of the height change amount in the function distribution contour map, various parameters of the single aspherical lens are determined.

[0089] In this embodiment, r′, r, l a , d, l b , f, and the aspherical coefficient of the light incident surface are determined according to the condition that Δy is at the minimum value.

[0090] In this embodiment, after determining various parameters of the single aspherical lens, it further includes:

[0091] Based on various parameters, optical simulation verification is carried out on the single aspherical lens, and it is judged whether the single aspherical lens meets the preset performance indicators according to the results of the optical simulation verification.

[0092] If the requirements are not met, return to S101 to change the initial parameters, namely the distance between the vertex of the light incident surface and the object point, the focal length of the single aspherical lens, the distance between the vertex of the light exit surface and the image point, and the central thickness of the single aspherical lens, and then perform S102, S103, S104, S105 and S106 to obtain the re-determined parameters of the single aspherical lens. Based on the re-determined parameters of the single aspherical lens, optical simulation verification is carried out on the single aspherical lens, and it is judged whether the single aspherical lens meets the requirements until the requirements are met, then the design of the single aspherical lens is completed. In this embodiment, the implementer can set the preset performance indicators according to actual needs.

[0093] In a possible implementation manner, after determining the parameters of the single aspherical lens, it further includes:

[0094] According to c i =w1a i +w2b i The parameters of the single aspherical lens are corrected.

[0095] Wherein, w1 is the first preset weight, w2 is the second preset weight, a i is the aspherical coefficient after fitting the ideal surface shape of the on-axis object point, b i is the aspherical coefficient after fitting the ideal surface shape of the off-axis object point, and c i is the aspherical coefficient after fitting the comprehensive preset surface shape.

[0096] In this embodiment, the aspheric coefficients obtained by fitting the ideal surface shape of the off-axis object point can be used to correct the aspheric coefficients obtained by fitting the ideal surface shape of the on-axis object point, so as to obtain the corrected aspheric coefficients obtained by fitting the ideal surface shape of the on-axis object point. The corrected aspheric coefficients obtained by fitting the ideal surface shape of the on-axis object point are the aspheric coefficients obtained by fitting the comprehensive surface shape. The aspheric coefficients obtained by fitting the corresponding ideal surface shapes of the on-axis object point and the off-axis object point are used, and the optimized aspheric coefficients obtained by fitting the comprehensive surface shape are obtained by taking weights, which can solve the problem of the balance of the field distribution. w1 and w2 can be determined according to actual needs and can be modified. The ideal surface shape of the on-axis object point (surface shape 1) is determined according to z1 = η(h1), and the ideal surface shape of the off-axis object point (surface shape 2) is determined according to z2 = ζ(h2). The comprehensive preset surface shape (comprehensive surface shape) is determined according to z = w1z1 + w2z2 = w1η(h1) + w2ζ(h2). By comparing the upper half surface shape z1 = η(h1), h1 > 0 and the lower half surface shape z1 = η(h1), h1 < 0 of the ideal surface shape of the on-axis object point (surface shape 1) through the imaging characteristics of the lens or the RMS radius of the spot diagram, if the upper half surface shape of the ideal surface shape of the on-axis object point (surface shape 1) is better than the lower half surface shape, the lower half surface shape z2 = ζ(h2), h2 < 0 of the ideal surface shape of the off-axis object point (surface shape 2) is used as discrete points for aspheric coefficient fitting. On the contrary, if the lower half surface shape of the ideal surface shape of the on-axis object point (surface shape 1) is better than the upper half surface shape, the upper half surface shape z2 = ζ(h2), h2 > 0 of the ideal surface shape of the off-axis object point (surface shape 2) is used as discrete points for aspheric coefficient fitting. Finally, the comprehensive surface shape with the final field balance effect is obtained by superimposing the weights of the ideal surface shape of the on-axis object point and the ideal surface shape of the off-axis object point.

[0097] It should be understood that the magnitudes of the sequence numbers of the steps in the above embodiments do not mean the order of execution. The order of execution of each process should be determined according to its function and internal logic, and should not constitute any limitation to the implementation process of the embodiments of the present application.

[0098] Hereinafter, the feasibility of the lens design method provided by the embodiments of the present application is verified.

[0099] Due to the narrow working spectral range of the lidar optical system, the chromatic aberration requirement is relatively low. The optical system uses low-dispersion material glasses, such as N-BK7, N-PK51, etc., and even plastic materials such as PMMA, which can meet the chromatic aberration requirements of the system. For the optical path transceiver system of the lidar, it belongs to non-imaging optics and the transceiver field of view is small. The single-lens design mainly considers correcting spherical aberration and coma. For the problem of spherical aberration or axial spherical aberration, due to its rotational symmetry, good correction can be obtained through the optimization of the parameters of the standard aspherical lens. For the off-axis coma problem, when the field angle and relative aperture are small, the off-axis coma can be corrected by correcting the primary coma or optimizing the primary coma coefficient. When the field angle or relative aperture becomes large, correcting the primary coma may not necessarily achieve coma correction because the influence of its higher-order coma on the off-axis coma increases, and the parameters with the primary coma corrected or the primary coma coefficient being zero do not necessarily correspond to the optimal surface shape parameters. Due to the non-rotational symmetry of coma, its influence in the meridional plane is greater than that in the sagittal plane. The primary meridional coma is three times the primary sagittal coma. In view of this, this application proposes to obtain the lens surface shape parameters for eliminating spherical aberration based on Fermat's principle and the law of optical refraction, and then according to the selection range of the distance from the vertex of the light exit surface to the image point and the central thickness of the lens, through the ray tracing method, obtain the function distribution contour of the change in the height of the off-axis image point at the intersection of the image plane in the meridional plane, and determine the lens surface shape parameters (parameters of the single aspherical lens) according to the optimal value within this selection range. Usually, coma is measured by the difference between the average value of the intersection heights of the pair of rays passing through the upper and lower edges of the lens with the image plane and the intersection height of the principal ray. However, this application uses the average value of the difference between the intersection height of the upper-edge ray with the image plane and the intersection height of the principal ray plus the average value of the difference between the intersection height of the lower-edge ray with the image plane and the intersection height of the principal ray, and then takes the average to measure the imaging characteristics of the off-axis object point in the meridional plane, avoiding the influence of the upper and lower edge rays on the result due to the height of the image point being distributed on both sides of the principal ray image point.

[0100] Figure 2 is the schematic diagram of the ray transmission of the single aspherical lens provided by the embodiment of this application. As Figure 2 shown, the refractive index of the lens material is n. The single aspherical lens includes a light incident surface and a light exit surface. The light exit surface is a spherical surface, and the light incident surface is an aspherical surface. The light incident surface coincides with the aperture stop surface. The distance from the vertex of the light incident surface to the object point is l a , the height of the object point is y a , the spherical radius is r, the distance from the vertex of the light exit surface to the image point is l b , the focal length is f, the semi-aperture height of the lens is h, the central thickness of the lens is d, and the radius of curvature at the vertex of the light incident surface is r'. Among them, r', r, l a , d, l b and f satisfy the paraxial object-image position relationship of the single lens. Given la 、 d, l b and f, the values of the radius of curvature at the vertex of the light incident surface and the value of the radius of curvature at the vertex of the light exit surface can be calculated and determined.

[0101]

[0102]

[0103] The path of the object point P on the optical axis of the lens passing through the light incident surface and the light exit surface of the lens to the image point P' satisfies the equal optical path condition, so that the axial spherical aberration is completely corrected. According to the above equal optical path condition, through r, n, l a 、 d, l b parameters, the following system of equations is established:

[0104]

[0105] where r is the value of the radius of curvature at the vertex of the light exit surface, n is the refractive index of the single aspherical lens, d is the central thickness of the single aspherical lens, l a is the distance from the vertex of the light incident surface to the object point, l b is the distance from the vertex of the light exit surface to the image point, L0 is the distance from the intersection point B of the incident light and the light exit surface to the image point P', L1 is the distance from the intersection point A of the light from the object point P and the light incident surface to the intersection point B of the light exit surface, L2 is the distance from the object point P to the intersection point A of the light incident surface, h p is the distance from the intersection point A of the incident light and the light incident surface to the optical axis, θ is the angle between the line connecting the intersection point B of the incident light and the light exit surface and the center o' of the light exit surface and the optical axis, α is the angle between the direction of the light beam after the light from the object point P passes through the light incident surface and the optical axis, u is the angle between the direction of the light beam after the light from the object point P passes through the single aspherical lens and is refracted and exits and the optical axis, z2 is the projection distance along the optical axis from the intersection point A of the incident light and the light incident surface to the image point, and z1 is the projection distance along the optical axis from the intersection point B of the incident light and the light exit surface to the image point.

[0106] The above system of equations consists of 8 equations, where r, l a 、 n, d, l b are known parameters, L0, L1, L2, h p 、 θ, α, u, z2, z1 are 9 parameters to be solved. Through 8 systems of equations, L0, L1, L2, h p 、 α, u, z2, z1 can be converted into parametric equations expressed by θ. By solving the above system of equations, the functional relationship of L1 with respect to θ, l a 、 l b 、 n and d is obtained, that is, L1 = f(θ, l a , l b, n, d). Then, through numerical calculation, take N discrete values of θ as θ i (i = 1…N), and calculate N L1 values L 1i (i = 1…N). Then, successively obtain L 0i , z 1i , z 2i , (i = 1…N) from the above equations, so as to obtain the relationship table of the sag z pi = l b + d - z 2i (i = 1…N), that is, (z pi , h pi )(i = 1…N). Introduce the radius of curvature r' at the vertex of the light incident surface to convert the aspheric discrete points (z pi , h pi )(i = 1…N) into the data group and Take x pi (i = 1…N) as the independent variable and y pi (i = 1…N) as the dependent variable for linear fitting to determine the value of the conic coefficient k.

[0107] Combine the values of the aspheric coefficient and the conic coefficient to determine the standard equation of the light incident surface.

[0108]

[0109] To solve the coefficients of the standard equation, a4, a6, a8, a 10 , a 12 and a 14 need to make achieve the minimum value, and convert it into a linear least squares method to solve M N×6 a 6×1 - zp N×1 weighted average sum of the minimum value, and obtain the coefficient matrix.

[0110] Among them, the linear matrix is:

[0111]

[0112] The coefficient matrix is:

[0113] a 6×1 = [a4 a6 a8 a 10 a 12 a 14 T

[0114] Column vector:

[0115] zp N×1 = [z p1 z​p2 … z pN T

[0116] It can be obtained that:

[0117] a 6×1 =(M N×6 T M N×6 ) -1 M N×6 T zp N×1

[0118] The coefficients a4, a6, a8, a 10 , a 12 , a 14 of the above standard equation can be selected according to the error value of numerical calculation. When the fitting surface error is below 10 -7 mm, the predetermined accuracy can be achieved, and the fitting order can be reduced, that is, the highest coefficient is 14th order a 14 reduced to 12th order a 12 or 10th order a 10 , or even lower. When the surface error cannot meet the accuracy requirements, the fitting order can be increased, and the highest order term can be changed to a 16 or higher. Usually, the error will decrease as the fitting order increases, but the higher the order, the smaller the impact on the accuracy, that is, the less obvious the improvement. According to the field of view or the object point height and the lens aperture, strict ray tracing is performed on the off-axis object point Q. The height of the intersection point Q' of the ray emitted from the off-axis object point Q passing through the vertex of the light incident surface (i.e., the chief ray) transmitted through the lens and the image plane is y b . The height of the intersection point Q1' of the ray emitted from the off-axis object point Q refracted into the lens from the upper edge A point of the light incident surface of the lens (or called the upper ray) and refracted out from the light exit surface and the image plane is y b1 . The height of the intersection point Q2' of the ray emitted from the off-axis object point Q passing through the lower edge of the light incident surface (or called the lower ray) transmitted through the lens and the image plane is y b2 . Calculate According to the actual optical characteristics of the lens, pairs of rays with different apertures (not the full aperture), such as the ray pair at 0.9 aperture, can be selected for ray tracing to calculate Δy. Or different object point heights (not the maximum object point height), such as the ray pair at 0.9y a , can be selected for ray tracing to calculate Δy. The above ray tracing is carried out as follows: The unit vector from the on-axis point P to point A can be determined by the coordinates of P to A , and then the unit vector from A to B can be determined by the coordinates of point A and point B Through and the normal vector of point A can be calculated​ The coordinates of off-axis point Q and point A can determine the unit vector from Q to A That is, the incident vector. Using Snell's law and the normal vector The refraction vector entering the lens can be calculated. Since the light exit surface is a known spherical surface, the intersection point B' of this refraction vector and the light exit surface and the corresponding normal vector can be solved Then, according to Snell's law, the unit vector exiting the lens can be obtained, and thus the coordinates of the image plane intersection point can be obtained. The calculation of the following rays is similar and will not be elaborated. According to the distance l from the vertex of the light exit surface to the image point b and the optional range of the central thickness d of the lens (l bmin ~l bmax , d min ~d max ), N1 and N2 values are taken respectively, that is Repeat the above S102, S103, S104 and S105, and draw the function distribution contour map of d and l b according to the ray tracing method. Determine r′, r, l according to the condition that Δy is at the minimum value a , d, l b , f and the aspheric coefficient of the light incident surface. The above values and point number divisions can be set according to the results of the function distribution contour map and the processing tolerance. When the function distribution contour map is relatively concentrated in some areas, the selection range of l b and d can be reduced (l′ bmin ~l′ bmax , d′ min ~d′ max ), and this can be done repeatedly. The number of calculation points is related to the division step size. The division step size b of l can be made less than or equal to the tolerance of l b , and the division step size of d can be made less than or equal to the tolerance of d to determine the number of calculation points. Perform ray tracing simulation verification on the single aspheric lens to check whether the results meet the requirements. If not, return to S101, change the initial parameters and then perform the following steps. If the requirements are met, the lens design is completed

[0119] Optionally, by completing the on-axis spherical aberration correction and minimizing the off-axis coma effect through the above steps, according to the optical characteristics of the lens, the image plane can be moved forward and backward to generate defocus so that the on-axis and off-axis imaging tend to be balanced

[0120] The following takes the laser radar emission lens as an example to illustrate the above design method. Since the laser radar emission field of view is usually small, assuming the full field of view is 1°, after the laser passes through the lens and is collimated and output, the object-image relationship can be regarded in reverse, and its object distance is regarded as infinity, la = ∞, the distance between the laser emitting surface and the vertex of the lens light emitting surface is l b , l b , according to the above formula, take l a = ∞, the curvature radii at the vertices of the light incident surface and the light emitting surface can be calculated and determined as follows:

[0121]

[0122] The laser operating wavelength is 905 nm. PMMA plastic is selected as the lens material, and the corresponding refractive index is n = 1.4843. The focal length of the lens is f = 24.00 mm. According to the divergence angle of the laser, the numerical aperture is set to 0.38, that is, the aperture is 20.00 mm.

[0123] l b The preset selection range is: 14.0 - 17.0 mm, and the preset selection range of d is: 14.0 - 17.0 mm. Take N1 = 66 and N2 = 64 discrete values respectively to calculate the function distribution contour diagrams of d and l b of of, as shown in Figure 3 the function distribution contour diagrams of d and l b of of. According to Figure 3 the calculation results, the minimum values of Δy are concentrated in the region of 15.0 mm to 16.5 mm of l b , and the value range of d is still 14.0 - 17.0 mm. Therefore, re - select l b The preset selection range is: 15.0 - 16.5 mm, and the preset selection range of d is: 14.0 - 17.0 mm. The step size is 0.01 mm, which is less than the processing error. Take N1 = 150 and N2 = 30 discrete values respectively to calculate |y b1 - y b |, |y b2 - y b |, the function distribution contour diagrams of d and l b of, as shown in Figure 4 , Figure 5 , Figure 6 shown.

[0124] According to Figure 4 , Figure 5 , Figure 6 , in the minimum value region where Δy is located, select l b = 15.12 mm, d = 16.88 mm, and calculate as the initial parameters to obtain r′ = 14.90 mm, r = - 33.32 mm. Through Fermat's principle of equal optical path combined with the refraction law, and numerical fitting, the parameters of the single - aspherical collimating lens are obtained as shown in Table 1.

[0125] Table 1 Parameter Table of Single Aspherical Collimating Lens Obtained by the Method of This Application

[0126]

[0127] In order to compare this application (the primary coma coefficient is 0.004222 and the primary coma is not fully corrected) with a lens with corrected primary coma, under the conditions of the same refractive index, lens focal length and numerical aperture, complete correction of on-axis aberration and correction of primary coma are achieved, that is, the parameter table of a single aspherical collimating lens with a primary coma coefficient of 0 is shown in Table 2.

[0128] Table 2 Parameter Table of Single Aspherical Collimating Lens with Corrected Primary Coma

[0129]

[0130] See Figure 7 and Figure 8 the spot diagram, aberration curve and lens contour diagram of the single aspherical lens shown. According to the above simulation results, it can be seen that both lenses have corrected the on-axis aberration. The RMS radii of this application and the single aspherical collimating lens with corrected primary coma at the 0° field of view are 0.08 μm and 0.11 μm respectively, and the geometric radii are 0.10 μm and 0.15 μm respectively. At the 0.25° field of view, the RMS radii are 1.22 μm and 3.50 μm respectively, and the geometric radii are 2.20 μm and 8.70 μm respectively. At the 0.5° field of view, the RMS radii are 2.52 μm and 7.14 μm respectively, and the geometric radii are 4.80 μm and 18.32 μm respectively. The optical characteristics of this application for off-axis fields are better than those of the single aspherical collimating lens with corrected primary coma, and most of the spots in the spot diagram are distributed near or equivalent to the Airy disk (points distributed within the Airy disk are usually regarded as perfect imaging). According to the aberration curves of the meridional plane and the sagittal plane, it can be seen that generally the meridional aberration is greater than the sagittal aberration. For the single aspherical lens with corrected primary coma, when the aperture is small, the aberration characteristics are better, but it deteriorates rapidly as the aperture increases, and the aberration curve shows a unidirectional increasing characteristic. However, for the lens characteristics constructed by this application through the method of searching numerical calculations to correct the marginal aberration, when the aperture is small and at the aperture edge, the aberration characteristics are better and gradually deteriorate towards the middle of the aperture, showing the compensation and optimization effect of primary aberration and higher-order aberration.

[0131] The lens parameters of this application are obtained by taking N = 2800 points, calculating the discrete points on the light incident surface according to formulas (1) to (3), and through the above least squares fitting, the fitting error reaches 10 -7 in the mm magnitude range when the highest order is 12, meeting the design requirements, and thus obtaining the lens parameters in Table 1. The fitting sagittal height errors of the aspherical coefficients at the highest orders of 10 and 12 are asFigure 9 as shown

[0132] Optionally, since there is a certain adjustment margin for the imaging of off-axis image points, such as being all within the Airy disk, in practical applications, it can be considered to make the imaging characteristics of different fields of view tend to be balanced by defocusing. By adjusting the image plane distance by 0.002 mm forward and backward, as Figure 10 shown

[0133] Furthermore, considering the ideal imaging conditions of off-axis object points according to Fermat's principle, the light exit surface is still spherical. Due to the rotational symmetry of on-axis points, it is required that the surface type parameters of the light incident surface are also rotationally symmetrically distributed. However, for off-axis points, since they deviate from the symmetry axis of the optical axis, to satisfy the ideal imaging conditions, the surface type must be asymmetrically distributed. Thus, it can be known that theoretically there does not exist a surface shape that satisfies both the ideal imaging of on-axis points and off-axis points. Refer to Figure 11 and Figure 12 , calculate the surface type 1 for the ideal imaging of on-axis points by Fermat's principle, with the function z1 = η(h1), and the surface type 2 for the ideal imaging of off-axis points, with the function z2 = ζ(h2). In the calculation process, the condition of being at the same intersection point with the optical axis is achieved through self-feedback iteration, that is, ζ(0) = η(0). The iteration method is to take an initial value l′ for off-axis points a calculate Δz = ζ(0) - η(0), and then perform the next iteration I' according to the feedback value a = I' a - φ(Δz) calculation. Repeat this process until Δz < ε is less than the predetermined error. Here, φ(Δz) is a function of the variable Δz, such as a simple linear function φ(Δz = k * Δz). Compared with the usual bisection method, this method does not require specifying the solution boundary, and the iteration steps change with the deviation. When the deviation is large, the iteration steps increase, and when the deviation decreases, the iteration steps decrease, showing good convergence

[0134] By comparing the imaging characteristics or the RMS radius of the spot diagram of the lens for the upper half surface type z1 = η(h1), h1 > 0 and the lower half surface type z1 = η(h1), h1 < 0 when the surface type is 1. If the upper half surface type is better than the lower half surface type, then use the lower half surface type z2 = ζ(h2), h2 < 0 of the surface type 2 as discrete points for aspheric coefficient fitting. Conversely, if the lower half surface type is better than the upper half surface type, then use the upper half surface type z2 = ζ(h2), h > 0 of the surface type 2 as discrete points for aspheric coefficient fitting. Finally, the combined surface type with the function of field balance is obtained by superimposing the weights of the two surface types, that is

[0135] z = w1z1 + w2z2 = w1η(h1) + w2ζ(h2). The aberration optimization weights for different fields of view in ordinary optical software are converted into the lens surface type parameters obtained by combining the ideal on-axis surface type with its own occupied weight and the ideal off-axis surface type with its own occupied weight, that is, c i = w1a i + w2b i , where a i , b i , c i are the aspheric coefficients after fitting for surface type 1, the aspheric coefficients after fitting for surface type 2, and the aspheric coefficients of the combined surface type respectively. w1 is the weight set for surface type 1, and w2 is the weight set for surface type 2. Figure 13 is the spot diagram of the combined surface type with balanced field of view obtained under the weights w1 = 0.95 and w2 = 0.05.

[0136] In particular, the highest order of the above standard equation can be lower than 14, such as 12, 10, 8, 6, 4.

[0137] In particular, the highest order of the above standard equation can be higher than 14, such as 16, 18, 20, 22, 24.

[0138] In particular, the above standard equation can adopt the nonlinear multivariable fitting method.

[0139] In particular, the calculated lens parameters above can be specifically optimized on the optical software according to requirements.

[0140] Furthermore, the calculated lens parameters above can be optimized by defocusing.

[0141] Furthermore, the calculated lens parameters above can achieve field balance by combining the ideal on-axis surface type and the ideal off-axis surface type according to weights.

[0142] The embodiment of the present application provides a single aspheric lens. The light incident surface of the single aspheric lens is aspheric, the light exit surface is spherical, and the parameters of the single aspheric lens are obtained according to any of the single aspheric lens design methods provided in the first aspect of the embodiment of the present application.

[0143] The above is only the specific implementation manner of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present application can easily think of various equivalent modifications or substitutions, and these modifications or substitutions should all be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A design method for a single aspherical lens, characterized in that, The light incident surface of the single aspherical lens is an aspherical surface, and the light exit surface is a spherical surface. The design method includes: Obtaining the distance from the vertex of the light incident surface to the object point, the focal length of the single aspherical lens, the distance from the vertex of the light exit surface to the image point, and the central thickness of the single aspherical lens that are preset; Based on the distance from the vertex of the light incident surface to the object point, the focal length of the single aspherical lens, the distance from the vertex of the light exit surface to the image point, and the central thickness of the single aspherical lens, determining the value of the radius of curvature at the vertex of the light incident surface and the value of the radius of curvature at the vertex of the light exit surface; According to the distance from the vertex of the light incident surface to the object point, the central thickness of the single aspherical lens, the distance from the vertex of the light exit surface to the image point, and the value of the radius of curvature at the vertex of the light exit surface, establishing a system of parametric relationship equations that enables the single aspherical lens to satisfy the equal optical path condition; Calculating the discrete points of the surface profile of the light incident surface according to the system of parametric relationship equations, fitting the discrete points of the surface profile of the light incident surface to obtain the value of the conic coefficient and the aspherical coefficient, and determining the standard equation of the light incident surface based on the value of the radius of curvature at the vertex of the light incident surface, the value of the conic coefficient, and the aspherical coefficient; After determining the standard equation of the light incident surface, determining the height change amounts of the intersection points of the marginal ray and the chief ray with the image plane according to the ray tracing method; Obtaining a function distribution contour map of the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens based on the height change amounts; based on the function distribution contour map, determining the various parameters of the single aspherical lens; Among them, the calculating the discrete points of the surface profile of the light incident surface according to the system of parametric relationship equations includes: Denote the center of the light-emitting surface as , denote the intersection point of the incident light ray and the light-emitting surface as B, and denote the included angle between the line segment B and the optical axis of the single aspherical lens as θ; Discretize θ, and calculate the distance of the intersection point A of the incident light ray and the light incident surface from the optical axis when θ takes different discrete values according to the parameter relation equations , and the projection distance of the intersection point A of the incident light ray and the light incident surface to the image point along the optical axis direction ; According to calculate the sagittal height of the light incident surface when θ takes different discrete values , and obtain the discrete points of the surface shape of the light incident surface when θ takes different discrete values ; The method for determining the height change amounts is: （5） Among them, is an off-axis object point The height of the intersection point of the light ray emitted by the off-axis object point and passing through the vertex of the light incident surface with the image plane after being transmitted through the single aspherical lens ; is an off-axis object point The height of the intersection point of the light ray emitted by the off-axis object point, refracted into the single aspherical lens from point A at the upper edge of the light incident surface of the single aspherical lens, and then refracted out of the light exit surface and reaching the image plane ; is an off-axis object point The height of the intersection point of the light ray emitted by the off-axis object point and passing through the lower edge of the light incident surface with the image plane after being transmitted through the single aspherical lens .

2. The single aspherical lens design method according to claim 1, characterized in that The method for determining the value of the radius of curvature at the vertex of the light incident surface is: （1） The method for determining the value of the radius of curvature at the vertex of the light exit surface is: （2） wherein, is the value of the radius of curvature at the vertex of the light incident surface, is the value of the radius of curvature at the vertex of the light exit surface, is the refractive index of the single aspherical lens, is the central thickness of the single aspherical lens, is the focal length of the single aspherical lens, is the distance from the vertex of the light incident surface to the object point, is the distance from the vertex of the light exit surface to the object point.

3. The aspherical lens design method according to claim 1, wherein The system of parametric relationship equations is: （3） Among them, is the value of the radius of curvature at the vertex of the light-emitting surface, is the refractive index of the single aspherical lens, is the central thickness of the single aspherical lens, is the distance from the vertex of the light-incident surface to the object point, is the distance from the vertex of the light-emitting surface to the image point, is the distance from the intersection point B of the incident light ray and the light-emitting surface to the image point , is the distance from the object point where the incident light ray enters to the intersection point B of the light-incident surface and the light-emitting surface, is the distance from the object point to the intersection point A of the light-incident surface, is the distance from the intersection point A of the incident light ray and the light-incident surface to the optical axis. θ is the angle between the line connecting the intersection point B of the incident light ray and the light-emitting surface and the center of the sphere of the light-emitting surface and the optical axis, , is the angle between the direction of the light beam after passing through the light-incident surface and the optical axis of the light ray incident from the object point , is the angle between the direction of the light beam after refraction by the single aspherical lens and the optical axis of the light ray incident from the object point , is the projection distance along the optical axis from the intersection point A of the incident light ray and the light-incident surface to the image point, is the projection distance along the optical axis from the intersection point B of the incident light ray and the light-emitting surface to the image point.

4. The aspheric lens design method according to claim 1, characterized in that, The method for determining the standard equation of the light incident surface is: （4） Among them, is the value of the conic coefficient, is the value of the radius of curvature at the vertex of the light incident surface, is the distance from the intersection point A of the incident light and the light incident surface to the optical axis, , , , , , are all coefficients of the standard equation.

5. The method for designing a single aspherical lens according to claim 1, wherein The obtaining a function distribution contour map of the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens based on the height change amounts includes: Re-obtaining the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens, re-determining the value of the radius of curvature at the vertex of the light incident surface, the value of the radius of curvature at the vertex of the light exit surface, the system of parametric relationship equations, the value of the conic coefficient, the aspherical coefficient, and the standard equation of the light incident surface, obtaining the height change amounts, and plotting a function distribution contour map of the height change amounts of the distance from the vertex of the light exit surface to the image point and the central thickness of the single aspherical lens.

6. The single aspherical lens design method according to claim 1, characterized in that, The based on the function distribution contour map, determining the various parameters of the single aspherical lens includes: Determining the various parameters of the single aspherical lens according to the minimum value of the height change amounts in the function distribution contour map.

7. The single aspherical lens design method according to claim 1, characterized in that, After determining the various parameters of the single aspherical lens, it further includes: According to correct each parameter of the single aspherical lens; Among them, is the first preset weight, is the second preset weight, is the aspherical coefficient after fitting the ideal surface shape of the object point on the axis, is the aspherical coefficient after fitting the ideal surface shape of the off-axis object point, is the aspherical coefficient after fitting the comprehensive preset surface shape.

8. A single aspherical lens, characterized in that, The light incident surface of the single aspherical lens is an aspherical surface, the light exit surface is a spherical surface, and the various parameters of the single aspherical lens are obtained according to the single aspherical lens design method described in any one of claims 1-7.

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