CN1854787A - Method for designing non-spherical lens - Google Patents

Abstract

A kind of design method of aspherical lens, key step include: index of refraction, refractive index and the diameter for setting the aspherical lens; Using spherical design, two radius of curvature of the aspherical lens are designed, reach the index of refraction of above-mentioned setting, and make the distortion minimum value of three visual fields using two radius of curvature; It is first aspherical and second is aspherical, the eyeglass aspheric design formula that it is designed using eyeglass aspheric design formula are as follows:

, Z (r) is mirror surface depth, and Cv is the curvature of aspheric vertex of surface, and r is that any point is to the vertical height of optical axis on mirror surface, and P is conic constant value, and B, C, D, E are aspherical high-order coefficient; It is aspherical and second aspherical optimizes to first using damped least square method; Wherein, when optimization design, the aspherical lens are made to eliminate aberration at least five visual fields, and obtain first aspherical and second aspherical asphericity coefficient P, B, C, D, E.

Description

The method for designing of aspherical lens

[technical field]

The present invention relates to a kind of method for designing of optical mirror slip, relate in particular to a kind of method for designing of aspherical lens.

[background technology]

Optical device, as the eyeglass that optical read head, camera lens, lens adopted, generally adopts sphere design or aspheric surface design at present.

When eyeglass adopts sphere design, because two refractive surfaces of eyeglass are all designed to sphere form, therefore be easy to manufacture and processing.Yet the sphere that the spherical divergence eyeglass that center thin edges is thick or center thick rim are thin is assembled eyeglass, can be along with the increase of (also claiming the number of degrees) of eyeglass index of refraction, the edge of eyeglass or center can obviously thicken.Wherein eyeglass index of refraction refers to the rear vertex lens power value of this eyeglass, and its value equals the inverse of the eyeglass paraxial back vertex focal length (distance from eyeglass image interface summit to rear focus) that Yi meter Wei unit records.Can be calculated by formula (1):

$F_v=\frac{1}{f_v}=\frac{{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="A20051003447400151.png"\; state="\{\{state\}\}">F</figure-callout>}}_1+F_2-\frac{t}{n}{F}_1{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20051003447400151.png,A20051003447400162.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}{1-\frac{t}{n}{F}_1}---\left(1\right)$

Wherein, f _vfor the paraxial back vertex focal length of eyeglass, the radius-of-curvature of getting the sphere of not being close to image space is R ₁, the radius-of-curvature of being close to the sphere of image space is R ₂, center of lens thickness is t, and eyeglass material refractive index is n, and the index of refraction of two spheres can be respectively F ₁=(n-1)/R ₁with F ₂=(1-n)/R ₂.

The unit of eyeglass index of refraction uses D (diopter) to represent conventionally, and the usual said eyeglass number of degrees are exactly F _vvalue to be multiplied by 100 be 1D=100 degree.From formula (1), when one timing of eyeglass material, the index of refraction of eyeglass is just by R ₁, R ₂and t value decides.

When spherical divergence eyeglass designs, if t is fixed, along with the increase of eyeglass index of refraction, R ₁and R ₂difference just larger, this not only makes the edge of spherical divergence eyeglass obviously thicken, and if optic diameter fix, will make whole lens thickness strengthen.

When sphere convergence eyeglass designs, due to sphere convergence eyeglass center thickness, t depends on R ₁, R ₂value, therefore, also can be by regulating R ₁and R ₂value regulates the index of refraction of eyeglass.From formula (1), sphere is assembled eyeglass along with the increase of eyeglass index of refraction, R ₁and R ₂difference also just larger, the center thickness t of eyeglass is just larger, makes the volume of whole eyeglass larger.

Therefore, the spherical divergence or the convergence eyeglass that adopt sphere method for designing to design, if for camera lens, can increase the volume of camera lens; If this spherical divergence or to assemble eyeglass be nearsighted eyeglass or Farsighted lens, had both affected attractive in appearancely, cause again glasses wearer's discomfort.

In addition,, when eyeglass designs, generally except considering, the easiness and eyeglass slimming of eyeglass manufacture and processing, also must consider the image quality of eyeglass.

Aberration is one of principal element affecting lens imaging quality, and the aberration of General Influence lens imaging quality comprises three kinds of aberrations such as oblique fire astigmatism, visual field bending and distortion.Wherein, oblique fire astigmatism is that the light beam sending due to the tiny light source from extra-axial object point is different with the focus point of sagitta of arc field in meridian field, and has astigmatism so that look like unintelligible while making imaging.Visual field bending refers to that planar object perpendicular to optical axis is inconsistent and make image planes visual field become curved surface in image planes position at Yu Xiang edge, imaging Shi，Xiang center, can claim again average index of refraction error, is commonly referred to index of refraction error.Distortion be due in dipped beam axle region and distance light axle region because magnification is different, and make imaging generation barrel distortion or pincushion distortion, this kind of aberration makes imaging occur to change for how much but the sharpness that do not affect imaging.

As the index of refraction of establishing imaging surface in meridian field is F _t' (D), in sagitta of arc field, the index of refraction of imaging surface is F _s' (D), the image height of ideal image is MQ ', the image height of true imaging is MQ ":

Oblique fire astigmatism=F _t'-F _s'

From formula (1), when eyeglass adopts sphere design, can only be by regulating the radius-of-curvature of two spheres to eliminate oblique fire astigmatism, index of refraction error and these three kinds of aberrations that distort.But in fact, iff eliminating aberration by the radius-of-curvature of two spheres, can eliminate some aberrations, will increase the phenomenon of other another two aberrations.

Therefore, eyeglass adopts sphere design, cannot make eyeglass not only thin but also can effectively eliminate oblique fire astigmatism, index of refraction error and the three kinds of aberrations that distort simultaneously.

For addressing this problem, more eyeglass all adopts aspheric surface design at present, and wherein aspherical lens refers to that wherein at least one refractive surface is aspheric surface.

Eyeglass adopts aspheric surface design, can effectively eliminate oblique fire astigmatism, index of refraction error and the three kinds of aberrations that distort.As be disclosed in the CN1212766 Chinese patent application prospectus on March 31st, 1999, disclose a kind of design of aspherical lens, it changes the curvature at eyeglass each point place by introducing high-order term, and then reduce the thickness difference at each point place, the high-order term of so introducing in this technology had both comprised odd item, also comprised even item, can cause eyeglass refractive surface asymmetric, easily form larger above-mentioned three kinds of aberrations, so be difficult to design and process satisfactory eyeglass.

Be disclosed in the prospectus of CN1412604 Chinese patent application on April 23rd, 2003, disclose the design of another kind of aspherical lens, wherein, at least one refractive surface of this eyeglass is aspheric surface, and this aspheric surface computing formula (2) adopts following form:

$z\left(r\right)=\frac{{\mathrm{<figure-callout\; id="2"\; label="cr"\; filenames="A20051003447400151.png,A20051003447400162.png"\; state="\{\{state\}\}">cr</figure-callout>}}^2}{1+\sqrt{1-c^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20051003447400151.png,A20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}}+a_1{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="A20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^4+a_2{r}^6+a_3{r}^8+a_4{r}^{10}+a_5{r}^{12}---\left(2\right)$

Z in formula (r) represents the degree of depth of minute surface, and c represents the curvature on aspheric surface summit, and r represents that lens surface point is from the vertical range of optical axis, a ₁, a ₂, a ₃, a ₄, a ₅represent aspheric surface high-order term coefficient.

In this eyeglass aspheric surface design formula, although designing aspherical lens, introducing even item make refractive surface symmetrical.But conic constant value is 1 in this design, the thickness that shows this aspherical lens is attenuate effectively, and r has power 12 times, and the more difficult while of aspherical lens of designing is effectively eliminated oblique fire astigmatism, index of refraction error and the three kinds of aberrations that distort.

[summary of the invention]

In view of this, be necessary to provide a kind of method for designing of aspherical lens, make this aspherical lens can effectively eliminate aberration.

A method for designing for aspherical lens, its key step comprises:

Set index of refraction, refractive index and the diameter of this aspherical lens;

Employing sphere design, designs two radius-of-curvature of this aspherical lens, makes its index of refraction that reaches above-mentioned setting, and to utilize these two radius-of-curvature to make the distortion of three visual fields be minimum value;

Adopt eyeglass aspheric surface design formula to design the first aspheric surface and second aspheric surface of this aspherical lens, this eyeglass aspheric surface design formula is:

$Z\left(r\right)=\frac{C_v{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20051003447400151.png,A20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{1+\sqrt{1-P{C}_v^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20051003447400151.png,A20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}}+{\mathrm{<figure-callout\; id="4"\; label="Br"\; filenames="A20051003447400162.png"\; state="\{\{state\}\}">Br</figure-callout>}}^4+{\mathrm{Cr}}^6+{\mathrm{Dr}}^8+{\mathrm{Er}}^{10}$

In formula, Z (r) represents the minute surface degree of depth, C _vthe curvature that represents aspheric surface summit, r represents that on minute surface, any point is to the vertical height of optical axis, and P represents conic constant value, and B, C, D, E represent aspheric high-order term coefficient;

Adopt damped least square method to be optimized design to the first aspheric surface and the second aspheric surface;

Wherein, during optimal design, make this aspherical lens at least five visual fields, eliminate aberrations, and draw above-mentioned the first aspheric surface and the second aspheric asphericity coefficient P, B, C, D, E.

Compared with prior art, the method for designing of described aspherical lens, designs two aspheric surfaces simultaneously and adopts at least five visual fields to be optimized design.Than employing, be less than the method for designing that five visual fields are optimized the aspherical lens of design, can further eliminate the aberration maximum value existing in some visual field, make the designed aspherical lens of method for designing of aspherical lens of the present invention, oblique fire astigmatism in the 0 whole field range in visual field, visual field to 1.0, index of refraction error and distortion are all less, when wherein 1.0 visual fields refer to image space deflecting light beams by rear focus and the angle of lens light axis be 30 degree positions.

[accompanying drawing explanation]

Fig. 1 is the design flow diagram of aspherical lens one preferred configuration method of the present invention.

Fig. 2 is the designed aspheric surface divergent mirror chip architecture schematic diagram going out of the method for designing of aspherical lens of the present invention.

Fig. 3 A is that the designed aspheric surface going out of the method for designing of aspherical lens of the present invention is dispersed eyeglass at oblique fire astigmatism and the index of refraction error curve diagram of five visual field optimal design.

Fig. 3 B is that the designed aspheric surface going out of the method for designing of aspherical lens of the present invention is dispersed eyeglass at the distortion curve figure of five visual field optimal design.

Fig. 4 is the designed aspherical focusing lens structural representation going out of the method for designing of aspherical lens of the present invention.

Fig. 5 A is that the designed aspherical focusing lens going out of the method for designing of aspherical lens of the present invention is at oblique fire astigmatism and the index of refraction error curve diagram of seven visual field optimal design.

Fig. 5 B is that the designed aspherical focusing lens going out of the method for designing of aspherical lens of the present invention is at the distortion curve figure of seven visual field optimal design.

[embodiment]

As shown in Figure 1, be the design flow diagram of aspherical lens one preferred configuration method of the present invention, its key step comprises:

The first step, index of refraction, refractive index and the diameter of the aspherical lens that setting will design.

Second step, adopts sphere design, designs two radius-of-curvature of this aspherical lens, makes its index of refraction that reaches above-mentioned setting, and utilizes these two radius-of-curvature to make its distortion in 0.5,0.7 and 1.0 visual fields for minimum value.

The 3rd step, adopts an eyeglass aspheric surface design formula to define the first aspheric surface and second aspheric surface of this aspherical lens.

This eyeglass aspheric surface design formula (3) is:

$Z\left(r\right)=\frac{C_v{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20051003447400151.png,A20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{1+\sqrt{1-{\mathrm{PC}}_v^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20051003447400151.png,A20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}}+{\mathrm{<figure-callout\; id="4"\; label="Br"\; filenames="A20051003447400162.png"\; state="\{\{state\}\}">Br</figure-callout>}}^4+{\mathrm{Cr}}^6+{\mathrm{Dr}}^8+{\mathrm{Er}}^{10}---\left(3\right)$

Wherein, Z in formula (r) represents the minute surface degree of depth, C _vthe curvature that represents aspheric surface summit, r represents that on minute surface, any point is to the vertical height of optical axis, and P represents conic constant value, and B, C, D, E represent aspheric high-order term coefficient.

The 4th step, adopts damped least square method to be optimized design, makes this aspherical lens in a plurality of visual fields, eliminate oblique fire astigmatism, index of refraction error and distortion.

Aspherical lens, in eliminating the optimal design of aberration, is generally to eliminate aberration in some specific field angle, and wherein field angle refers to when image space deflecting light beams passes through rear focus and the angle of lens light axis.Therefore, while carrying out aspherical lens design in this flow process, start to adopt and five visual fields, eliminate oblique fire astigmatism, index of refraction error and distortion.

The optimal design of the method for designing of this aspherical lens can adopt damped least square method, and its performance function (4) can be defined as:

$\mathrm{\&phi;}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left[w_i(e_i-t_i)\right]}^2---\left(4\right)$

Wherein, w in formula _ifor weight factor, its value is taken as w _i> 0, and weight factor value is to decide according to the importance of the corresponding aberration of place item, and very strict if the aberration that will eliminate place item requires, that weight factor value can obtain larger; The item number of m for optimizing, its value is for being more than or equal to 1 integer; e _ifor considered correction term is certain aberration, consider e _iitem number be numerical value m; t _ifor the desired value of certain aberration, desired value t _ivalue according to e _isituation and determining.

In five visual fields, eliminate oblique fire astigmatism, index of refraction error and the three kinds of aberrations that distort,, in these five visual fields, make the desired value t of these three kinds of aberrations in performance function (4) _ibe zero.

The 5th step, calculates the first aspheric surface of this aspherical lens and the second aspheric asphericity coefficient P, B, C, D, E by the solution of damped least square method.

As this oblique fire astigmatism, index of refraction error and the desired value t of three kinds of aberrations in performance function (4) that distort _iwhile being zero, by the solution of damped least square method, obtained the first aspheric surface and the second aspheric asphericity coefficient of this aspherical lens, draw the design result of this aspherical lens.

The 6th step, judges whether oblique fire astigmatism, index of refraction error and the distortion of this aspherical lens in the whole field range of 0 visual field, visual field to 1.0 all can meet the demands.

Can judge by making oblique fire astigmatism, index of refraction error and the curve map of distortion in 0 visual field, visual field to 1.0, judge that relevant oblique fire astigmatism, index of refraction error and the distortion of these curve maps are in the whole field range of 0 visual field, visual field to 1.0, whether aberration maximum value meets the demands.

The 7th step, by judged result, determine whether that also needing to increase visual field is optimized design, if these three kinds of aberrations can not meet the demands in certain visual field, the visual field that optimal design can not meet the demands one by one, eliminate the oblique fire astigmatism, index of refraction error and the distortion that exist aberration maximum value to surpass certain visual field requiring, until reach requirement.

The method for designing of above-mentioned aspherical lens, in at least five visual fields, eliminate oblique fire astigmatism, index of refraction error and distortion, so just make to adopt the designed aspherical lens of method for designing of this aspherical lens, the oblique fire astigmatism in the whole field range of 0 visual field, visual field to 1.0, index of refraction error and these three kinds of aberrations that distort are all less.Therefore the method for designing of this aspherical lens can be designed the good aspherical lens of optical property.

As shown in Figure 2, the aspheric surface going out for the method for designing of above-mentioned aspherical lens is designed is dispersed the structural representation of eyeglass, and this aspheric surface is dispersed eyeglass and comprised that the radius-of-curvature of the first aspheric surface 1 and the second aspheric surface 2, the first aspheric surfaces 1 is R ₁, the radius-of-curvature of the second aspheric surface 2 is R ₂, center of lens thickness is t ₁, optic diameter is DA ₁.

This aspheric surface is dispersed the method for designing of eyeglass, can adopt eyeglass aspheric surface design formula (3) to design, and wherein, the asphericity coefficient of establishing the first aspheric surface 1 is P ₁, B ₁, C ₁, D ₁, E ₁, the asphericity coefficient P of the second aspheric surface 2 ₂, B ₂, C ₂, D ₂, E ₂, P wherein ₁, P ₂be respectively the conic constant value of the first aspheric surface 1 and the second aspheric surface 2, B ₁, C ₁, D ₁, E ₁and B ₂, C ₂, D ₂, E ₂be respectively the high-order term coefficient of the first aspheric surface 1 and the second aspheric surface 2.

The design that this aspheric surface is dispersed eyeglass adopts damped least square method to be optimized design, and the performance function of damped least square method is as shown in formula (4).The design that this aspheric surface is dispersed eyeglass adopts at least five visual fields to eliminate aberration,, makes the desired value t of performance function (4) that is _iin at least five visual fields, be zero.

In performance function (4), this aspheric surface is dispersed the design of eyeglass, aberration correction, to the procedural representation of desired value, is to be provided with 10 variable design parameters, i.e. 10 design variable performance functions.With x ₁, x ₂, x ₃... x ₉, x ₁₀the asphericity coefficient P that represents the first aspheric surface 1 ₁, B ₁, C ₁, D ₁, E ₁asphericity coefficient P with the second aspheric surface 2 ₂, B ₂, C ₂, D ₂, E ₂.

By performance function (4), known, optimizing item number has m, and this aspheric surface is dispersed the method for designing of eyeglass, can adopt m/3 item wherein to eliminate oblique fire astigmatism, and its time is according to visual field size 1.0 visual fields and determining, then adopt m/3 item to eliminate index of refraction error and m/3 item is eliminated distortion.An error function of definable (5) is:

f _i＝W _i(e _i-t _i)＝f _i(x ₁，x ₂，x ₃...x _n)，i＝1，2，......，m (5)

For calculating the asphericity coefficient P of the first aspheric surface 1 ₁, B ₁, C ₁, D ₁, E ₁asphericity coefficient P with the second aspheric surface 2 ₂, B ₂, C ₂, D ₂, E ₂value.If the variable before optimizing is with x ₁₀, x ₂₀, x ₃₀..., x _n0represent n=10; Aberration f ₁₀, f ₂₀, f ₃₀... f _m0represent, the variable after optimization is with x ₁, x ₂, x ₃... x ₉, x _nrepresent n=10; Aberration f ₁, f ₂, f ₃... f _m-1, f _mrepresent.

Because the solution (6) of damped least square method is:

X＝(A ^TA+pI) ^-1A ^Tf ₀ (6)

Symbol in formula can be used defined matrix:

$x_0=\left(\begin{array}{c}{x}_{10}\\ x_{20}\\ x_{30}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\mathrm{<figure-callout\; id="0"\; label="x\; n"\; filenames="A20051003447400172.png"\; state="\{\{state\}\}">x</figure-callout>}}_n\end{array}\right),x=\left(\begin{array}{c}{x}_1\\ x_2\\ x_3\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ x_n\end{array}\right),{\mathrm{<figure-callout\; id="0"\; label="f"\; filenames="A20051003447400172.png"\; state="\{\{state\}\}">f</figure-callout>}}_0=\left(\begin{array}{c}{f}_{10}\\ f_{20}\\ f_{30}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ {\mathrm{<figure-callout\; id="0"\; label="f\; m"\; filenames="A20051003447400172.png"\; state="\{\{state\}\}">f</figure-callout>}}_m\end{array}\right),f=\left(\begin{array}{c}{f}_1\\ f_2\\ {\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="A20051003447400162.png"\; state="\{\{state\}\}">f</figure-callout>}}_3\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ f_m\end{array}\right),X={x-x}_0=\left(\begin{array}{c}{x}_1-x_{10}\\ x_2-x_{20}\\ x_3-x_{30}\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ x_n-{\mathrm{<figure-callout\; id="0"\; label="x\; n"\; filenames="A20051003447400172.png"\; state="\{\{state\}\}">x</figure-callout>}}_n\end{array}\right)$

A is the matrix of a m * n, wherein $A_{\mathrm{ij}}=\frac{{\&PartialD;f}_i}{{\&PartialD;x}_j},$ i＝1，2，....，m，j＝1，2，....，n，n＝10。

A wherein ^tfor the transposed matrix of A, p is damping factor, and I is unit matrix, (A ^ta+pI) ^-1expression is to (A ^ta+pI) matrix of negating, by the computing of above matrix, can obtain the operation values of X, passes through x=x ₀+ X, can determine the value of x, and then can draw the P after correction ₁, B ₁, C ₁, D ₁, E ₁, P ₂, B ₂, C ₂, D ₂, E ₂value.

If the designed aspheric surface of the method for designing of above-mentioned aspherical lens is dispersed eyeglass, employing in 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field and 1.0 Wu Ge visual fields, visual field are optimized design, wherein to disperse the material of eyeglass be a kind of plastics to this aspheric surface, refractive index is 1.586, and it is as shown in table 1 that this aspheric surface is dispersed the design parameter of eyeglass.

Table 1

Eyeglass index of refraction F v=-14D, optic diameter DA 1=30mm, center thickness t 1＝1mm
						The first aspheric surface 1			The second aspheric surface 2
Radius of curvature R 1(cm)		36.07206	Radius of curvature R 1(cm)		19.26784
						Quadric surface constant value P 1		-3.146794	Quadric surface constant value P 2		-1.309141
Aspheric high-order term coefficient	B 1	1.45672×10 -4	Aspheric high-order term coefficient	B 2	1.877927×10 -4
						C 1	-7.260429×10 -7	C 2	-3.682191×10 -7
	D 1	2.68586×10 -9		D 2	-2.583728×10 -10
						E 1	-3.404548×10 -12	E 2	1.296844×10 -11

In performance function (4), adopt weight factor w ₁=w ₂=...=w ₁₄=w ₁₅=1, desired value t ₁=t ₂=...=t ₁₄=t ₁₅=0, by calculating, can show that the aspheric surface going out for the method for designing of this aspherical lens is designed as Fig. 3 A disperses eyeglass at oblique fire astigmatism and the index of refraction error curve diagram of five visual field optimal design, the designed aspheric surface going out of method for designing that Fig. 3 B is this aspherical lens is dispersed eyeglass at the distortion curve figure of five visual field optimal design.

Wherein, in Fig. 3 A, abscissa axis represents the size of index of refraction, and axis of ordinates represents the size of field angle; In Fig. 3 B, abscissa axis represents the size of distortion, and axis of ordinates represents the size of field angle.F ' in Fig. 3 A _tfor the index of refraction of imaging surface in meridian field, F ' _sfor the index of refraction of imaging surface in sagitta of arc field, FPS=F _vfor eyeglass index of refraction, the curve in Fig. 3 B is the size of distortion in each visual field:

Oblique fire astigmatism=F ' _t-F ' _s;

By Fig. 3 A and Fig. 3 B, can find out that the designed aspheric surface going out of the method for designing of this aspherical lens disperses eyeglass, in the whole field range of 0 visual field, visual field to 1.0, oblique fire astigmatism is less than 0.044D, index of refraction error is less than 0.041D, distortion is less than 0.067%, and it is very little that these three kinds of aberration value are all proofreaied and correct, therefore effectively eliminate preferably oblique fire astigmatism, index of refraction error and the three kinds of aberrations that distort.

As shown in Figure 4, the structural representation of the aspherical focusing lens going out for the method for designing of this aspherical lens is designed, this aspherical focusing lens comprises that the radius-of-curvature of the first aspheric surface 3 and the second aspheric surface 4, the first aspheric surfaces 3 is R ₃, the radius-of-curvature of the second aspheric surface 4 is R ₄, center of lens thickness is t ₂, optic diameter is DA ₂.

To disperse the method for designing of eyeglass identical with above-mentioned aspheric surface substantially for the method for designing of this aspherical focusing lens, its difference is in the method for designing of this aspherical focusing lens, is that adopting at least 7 is elimination oblique fire astigmatism, index of refraction error and distortion in visual field.

If the aspherical focusing lens that the method for designing of this aspherical lens is designed, employing in 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field, 0.9 visual field, 0.95 visual field and 1.0 Qi Ge visual fields, visual field are optimized design, wherein the material of this aspherical focusing lens is a kind of plastics, refractive index is 1.586, and the design parameter of this aspherical focusing lens is as shown in table 2.

Table 2

Eyeglass index of refraction F v=14.00D, optic diameter DA 2=32mm, center thickness t 2＝9.2mm
						The first aspheric surface 3			The second aspheric surface 4
Radius of curvature R 3(cm)		26.27803	Radius of curvature R 4(cm)		50.45961
						Quadric surface constant value P 1		-3.961846	Quadric surface constant value P 2		-3.228008
Aspheric high-order term coefficient	B 1	1.989787×10 -5	Aspheric high-order term coefficient	B 2	-2.220448×10 -5
						C 1	-8.046623×10 -8	C 2	-1.609468×10 -7
	D 1	-1.679019×10 -10		D 2	5.014807×10 -10
						E 1	1.10465×10 -13	E 2	-6.264007×10 -13

In performance function (4), select w ₁=2, w ₂=4, w ₃=5, w ₄=8, w ₅=9, w ₆=9, w ₇=10 for oblique fire astigmatism weight factor, selects w ₈=1, w ₉=2, w ₁₀=3, w ₁₁=10, w ₁₂=12, w ₁₃=12, w ₁₄=14 is index of refraction error weight factor, selects w ₁₅=0.2, w ₁₆=0.5, w ₁₇=0.5, w ₁₈=0.8, w ₁₉=1, w ₂₀=1, w ₂₁=1.8 is distortion weight factor, desired value t ₁=t ₂=...=t ₂₀=t ₂₁=0, by calculating, can show that the aspherical focusing lens that goes out for the method for designing of this aspherical lens is designed as Fig. 5 A is at oblique fire astigmatism and the index of refraction error curve diagram of seven visual field optimal design, the designed aspherical focusing lens going out of method for designing that Fig. 5 B is this aspherical lens is at the distortion curve figure of seven visual field optimal design.

Wherein, in Fig. 5 A, abscissa axis represents the size of index of refraction, and axis of ordinates represents the size of field angle; In Fig. 5 B, abscissa axis represents the size of distortion, and axis of ordinates represents the size of field angle.F ' in Fig. 5 A _tfor the index of refraction of imaging surface in meridian field, F ' _sfor the index of refraction of imaging surface in sagitta of arc field, FPS=F _vfor the index of refraction of eyeglass, the curve in Fig. 5 B is the size of distortion in each visual field:

Oblique fire astigmatism=F ' _t-F ' _s;

By Fig. 5 A and Fig. 5 B, can find out the designed aspherical focusing lens going out of the method for designing of this aspherical lens, in the whole field range of 0 visual field, visual field to 1.0, oblique fire astigmatism is less than 0.0377D, index of refraction error is less than 0.0815D, distortion is less than 1.1493%, and it is very little that these three kinds of aberration value are all proofreaied and correct, therefore effectively eliminate preferably oblique fire astigmatism, index of refraction error and distortion simultaneously.

In sum, the method for designing of this aspherical lens, can realize the object of effective elimination aberration.So, the foregoing is only this preferred embodiments, be such as familiar with the personage of this case technology, helping the equivalence modification of doing according to this case creation spirit or changing, all should be contained in following claim.

Claims (10)

1. a method for designing for aspherical lens, the method for designing key step of this aspherical lens comprises: index of refraction, refractive index and the diameter of setting this aspherical lens;

Employing sphere design, designs two radius-of-curvature of this aspherical lens, makes its index of refraction that reaches above-mentioned setting, and to utilize these two radius-of-curvature to make the distortion of three visual fields be minimum value;

Adopt eyeglass aspheric surface design formula to design the first aspheric surface and second aspheric surface of this aspherical lens, this eyeglass aspheric surface design formula is:

$Z\left(r\right)=\frac{C_v{r}^2}{1+\sqrt{1-P{C}_v^2{r}^2}}+{\mathrm{Br}}^4+{\mathrm{Cr}}^6+{\mathrm{Dr}}^8+{\mathrm{Er}}^{10}$

In formula, Z (r) represents the minute surface degree of depth, C _vthe curvature that represents aspheric surface summit, r represents that on minute surface, any point is to the vertical height of optical axis, and P represents conic constant value, and B, C, D, E represent aspheric high-order term coefficient;

Adopt damped least square method to be optimized design to the first aspheric surface and the second aspheric surface;

It is characterized in that: be optimized when design, make this aspherical lens eliminate aberrations at least five visual fields, and draw above-mentioned the first aspheric surface and the second aspheric asphericity coefficient P, B, C, D, E.

2. the method for designing of aspherical lens as claimed in claim 1, is characterized in that: these three visual fields are 0.5,0.7 and 1.0 visual fields.

3. the method for designing of aspherical lens as claimed in claim 1, is characterized in that: this aspherical lens can be aspherical focusing lens, and optimal design is to eliminate aberration at least seven visual fields.

4. the method for designing of the aspherical lens as described in claim 1 or 3, is characterized in that: this optimal design adopts the performance function of damped least square method to be:

$\mathrm{\&phi;}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left[w_i(e_i-t_i)\right]}^2$

Wherein, w in formula _ifor weight factor, the item number of m for optimizing, e _ifor considered correction term is certain aberration, t _idesired value for certain aberration.

5. the method for designing of aspherical lens as claimed in claim 4, is characterized in that: in the item number m of this optimization, m/3 item is used for eliminating oblique fire astigmatism, and m/3 item is used for eliminating index of refraction error, and m/3 item is used for eliminating distortion.

6. the method for designing of the aspherical lens as described in claim 1 or 3, is characterized in that: this optimal design is eliminated aberration in 0 visual field to 1.0 field range, and wherein 1.0 visual fields refer to that field angle is the position of 30 degree.

7. the method for designing of aspherical lens as claimed in claim 1, is characterized in that: these five visual fields can be 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field and 1.0 visual fields.

8. the method for designing of aspherical lens as claimed in claim 7, it is characterized in that: this aspherical lens is that aspheric surface is dispersed eyeglass, the index of refraction of dispersing eyeglass when this aspheric surface of setting is-14.00D, refractive index is 1.586, optic diameter is 30mm, center thickness is 1mm, the first aspheric radius-of-curvature is 36.07206cm, the second aspheric radius-of-curvature is 19.26785cm, and in this 0.3 visual field, 0.5 visual field, 0.7 visual field, oblique fire astigmatism is eliminated in these five visual fields of 0.85 visual field and 1.0 visual fields, when index of refraction error and distortion, this aspheric surface is dispersed the first aspheric surface of eyeglass and the second aspheric asphericity coefficient as following table: The first aspheric surface The second aspheric surface Quadric surface constant value P ₁ -3.146794 Quadric surface constant value P ₂ -1.309141 Aspheric high-order term coefficient B ₁ 1.45672×10 ^-4 Aspheric high-order term coefficient B ₂ 1.877927×10 ^-4 C ₁ -7.260429×10 ^-7 C ₂ -3.682191×10 ^-7 D ₁ 2.68586×10 ^-9 D ₂ -2.583728×10 ^-10 E ₁ -3.404548×10 ^-12 E ₂ 1.296844×10 ^-11

9. the method for designing of aspherical lens as claimed in claim 3, is characterized in that: these seven visual fields can be 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field, 0.9 visual field, 0.95 visual field and 1.0 visual fields.

10. the method for designing of aspherical lens as claimed in claim 9, it is characterized in that: when setting the index of refraction of this aspherical focusing lens, be 14.00D, refractive index is 1.586, optic diameter is 32mm, center thickness is 9.2mm, the first aspheric radius-of-curvature is 26.27803cm, the second aspheric radius-of-curvature is 50.45961cm, and in this 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field, 0.9 visual field, oblique fire astigmatism is eliminated in 0.95 visual field and 1.0 Qi Ge visual fields, visual field, when index of refraction error and distortion, the first aspheric surface of this aspherical focusing lens and the second aspheric asphericity coefficient are as following table: The first aspheric surface The second aspheric surface Quadric surface constant value P ₁ -3.961846 Quadric surface constant value P ₂ -3.228008 Aspheric high-order term coefficient B ₁ 1.989787×10 ^-5 Aspheric high-order term coefficient B ₂ -2.220448×10 ^-5 C ₁ -8.046623×10 ^-10 C ₂ -1.609468×10 ^-7 D ₁ -1.679019×10 ^-10 D ₂ 5.014807×10 ^-10 E ₁ 1.10465×10 ^-13 E ₂ -6.264007×10 ^-13

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