CN100426038C - Method for designing non-spherical lens - Google Patents

Abstract

The present invention relates to a method for designing an aspherical lens. The present invention has the main steps that the refraction rate, the refractive index and the diameter of the aspherical lens are set, the two curvature radiuses of the aspherical lens are designed by adopting the spherical design to enable the aspherical lens to achieve the set refraction rate, and the two curvature radiuses are used for minimizing the distortion of three viewing fields; a first aspheric surface and a second aspheric surface are designed by adopting the aspherical design formula of the lens, and the aspherical design formula of the lens is Z (r) =*+Br<4>+Cr<6>+Dr<8>+Er<10>, wherein Z (r) is the deepness of the lens, Cv is the curvature of the apex of each of the aspheric surfaces, r is the vertical height between any point and an optical axis on a lens surface, P is the constant value of a secondary curve, and B, C, D and E are the high-order term coefficients of the aspheric surfaces; the first aspheric surface and the second aspheric surface are designed to be optimized by adopting a damping least square method, wherein during the optimizing design, the chromatic aberration of the aspherical lens is eliminated in at least five viewing fields, and the aspherical coefficients P, B, C, D and E of the first aspheric surface and the second aspheric surface are obtained.

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]

The eyeglass that present optical device such as optical read head, camera lens, lens are adopted generally adopts sphere design or aspheric surface design.

When eyeglass adopts the sphere design, because two refractive surfaces of eyeglass all are designed to the sphere form, so be easy to make and processing.Yet the sphere that spherical divergence eyeglass that the 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, and the edge of eyeglass or center can obviously thicken.Wherein the eyeglass index of refraction is meant the back vertex lens power value of this eyeglass, and it is the inverse of the paraxial consequent focal length of eyeglass (distance from eyeglass picture side surface vertices to rear focus) that records of unit that its value equals with rice.Can calculate by formula (1):

$F_v=\frac{1}{f_v}=\frac{{\mathrm{<figure-callout\; id="1"\; label="F"\; filenames="C20051003447400151.png"\; state="\{\{state\}\}">F</figure-callout>}}_1+F_2-\frac{t}{n}{F}_1{\mathrm{<figure-callout\; id="2"\; label="F"\; filenames="C20051003447400151.png,C20051003447400162.png"\; state="\{\{state\}\}">F</figure-callout>}}_2}{1-\frac{t}{n}{F}_1}---\left(1\right)$

Wherein, f _vBe the paraxial back focal distance of eyeglass, the radius-of-curvature of getting the sphere of not being close to picture side is R ₁, the radius-of-curvature of being close to the sphere of picture side is R ₂, center of lens thickness is t, and eyeglass material refractive index is n, and then 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) expression usually, and the usual said eyeglass number of degrees are exactly F _vOn duty be the 1D=100 degree with 100.From formula (1), when one timing of eyeglass material, the index of refraction of eyeglass is just by R ₁, R ₂And the t value decides.

When the spherical divergence eyeglass designs, if t is fixed, then along with the increase of eyeglass index of refraction, R ₁And R ₂Difference just big more, 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,, sphere depends on R because assembling eyeglass center thickness t ₁, R ₂Value, therefore, also can be by regulating R ₁And R ₂Value is regulated the index of refraction of eyeglass.By formula (1) as can be known, sphere is assembled the increase of eyeglass along with the eyeglass index of refraction, R ₁And R ₂Difference also just big more, then the center thickness t of eyeglass is just big more, makes that the volume of whole eyeglass is bigger.

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

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

Aberration is one of principal element that influences lens imaging quality, and the aberration that generally influences lens imaging quality comprises three kinds of aberrations such as oblique fire astigmatism, visual field bending and distortion.Wherein, the oblique fire astigmatism is because the light beam that sends from the tiny light source of extra-axial object point is different with the focus point of sagitta of arc field in the meridian field, and has astigmatism so that picture is unintelligible when making imaging.The visual field bending is meant perpendicular to the planar object of optical axis when the imaging, as the edge of center and picture inconsistent and make the image planes visual field become curved surface in the image planes position, can claim average index of refraction error again, be commonly referred to the index of refraction error.Distortion is because different because of magnification with distance light axle zone in dipped beam axle zone, and makes imaging generation barrel distortion or pincushion distortion, and this kind aberration makes imaging that how much changes take place but do not influence the sharpness of imaging.

As the index of refraction of establishing imaging surface in the meridian field is F ' _T(D), the index of refraction of imaging surface is T ' in the sagitta of arc field _S(D), the image height of ideal image is MQ ', and the image height of true imaging is MQ ", then:

Oblique fire astigmatism=F ' _T-F ' _S

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

Therefore, eyeglass adopts the sphere design, can't 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 the aspheric surface design at present, and wherein aspherical lens is meant that wherein at least one refractive surface is an aspheric surface.

Eyeglass adopts the 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 is by introducing the curvature that high-order term changes eyeglass each point place, and then reduce the thickness difference at each point place, the high-order term of introducing in right this technology had both comprised odd item, also comprised the even item, can cause the eyeglass refractive surface asymmetric, form bigger above-mentioned three kinds of aberrations easily, so be difficult to design and process satisfactory eyeglass.

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

$z\left(r\right)=\frac{{\mathrm{<figure-callout\; id="2"\; label="cr"\; filenames="C20051003447400151.png,C20051003447400162.png"\; state="\{\{state\}\}">cr</figure-callout>}}^2}{1+\sqrt{1-c^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C20051003447400151.png,C20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}}+a_1{\mathrm{<figure-callout\; id="4"\; label="r"\; filenames="C20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^4+a_2{r}^6+a_3{r}^8+a_4{r}^{10}+a_5{r}^{12}---\left(2\right)$

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

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

[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 kind of method for designing of aspherical lens, its key step comprises:

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

The employing sphere designs, and 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 the distortion of 0.5 visual field, 0.7 visual field and 1.0 visual fields be minimum value;

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

$Z\left(r\right)=\frac{C_v{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C20051003447400151.png,C20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{1+\sqrt{1-{\mathrm{PC}}_v^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C20051003447400151.png,C20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}}+{\mathrm{<figure-callout\; id="4"\; label="Br"\; filenames="C20051003447400162.png"\; state="\{\{state\}\}">Br</figure-callout>}}^4+{\mathrm{Cr}}^6+{\mathrm{Dr}}^8+{\mathrm{Er}}^{10}$

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

Adopt damped least square method that first aspheric surface and second aspheric surface are optimized design;

Wherein, during optimal design, make this aspherical lens eliminate aberrations at least five visual fields, and draw above-mentioned 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.Be less than the method for designing that five visual fields are optimized the aspherical lens of design than employing, can further eliminate the aberration maximum value that exists 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 whole field range in visual field, 0 visual field to 1.0, index of refraction error and distortion are all less, are 30 to spend positions with the angle of lens light axis when wherein 1.0 visual fields are meant as square deflecting light beams by rear focus.

[description of drawings]

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

The aspheric surface divergent mirror chip architecture synoptic diagram that Fig. 2 goes out for the method for designing of aspherical lens of the present invention is designed.

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

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

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

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

The aspherical focusing lens that Fig. 5 B goes out for the method for designing of aspherical lens of the present invention is designed 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, adopt the sphere design, design two radius-of-curvature of this aspherical lens, make its index of refraction that reaches above-mentioned setting, and utilize these two radius-of-curvature to make its distortion be minimum value in 0.5,0.7 and 1.0 visual fields.

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

This eyeglass aspheric surface design formula (3) is:

$Z\left(r\right)=\frac{C_v{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C20051003447400151.png,C20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}{1+\sqrt{1-{\mathrm{PC}}_v^2{\mathrm{<figure-callout\; id="2"\; label="r"\; filenames="C20051003447400151.png,C20051003447400162.png"\; state="\{\{state\}\}">r</figure-callout>}}^2}}+{\mathrm{<figure-callout\; id="4"\; label="Br"\; filenames="C20051003447400162.png"\; state="\{\{state\}\}">Br</figure-callout>}}^4+{\mathrm{Cr}}^6+{\mathrm{Dr}}^8+{\mathrm{Er}}^{10}---\left(3\right)$

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

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

Aspherical lens generally is to eliminate aberration in some specific field angle in the optimal design of eliminating aberration, and wherein field angle is meant when picture side's deflecting light beams passes through rear focus and the angle of lens light axis.So, when carrying out the aspherical lens design in this flow process, begin to adopt and eliminate oblique fire astigmatism, index of refraction error and distortion five visual fields.

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 the formula _iBe weight factor, its value is taken as w _i＞0, the weight factor value is that the importance according to the corresponding aberration of place item decides, and very strict if the aberration that will eliminate the place item requires, then that weight factor value can obtain bigger; The item number of m for optimizing, its value are the integer more than or equal to 1; e _iFor the correction term of being considered is certain aberration, consider e _iItem number be numerical value m; t _iBe the desired value of certain aberration, desired value t _iValue according to e _iSituation and deciding.

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

In the 5th step, calculate first aspheric surface of this aspherical lens and the second aspheric asphericity coefficient P, B, C, D, E by separating 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 _iWhen being zero, obtain first aspheric surface and the second aspheric asphericity coefficient of this aspherical lens, draw the design result of this aspherical lens by separating of damped least square method.

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

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

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

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

As shown in Figure 2, the aspheric surface that goes 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 first aspheric surface 1 and second aspheric surface, 2, the first aspheric surfaces 1 is R ₁, the radius-of-curvature of 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 first aspheric surface 1 is P ₁, B ₁, C ₁, D ₁, E ₁, the asphericity coefficient P of second aspheric surface 2 ₂, B ₂, C ₂, D ₂, E ₂, P wherein ₁, P ₂Be respectively the conic constant value of first aspheric surface 1 and 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 first aspheric surface 1 and second aspheric surface 2.

This aspheric surface is dispersed the design of eyeglass and is adopted damped least square method to be optimized design, and then the performance function of damped least square method as shown in Equation (4).This aspheric surface is dispersed the design of eyeglass and is adopted at least five visual fields to eliminate aberration,, makes the desired value t of performance function (4) that is _iBe zero at least five visual fields.

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

Known that by performance function (4) optimizing item number has m, this aspheric surface is dispersed the method for designing of eyeglass, can adopt m/3 item wherein to eliminate the oblique fire astigmatism, and its time is according to the visual field size

1.0 visual field and deciding is adopted the m/3 item to eliminate index of refraction sum of errors m/3 item again and is eliminated distortion.Then 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 first aspheric surface 1 ₁, B ₁, C ₁, D ₁, E ₁Asphericity coefficient P with 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 _N0Expression, n=10; Aberration f ₁₀, f ₂₀, f ₃₀..., f _M0Expression, the variable after the optimization is with x ₁, x ₂, x ₃... x ₉, x _nExpression, n=10; Aberration f ₁, f ₂, f ₃... f _M-1, f _mExpression.

Because separate (6) of damped least square method are:

X＝(A ^TA+pI) ^-1A ^Tf ₀(6)

Symbol in the formula can be used defined matrix:

$x_0=\left(\begin{array}{c}{x}_{10}\\ x_{20}\\ x_{30}\\ .\\ .\\ .\\ .\\ .\\ .\\ x_{n0}\end{array}\right),$ $x=\left(\begin{array}{c}{x}_1\\ x_2\\ x_3\\ .\\ .\\ .\\ .\\ .\\ .\\ x_n\end{array}\right),$ $f_0=\left(\begin{array}{c}{f}_{10}\\ f_{20}\\ f_{30}\\ .\\ .\\ .\\ .\\ .\\ .\\ f_{m0}\end{array}\right),$ $f=\left(\begin{array}{c}{f}_1\\ f_2\\ {\mathrm{<figure-callout\; id="3"\; label="f"\; filenames="C20051003447400162.png"\; state="\{\{state\}\}">f</figure-callout>}}_3\\ .\\ .\\ .\\ .\\ .\\ .\\ f_m\end{array}\right),$ $X=x-x_0=\left(\begin{array}{c}{x}_1-x_{10}\\ x_2-x_{20}\\ x_3-x_{30}\\ .\\ .\\ .\\ .\\ .\\ .\\ x_n-x_{n0}\end{array}\right)$

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 ^TBe the transposed matrix of A, p is a damping factor, and I is a unit matrix, (A ^TA+pI) ^-1Expression is to (A ^TA+pI) matrix of negating by the computing of above matrix, can get the operation values of X, passes through x=x ₀+ X can determine the value of x, and then can draw the P after the 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, five visual fields in 0.85 visual field and 1.0 visual fields be 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

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 draw the aspheric surface that goes out for the method for designing of this aspherical lens is designed as Fig. 3 A and disperse oblique fire astigmatism and the index of refraction error curve diagram of eyeglass five visual field optimal design, the aspheric surface that Fig. 3 B goes out for the method for designing of this aspherical lens is designed is dispersed the distortion curve figure of eyeglass five visual field optimal design.

Wherein, among Fig. 3 A, abscissa axis is represented the size of index of refraction, and axis of ordinates is represented the size of field angle; Among Fig. 3 B, abscissa axis is represented the size that distorts, and axis of ordinates is represented the size of field angle.F ' among Fig. 3 A _TBe the index of refraction of imaging surface in the meridian field, F ' _SBe the index of refraction of imaging surface in the sagitta of arc field, FPS=F _vBe the eyeglass index of refraction, the curve among Fig. 3 B is the size of distortion in each visual field, then:

Oblique fire astigmatism=F ' _T-F ' _S

By Fig. 3 A and Fig. 3 B, can find out that the designed aspheric surface that goes out of the method for designing of this aspherical lens disperses eyeglass, in the whole field range of visual field, 0 visual field to 1.0, the oblique fire astigmatism is less than 0.044D, the 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, so effectively eliminate oblique fire astigmatism, three kinds of aberrations of index of refraction sum of errors distortion preferably.

As shown in Figure 4, the structural representation of the aspherical focusing lens that goes out for the method for designing of this aspherical lens is designed, this aspherical focusing lens comprise that the radius-of-curvature of first aspheric surface 3 and second aspheric surface, 4, the first aspheric surfaces 3 is R ₃, the radius-of-curvature of 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 basically 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 the 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, seven visual fields in 0.95 visual field and 1.0 visual fields be 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

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 are oblique fire astigmatism weight factor, select 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 are distortion weight factor, desired value t ₁=t ₂=...=t ₂₀=t ₂₁=0, by calculating, can draw the aspherical focusing lens that goes out for the method for designing of this aspherical lens is designed as Fig. 5 A oblique fire astigmatism and the index of refraction error curve diagram seven visual field optimal design, Fig. 5 B is the distortion curve figure of the designed aspherical focusing lens that goes out of the method for designing of this aspherical lens seven visual field optimal design.

Wherein, among Fig. 5 A, abscissa axis is represented the size of index of refraction, and axis of ordinates is represented the size of field angle; Among Fig. 5 B, abscissa axis is represented the size that distorts, and axis of ordinates is represented the size of field angle.F ' among Fig. 5 A _TBe the index of refraction of imaging surface in the meridian field, F ' _SBe the index of refraction of imaging surface in the sagitta of arc field, FPS=F _vBe the index of refraction of eyeglass, the curve among Fig. 5 B is the size of distortion in each visual field, then:

Oblique fire astigmatism=F ' _T-F ' _S

By Fig. 5 A and Fig. 5 B, can find out the designed aspherical focusing lens that goes out of the method for designing of this aspherical lens, in the whole field range of visual field, 0 visual field to 1.0, the oblique fire astigmatism is less than 0.0377D, the 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, so effectively eliminate oblique fire astigmatism, index of refraction error and distortion preferably simultaneously.

In sum, the method for designing of this aspherical lens can realize effectively eliminating the purpose of aberration.So, the above only is this better embodiment, is familiar with the personage of this case technology such as, helping the equivalence modification of being done according to this case creation spirit or changing, all should be contained in the following claim.

Claims (9)

1. the method for designing of an 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;

The employing sphere designs, and 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 the distortion of 0.5 visual field, 0.7 visual field and 1.0 visual fields be minimum value;

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

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

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

Adopt damped least square method that first aspheric surface and second aspheric surface are optimized design;

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

2. the method for designing of aspherical lens as claimed in claim 1, it is characterized in that: this aspherical lens is an aspherical focusing lens, then optimal design is to eliminate aberrations at least seven visual fields.

3. the method for designing of aspherical lens as claimed in claim 1 or 2 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 the formula _iBe weight factor, the item number of m for optimizing, e _iFor the correction term of being considered is certain aberration, t _iDesired value for certain aberration.

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

5. the method for designing of aspherical lens as claimed in claim 1 or 2, it 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 are meant that field angle is the position of 30 degree.

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

7. the method for designing of aspherical lens as claimed in claim 6, 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, 0.85 the oblique fire astigmatism is eliminated in these five visual fields of visual field and 1.0 visual fields, during the distortion of index of refraction sum of errors, this aspheric surface is dispersed first aspheric surface and the second aspheric asphericity coefficient such as the following table of eyeglass:

8. the method for designing of aspherical lens as claimed in claim 2, it is characterized in that: these seven visual fields are 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.

9. the method for designing of aspherical lens as claimed in claim 8, it is characterized in that: when the index of refraction of setting this aspherical focusing lens is 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, 0.95 the oblique fire astigmatism is eliminated in seven visual fields in visual field and 1.0 visual fields, during the distortion of index of refraction sum of errors, first aspheric surface of this aspherical focusing lens and second aspheric asphericity coefficient such as the following table:

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