CN1841113A - Aspherical lens - Google Patents

Abstract

A kind of aspherical lens, including first is aspherical and second is aspherical, the index of refraction of the aspherical lens changes within the scope of 1D, the first aspherical fixation, and makes the aspherical lens at least five visual field, makes performance function Target value ti be zero, wherein wi is weight factor, and m be the item number of optimization, and ei is correction term i.e. some aberration for being considered, ti for some aberration target value.

Description

Aspherical lens

[technical field]

The present invention relates to a kind of eyeglass, relate in particular to a kind of aspherical lens.

[background technology]

Optical device, as the eyeglass that optical read head, camera lens, lens adopted, generally has spheric glass or aspherical lens at present.

For spheric glass, because two refractive surface is sphere form, therefore be all easier to man-hour with adding manufacturing.Yet ，Dui center thin edges is thick, disperse spheric glass, along with the increase of (also claiming the number of degrees) of eyeglass index of refraction, the edge of eyeglass 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):

$F_v=\frac{1}{f_v}=\frac{{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="A20051003393500173.png"\; state="\{\{state\}\}">F</figure-callout>}}_1+F_2-\frac{t}{n}{F}_1{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="A20051003393500173.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}{1-\frac{t}{n}{F}_1}---\left(1\right)$

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 public (1) formula, when one timing of eyeglass material, the index of refraction of eyeglass is just by R ₁, R ₂and t value decides.Therefore, if t value is fixing, just could be by would regulating R ₁and R ₂value regulates the index of refraction of eyeglass.

Therefore for dispersing spheric glass, if t is fixed, along with the increase of eyeglass index of refraction, R ₁and R ₂difference will be larger, this not only makes the edge of dispersing spheric glass obviously thicken, and if optic diameter fix, will make whole lens thickness strengthen.If this disperses spheric glass for camera lens, can increase the volume of camera lens; If this disperses spheric glass is nearsighted eyeglass, both affected attractive in appearancely, cause again glasses wearer's discomfort.

In addition,, for eyeglass, 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 visual field become curved surface 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), for dispersing spheric glass, if center of lens thickness is fixed, can only slant astigmatism, index of refraction error and these three kinds of aberrations that distort by regulating the radius-of-curvature of two spheres to eliminate.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.As disperse when spheric glass only has a curvature mirror radius and can proofread and correct oblique fire astigmatism, but can increase index of refraction error and these two kinds of aberrations of distortion.

Therefore, general spheric glass cannot be designed to not only thin but also can effectively eliminate the eyeglass of 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 one of them refractive surface is aspheric surface, and aspheric surface can be ellipsoid, hyperboloid, parabola etc.

Eyeglass adopts aspheric surface design, and the eyeglass that can offset the sphere formation of two different curvature does not wait the whole thickening of the eyeglass causing at center and peripheral thickness, and can effectively eliminate again oblique fire astigmatism, index of refraction error and the three kinds of aberrations that distort.As be disclosed in the Chinese patent application CN1212766A on March 31st, 1999, disclosed a kind 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 the eyeglass meeting the requirements.

The Chinese patent application CN1412604A that is disclosed on April 23rd, 2003, has disclosed another kind of aspherical lens, and wherein, at least one refractive surface of this eyeglass is aspheric surface, and this aspheric surface computing formula (2) adopts following form:

$z\left(r\right)=\frac{{\mathrm{<figure-callout\; id="2"\; label="cr"\; filenames="A20051003393500173.png"\; state="\{\{state\}\}">cr</figure-callout>}}^2}{1+\sqrt{1-c^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="A20051003393500173.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}}+a_1{r}^4+a_2{r}^6+a_3{r}^8+a_4{r}^{10}+a_5{r}^{12}---\left(2\right)$

The rise that in formula, z is surperficial somewhere, c represents the curvature on aspheric surface summit, r represents the distance from optical axis, a ₁, a ₂, a ₃, a ₄, a ₅for aspheric high-order term coefficient.

In this aspheric surface formula, although designing aspherical lens, introducing even item make refractive surface symmetrical,, in its formula, r has power 12 times, 5 values of aspheric surface high-order term coefficients by using.If only have a refractive surface to adopt this formula to carry out aspheric surface design, the further attenuate of the thickness of eyeglass, and the above-mentioned three kinds of aberrations of more difficult effective elimination.If two refractive surfaces all adopt this formula to carry out aspheric surface design, when the index of refraction of eyeglass changes, the aspheric surface design of two refractive surfaces all can change, will increase the use amount of aspheric surface design, make to manufacture difficulty, cost increases, and carries out aspheric surface design simultaneously, makes the more difficult while effectively eliminate above-mentioned three kinds of aberrations.

Aspherical lens is in optimization (aberration is minimized) design of eliminating aberration, generally to eliminate aberration in some specific field angle, the corresponding meeting of the aberration of other field angle becomes less, and wherein field angle refers to the angle of image space deflecting light beams and lens light axis.

At present, for effectively eliminating the aberration of aspherical lens, conventionally adopt damped least square method to carry out optimal design aspherical lens, first define a performance function (3):

$\mathrm{\&phi;}=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\left[w_i(e_i-t_i)\right]}^2---\left(3\right)$

W wherein _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.

Be provided with an aspherical lens, comprise the first aspheric surface and the second aspheric surface, wherein the first aspheric asphericity coefficient P ₁, B ₁, C ₁, D ₁, E ₁, the second aspheric asphericity coefficient P ₂, B ₂, C ₂, D ₂, E ₂, P wherein ₁, P ₂for conic constant value (Conic Constant), B ₁, C ₁, D ₁, E ₁and B ₂, C ₂, D ₂, E ₂be respectively the first aspheric surface and the second aspheric high-order term coefficient (High ordercoefficients).

When this aspherical lens adopts the optimal design of three visual fields, as adopt 0.5 visual field, 0.7 visual field and 1.0 visual fields to optimize, wherein 1.0 visual fields refer to that the angle of image space deflecting light beams and lens light axis is 30 degree positions, and the parameter of establishing this aspherical lens is as shown in table 1.

Table 1

Eyeglass index of refraction F v=-14D, optic diameter DA=30mm, center thickness t=1mm
						The first aspheric surface			The second aspheric surface
Radius of curvature R 1(cm)		36.07184	Radius of curvature R 1(cm)		19.26777
						Quadric surface constant P 1		-3.386493	Quadric surface constant P 2		-1.528979
The first aspheric asphericity coefficient	B 1	1.198016×10 -4	The second aspheric asphericity coefficient	B 2	1.674289×10 -4
						C 1	-4.77547×10 -7	C 2	-4.371044×10 -7
	D 1	2.24246×10 -9		D 2	4.644352×10 -9
						E 1	-4.148246×10 -12	E 2	-9.825316×10 -12

In performance function (3), weight factor w ₁=w ₂=...=w ₈=w ₉=1, desired value t ₁=t ₂=...=t ₈=t ₉=0, by calculating, can be oblique fire astigmatism and the index of refraction error curve diagram that existing aspherical lens three visual fields are optimized as Figure 1A, Figure 1B is the distortion curve figure that existing aspherical lens three visual fields are optimized.

Wherein, in Figure 1A, abscissa axis represents the index of refraction of index of refraction, and axis of ordinates represents the size of field angle; In Figure 1B, abscissa axis represents the size of distortion, and axis of ordinates represents the size of field angle.F in Figure 1A _t' be the index of refraction of imaging surface in meridian field, F _s' be the index of refraction of imaging surface in sagitta of arc field, FPS=F _vfor the index of refraction of eyeglass, the curve in Figure 1B is the size of distortion in each visual field:

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

By Figure 1A and Figure 1B, obviously can find out in 0.5 visual field, 0.7 visual field and 1.0 visual fields, oblique fire astigmatism, index of refraction error and distortion all have a minimum value.But oblique fire astigmatism has a maximal value in 0.87 visual field, by being calculated as 1.816D; Index of refraction error has a maximal value in 0.88 visual field, by being calculated as 0.941D; Distortion has a maximal value in 0.89 visual field, by being calculated as 0.544%, therefore effect is poor.

When increasing a visual field and optimize, as while adopting 0.5 visual field, 0.7 visual field, 0.85 visual field and 1.0 visual fields to optimize, the parameter of establishing this aspherical lens is as shown in table 2.

Table 2

Eyeglass index of refraction F v=-14D, optic diameter DA=30mm, center thickness t=1mm
						The first aspheric surface			The second aspheric surface
Radius of curvature R 1(cm)		36.07206	Radius of curvature R 1(cm)		19.26784
						Quadric surface constant P 1		-2.35129	Quadric surface constant P 2		-0.984932
The first aspheric asphericity coefficient	B 1	1.483993×10 -4	The first aspheric asphericity coefficient	B 2	1.900389×10 -4
						C 1	-7.892148×10 -7	C 2	-4.748713×10 -7
	D 1	2.9497×10 -9		D 2	1.432663×10 -10
						E 1	-3.773838×10 -12	E 2	1.272448×10 -11

In performance function (3), weight factor w ₁=w ₂=...=w ₁₁=w ₁₂=1, desired value t ₁=t ₂=...=t ₁₁=t ₁₂=0, by calculating, can draw as Fig. 2 A to be oblique fire astigmatism and the index of refraction error curve diagram of existing aspherical lens four visual fields optimizations, Fig. 2 B is the distortion curve figure that existing aspherical lens four visual fields are optimized.

Wherein, in Fig. 2 A, abscissa axis represents the index of refraction of index of refraction, and axis of ordinates represents the size of field angle; In Fig. 2 B, abscissa axis represents the size of distortion, and axis of ordinates represents the size of field angle.F in Fig. 2 A _t' be the index of refraction of imaging surface in meridian field, F _s' be 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. 2 B is the size of distortion in each visual field:

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

By Fig. 2 A and Fig. 2 B, obviously can find out that the effect of optimization that adopts four visual fields to optimize is better than the effect of optimization that above-mentioned employing 0.5 visual field, 0.7 visual field and 1.0 visual fields are optimized.But, in 0.3 place, visual field oblique fire astigmatism, index of refraction error and distortion, but there is a maximal value.

Therefore aspherical lens adopts three or four visual fields optimizations, all can not eliminate preferably aberration.

[summary of the invention]

In view of this, be necessary to design a kind of eyeglass, make this eyeglass cost easy to manufacture lower, and not only thin but also can effectively eliminate aberration.

An aspherical lens, comprises the first aspheric surface and the second aspheric surface, and wherein the index of refraction of this aspherical lens changes within the scope of 1D, and the first aspheric surface is fixed, and makes this aspherical lens at least 5 visual fields, makes performance function

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

Desired value t _ibe zero, w wherein _ifor weight factor, the item number of m for optimizing, e _ifor considered correction term is certain aberration, t _idesired value for certain aberration.

Compared with prior art, this aspherical lens is owing to being changed within the scope of 1D at index of refraction, and the first aspheric surface is fixed, and is optimized design at least 5 visual fields, so have the following advantages:

1. than changing with eyeglass index of refraction, two aspherical lens that aspheric surface design need change simultaneously, aspherical lens of the present invention has reduced aspheric surface design use amount, therefore cost easy to manufacture is lower.

2. than being less than 5 visual fields and being optimized the aspherical lens of design, the oblique fire astigmatism of aspherical lens of the present invention, index of refraction error and distortion are all less in 0 visual field to 1.0 field range.

3. than eyeglass index of refraction variation range, be greater than the aspherical lens of 1D, aspherical lens of the present invention has reduced the difficulty of eliminating aberration.

[accompanying drawing explanation]

Figure 1A is oblique fire astigmatism and the index of refraction error curve diagram that existing aspherical lens three visual fields are optimized.

Figure 1B is the distortion curve figure that existing aspherical lens three visual fields are optimized.

Fig. 2 A is oblique fire astigmatism and the index of refraction error curve diagram that existing aspherical lens four visual fields are optimized.

Fig. 2 B is the distortion curve figure that existing aspherical lens four visual fields are optimized.

Fig. 3 is aspherical lens structural representation of the present invention.

Fig. 4 A is oblique fire astigmatism and the index of refraction error curve diagram that aspherical lens of the present invention five visual fields are optimized.

Fig. 4 B is the distortion curve figure that aspherical lens of the present invention five visual fields are optimized.

[embodiment]

As shown in Figure 3, be aspherical lens structural representation of the present invention, this aspherical lens comprises 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, optic diameter is DA.

Aspherical lens of the present invention adopts damped least square method to carry out optimal design.In performance function (3), aspherical lens design of the present invention is the process to desired value aberration correction, is expressed as and is provided with 10 variable design parameters, be 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, P wherein ₁, P ₂for conic constant value, B ₁, C ₁, D ₁, E ₁and B ₂, C ₂, D ₂, E ₂be respectively the first aspheric surface and the second aspheric surface high-order term coefficient.

From performance function (3), optimizing item number has m, and aspherical lens of the present invention can adopt m/3 item wherein to eliminate oblique fire astigmatism while optimizing, and its time is according to visual field size 1.0 visual fields and determining, when wherein 1.0 visual fields refer to eyeglass imaging, deflecting light beams and lens light axis angle are 30 degree, then adopt m/3 item to eliminate index of refraction error and m/3 item is eliminated distortion.An error function of definable (4) is:

f _i＝W _i(e _i-t _i)＝f _i(x ₁，x ₂，x ₃...x _n)，i＝1，2，......，m (4)

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 of damped least square method is (5)

X＝(A ^TA+pI) ^-1A ^Tf ₀ (5)

Symbol in formula can be used defined matrix:

$x_0=\left(\begin{array}{c}{x}_{10}\\ x_{20}\\ x_{30}\\ .\\ .\\ .\\ .\\ .\\ .\\ x_{n0}\end{array}\right),$ $x=\left(\begin{array}{c}{x}_1\\ x_2\\ x_3\\ .\\ .\\ .\\ .\\ .\\ .\\ x_n\end{array}\right),$ $f_0=\left(\begin{array}{c}{f}_{10}\\ f_{20}\\ f_{30}\\ .\\ .\\ .\\ .\\ .\\ .\\ f_{m0}\end{array}\right),$ $f=\left(\begin{array}{c}{f}_1\\ f_2\\ f_3\\ .\\ .\\ .\\ .\\ .\\ .\\ f_m\end{array}\right),$ $X=x-x_0=\left(\begin{array}{c}{x}_1-x_{10}\\ x_2-x_{20}\\ x_3-x_{30}\\ .\\ .\\ .\\ .\\ .\\ .\\ x_n-x_{n0}\end{array}\right)$

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.

Aspherical lens of the present invention is to adopt two aspheric surface designs, index of refraction at this aspherical lens is changed within the scope of 1D, the first aspheric surface 1 design is fixing, and in 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field and 1.0 visual fields eliminate oblique fire astigmatism, index of refraction error and distortion.

If aspherical lens of the present invention be eyeglass index of refraction for-14D to-14.75D or-20D carries out aspheric surface design to-20.75D.First design eyeglass index of refraction for-14D or-two aspheric surfaces of 20D, while changing in the index of refraction of this aspherical lens scope at 1D, the index of refraction of this aspherical lens be-14.25D ,-14.50D ,-14.75D or-during certain value of 20.25D ,-20.50D ,-20.75D, the second aspheric surface 2 is carried out to aspheric surface design.Wherein, the aspheric surface design of the second aspheric surface 2 is mainly two aspects, the first when the index of refraction of this aspherical lens be-14.25D ,-14.50D ,-14.75D or-when 20.25D ,-the 20.50D ,-some values of 20.75D, the aspheric surface design of the second aspheric surface 2 makes this aspherical lens can reach this value; Its two be in 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field and these five visual fields, 1.0 visual fields are optimized, and effectively eliminate oblique fire astigmatism, index of refraction error and the distortion of these five visual fields.

Because aspherical lens of the present invention is to adopt two aspheric surfaces designs, than the eyeglass that only adopts an aspheric surface design can be further effective attenuate and eliminate aberration.

Aspheric surface design due to aspherical lens of the present invention, be first design eyeglass index of refraction for-14D or-two aspheric surfaces of 20D, while changing in the index of refraction of this aspherical lens scope at 1D, the index of refraction of this aspherical lens be-14.25D ,-14.50D ,-14.75D or-during certain value of 20.25D ,-20.50D ,-20.75D, the second aspheric surface 2 is carried out to aspheric surface design.Than the change with eyeglass index of refraction, need change the aspherical lens of two aspheric surface designs simultaneously, can reduce the use amount of aspheric surface design, therefore make aspherical lens of the present invention cost easy to manufacture lower.

And large or two aspherical lens that aspheric surface design need change, have reduced the difficulty of eliminating aberration than eyeglass index of refraction variation range simultaneously.

Aspherical lens of the present invention in 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field and 1.0 visual fields are optimized, than being less than 5 visual fields and being optimized the aspherical lens of design, the oblique fire astigmatism of aspherical lens of the present invention, index of refraction error and distortion are all less in 0 visual field, visual field to 1.0.

If aspherical lens parameter of the present invention is as shown in table 3, adopts and in 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field and 1.0 visual fields, eliminate oblique fire astigmatism, index of refraction error and distortion.

Table 3

Eyeglass index of refraction F v=-14D, optic diameter DA=30mm, center thickness t=1mm
						The first aspheric surface			The second aspheric surface
Radius of curvature R 1(cm)		36.07206	Radius of curvature R 1(cm)		19.26784
						Quadric surface constant P 1		-3.146794	Quadric surface constant P 2		-1.309141
The first aspheric asphericity coefficient	B 1	1.45672×10 -4	The first aspheric asphericity 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 (3), 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 draw as Fig. 4 A to be oblique fire astigmatism and the index of refraction error curve diagram of aspherical lens five visual fields optimizations of the present invention, Fig. 4 B is the distortion curve figure that aspherical lens of the present invention five visual fields are optimized.

Wherein, in Fig. 4 A, abscissa axis represents the index of refraction of index of refraction, and axis of ordinates represents the size of field angle; In Fig. 4 B, abscissa axis represents the size of distortion, and axis of ordinates represents the size of field angle.F in Fig. 4 _t' be the index of refraction of imaging surface in meridian field, F _s' be the index of refraction of imaging surface in sagitta of arc field, FPS=F _vfor eyeglass index of refraction, the curve in Fig. 4 B is the size of distortion in each visual field:

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

By Fig. 4 A and Fig. 4 B, can find out that the effect of optimization of oblique fire astigmatism, index of refraction error and distortion is obviously better than adopting the effect of optimization of three visual fields and four visual fields.Known by calculating, in whole 0 visual field to 1.0 field range, oblique fire astigmatism is less than 0.044D, and index of refraction error is less than 0.041D, and 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 aberration.

For further illustrating aspherical lens of the present invention, at index of refraction, be changed within the scope of 1D, the first aspheric surface 1 is fixing, and at least 5 visual fields, is optimized the superiority of design, can describe by table 4 and the design result of table 5.

Table 4 is a kind of aspheric surface design result of aspherical lens, get in variation range is 1D-14.00D of the index of refraction of this aspherical lens,-14.25D,-14.50D and-tetra-values of 14.75D, first design-14.00D double-sized non-spherical lens, p-14.25D again,-14.50D or-14.75D lens design, fix the first aspheric surface 1, optimize the second aspheric surface 2, make this aspherical lens index of refraction can for wherein-14.25D,-14.50D or-value of 14.75D, in design process, adopt 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field and 1.0 visual fields are optimized, this design result makes to slant astigmatism, it is all less when index of refraction error and distortion are spent in u '=30, maximum field of view angle.

Table 4

Aspheric surface negative lens density=1.25g/cm 3, diameter=32mm, eyeglass index of refraction
						Project		-14.00D	-14.25D	-14.50D	-14.75D
The first aspheric curvature radius R 1(cm)		36.07206	36.07206	36.07206	36.07206
						Quadric surface constant P 1		-3.146794	-3.146794	-3.146794	-3.146794
First is non-	B 1	1.45672×10 -4	1.45672×10 -4	1.45672×10 -4	1.45672×10 -4

Sphere asphericity coefficient	C 1	-7.260429×10 -7	-7.260429×10 -7	-7.260429×10 -7	-7.260429×10 -7
						D 1	2.68586×10 -9	2.68586×10 -9	2.68586×10 -9	2.68586×10 -9
	E 1	-3.404548×10 -12	-3.404548×10 -12	-3.404548×10 -12	-3.404548×10 -12
						The second aspheric curvature radius R 2(cm)		19.26784	19.11074	18.95619	18.80412
Quadric surface constant P 2		-1.309141	-1.284449	-1.260122	-1.236141
						The second aspheric surface asphericity coefficient	B 2	1.877927×10 -4	1.877966×10 -4	1.877788×10 -4	1.877387×10 -4
C 2	-3.682191×10 -7	-3.445407×10 -7	-3.200215×10 -7	-2.946401×10 -7
					D 2		-2.583728×10 -10	-4.804301×10 -10	-7.123628×10 -10	-9.544794×10 -10
E 2	1.296844×10 -11	1.394786×10 -11	1.49707×10 -11	1.603837×10 -11
					Center thickness (cm)		1	1	1	1
Oblique fire astigmatism (D) is in u '=30 °		-0.0005	0.0083	0.0181							0.0289
					Refractive index error (D) is in u '=30 °		0.0033	0.0133	0.0235	0.0341
Distortion (%) is in u '=30 °		0.0014	0.0017	0.0026							0.0041

Table 5 be aspherical lens index of refraction for-20.00D ,-20.25D ,-20.50D be to the design result of-20.75D, its design concept is identical with the aspheric surface design concept of table 4, only get-20.00D of the index of refraction of this aspherical lens ,-20.25D ,-20.50D or-four values of 20.75D.

Table 5

Aspheric surface negative lens density=1.25g/cm 3, diameter=32mm eyeglass index of refraction
						Project		-20.00D	-20.25D	-20.50D	-20.75D
The first aspheric curvature radius R 1(cm)		37.80645	37.80645	37.80645	37.80645
						Quadric surface constant P 1		-3.715908	-3.715908	-3.715908	-3.715908
The first aspheric surface asphericity coefficient	B 1	1.803131×10 -4	1.803131×10 -4	1.803131×10 -4	1.803131×10 -4
						C 1	-1.097598×10 -6	-1.097598×10 -6	-1.097598×10 -6	-1.097598×10 -6
	D 1	4.370386×10 -9	4.370386×10 -9	4.370386×10 -9	4.370386×10 -9
						E 1	-6.18553×10 -12	-6.18553×10 -12	-6.18553×10 -12	-6.18553×10 -12
	The second aspheric curvature radius R 2(cm)		16.43621	16.32177	16.2089						16.09758
Quadric surface constant P 2						-0.9781556	-0.9592829	-0.9404506	-0.9216419
		The second aspheric surface aspheric surface system	B 2	2.377542×10 -4	2.372966×10 -4					2.36804×10 -4	2.362768×10 -4
C 2	-3.355765×10 -7					-2.893335×10 -7	-2.417788×10 -7	-1.929284×10 -7
			D 2	-3.57117×10 -9	-4.085584×10 -9				-4.617866×10 -9	-5.168016×10 -9

Number	E 2	3.847443×10 -11	4.084677×10 -11	4.330295×10 -11	4.58434×10 -11
						Center thickness (cm)		1	1	1	1
Oblique fire astigmatism (D) is in u '=30 °		0.0050	0.0340	0.0645	0.0965
						Refractive index error (D) is in u '=30 °		-0.0058	0.0062	0.0193	0.0334
Distortion (%) is in u '=30 °		0.0022	0.0135	0.0265	0.0411

By table 4 and table 5, can be found out, the index of refraction of this aspherical lens-14.00D to-14.75D and-20.00D to-20.75D in, at degree place, u '=30, maximum field of view angle, oblique fire astigmatism be-0.0005D extremely-0.0965D, index of refraction error is-0.0058D to 0.0341D, and distort 0.0014% to 0.0411%, these three kinds of aberrations are all less.

For the aberration of explanation other field angle in the degree of maximum field of view angle 30, by can be calculated as table 6, table 7, shown in table 8, be respectively-14.00D to-14.75D and-20.00D extremely-details of oblique fire astigmatism, index of refraction error and the distortion of 20.75D.

Table 6

Visual field ratio	Oblique fire astigmatism (D) eyeglass index of refraction
									-14.00D	-14.25D	-14.50D	-14.75D	-20.00D	-20.25D	-20.50D	-20.75D
	0.05	-0.0036	0.0048	0.0060	0.0074	0.0106	0.01290	0.0152									0.0175
0.10									0.0119	0.0160	0.0203	0.0247	0.0345	0.0418	0.0494	0.0571
	0.15	0.0195	0.0263	0.0333	0.0405	0.0533	0.0645	0.0759									0.0875
0.20									0.0217	0.0287	0.0358	0.0431	0.0516	0.0609	0.0702	0.0794
	0.25	0.0177	0.0211	0.0242	0.0272	0.0282	0.0276	0.0266									0.0249
0.30									0.0105	0.0067	0.0023	-0.0027	-0.0036	-0.0201	-0.0377	-0.0565
	0.35	0.0029	-0.0093	-0.0224	-0.0366	-0.0288	-0.0613	-0.0955									-0.1313
0.40									-0.0060	-0.0243	-0.0438	-0.0644	-0.0427	-0.0838	-0.1268	-0.1715
	0.45	-0.0191	-0.0382	-0.0583	-0.0794	-0.0471	-0.0846	-0.1234									-0.1637
0.50									-0.0346	-0.0481	-0.0621	-0.0766	-0.0405	-0.0617	-00835	-0.1060
	0.55	-0.0435	-0.0464	-0.0493	-0.0521	-0.0177	-0.0154	-0.0129									-0.0101
0.60									-0.0363	-0.0277	-0.0185	-0.0086	0.0140	0.0381	0.0630	0.0888
	0.65	-0.0130	0.0032	0.0203	0.0383	0.0308	0.0654	0.1011									0.1376
0.70									0.0140	0.0298	0.0464	0.0636	0.0134	0.0416	0.0701	0.0990
	0.75	0.0290	0.0354	0.0418	0.0484	-0.0242	-0.0183	-0.0130									-0.0082
0.80									0.0242	0.0151	0.0053	-0.0051	-0.0382	-0.0609	-0.0850	-0.1105
	0.85	0.0030	-0.0208	-0.0457	-0.0718	-0.0004	-0.0437	-0.0887									-0.1354
0.90									-0.0234	-0.0527	-0.0831	-0.1145	0.0613	0.0177	-0.0271	-0.0729

0.95	-0.0357	-0.0548	-0.0742	-0.0941	0.0809	0.0626	0.0443	0.0260
									1.00	-0.0005	0.0083	0.0181	0.0289	0.0050	0.0340	0.0645	0.0965

Table 7

Visual field ratio	Index of refraction error (D) eyeglass index of refraction
									-14.00D	-14.25D	-14.50D	-14.75D	-20.00D	-20.25D	-20.50D	-20.75D
	0.05	0.0044	0.0056	0.0069	0.0082	0.0110	0.0132	0.0155									0.0179
0.10									0.0154	0.0198	0.0242	0.0289	0.0374	0.0452	0.0531	0.0613
	0.15	0.0280	0.0358	0.0439	0.0523	0.0641	0.0774	0.0911									0.1049
0.20									0.0372	0.0472	0.0574	0.0678	0.0766	0.0921	0.1076	0.1234
	0.25	0.0411	0.0504	0.0599	0.0695	0.0714	0.0829	0.0943									0.1056
0.30									0.0413	0.0471	0.0529	0.0584	0.0559	0.0581	0.0598	0.0608
	0.35	0.0403	0.0409	0.0411	0.0408	0.0415	0.0323	0.0221									0.0109
0.40									0.0381	0.0339	0.0291	0.0236	0.0333	0.0153	-0.0038	-0.0242
	0.45	0.0325	0.0261	0.0190	0.0112	0.029	0.0096	-0.0116									-0.0340
0.50									0.0224	0.0175	0.0121	0.0061	0.0292	0.0148	-0.0004	-0.0164
	0.55	0.0108	0.0108	0.0106	0.0102	0.0328	0.0297	0.0264									0.0228
0.60									0.0028	0.0092	0.0158	0.0224	0.0373	0.0466	0.0561	0.0657
	0.65	0.0004	0.0120	0.0239	0.0362	0.0321	0.0493	0.0669									0.0848
0.70									0.0003	0.0134	0.0268	0.0404	0.0094	0.0259	0.0426	0.0595
	0.75	-0.0023	0.0074	0.0171	0.0269	-0.0216	-0.0148	-0.0081									-0.0015
0.80									-0.0091	-0.0065	-0.0043	-0.0024	-0.0357	-0.0432	-0.0511	-0.0596
	0.85	-0.0175	-0.0224	-0.0279	-0.0341	-0.0162	-0.0353	-0.0550									-0.0754
0.90									-0.0232	-0.0315	-0.0404	-0.0500	0.0212	-0.0001	-0.0219	-0.0439
	0.95	-0.0203	-0.0242	-0.0284	-0.0329	0.0363	0.0256	0.0151									0.0050
1.00									0.0033	0.0133	0.0235	0.0341	-0.0058	0.0062	0.0193	0.0334

Table 8

Visual field ratio	Distortion (%) eyeglass index of refraction
									-14.00D	-14.25D	-14.50D	-14.75D	-20.00D	-20.25D	-20.50D	-20.75D
	0.05	-0.0020	-0.0011	-0.0001	0.0008	-0.0011	0.0006	0.0024									0.0041
0.10									-0.0085	-0.0052	-0.0017	0.0018	-0.0063	-0.0002	0.0061	0.0124
	0.15	-0.0206	-0.0142	-0.0076	-0.0008	-0.0200	-0.0085	0.0033									0.0152
0.20									-0.0374	-0.0286	-0.0196	-0.0101	-0.0436	-0.0279	-0.0120	0.0041
	0.25	-0.0551	-0.0456	-0.0357	-0.0256	-0.0712	-0.0546	-0.0380									0.0212
0.30									-0.0665	-0.0584	-0.0501	-0.0417	-0.0898	-0.0766	-0.0633	-0.0501
	0.35	-0.0641	-0.0597	-0.0552	-0.0506	-0.0863	-0.0796	-0.0732									-0.0671

0.40	-0.0454	-0.0457	-0.0462	-0.0469	-0.0566	-0.0579	-0.0596	-0.0618
									0.45	-0.0149	-0.0200	-0.0254	-0.0310	-0.0110	-0.0191	-0.0277	-0.0369
0.50	0.0159	0.0075	-0.0012	-0.0102	0.0313	0.0195	0.0074	-0.0053
									0.55	0.0353	0.0257	0.0160	0.0060	0.0528	0.0416	0.0301	0.0183
0.60	0.0365	0.0282	0.0198	0.0113	0.0467	0.0397	0.0328	0.0258
									0.65	0.0212	0.0159	0.0102	0.0056	0.0179	0.0176	0.0175	0.0178
0.70	-0.0015	-0.0031	-0.0045	-0.0056	-0.0189	-0.0123	-0.0053	0.0025
									0.75	-0.0190	-0.0174	-0.0154	-0.0130	-0.0435	-0.0317	-0.0191	-0.0057
0.80	-0.0197	-0.0164	-0.0125	-0.0081	-0.0366	-0.0222	-0.0068	0.0096
									0.85	0.0000	0.0036	0.0077	0.0123	0.0073	0.0218	-0.0373	0.0541
0.90	0.0301	0.0327	0.0357	0.0393	0.0659	0.0787	0.0930	0.1087
									0.95	0.0434	0.0445	0.0461	0.0483	0.0859	0.0974	0.1103	0.1247
1.00	0.0141	0.0017	0.0026	0.0041	0.0022	0.0135	0.0265	0.0411

From table 6, table 7, table 8 is known, in the whole field range of 0 degree to 30 degree, slant astigmatism and be less than 0.1715D, index of refraction error is less than 0.1234D, distortion is less than 0.1247%, and this aberration of three kinds is all less, therefore aspherical lens of the present invention can effectively be eliminated oblique fire astigmatism, index of refraction error and the three kinds of aberrations that distort preferably simultaneously.

In sum, aspherical lens of the present invention, can realize cost easy to manufacture lower, and not only thin but also effectively eliminate the object of aberration.Only, the foregoing is only preferred embodiment of the present invention, 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 (7)

1. an aspherical lens, comprises the first aspheric surface and the second aspheric surface, it is characterized in that: the index of refraction of this aspherical lens changes within the scope of 1D, and the first aspheric surface is fixed, and makes this aspherical lens at least 5 visual fields, makes performance function

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

Desired value t _ibe zero, w wherein _ifor weight factor, the item number of m for optimizing, e _ifor considered correction term is certain aberration, t _idesired value for certain aberration.

2. aspherical lens as claimed in claim 1, is characterized in that: this aspheric surface is to disperse aspherical lens.

3. aspherical lens as claimed in claim 1, is characterized in that: this performance function has 10 Variable Designing Of parameters.

4. aspherical lens as claimed in claim 3, is characterized in that: these 10 Variable Designing Of parameters are P ₁, P ₂, B ₁, C ₁, D ₁, E ₁, B ₂, C ₂, D ₂and E ₂, P wherein ₁, P ₂be respectively the first aspheric surface and the second aspheric conic constant value, B ₁, C ₁, D ₁, E ₁be the first aspheric surface high-order term coefficient, B ₂, C ₂, D ₂, E ₂it is the second aspheric surface high-order term coefficient.

5. the aspherical lens as described in claim 3 or 4, is characterized in that: these 10 Variable Designing Of parameters are to calculate performance function gained by damped least square method.

6. aspherical lens as claimed in claim 1, is characterized in that: these 5 visual fields can be respectively 0.3 visual field, 0.5 visual field, 0.7 visual field, 0.85 visual field and 1.0 visual fields.

7. aspherical lens as claimed in claim 6, is characterized in that: 1.0 visual fields are that the field angle at this aspherical lens is the position of 30 degree.

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