阅读说明：本技术 一种双面非球面镜片及其设计方法 (Double-sided aspheric lens and design method thereof ) 是由 谢公兴 赵志刚 张佳康 于 2020-12-14 设计创作，主要内容包括：本发明涉及一种双面非球面镜片,包括前表面和后表面,所述前表面、后表面的曲面均为非球面折射面,所述非球面折射面由以下圆锥曲线函数确定：。依照本发明的方法设计出的镜片,同时兼顾了镜片的厚度和主要用眼区域的像质情况,通过调整镜片前表面的面形主要参数,可以直接计算出整个镜片的关键像差,以便于根据客户的具体需求,得到最佳设计结果。(The invention relates to a double-sided aspheric lens, which comprises a front surface and a rear surface, wherein the curved surfaces of the front surface and the rear surface are aspheric refraction surfaces, and the aspheric refraction surfaces are determined by the following conic curve functions: . The lens designed according to the method of the invention simultaneously considers the thickness of the lens and the image quality condition of the main eye area, and the key aberration of the whole lens can be directly calculated by adjusting the main parameters of the surface shape of the front surface of the lens, so as to obtain the optimal design result according to the specific requirements of customers.)

1. A double-sided aspheric lens comprising an anterior surface and a posterior surface, wherein the curved surfaces of the anterior and posterior surfaces are aspheric refractive surfaces defined by conic functions:

wherein the content of the first and second substances,the rise of the face shape is shown,the radius of curvature of the center point is represented,represents the distance between the evaluation point and the optical axis, and，is the conic coefficient.

2. A design method of a double-sided aspheric lens is characterized by comprising the following steps:

in the first step, the front and back surfaces of the lens are described by the following conic coefficient formula:

in the formula (I), the compound is shown in the specification,the rise of the face shape is shown,the radius of curvature of the center point is represented,represents the distance between the evaluation point and the optical axis, and，is the cone coefficient;

second, the central curvature of the front surface of the lens is recorded asThe conic coefficient of the front surface of the lens is recorded；

Third, the central curvature of the back surface of the lens is recorded asCalculating the central curvature of the back surface of the lens according to the following formula,

in the formula (I), the compound is shown in the specification,which represents the optical power of the lens,represents the refractive index of the lens;

the conic coefficient of the rear surface of the lens is recordedThe conic coefficient of the back surface is calculated according to the following equation:

in the formula (I), the compound is shown in the specification,the local curvature of the front lens surface at the lens edge location, the local curvature of the back lens surface at the lens edge location,is the abscissa of the edge position of the lens on the aspherical refracting surface of the lens,is the local power of the lens edge position and；

fourthly, evaluating the quality of the lens design by adopting the thickness of the edge position of the lens and the aberration of the investigation position on the lens;

and fifthly, drawing a point array diagram by taking the thickness of the lens at the edge position as a vertical coordinate and the aberration of the lens at the investigation position as a horizontal coordinate, and then selecting an optimal scheme in the point array diagram according to the user requirement.

3. The method of claim 2, wherein in the fourth step, the thickness of the lens center is set asThe thickness of the edge of the lens isCalculating the thickness of the edge of the lens according to the following formula,

；

let the lens aberration be Asti, calculate the lens aberration according to the following formula,

Asti = Asti_f + Asti_b

in the formula, Asti_fDenotes the astigmatism of the front surface of the lens, Asti_bAstigmatism of the back surface of the lens is shown.

4. A method for designing a double-sided aspherical lens according to claim 3, wherein astigmatism of the front surface of the lens is calculated according to the following formula,

Asti_f = (n – 1)* (s_f1 – s_f2)

in the formula, s_f1 denotes the maximum curvature of the front surface of the lens at the investigation position, s_f2 denotes the minimum curvature of the front surface of the lens in the investigation position;

astigmatism of the rear surface of the lens is calculated according to the following formula,

Asti_b = (n – 1)* (s_b1 – s_b2)

in the formula, s_b1 denotes the maximum curvature of the rear surface of the lens at the investigation position, s_b2 denotes the minimum curvature of the rear surface of the lens at the position of investigation.

5. A method of designing a double-sided aspherical lens as claimed in claim 4, wherein the edge of the lens is positioned at a lens diameter of 70 mm; the lens was examined at a position where the lens was at 50mm in diameter.

Technical Field

The invention relates to a double-sided aspheric lens and a design method thereof.

Background

At present, the lenses used in optical devices, such as optical pick-up heads, camera lenses, and spectacle lenses, generally include two types, i.e., spherical lenses and aspherical lenses. For spherical lenses, since both refractive surfaces are spherical, the manufacturing and processing are easy. However, in addition to the ease of manufacturing and processing of the lens and the thinning of the lens, the lens must also take into consideration the imaging quality of the lens. Conventionally, in order to obtain a thin lens, it is necessary to change the curved surface of the lens, and the spherical design is adopted to increase aberration and distortion, resulting in such undesirable phenomena as a clear image, a distorted view, and a narrow field of view.

In order to solve the problem, most of the existing lenses adopt an aspheric surface design, wherein the aspheric surface means that one of the refraction surfaces is an aspheric surface, and the aspheric surface can be an ellipsoid, a hyperboloid, a paraboloid and the like. The lens adopts the aspheric surface design, so that the image is corrected, the problems of distorted vision and the like are solved, and meanwhile, the lens is lighter, thinner and flatter. Moreover, the excellent impact resistance is still maintained, making the wearer safe to use.

Although the current design of the aspheric lens for the glasses does not lack a special design method, the design methods are relatively complex and have certain requirements on design experience, so an effective design method needs to be designed, and the design method of the aspheric lens with good imaging effect can be realized.

Disclosure of Invention

The invention aims to solve the technical problem of providing a double-sided aspheric lens and a design method thereof according to the defects of the prior art.

The invention provides a double-sided aspheric lens, which comprises a front surface and a rear surface, wherein the curved surfaces of the front surface and the rear surface are aspheric refraction surfaces, and the aspheric refraction surfaces are determined by the following conic curve functions:

wherein the content of the first and second substances,the rise of the face shape is shown,center of representationThe radius of curvature of the point(s),represents the distance between the evaluation point and the optical axis, and（a coordinate representing a point on the aspherical refractive surface),the conic coefficient represents the degree of deviation of the surface form from the spherical surface.

The invention adopts the representation method aiming at the aspheric surface, can ensure the smoothness of the surface shape and can not generate local inflection points; the number of the aspheric surface coefficients is limited, so that optimization is facilitated, and the design with good image quality and light weight can be quickly found. Therefore, the aspheric lens designed by the representation method has the advantages of thin thickness, light weight, good imaging quality, easy processing and the like.

The invention also provides a design method of the double-sided aspheric lens, which comprises the following steps:

the first step, the description mode of the lens surface shape, namely the front surface and the back surface of the lens are described by the following cone coefficient formula:

in the formula (I), the compound is shown in the specification,the rise of the face shape is shown,the radius of curvature of the center point is represented,represents the distance between the evaluation point and the optical axis, and，is the cone coefficient; thus only two variables are requiredAndthe surface shape of a surface can be determined;

second step, design variable-recording the central curvature of the front surface of the lens asThe conic coefficient of the front surface of the lens is recorded；

Third, calculating the parameters of the back surface of the lens-recording the central curvature of the back surface of the lensCalculating the central curvature of the back surface of the lens according to the following formula,

in the formula (I), the compound is shown in the specification,which represents the optical power of the lens,representing the refractive index of the lens, which are respectively the design target and the known parameters of the invention;

the conic coefficient of the rear surface of the lens is recordedThe conic coefficient of the lens back surface is calculated according to the following equation:

in the formula (I), the compound is shown in the specification,is the local curvature of the front lens surface at the location of the lens edge,is the local curvature of the lens back surface at the location of the lens edge,is the abscissa of the edge position of the lens on the aspherical refracting surface of the lens,is the local power of the lens edge position and；

fourthly, evaluating indexes, namely evaluating the quality of the lens design by adopting the thickness of the edge position of the lens and the aberration of the inspected position on the lens;

and fifthly, an optimization process, namely drawing a point list by taking the thickness of the lens at the edge position as a vertical coordinate and the aberration of the lens at the investigation position as a horizontal coordinate, and then selecting an optimal scheme in the point list according to the requirements of a user.

In the present invention,andall are variables, a set of calculation formula is deduced by adopting the method of the invention, and the variables are established、The association of the combination of (a) and the evaluation index (i.e. the thickness of the lens at a diameter of 70mm, the aberration of the lens at a diameter of 50 mm).

In the fourth step, the center thickness of the lens is set toThe thickness of the edge of the lens isCalculating the thickness of the edge of the lens according to the following formula,

；

let the lens aberration be Asti, calculate the lens aberration according to the following formula,

Asti = Asti_f + Asti_b

in the formula, Asti_fDenotes the astigmatism of the front surface of the lens, Asti_bAstigmatism of the back surface of the lens is shown.

The method for calculating the astigmatism of the front and back surfaces of the lens is as follows: astigmatism of the front surface of the lens is calculated according to the following formula,

Asti_f = (n – 1)* (s_f1 – s_f2)

in the formula, s_f1 denotes the maximum curvature of the front surface of the lens at the investigation position, s_f2 denotes the minimum curvature of the front surface of the lens in the investigation position;

astigmatism of the rear surface of the lens is calculated according to the following formula,

Asti_b = (n – 1)* (s_b1 – s_b2)

in the formula, s_b1 denotes the maximum curvature of the rear surface of the lens at the investigation position, s_b2 denotes the minimum curvature of the rear surface of the lens at the position of investigation. The position considered here is at a lens diameter of 50 mm.

Further, the edge position of the lens is that the lens is at the diameter of 70 mm; the lens was examined at a position where the lens was at 50mm in diameter.

The invention provides a novel design method, which establishes a relation between the aspheric surface coefficient and the final lens performance through a simple calculation formula, thereby conveniently obtaining the aspheric surface coefficient corresponding to the lens with excellent performance. The lens is designed according to the method provided by the invention, the thickness of the lens and the image quality condition of a main eye area (within 50mm of the diameter) are considered, and the main parameters (namely the surface shape of the front surface of the lens) are adjusted) The key aberration of the whole lens can be directly calculated, so that the optimal design result can be obtained according to the specific requirements of a customer.

Drawings

The invention is further described below with reference to the accompanying drawings.

FIG. 1 is a schematic structural view of a lens of the present invention.

FIG. 2 is a schematic view showing the position of an evaluation index on a lens according to the present invention.

FIG. 3 is a diagram illustrating the results of the two-sided aspheric design of the present invention.

Detailed Description

Example 1

The embodiment provides a design method of a double-sided aspheric lens, which comprises the following steps:

first step, lens surface shape description mode

The anterior and posterior surfaces of the lens are described by the conic coefficient formula:

in the formula (I), the compound is shown in the specification,the rise of the face shape is shown,the radius of curvature of the center point is represented,represents the distance between the evaluation point and the optical axis, and，is the cone coefficient; thus only two variables are requiredAndthe profile of a surface can be determined.

Second step, design variablesAnd

the central curvature of the front surface of the lens is notedThe conic coefficient of the front surface of the lens is recorded. The method of the invention is to deduce a set of calculation formula and establish variables、The association of the combination of (a) and the evaluation index (i.e. the thickness of the lens at a diameter of 70mm, the aberration of the lens at a diameter of 50 mm).

Third step, calculating parameters of back surface of lens

For lenses of known power, such as-8D, from a simple formula for lens power calculation, it can be seen that:

it is known thatAndunder the precondition of (1), the pressure of the gas,it can be simply calculated according to the following formula: the central curvature of the back surface of the lens is notedCalculating the central curvature of the back surface of the lens according to the following formula,

in the formula (I), the compound is shown in the specification,representing the central curvature of the back surface of the lens,which represents the optical power of the lens,represents the refractive index of the lens, andfor design purposes, known parameters.

For an arbitrary curve on the lens, z = f (x), the local curvature formula of the curve is:

wherein the content of the first and second substances,、first and second order differentials, respectively, of the function f (x). For the front and back curved surfaces of the lens, an analytical expression can be used for description.

Thus, for，

Order toThen, the corresponding first and second order differential equations of the curved surface can be derived:

in the formula (I), the compound is shown in the specification,the abscissa representing a point on the aspherical refracting surface of the lens (i.e. the abscissa at a lens diameter of 70mm, in general=35）。

In the prior art are knownAndunder the precondition of (1), the local curvature at a certain position can be calculated by the following formula:

then, for the front lens surface at the lens edge, i.e. at a diameter of 70 mm: (= 35) local curvature thereofComprises the following steps:

for the lens posterior surface at the lens edge, i.e. 70mm diameter: (= 35) local curvature thereofComprises the following steps:

at the lens edge (i.e. at the position of 70mm diameter), its local curvature formula also satisfies the following simplified power formula, i.e. for the local power at the lens edge, there is:

in the formula (I), the compound is shown in the specification,denotes the local power of the lens at a diameter of 70mm and n represents the refractive index of the material of the lens. If it is desired that the local power at the edge of the lens remains the same as the power in the center of the lens, thenI.e. byIs a known design target value. Thus, from the above formula, it is known、、、Andin the case of (2), can be calculated to obtainThe value of (c).

Fourth, evaluation index

There are two main criteria for evaluating the quality of lens design.

(1) Thickness of lens

For a near-sighted lens, the central thickness of the near-sighted lens is fixed in advance (generally set to be 1.2 mm), and for different lens designs, the edge thickness of the near-sighted lens is an important index for judging the quality of the lens. For user comfort and aesthetics, the thinner the lens the better, but the thinner the lens, the more astigmatism the lens is typically designed to have.

If we look at the edge thickness of a lens at 70mm diameter, as shown in figures 1 and 2, then assume that the lens center thickness isThe radius of curvature of the center of the front surface of the lens isThe front surface of the lens has a conic coefficient ofThe central radius of curvature of the back surface of the lens isThe back surface conic coefficient of the lens isThen the edge thickness of the lens is calculated using the following equation：

,

Wherein the content of the first and second substances,=35。

(2) aberration size at 50mm diameter (main eye area) on lens

As shown in FIG. 2, s_fIs the local curvature, s, of any point on the front surface of the lens_bIs the local curvature of any point on the posterior surface of the lens. Given the knowledge of the formula describing the lens profile, the following equation can be usedThe principal curvatures s1 and s2 are calculated for any point on the anterior (posterior) surface of the lens, where s1 is the maximum curvature and s2 is the minimum curvature, both perpendicular to each other.

The formula for calculating the principal curvature of any point on the curved surface can be described as follows:

=

wherein the content of the first and second substances,. For aspheric surfaceThe surface shape can be expressed by analytic formula, so that the first and second partial derivativesCan be directly obtained.

As a result of this, the number of the,the astigmatism at any point on the lens surface can be approximated as:

Asti = (n – 1)* (s1 – s2)

where n represents the refractive index of the material of the lens, a known variable.

The astigmatism of the front and back surfaces of the lens is then calculated as follows:

astigmatism of the front surface of the lens is calculated according to the following formula,

Asti_f = (n – 1)* (s_f1 – s_f2)

in the formula, s_f1 denotes the maximum curvature of the front surface of the lens at a diameter of 50mm, s_f2 denotes that the front surface of the lens is straightMinimum curvature at diameter 50 mm;

astigmatism of the rear surface of the lens is calculated according to the following formula,

Asti_b = (n – 1)* (s_b1 – s_b2)

in the formula, s_b1 denotes the maximum curvature of the back surface of the lens at a diameter of 50mm, s_b2 denotes the minimum curvature of the back surface of the lens at 50mm diameter.

For a lens aberration Asti at a diameter of 50mm, it can be approximately expressed by the superposition of the astigmatism of the front and back surfaces:

Asti = Asti_f + Asti_b

in the formula, Asti_fDenotes the astigmatism of the front surface of the lens, Asti_bAstigmatism of the back surface of the lens is shown.

Fifth step, optimization procedure

The center curvature and the cone coefficient of the front surface of the lens are used as variables to obtain a series of variable combinations of the lens, and then a series of formulas in the steps are used to obtain combinations of the edge thickness and the aberration value of the lens under the combination conditions, and the combinations are drawn into a point chart as shown in figure 3 (namely, the thickness of the lens at the position of 70mm diameter is used as an ordinate, and the aberration of the lens at the position of 50mm diameter is used as an abscissa), so that the optimal solution can be selected in the point chart according to the requirements of users. Specifically, after the point alignment chart is obtained, a design with the minimum astigmatism can be selected in the point alignment chart according to the requirement of the lens thickness; the design with the smallest thickness can also be selected in the dot diagram according to the requirements of astigmatism.

When the central curvature radius of the front surface of the lens is 500mm, 400mm and 300mm, respectively, the front surface conic coefficient is from-200 to 5, and when the front surface conic coefficient is changed in 5 steps, the design results of the obtained double-sided aspheric surface are shown in fig. 3.

If a certain aberration index is used as a selection criterion, for example, astigmatism at 50mm of the lens diameter is less than 1.5, then the lens double-sided aspheric surface design result with the minimum edge thickness can be obtained, and the minimum edge thickness is 8.5mm. In the dot-column diagram, for a number of data points with an abscissa of-1.5, the data point with the smallest ordinate (edge thickness) (as the dot in fig. 3) is selected, and the corresponding lens parameters are shown in the table below.

The refractive index n = 1.7 of the lens and the central thickness = 1.0 of the lens

Front surface center radius of curvature	Front surface cone coefficient	Radius of curvature of center of rear surface	Coefficient of back surface cone	Astigmatism at 50mm diameter	Edge thickness at 70mm diameter
						500	-100	74.46	-2.34	-1.497	8.499

The invention selects the front and back surfaces of the lens, adopts the aspheric surface description equation of the basic form, and provides a novel double-sided aspheric surface lens design method.

In addition to the above embodiments, the present invention may have other embodiments. All technical solutions formed by adopting equivalent substitutions or equivalent transformations fall within the protection scope of the claims of the present invention.